goldreich

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Author name code: goldreich
ADS astronomy entries on 2022-09-14
author:Goldreich, Peter

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Title: DAVs: Red Edge and Outbursts
Authors: Luan, Jing; Goldreich, Peter
2018ApJ...863...82L Altcode: 2017arXiv171106367L
As established by photometric surveys, white dwarfs with hydrogen
atmospheres and surface gravity, log(g) ≈ 8.0 pulsate as they
cool across the temperature range of 12,500 K ≳ T eff
≳ 10,800 K. Known as DAVs or ZZ Ceti stars, their oscillations are
attributed to gravity modes excited by convective driving. Overstability
requires convective driving to exceed radiative damping. Previous works
have demonstrated that ω ≳ max(τ c -1,
L ℓ,b ) is a necessary and sufficient condition for
overstability. Here τ c and L ℓ,b are
the effective thermal timescale and Lamb frequency at the base of the
surface convection zone. Below the observational red edge, L 
ℓ,b ≫ τ c -1, so overstable modes
all have ωτ c ≫ 1. Consequently, their photometric
amplitudes are reduced by that large factor rendering them difficult to
detect. Although proposed previously, the condition ω ≳ L ℓ,b
 has not been clearly interpreted. We show that modes with ω &lt;
L ℓ,b suffer enhanced radiative damping that exceeds
convective driving rendering them damped. A quasi-adiabatic analysis is
adequate to account for this enhancement. Although this approximation
is only marginally valid at the red edge, it becomes increasingly
accurate toward both higher and lower {T}eff}. Recently,
Kepler discovered a number of cool DAVs that exhibit sporadic flux
outbursts. Typical outbursts last several hours, are separated by
days, and release ∼1033-1034 erg. We attribute
outbursts to limit cycles arising from sufficiently resonant 3-mode
couplings between overstable parent modes and pairs of radiatively
damped daughter modes. Limit cycles account for the durations and
energies of outbursts and their prevalence near the red edge of the
DAV instability strip.

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Title: Dense Regions in Supersonic Isothermal Turbulence
Authors: Robertson, Brant; Goldreich, Peter
2018ApJ...854...88R Altcode: 2018arXiv180105440R
The properties of supersonic isothermal turbulence influence a variety
of astrophysical phenomena, including the structure and evolution of
star-forming clouds. This work presents a simple model for the structure
of dense regions in turbulence in which the density distribution
behind isothermal shocks originates from rough hydrostatic balance
between the pressure gradient behind the shock and its deceleration
from ram pressure applied by the background fluid. Using simulations
of supersonic isothermal turbulence and idealized waves moving through
a background medium, we show that the structural properties of dense,
shocked regions broadly agree with our analytical model. Our work
provides a new conceptual picture for describing the dense regions,
which complements theoretical efforts to understand the bulk statistical
properties of turbulence and attempts to model the more complex
features of star-forming clouds like magnetic fields, self-gravity,
or radiative properties.

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Title: Enceladus: three-act play and current state
Authors: Luan, J.; Goldreich, P.
2017AGUFM.P51F..04L Altcode:
Eccentricity (e) growth as Enceladus migrates deeper into mean motion
resonance with Dione results in increased tidal heating. As the bottom
of the ice shell melts, the rate of tidal heating jumps and runaway
melting ensues. At the end of run-away melting, the shell's thickness
has fallen below the value at which the frequency of free libration
equals the orbital mean motion and e has damped to well below its
current value. Subsequently, both the shell thickness and e partake in a
limit cycle. As e damps toward its minimum value, the shell's thickness
asymptotically approaches its resonant value from below. After minimum
e, the shell thickens quickly and e grows even faster. This cycle is
likely to have been repeated multiple times in the past. Currently,
e is much smaller than its equilibrium value corresponding to the
shell thickness. Physical libration resonance resolves this mystery,
it ensures that the low-e and medium-thickness state is present for
most of the time between consecutive limit cycles. It is a robust
scenario that avoids fine tuning or extreme parameter choice, and
naturally produces episodic stages of high heating, consistent with
softening of topographical features on Enceladus.

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Title: Classification of Satellite Resonances in the Solar System
Authors: Luan, Jing; Goldreich, Peter
2017AJ....153...17L Altcode:
Several pairs of solar system satellites occupy mean motion resonances
(MMRs). We divide these into two groups according to their proximity
to exact resonance. Proximity is measured by the existence of a
separatrix in phase space. MMRs between Io-Europa, Europa-Ganymede, and
Enceladus-Dione are too distant from exact resonance for a separatrix
to appear. A separatrix is present only in the phase spaces of the
Mimas-Tethys and Titan-Hyperion MMRs, and their resonant arguments
are the only ones to exhibit substantial librations. Could there be a
causal connection between the libration amplitude and the presence of a
separatrix? Our suspicions were aroused by Goldreich &amp; Schlichting,
who demonstrate that sufficiently deep in a MMR, eccentricity damping
could destabilize librations. However, our investigation reveals that
libration amplitudes in both the Mimas-Tethys and Titan-Hyperion
MMRs are fossils. Although the Mimas-Tethys MMR is overstable, its
libration amplitude grows on the tidal damping timescale of Mimas’s
inclination, which is considerably longer than a Hubble time. On the
other hand, the Titan-Hyperion MMR is stable, but tidal damping of
Hyperion’s eccentricity is too weak to have affected the amplitude
of its libration.

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Title: Understanding Enceladus
Authors: Luan, Jing; Goldreich, Peter
2016DPS....4822504L Altcode:
We offer answers to the following questions?1, How did the global ocean
form?2, Why is thermal activity concentrated at the south pole?3,
What maintains the current small orbital eccentricity?4, How is the
thickness of the ice shell changing?5, Why are the tiger stripes so
hot?6, What sets the area of the south polar terrain?

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Title: Thermal Conductivity of Rubble Piles
Authors: Luan, Jing; Goldreich, Peter
2015ApJ...814...36L Altcode: 2015arXiv151005295L
Rubble piles are a common feature of solar system bodies. They are
composed of monolithic elements of ice or rock bound by gravity. Voids
occupy a significant fraction of the volume of a rubble pile. They can
exist up to pressure P≈ {ɛ }Yμ , where {ɛ }Y
is the monolithic material's yield strain and μ its rigidity. At low P,
contacts between neighboring elements are confined to a small fraction
of their surface areas. As a result, the effective thermal conductivity
of a rubble pile, {k}{con}≈ k{(P/({ɛ }Yμ
))}1/2, can be orders of magnitude smaller than the
thermal conductivity of its monolithic elements, k. In a fluid-free
environment, only radiation can transfer energy across voids. It
contributes an additional component, {k}{rad}=16{\ell
}σ {T}3/3, to the total effective conductivity,
{k}{eff}={k}{con}+{k}{rad}. Here ℓ,
the inverse of the opacity per unit volume, is of the order of the
size of the elements, and voids. An important distinction between
{k}{con} and {k}{rad} is that the former
is independent of the size of the elements, whereas the latter is
proportional to it. Our expression for {k}{eff} provides
a good fit to the depth dependence of thermal conductivity in the
top 140 cm of the lunar regolith. It also offers a good starting
point for detailed modeling of thermal inertias for asteroids and
satellites. Measurement of the response of surface temperature to
variable insolation is a valuable diagnostic of a regolith. There is
an opportunity for careful experiments under controlled laboratory
conditions to test models of thermal conductivity such as the one
we outline.

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Title: Secular Evolution of the Pulsar Triple System J0337+1715
Authors: Luan, Jing; Goldreich, Peter
2014ApJ...790...82L Altcode: 2014arXiv1405.2374L
The pulsar triple system J0337+1715 is remarkably regular and highly
hierarchical. Secular interactions transfer angular momentum between
inner and outer orbits unless their apsidal lines are parallel or
anti-parallel. These choices correspond to orthogonal eigenmodes p
and are characterized by e p, 1/e p, 2 ~ a
1/a 2 and e a, 1/e a, 2
~ (a 1/a 2)-3/2(m 2/m
1). Mode p dominates the current state so e 1/e
2 remains close to e p, 1/e p, 2. A
small contribution by Mode a causes e 1 and e 2 to
oscillate with a period of ~103 yr which should be apparent
in a few years. These will reveal the effects of general relativity, and
possibly the distortion of the inner white dwarf (WD). Phinney proposes
that the epicyclic energy of a WD-pulsar binary reaches equipartition
with the kinetic energy of a single convective eddy when the WD's
progenitor fills its Roche lobe. We extend Phinney's theory to apply
to modes rather than individual orbits. Thus we predict that Mode p and
Mode a achieved equipartition with eddies in the giant envelopes of the
progenitors of the outer and inner WD, respectively. The most effective
eddies are those with lifetimes closest to the orbit period. These were
far more energetic in the progenitor of the outer WD. This explains
why Mode p overwhelms Mode a, and also why the inner binary's orbit is
far more eccentric than orbits of other WD-pulsar binaries with similar
orbit periods. Mode a's small but finite amplitude places a lower bound
of Q ~ 106 on the tidal quality parameter of the inner WD.

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Title: Physical Constraints on Fast Radio Bursts
Authors: Luan, Jing; Goldreich, Peter
2014ApJ...785L..26L Altcode: 2014arXiv1401.1795L
Fast radio bursts (FRBs) are isolated, ms radio pulses with dispersion
measure (DM) of order 103 pc cm-3. Galactic
candidates for the DM of high latitude bursts detected at GHz
frequencies are easily dismissed. DM from bursts emitted in stellar
coronas are limited by free-free absorption and those from H II
regions are bounded by the nondetection of associated free-free
emission at radio wavelengths. Thus, if astronomical, FRBs are probably
extragalactic. FRB 110220 has a scattering tail of ~5.6 ± 0.1 ms. If
the electron density fluctuations arise from a turbulent cascade, the
scattering is unlikely to be due to propagation through the diffuse
intergalactic plasma. A more plausible explanation is that this burst
sits in the central region of its host galaxy. Pulse durations of
order ms constrain the sizes of FRB sources implying high brightness
temperatures that indicates coherent emission. Electric fields near
FRBs at cosmological distances would be so strong that they could
accelerate free electrons from rest to relativistic energies in a
single wave period.

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Title: Overstable Librations can Account for the Paucity of Mean
Motion Resonances among Exoplanet Pairs
Authors: Goldreich, Peter; Schlichting, Hilke E.
2014AJ....147...32G Altcode: 2013arXiv1308.4688G
We assess the multi-planet systems discovered by the Kepler satellite
in terms of current ideas about orbital migration and eccentricity
damping due to planet-disk interactions. Our primary focus is on
first order mean motion resonances, which we investigate analytically
to lowest order in eccentricity. Only a few percent of planet pairs
are in close proximity to a resonance. However, predicted migration
rates (parameterized by \tau _n=n/{|\dot{n}|}) imply that during
convergent migration most planets would have been captured into
first order resonances. Eccentricity damping (parameterized by
\tau _e=e/{|\dot{e}|}) offers a plausible resolution. Estimates
suggest τ e /τ n ~ (h/a)2
~ 10-2, where h/a is the ratio of disk thickness to
radius. Together, eccentricity damping and orbital migration give
rise to an equilibrium eccentricity, e eq ~ (τ e
/τ n )1/2. Capture is permanent provided
e eq &lt;~ μ1/3, where μ denotes the planet
to star mass ratio. But for e eq &gt;~ μ1/3,
capture is only temporary because librations around equilibrium
are overstable and lead to passage through resonance on timescale
τ e . Most Kepler planet pairs have e eq
&gt; μ1/3. Since τ n Gt τ e 
is the timescale for migration between neighboring resonances, only
a modest percentage of pairs end up trapped in resonances after the
disk disappears. Thus the paucity of resonances among Kepler pairs
should not be taken as evidence for in situ planet formation or the
disruptive effects of disk turbulence. Planet pairs close to a mean
motion resonance typically exhibit period ratios 1%-2% larger than
those for exact resonance. The direction of this shift undoubtedly
reflects the same asymmetry that requires convergent migration for
resonance capture. Permanent resonance capture at these separations
from exact resonance would demand μ(τ n /τ e
)1/2 &gt;~ 0.01, a value that estimates of μ from
transit data and (τ e /τ n )1/2
from theory are insufficient to match. Plausible alternatives involve
eccentricity damping during or after disk dispersal. The overstability
referred to above has applications beyond those considered in this
investigation. It was discovered numerically by Meyer &amp; Wisdom in
their study of the tidal evolution of Saturn's satellites.

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Title: A Simple Model for Orbital Resonances with Dissipation and
its Application to Multiple-Planet Systems
Authors: Schlichting, Hilke; Goldreich, P.
2013DPS....4511303S Altcode:
Data from multi-planet systems discovered by Kepler show that
most planets currently do not reside in or close to mean motion
resonances. There is however a significant excess of planet pairs with
period ratios close to but 1-2% larger than those of exact resonance. We
present a simple model for orbital resonance including dissipation
and apply it to exoplanet systems. Our results demonstrate that
there are three possible outcomes for a pair of planets encountering
a resonance. These three different outcomes are due to eccentricity
damping that can drive an instability of the amplitude of libration
about exact resonance. Damping promotes instability because the
effective potential is maximal at exact resonance. The instability
manifests itself in systems for which eccentricity damping occurs
more rapidly than semi-major axis migration. Our results indicate that
only about 10% of planet pairs should currently reside in or near mean
motion resonances. Thus the small fraction of near commensurate orbits
in multi-planet systems discovered by Kepler is fully consistent with
disk migration of low mass planets. Furthermore, for planet pairs
massive enough to be permanently captured into resonance, our model
can account for the deficit of planet pairs at exact resonance and
for the corresponding excess of pairs with slightly greater separation.

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Title: Adiabatic Heating of Contracting Turbulent Fluids
Authors: Robertson, Brant; Goldreich, Peter
2012ApJ...750L..31R Altcode: 2012arXiv1203.4815R
Turbulence influences the behavior of many astrophysical systems,
frequently by providing non-thermal pressure support through random
bulk motions. Although turbulence is commonly studied in systems with
constant volume and mean density, turbulent astrophysical gases often
expand or contract under the influence of pressure or gravity. Here,
we examine the behavior of turbulence in contracting volumes using
idealized models of compressed gases. Employing numerical simulations
and an analytical model, we identify a simple mechanism by which
the turbulent motions of contracting gases "adiabatically heat,"
experiencing an increase in their random bulk velocities until
the largest eddies in the gas circulate over a Hubble time of the
contraction. Adiabatic heating provides a mechanism for sustaining
turbulence in gases where no large-scale driving exists. We describe
this mechanism in detail and discuss some potential applications to
turbulence in astrophysical settings.

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Title: Why do we see the man in the Moon?
Authors: Aharonson, Oded; Goldreich, Peter; Sari, Re'em
2012Icar..219..241A Altcode:
Numerical simulations and analysis show that the Moon locks into
resonance with a statistical preference of facing either the current
near-side or far-side toward Earth. The near-side is largely covered
by dense, topographically low, dark mare basalts, the pattern of which
to some, resembles the image of a man's face. Although the Moon is
locked in this configuration at present, the opposite one, with the
current far-side facing Earth, is of lower potential energy and hence
might be naively expected. Instead, we find that the probability of
selecting each configuration depends upon the ratio of the asymmetry
of the potential energy maxima, dominated by the octupole moment of the
Moon, to the energy dissipated per tidal cycle within the Moon. If this
ratio is small, the two configurations are equally likely. Otherwise,
interesting dynamical behavior ensues. In the Moon's present orbit, with
the best-estimated geophysical parameters and dissipation parameter
Q = 35, trapping into the current higher-energy configuration is
preferred. With Q = 100 in analogy with the solid Earth, the current
configuration is nearly certain. The ratio of energies and corresponding
probabilities were different in the past. Relative crater counts on the
leading and trailing faces indicate an impact may have unlocked the
Moon before it settled into the present configuration. Our analysis
constrains the geophysical parameters at the time of the last such
event.

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Title: Why do We See the Man in the Moon?
Authors: Aharonson, O.; Goldreich, P.; Sari, R.
2012LPI....43.2532A Altcode:
Numerical simulations and analysis show that the Moon locks into
resonance with a statistical preference of facing either the current
nearside or farside toward Earth.

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Title: Why do We See the Man in the Moon?
Authors: Aharonson, O.; Goldreich, P.; Sari, R.
2010AGUFM.P51C1464A Altcode:
The Moon's current spin-orbit resonance results in it continuously
pointing the same side towards the Earth. This is the side largely
covered by dense, dark mare basalts, the pattern of which, to some,
resembles the shape of a man's face. For dynamical stability, the
Moon must spin about its axis of maximum moment of inertia, and point
its axis of minimum inertia in direction of the Earth, leaving two
options of facing the current near-side or far-side towards us. While
both configurations are local potential energy minima, we show that
under certain conditions, breaking and locking into resonance from a
state of rapid rotation preferentially selects one configuration over
the other. We analytically and numerically simulate the locking of
the Moon into resonance and consider the dependence on the relevant
geophysical parameters at the time of last resonance locking. The
probability of each configuration depends upon the gravitational
potential energy asymmetry dominated by the octupole moment of the Moon,
and by the energy dissipated per tidal cycle dominated by the internal
properties of the Moon. If these energies are widely separated, the two
configurations are equally likely. If these energies are comparable,
interesting dynamical behavior results. For example, we find that in
the current orbit with the current best-estimated parameters, the Moon
is more likely to fall into the higher of the two energy configurations
facing the near-side towards the Earth with a preference of ~3:1.

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Title: Elastic ice shells of synchronous moons: Implications for
cracks on Europa and non-synchronous rotation of Titan
Authors: Goldreich, Peter M.; Mitchell, Jonathan L.
2010Icar..209..631G Altcode: 2009arXiv0910.0032G
A number of synchronous moons are thought to harbor water oceans beneath
their outer ice shells. A subsurface ocean frictionally decouples the
shell from the interior. This has led to proposals that a weak tidal
or atmospheric torque might cause the shell to rotate differentially
with respect to the synchronously rotating interior. Applications along
these lines have been made to Europa and Titan. However, the shell is
coupled to the ocean by an elastic torque. As a result of centrifugal
and tidal forces, the ocean would assume an ellipsoidal shape with its
long axis aligned toward the parent planet. Any displacement of the
shell away from its equilibrium position would induce strains thereby
increasing its elastic energy and giving rise to an elastic restoring
torque. In the investigation reported on here, the elastic torque is
compared with the tidal torque acting on Europa and the atmospheric
torque acting on Titan. Regarding Europa, it is shown that the tidal
torque is far too weak to produce stresses that could fracture the ice
shell, thus refuting an idea that has been widely advocated. Instead,
it is suggested that the cracks arise from time-dependent stresses due
to non-hydrostatic gravity anomalies from tidally driven, episodic
convection in the satellite's interior. Two years of Cassini RADAR
observations of Titan's surface have been interpreted as implying
an angular displacement of ∼0.24° relative to synchronous
rotation. Compatibility of the amplitude and phase of the observed
non-synchronous rotation with estimates of the atmospheric torque
requires that Titan's shell be decoupled from its interior. We find
that the elastic torque balances the seasonal atmospheric torque at
an angular displacement ≲0.05°, effectively coupling the shell to
the interior. Moreover, if Titan's surface were spinning faster than
synchronous, the tidal torque tending to restore synchronous rotation
would almost certainly be larger than the atmospheric torque. There must
either be a problem with the interpretation of the radar observations,
or with our basic understanding of Titan's atmosphere and/or interior.

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Title: Elastic Ice Shells of Synchronous Moons
Authors: Mitchell, Jonathan L.; Goldreich, P. M.
2009DPS....41.6605M Altcode:
A growing number of water-rich, synchronous moons are thought to contain
subsurface water oceans below an icy shell, most notably Europa and
Titan. Under tidal and rotational stresses, these shells deform and
store elastic energy unless the shell yields or viscously deforms on
a timescale that is fast compared to the forcing period. Otherwise,
the deformed shell experiences a back-torque tending to keep it
aligned with the satellite-planet line. The shell will rotate an
angle given by the balance between the elastic torque and the spinup
torque. For Europa, it has been widely advocated that stresses arising
from non-synchronous rotation of the shell are responsible for the
large cracks on its surface. The angle giving balance between the
tidal and elastic torques is exceedingly small -- of order 10^-6
radians -- and associated stresses are only of the order 1 Pa, well
below that needed to crack the shell; this poses a challenge to the
prevailing ideas of surface cracking on Europa. Time-dependent gravity
anomalies from mantle convection in Europa is a more likely mechanism
for producing large surface cracks. On Titan, it has been reported that
the surface spin is faster than synchronous, which has been interpreted
as resulting from a seasonally varying atmospheric torque on the surface
shell. The maximum atmospheric torque could rotate an elastic shell
relative to the underlying hydrostatic shape of order 10^-3 radians,
implying the shell is effectively coupled to the interior. Therefore,
the atmospheric torque forces a libration of the entire figure that is
180 degrees out-of-phase with the forcing and with a smaller amplitude
than has been reported.

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Title: Tidal Evolution of Rubble Piles
Authors: Goldreich, Peter; Sari, Re'em
2009ApJ...691...54G Altcode: 2007arXiv0712.0446G
Many small bodies in the solar system are believed to be rubble piles,
a collection of smaller elements separated by voids. We propose a model
for the structure of a self-gravitating rubble pile. Static friction
prevents its elements from sliding relative to each other. Stresses
are concentrated around points of contact between individual
elements. The effective dimensionless rigidity, \tilde{μ}_rubble,
is related to that of a monolithic body of similar composition
and size, \tilde{μ} by \tilde{μ}_rubble ∼ \tilde{μ}^{1/2}
ɛ_Y^{-1/2}, where epsilon Y ~ 10-2 is the
yield strain. This represents a reduction in effective rigidity
below the maximum radius, R max ~ [μepsilon
Y /(Gρ2)]1/2 ~ 103 km, at
which a rubble pile can exist. Our model for the rigidity of rubble
piles is compatible with laboratory experiments on the speed of shear
waves in sand. Densities derived for binary asteroids imply that they
are rubble piles. Thus their tidal evolution proceeds faster than it
would if they were monoliths. Binary orbit evolution is also driven by
torques resulting from the asymmetrical scattering and reradiation of
sunlight (YORP and BYORP effects). The tidal torque probably overcomes
the radiative (YORP) torque and synchronizes the spins of secondaries in
near-Earth binary asteroids and it definitely does so for secondaries
of main-belt binary asteroids. Synchronization is a requirement for
the radiative (BYORP) torque to act on the binary orbit. This torque
clearly dominates the tidal torque for all near-Earth binary asteroids
and for some binaries in the main belt. For other main-belt binaries,
the tidal torque appears to be at least comparable in strength to
the BYORP torque. An exciting possibility is that in these systems
the angular momentum added to the orbit by the tidal torque might be
removed by the radiative torque.

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Title: MHD turbulence
Authors: Goldreich, Peter
2009SchpJ...4.2350G Altcode:
No abstract at ADS

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Title: Constraints on deep-seated zonal winds inside Jupiter and
Saturn
Authors: Liu, Junjun; Goldreich, Peter M.; Stevenson, David J.
2008Icar..196..653L Altcode: 2007arXiv0711.3922L
The atmospheres of Jupiter and Saturn exhibit strong and stable
zonal winds. How deep the winds penetrate unabated into each planet
is unknown. Our investigation favors shallow winds. It consists of
two parts. The first part makes use of an Ohmic constraint; Ohmic
dissipation associated with the planet's magnetic field cannot exceed
the planet's net luminosity. Application to Jupiter (J) and Saturn
(S) shows that the observed zonal winds cannot penetrate below a depth
at which the electrical conductivity is about six orders of magnitude
smaller than its value at the molecular-metallic transition. Measured
values of the electrical conductivity of molecular hydrogen yield radii
of maximum penetration of 0.96R and 0.86R, with uncertainties of a few
percent of R. At these radii, the magnetic Reynolds number based on the
zonal wind velocity and the scale height of the magnetic diffusivity
is of order unity. These limits are insensitive to difficulties
in modeling turbulent convection. They permit complete penetration
along cylinders of the equatorial jets observed in the atmospheres
of Jupiter and Saturn. The second part investigates how deep the
observed zonal winds actually do penetrate. As it applies heuristic
models of turbulent convection, its conclusions must be regarded as
tentative. Truncation of the winds in the planet's convective envelope
would involve breaking the Taylor-Proudman constraint on cylindrical
flow. This would require a suitable nonpotential acceleration which
none of the obvious candidates appears able to provide. Accelerations
arising from entropy gradients, magnetic stresses, and Reynolds stresses
appear to be much too weak. These considerations suggest that strong
zonal winds are confined to shallow, stably stratified layers, with
equatorial jets being the possible exception.

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Title: How much oxygen is too much? Constraining Saturn's ring
atmosphere
Authors: Farmer, Alison J.; Goldreich, Peter
2007Icar..188..108F Altcode:
The discovery of a molecular oxygen atmosphere around Saturn's
rings has important implications for the electrodynamics of the
ring system. Its existence was inferred from the Cassini in situ
detection of molecular oxygen ions above the rings during Saturn Orbit
Insertion in 2004. Molecular oxygen is difficult to observe remotely,
and theoretical estimates have yielded only a lower limit ( N≳10 cm)
to the O 2 column density. Comparison with observations has
previously concerned matching ion densities at spacecraft altitudes far
larger than the scale height of the neutral atmosphere. This is further
complicated by charged particle propagation effects in Saturn's offset
magnetic field. In this study we adopt a complementary approach,
by focusing on bulk atmospheric properties and using additional
aspects of the Cassini observations to place an upper limit on the
column density. We develop a simple analytic model of the molecular
atmosphere and its photo-ionization and dissociation products, with N
a free parameter. Heating of the neutrals by viscous stirring, cooling
by collisions with the rings, and torquing by collisions with pickup
ions are all included in the model. We limit the neutral scale height
to h≲3000 km using the INMS neutral density nondetection over the A
ring. A first upper limit to the neutral column is derived by using
our model to reassess O 2 production and loss rates. Two
further limits are then obtained from Cassini observations: corotation
of the observed ions with the planet implies that the height-integrated
conductivity of the ring atmosphere is less than that of Saturn's
ionosphere; and the nondetection of fluorescent atomic oxygen over the
rings constrains the molecular column from which it is produced via
photo-dissociation. These latter limits are independent of production
and loss rates and are only weakly dependent on temperature. From
the three independent methods described, we obtain similar limits:
N≲2×10 cm. The mean free path for collisions between neutrals thus
cannot be very much smaller than the scale height.

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Title: Spontaneous axisymmetry breaking of the external magnetic
field at Saturn
Authors: Goldreich, Peter; Farmer, Alison J.
2007JGRA..112.5225G Altcode: 2007JGRA..11205225G; 2006astro.ph..8296G
Saturn's magnetic field is remarkably axisymmetric. Early evidence for
nonaxisymmetry came from the periodicity of Saturn's kilometric radio
bursts (SKR). Subsequently, percent-level variations of the SKR period
were found to occur on timescales of years. A recent breakthrough has
been the direct detection of a nonaxisymmetric component of the field
that rotates with a period close to that of the SKR and whose magnitude
varies only weakly with distance from Saturn. The latter implies that
it must be supported by currents external to the planet. We explore the
hypothesis that centrifugally driven convection spontaneously breaks
the axisymmetry of the external magnetic field at Saturn. The density
of the outflowing plasma close to its source is assumed to contain
a substantial part that varies as cos? and rotates uniformly. We
demonstrate that the plasma stream must narrow with distance from the
planet, while the field-aligned currents joining stream to ionosphere
increase rapidly. These currents produce a nonaxisymmetric component
of magnetic field whose magnitude varies inversely with radial
distance in the planet's equatorial plane. For a rate of plasma
outflow 104 ≲ ? ≲ 105g s-1, this
component's strength is compatible with that observed. Additionally,
we postulate that the SKR is associated with the narrow range of
longitudes over which large currents flow along magnetic field lines
connecting the tip of the outflow to the auroral ionosphere.

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Title: Imbalanced Strong MHD Turbulence
Authors: Lithwick, Y.; Goldreich, P.; Sridhar, S.
2007ApJ...655..269L Altcode: 2006astro.ph..7243L
We present a phenomenological model of imbalanced MHD turbulence
in an incompressible magnetofluid. The steady state cascades, of
waves traveling in opposite directions along the mean magnetic field,
carry unequal energy fluxes to small length scales, where they decay
as a result of viscous and resistive dissipation. The inertial range
scalings are well understood when both cascades are weak. We study
the case in which both cascades are, in a sense, strong. The inertial
range of this imbalanced cascade has the following properties: (1)
The ratio of the rms Elsässer amplitudes is independent of scale
and is equal to the ratio of the corresponding energy fluxes. (2) In
common with the balanced strong cascade, the energy spectra of both
Elsässer waves are of the anisotropic Kolmogorov form, with their
parallel correlation lengths equal to each other on all scales, and
proportional to the two-thirds power of the transverse correlation
length. (3) The equality of cascade time and wave period (critical
balance) that characterizes the strong balanced cascade does not
apply to the Elsässer field with the larger amplitude. Instead,
the more general criterion that always applies to both Elsässer
fields is that the cascade time is equal to the correlation time of
the straining imposed by oppositely directed waves. (4) In the limit
of equal energy fluxes, the turbulence corresponds to the balanced
strong cascade. Our results are particularly relevant for turbulence
in the solar wind. Spacecraft measurements have established that in
the inertial range of solar wind turbulence, waves traveling away from
the Sun have higher amplitudes than those traveling toward it. Result 1
allows us to infer the turbulent flux ratios from the amplitude ratios,
thus providing insight into the origin of the turbulence.

---------------------------------------------------------
Title: Spontaneous Axisymmetry Breaking of Saturn's External
Magnetic Field
Authors: Farmer, A. J.; Goldreich, P.
2006AGUFMSM22B..08F Altcode:
Saturn's magnetic field is remarkably axisymmetric: its dipole axis is
inclined by less than 0.2° with respect to its rotation axis. Recent
Cassini observations have revealed small non-axisymmetric field
components which rotate slightly more slowly than any atmospheric
feature. We show that rotationally driven convection of magnetospheric
plasma is responsible for the axisymmetry-breaking. Field-aligned
currents transfer angular momentum from the planet to a tongue of
outflowing plasma. This transfer slows the rate of rotation of the
ionosphere relative to that of the underlying atmosphere. The currents
are the source for the non- axisymmetric components of the field. The
common rotation rates of these components and Saturn's kilometric radio
(SKR) bursts is that of the plasma near the orbit of Enceladus, and by
extension the rotation rate in the ionosphere to which this plasma is
coupled. That rate tells us nothing about the rotation rate of Saturn's
deep interior. Of that we remain ignorant. Magnetic perturbations with
magnitudes similar to those observed by Cassini are produced for \dot
M ~ 104 g/s, a value similar to estimates for the rate of production
of plasma from Saturn's E-ring. Enhancement of the SKR occurs in a
narrow range of longitudes where the tip of the outgoing plasma stream
connects to the auroral ionosphere, via field lines that are bowed
outwards by currents that supply the plasma's centripetal acceleration.

---------------------------------------------------------
Title: Ohmic Dissipation Constraint on Deep-seated Zonal Winds in
Jupiter and Saturn
Authors: Liu, Junjun; Goldreich, P. M.; Stevenson, D. J.
2006DPS....38.0205L Altcode: 2006BAAS...38..483L
The atmospheres of Jupiter and Saturn exhibit strong and stable zonal
winds. Busse (1976) suggested that they might be the surface expression
of deep flows on cylinders. This hypothesis experiences difficulty
when account is taken of the electrical conductivity of molecular
hydrogen as measured in shockwave experiments. The deep zonal flow of an
electrically conducting fluid would produce a toroidal magnetic field,
an associated poloidal electrical current, and Ohmic dissipation. In
steady state, the total Ohmic dissipation cannot exceed the planet's
net luminosity. If we assume that the observed zonal flow penetrates
along cylinders until it is truncated to (near) zero at some spherical
radius, the upper bound on Ohmic dissipation constrains this radius
to be no smaller than 0.96 Jupiter radius and 0.86 Saturn radius. The
truncation of the cylindrical flow in the convective envelope requires
an appropriate force to break the Taylor-Proudman constraint. We have
been unable to identify any plausible candidate. The Lorentz force
is much too weak. Order of magnitude considerations suggest that
both divergence of the Reynolds stress and the buoyancy force are
inadequate. Therefore, we claim that the assumed deep-seated flows
do not exist. Equatorial jets could maintain constant velocities
on cylinders through the planet provided their half-widths were no
greater than 21° for Jupiter and 31° for Saturn. These boundaries
are similar to those of the equatorial jets observed in the planets’
atmospheres. We speculate that the Reynolds stress associated with
turbulent convection promotes differential rotation throughout the
interiors of the giant planets. Along cylinders that pass through the
maximum penetration depth, the Maxwell stress balances the Reynolds
stress resulting in small differential rotation except in the stably
stratified atmosphere. Equatorial jets are unencumbered by the Maxwell
stress. They pass through the planets and maintain velocities limited
by parasitic instabilities.

---------------------------------------------------------
Title: Magnetospheric Eclipses in the Double Pulsar System J0737-3039
Authors: Rafikov, R. R.; Goldreich, P.
2006IAUJD...2E..32R Altcode:
Recently discovered double pulsar system J0737-3039 consisting
of millisecond and normal pulsars in a 2.4 hour orbit provides us
with unprecedented tests of general relativity and magnetospheric
effects. One of the most interesting phenomena observed in this
system is the eclipse of the millisecond pulsar in the radio at its
conjunction with the normal pulsar. I will describe a theory which
explains this observation as a result of synchrotron absorption of
the millisecond pulsar radiobeam in the magnetosphere of the normal
pulsar. Absorption is "induced" in a sense that the intense radiobeam
of millisecond pulsar itself strongly modifies the properties of
the plasma in the closed part of the normal pulsar magnetosphere:
absorption of high-brightness temperature radio emission heats up
particles already present there and also allows additional pair plasma
to be trapped in this region by magnetic bottling effect. This theory
self-consistently predicts the size of the eclipsing region which agrees
very well with the observed duration of eclipse. Recent observations
of the variability of transmission during the eclipse modulated at
the rotation period of the normal pulsar have been interpreted as
resulting from the absorption by the rigidly rotating dipolar-shaped
magnetosphere which is in perfect agreement with our theory.

---------------------------------------------------------
Title: Spherical Accretion
Authors: Sari, Re'em; Goldreich, Peter
2006ApJ...642L..65S Altcode: 2006astro.ph..3293S
We compare different examples of spherical accretion onto a
gravitating mass. Limiting cases include the accretion of a
collisionally dominated fluid and the accretion of collisionless
particles. We derive expressions for the accretion rate and density
profile for semicollisional accretion, which bridges the gap between
these limiting cases. Particle crossing of the Hill sphere during the
formation of the outer planets is likely to have taken place in the
semicollisional regime.

---------------------------------------------------------
Title: Folded Fields as the Source of Extreme Radio-Wave Scattering
in the Galactic Center
Authors: Goldreich, Peter; Sridhar, S.
2006ApJ...640L.159G Altcode: 2006astro.ph..2532G
A strong case has been made that radio waves from sources within about
half a degree of the Galactic center undergo extreme diffractive
scattering. However, problems arise when standard (“Kolmogorov”)
models of electron density fluctuations are employed to interpret the
observations of scattering in conjunction with those of free-free radio
emission. Specifically, the outer scale of a Kolmogorov spectrum of
electron density fluctuations is constrained to be so small that it is
difficult to identify an appropriate astronomical setting. Moreover, an
unacceptably high turbulent heating rate results if the outer scale of
the velocity field coincides with that of the density fluctuations. We
propose an alternative model based on folded magnetic field structures
that have been reported in numerical simulations of small-scale
dynamos. Nearly isothermal density variations across thin current
sheets suffice to account for the scattering. There is no problem of
excess turbulent heating, because the outer scale for the velocity
fluctuations is much larger than the widths of the current sheets. We
speculate that interstellar magnetic fields could possess geometries
that reflect their origins: fields maintained by the Galactic dynamo
could have large correlation lengths, whereas those stirred by local
energetic events might exhibit folded structures.

---------------------------------------------------------
Title: Understanding the behavior of Prometheus and Pandora
Authors: Farmer, Alison J.; Goldreich, Peter
2006Icar..180..403F Altcode: 2005astro.ph.11055F
We revisit the dynamics of Prometheus and Pandora, two small moons
flanking Saturn's F ring. Departures of their orbits from freely
precessing ellipses result from mutual interactions via their 121:118
mean motion resonance. Motions are chaotic because the resonance is
split into four overlapping components. Orbital longitudes were observed
to drift away from predictions based on Voyager ephemerides. A sudden
jump in mean motions took place close to the time at which the orbits'
apses were antialigned in 2000. Numerical integrations reproduce both
the longitude drifts and the jumps. The latter have been attributed to
the greater strength of interactions near apse antialignment (every
6.2 yr), and it has been assumed that this drift-jump behavior
will continue indefinitely. We re-examine the dynamics of the
Prometheus-Pandora system by analogy with that of a nearly adiabatic,
parametric pendulum. In terms of this analogy, the current value of
the action of the satellite system is close to its maximum in the
chaotic zone. Consequently, at present, the two separatrix crossings
per precessional cycle occur close to apse antialignment. In this state
libration only occurs when the potential's amplitude is nearly maximal,
and the "jumps" in mean motion arise during the short intervals of
libration that separate long stretches of circulation. Because chaotic
systems explore the entire region of phase space available to them,
we expect that at other times the Prometheus-Pandora system would
be found in states of medium or low action. In a low action state it
would spend most of the time in libration, and separatrix crossings
would occur near apse alignment. We predict that transitions between
these different states can happen in as little as a decade. Therefore,
it is incorrect to assume that sudden changes in the orbits only happen
near apse antialignment.

---------------------------------------------------------
Title: Spoke formation under moving plasma clouds
Authors: Farmer, Alison J.; Goldreich, Peter
2005Icar..179..535F Altcode: 2005astro.ph..9306F
Goertz and Morfill [Goertz, C.K., Morfill, G., 1988. Icarus 53,
219-229] propose that spokes on Saturn's rings form under radially
moving plasma clouds produced by meteoroid impacts. We demonstrate
that the speed at which a plasma cloud can move relative to the ring
material is bounded from above by the difference between the Keplerian
and corotation velocities. The radial orientation of new spokes requires
radial speeds that are at least an order of magnitude larger than this
upper limit, thus the model advanced by Goertz and Morfill fails to
make radial spokes.

---------------------------------------------------------
Title: Magnetospheric Eclipses in the Double-Pulsar System PSR
J0737-3039
Authors: Rafikov, Roman R.; Goldreich, Peter
2005ApJ...631..488R Altcode: 2004astro.ph.12355R
We argue that eclipses of radio emission from the millisecond
pulsar A in the double-pulsar system PSR J0737-3039 are due to
synchrotron absorption by plasma in the closed field line region of
the magnetosphere of its normal pulsar companion B. On the basis of
a plausible geometric model, pulsar A's radio beam only illuminates
pulsar B's magnetosphere for about 10 minutes surrounding the time of
eclipse. During this time it heats particles at r&gt;~109
cm to relativistic energies and enables extra plasma, beyond that
needed to maintain the corotation electric field, to be trapped by
magnetic mirroring. An enhancement of the plasma density by a factor of
~102 is required to match the duration and optical depth of
the observed eclipses. The extra plasma might be supplied by a source
near B through Bγ pair creation by energetic photons produced in
B's outer gap. Relativistic pairs cool by synchrotron radiation close
to where they are born. Reexcitation of their gyrational motions by
cyclotron absorption of A's radio beam can result in their becoming
trapped between conjugate mirror points in B's magnetosphere. Because
the trapping efficiency decreases with increasing optical depth,
the plasma density enhancement saturates even under steady state
illumination. The result is an eclipse with finite, frequency-dependent
optical depth. After illumination by A's radio beam ceases, the trapped
particles cool and are lost. The entire cycle repeats every orbital
period. We speculate that the asymmetries between eclipse ingress and
egress result in part from the magnetosphere's evolution toward a steady
state when illuminated by A's radio beam. We predict that A's linear
polarization varies with both eclipse phase and B's rotational phase.

---------------------------------------------------------
Title: Spokes in Saturn's Rings
Authors: Farmer, A. J.; Goldreich, P.
2004AAS...205.4307F Altcode: 2004BAAS...36.1412F
The “spokes” in Saturn's rings have eluded explanation since
their discovery by the Voyager spacecraft. These ghostly radial dust
lanes spring into existence in under five minutes, then fade away in
hours as the Keplerian rotation of the rings distorts them. I shall
present a new model for spoke formation which looks set to reproduce
the observations. In particular we can account for the occurrence of
spokes around the radius of corotation of the planet with its rings,
a point which has evaded previous studies. New data from the Cassini
mission should provide even more stringent tests of our theory.

---------------------------------------------------------
Title: Chaos in the F Ring
Authors: Rappaport, N. J.; Goldreich, P.
2004DPS....36.0704R Altcode: 2004BAAS...36.1078R
We have been applying the methods developed in our studies of the
chaotic motion of Prometheus and Pandora to study the chaotic motion
of particles in the F ring. This work is still in progress at the
time this abstract is written. We hope to present results that will
be consistent with some of the characteristic features of the F ring.

---------------------------------------------------------
Title: Final Stages of Planet Formation
Authors: Goldreich, Peter; Lithwick, Yoram; Sari, Re'em
2004ApJ...614..497G Altcode: 2004astro.ph..4240G
We address three questions regarding solar system planets: What
determined their number? Why are their orbits nearly circular and
coplanar? How long did they take to form? Runaway accretion in a
disk of small bodies resulted in a tiny fraction of the bodies growing
much larger than all the others. These big bodies dominated the viscous
stirring of all bodies. Dynamical friction by small bodies cooled the
random velocities of the big ones. Random velocities of small bodies
were cooled by mutual collisions and/or gas drag. Runaway accretion
terminated when the orbital separations of the big bodies became as
wide as their feeding zones. This was followed by oligarchic growth
during which the big bodies maintained similar masses and uniformly
spaced semimajor axes. As the oligarchs grew, their number density
decreased, but their surface mass density increased. We depart
from standard treatments of planet formation by assuming that as
the big bodies got bigger, the small ones got smaller as the result
of undergoing a collisional fragmentation cascade. It follows that
oligarchy was a brief stage in solar system evolution. When the
oligarchs' surface mass density matched that of the small bodies,
dynamical friction was no longer able to balance viscous stirring,
so their velocity dispersion increased to the extent that their orbits
crossed. This marked the end of oligarchy. What happened next differed
in the inner and outer parts of the planetary system. In the inner
part, where the ratios of the escape velocities from the surfaces of
the planets to the escape velocities from their orbits are smaller than
unity, big bodies collided and coalesced after their random velocities
became comparable to their escape velocities. In the outer part,
where these ratios are larger than unity, the random velocities of
some of the big bodies continued to rise until they were ejected. In
both parts, the number density of the big bodies eventually decreased
to the extent that gravitational interactions among them no longer
produced large-scale chaos. After that their orbital eccentricities
and inclinations were damped by dynamical friction from the remaining
small bodies. The last and longest stage in planet formation
was the cleanup of small bodies. Our understanding of this stage is
fraught with uncertainty. The surviving protoplanets cleared wide
gaps around their orbits that inhibited their ability to accrete
small bodies. Nevertheless, in the inner planet system, all of the
material in the small bodies ended up inside planets. Small bodies in
the outer planet system probably could not have been accreted in the
age of the solar system. A second generation of planetesimals may have
formed in the disk of small bodies, by either collisional coagulation
or gravitational instability. In the outer planet system, bodies of
kilometer size or larger would have had their random velocities excited
until their orbits crossed those of neighboring protoplanets. Ultimately
they would have either escaped from the Sun or become residents of the
Oort Cloud. An important distinction is that growth of the inner planets
continued through cleanup, whereas assembly of the outer planets was
essentially complete by the end of oligarchy. These conclusions imply
that the surface density of the protoplanetary disk was that of the
minimum solar mass nebula in the inner planet region but a few times
larger in the outer planet region. The timescale through cleanup was
set by the accretion rate at the geometrical cross section in the inner
planet region and by the ejection rate at the gravitationally enhanced
cross section in the outer planet region. It was a few hundred million
years in the former and a few billion years in the latter. However,
since Uranus and Neptune acquired most of their mass by the end of
oligarchy, they may have formed before Earth! A few implications
of the above scenario are worth noting. Impacts among protoplanets
of comparable size were common in the inner planet system but not in
the outer. Ejections from the outer planet system included several
bodies with masses in excess of Earth after oligarchy and an adequate
number of kilometer-size bodies to populate the Oort comet cloud during
cleanup. Except at the very end of cleanup, collisions prevented Uranus
and Neptune from ejecting kilometer-size objects. Only Jupiter and,
to a much lesser extent, Saturn were capable of populating the Oort
Cloud with comets of kilometer size.

---------------------------------------------------------
Title: Planet Formation by Coagulation: A Focus on Uranus and Neptune
Authors: Goldreich, Peter; Lithwick, Yoram; Sari, Re'em
2004ARA&A..42..549G Altcode: 2004astro.ph..5215G
Planets form in the circumstellar disks of young stars. We review the
basic physical processes by which solid bodies accrete each other and
alter each others' random velocities, and we provide order-of-magnitude
derivations for the rates of these processes. We discuss and exercise
the two-groups approximation, a simple yet powerful technique for
solving the evolution equations for protoplanet growth. We describe
orderly, runaway, neutral, and oligarchic growth. We also delineate the
conditions under which each occurs. We refute a popular misconception
by showing that the outer planets formed quickly by accreting small
bodies. Then we address the final stages of planet formation. Oligarchy
ends when the surface density of the oligarchs becomes comparable
to that of the small bodies. Dynamical friction is no longer able
to balance viscous stirring and the oligarchs' random velocities
increase. In the inner-planet system, oligarchs collide and coalesce. In
the outer-planet system, some of the oligarchs are ejected. In both the
inner- and outer-planet systems, this stage ends once the number of big
bodies has been reduced to the point that their mutual interactions no
longer produce large-scale chaos. Subsequently, dynamical friction by
the residual small bodies circularizes and flattens their orbits. The
final stage of planet formation involves the clean up of the residual
small bodies. Clean up has been poorly explored.

---------------------------------------------------------
Title: Planet-Disk Symbiosis
Authors: Sari, Re'em; Goldreich, Peter
2004ApJ...606L..77S Altcode: 2003astro.ph..7107S
Planets form in disks around young stars. Interactions with these disks
cause them to migrate and thus affect their final orbital periods. We
suggest that the connection between planets and disks may be deeper
and involve a symbiotic evolution. By contributing to the outward
transport of angular momentum, planets promote disk accretion. Here we
demonstrate that planets sufficiently massive to open gaps could be
the primary agents driving disk accretion. Those having masses below
the gap opening threshold drift inward more rapidly than the disk
material and can only play a minor role in its accretion. An even more
intimate symbiosis involving gap opening planets may result if they
acquire most of their mass prior to gap formation. Given a small initial
eccentricity, just a fraction of a percent, the orbital eccentricity of
a massive planet may grow rapidly once a mass in excess of the planet's
mass has been repelled to form a gap around the planet's orbit. Then,
as the planet's radial excursions approach the gap's width, subsequent
eccentricity growth slows so that the planet's orbit continues to be
confined within the gap.

---------------------------------------------------------
Title: Wave Damping by Magnetohydrodynamic Turbulence and Its Effect
on Cosmic-Ray Propagation in the Interstellar Medium
Authors: Farmer, Alison J.; Goldreich, Peter
2004ApJ...604..671F Altcode: 2003astro.ph.11400F
Cosmic rays scatter off magnetic irregularities (Alfvén waves) with
which they are resonant, that is, waves of wavelength comparable to
their gyroradii. These waves may be generated either by the cosmic
rays themselves, if they stream faster than the Alfvén speed, or by
sources of MHD turbulence. Waves excited by streaming cosmic rays are
ideally shaped for scattering, whereas the scattering efficiency of
MHD turbulence is severely diminished by its anisotropy. We show that
MHD turbulence has an indirect effect on cosmic-ray propagation by
acting as a damping mechanism for cosmic-ray-generated waves. The hot
(“coronal”) phase of the interstellar medium is the best candidate
location for cosmic-ray confinement by scattering from self-generated
waves. We relate the streaming velocity of cosmic rays to the rate of
turbulent dissipation in this medium for the case in which turbulent
damping is the dominant damping mechanism. We conclude that cosmic
rays with up to 102 GeV could not stream much faster than
the Alfvén speed but 106 GeV cosmic rays would stream
unimpeded by self-generated waves, unless the coronal gas were
remarkably turbulence-free.

---------------------------------------------------------
Title: Sackler Lecture: Final Stages of Planet Formation
Authors: Goldreich, Peter
2004cfa..collE..15G Altcode:
My lecture will address three major questions regarding solar system
planets. What determined their number? Why are their orbits nearly
circular and coplanar? How long did they take to form? Answers to
these will be given in terms of: stability against large scale chaos;
dynamical friction by small bodies; and the accretion rate at the
geometrical cross section in the inner planet region and the ejection
rate at the gravitationally enhanced cross section in the outer.

---------------------------------------------------------
Title: Gauge freedom in the N-body problem of celestial mechanics
Authors: Efroimsky, M.; Goldreich, P.
2004A&A...415.1187E Altcode: 2003astro.ph..7130E
The goal of this paper is to demonstrate how the internal symmetry
of the N-body celestial-mechanics problem can be exploited in orbit
calculation. We start with summarising research reported in
(Efroimsky \cite{Efr02}, \cite{Efr03}; Newman &amp; Efroimsky
\cite{New03}; Efroimsky &amp; Goldreich \cite{Efro03}) and develop
its application to planetary equations in non-inertial frames. This
class of problems is treated by the variation-of-constants method. As
explained in the previous publications, whenever a standard system of
six planetary equations (in the Lagrange, Delaunay, or other form) is
employed for N objects, the trajectory resides on a 9(N-1)-dimensional
submanifold of the 12(N-1)-dimensional space spanned by the orbital
elements and their time derivatives. The freedom in choosing
this submanifold reveals an internal symmetry inherent in the
description of the trajectory by orbital elements. This freedom is
analogous to the gauge invariance of electrodynamics. In traditional
derivations of the planetary equations this freedom is removed by
hand through the introduction of the Lagrange constraint, either
explicitly (in the variation-of-constants method) or implicitly (in
the Hamilton-Jacobi approach). This constraint imposes the condition
(called “osculation condition”) that both the instantaneous position
and velocity be fit by a Keplerian ellipse (or hyperbola), i.e., that
the instantaneous Keplerian ellipse (or hyperbola) be tangential to the
trajectory. Imposition of any supplementary constraint different from
that of Lagrange (but compatible with the equations of motion) would
alter the mathematical form of the planetary equations without affecting
the physical trajectory. However, for coordinate-dependent
perturbations, any gauge different from that of Lagrange makes the
Delaunay system non-canonical. Still, it turns out that in a more
general case of disturbances dependent also upon velocities, there
exists a “generalised Lagrange gauge”, i.e., a constraint under
which the Delaunay system is canonical (and the orbital elements are
osculating in the phase space). This gauge reduces to the regular
Lagrange gauge for perturbations that are velocity-independent. Finally, we provide a practical example illustrating how the gauge
formalism considerably simplifies the calculation of satellite motion
about an oblate precessing planet.

---------------------------------------------------------
Title: Origin of chaos in the Prometheus-Pandora system
Authors: Goldreich, Peter; Rappaport, Nicole
2003Icar..166..320G Altcode: 2003astro.ph..7259G
We demonstrate that the chaotic orbits of Prometheus and Pandora
are due to interactions associated with the 121:118 mean motion
resonance. Differential precession splits this resonance into a quartet
of components equally spaced in frequency. Libration widths of the
individual components exceed the splitting, resulting in resonance
overlap which causes the chaos. Mean motions of Prometheus and Pandora
wander chaotically in zones of width 1.8 and 3.1 deg yr -1,
respectively. A model with 1.5 degrees of freedom captures the essential
features of the chaotic dynamics. We use it to show that the Lyapunov
exponent of 0.3 yr -1 arises because the critical argument
of the dominant member of the resonant quartet makes approximately
two separatrix crossings every 6.2 year precessional cycle.

---------------------------------------------------------
Title: Gauge symmetry of the N-body problem in the Hamilton-Jacobi
approach
Authors: Efroimsky, Michael; Goldreich, Peter
2003JMP....44.5958E Altcode: 2003JMPS...44.5958E; 2003JMP...44..5958E; 2003astro.ph..5344E
In most books the Delaunay and Lagrange equations for the orbital
elements are derived by the Hamilton-Jacobi method: one begins with
the two-body Hamilton equations in spherical coordinates, performs
a canonical transformation to the orbital elements, and obtains the
Delaunay system. A standard trick is then used to generalize the
approach to the N-body case. We reexamine this step and demonstrate
that it contains an implicit condition which restricts the dynamics
to a 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space
spanned by the elements and their time derivatives. The tacit condition
is equivalent to the constraint that Lagrange imposed “by hand”
to remove the excessive freedom, when he was deriving his system of
equations by variation of parameters. It is the condition of the orbital
elements being osculating, i.e., of the instantaneous ellipse (or
hyperbola) being always tangential to the physical velocity. Imposure
of any supplementary condition different from the Lagrange constraint
(but compatible with the equations of motion) is legitimate and
will not alter the physical trajectory or velocity (though will
alter the mathematical form of the planetary equations). This
freedom of nomination of the supplementary constraint reveals a
gauge-type internal symmetry instilled into the equations of celestial
mechanics. Existence of this internal symmetry has consequences for
the stability of numerical integrators. Another important aspect of
this freedom is that any gauge different from that of Lagrange makes
the Delaunay system noncanonical. In a more general setting, when the
disturbance depends not only upon positions but also upon velocities,
there is a “generalized Lagrange gauge” wherein the Delaunay system
is symplectic. This special gauge renders orbital elements that are
osculating in the phase space. It coincides with the regular Lagrange
gauge when the perturbation is velocity independent.

---------------------------------------------------------
Title: Gauge-invariant disturbing function in precessing frames
of reference.
Authors: Efroimsky, M.; Goldreich, P.
2003DDA....34.0903E Altcode: 2003BAAS...35.1042E
In most books the Lagrange and Delaunay systems of equations for the
orbital elements are derived in the Hamilton-Jacobi approach: one
begins with two-body Hamilton equations in spherical or Cartesian
coordinates; then carries out a canonical transformation to the
orbital elements and, thus, arrives to the Delaunay or Lagrange
system. A standard trick then enables one to generalize the approach
to the N-body case. We carefully re-examine this step and demonstrate
that it contains an implicit condition which restricts the orbit to a
certain 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space
spanned by the orbital elements and their time derivatives. This tacit
assumption is equivalent to the so-called Lagrange constraint, one that
Lagrange imposed “by hand” in order to remove the excessive freedom,
when he was deriving his system of equations by the method of variation
of parameters. The physical meaning of this implicit condition,
tacitly present also in the Hamilton-Jacobi treatment of the N-body
problem, is transparent: it is the condition of the orbital elements
being osculating (i.e., of the velocity being expressed through the
orbital elements in the same manner as in the two-body case). The
imposure of any supplementary condition, which is different from the
Lagrange constraint (but is compatible with the equations of motion), is
legitimate. However, it will alter the form of the Lagrange and Delaunay
equations (Efroimsky 2002, Newman &amp; Efroimsky 2003) and will have
consequences for numerical integrators (Efroimsky 2002, Murison &amp;
Efroimsky 2003). Another important alteration of the Lagrange and
Delaunay systems will be in order when the disturbing function depends
not only upon the coordinates but also upon the velocities, i.e., when
the orbital elements are defined in a non-inertial coordinate system
(Goldreich 1965). In the current presentation we consider interplay
between these two issues: the freedom of gauge fixing and the freedom
of reference-system choice. We apply our results to description of a
satellite motion about a precessing planet.

---------------------------------------------------------
Title: The origin of chaos in the dynamics of the Prometheus-Pandora
System
Authors: Rappaport, N. J.; Goldreich, P.
2003DPS....35.4603R Altcode: 2003BAAS...35.1010R
In 2002, Rappaport and Goldreich demonstrated that the motions
of Prometheus and Pandora are chaotic. The chaos arises from the
gravitational interactions between the satellites. Sudden changes in
mean motions occur every 6.2 years when the periapsis of Pandora's
orbit is aligned and on the same side of Saturn with the apoapsis
of Prometheus' orbit, and the gravitational interactions between the
two bodies are greatly enhanced. We followed up this work by a
search for the origin of the chaos. We found that the chaos is due to
overlapping of the four resonances associated with the same 121:118
ratio of mean motions and the four possible combinations of periapsis
longitudes of Prometheus and Pandora. Mean motion of Prometheus and
Pandora wander chaotically in zones of width 1.8 and 3.1 degrees per
year, respectively. Furthermore, we demonstrated that the whole
system can be represented by a single degree of freedom model that
captures the full chaotic dynamics. References: (1) Rappaport,
N.J., and P. Goldreich 2002: The Chaotic Dynamics of Prometheus and
Pandora, BAAS 34, 883. (2) Goldreich, P., and N. Rappaport 2003:
Chaotic motions of Prometheus and Pandora, Icarus 162, 391-399. This research was supported by NASA Planetary Geology and Geophysics
grant 344-30-53-02 and by NSF grant AST-0098301.

---------------------------------------------------------
Title: Formation of Kuiper Belt Binaries
Authors: Sari, R.; Goldreich, P.; Lithwick, Y.
2003DPS....35.4909S Altcode: 2003BAAS...35.1017S
At least several percent of large Kuiper belt objects are
members of wide binaries. We argue that binaries formed during
runaway accretion. Collisionless gravitational interactions provide
two channels for binary formation. The initial step is always the
formation of a transient binary when two large bodies penetrate each
other's Hill spheres. Then, either dynamical friction due to small
bodies or the scattering of a third large body can carry away the
energy needed for permanent binding. We predict that most objects
of size comparable to those currently observed in the Kuiper belt
are members of multiple systems: outside of a critical separation of
3”, the binary probability is about 0.3%; inside that separation,
the probability increases inversely with separation. This prediction
is compatible with results from current surveys.

---------------------------------------------------------
Title: Chaotic motions of prometheus and pandora
Authors: Goldreich, Peter; Rappaport, Nicole
2003Icar..162..391G Altcode:
Recent HST images of the saturnian satellites Prometheus and Pandora
show that their longitudes deviate from predictions of ephemerides
based on Voyager images. Currently Prometheus is lagging and Pandora
leading these predictions by somewhat more than 20°. We show
that these discrepancies are fully accounted for by gravitational
interactions between the two satellites. These peak every 24.8 days
at conjunctions and excite chaotic perturbations. The Lyapunov
exponent for the Prometheus-Pandora system is of order 0.3 year
-1 for satellite masses based on a nominal density of 0.63
g cm -3. Interactions are strongest when the orbits come
closest together. This happens at intervals of 6.2 years when their
apses are antialigned. In this context, we note the sudden changes of
opposite signs in the mean motions of Prometheus and Pandora at the end
of 2000 occurred around the time their apsidal lines were antialigned.

---------------------------------------------------------
Title: Eccentricity Evolution for Planets in Gaseous Disks
Authors: Goldreich, Peter; Sari, Re'em
2003ApJ...585.1024G Altcode: 2002astro.ph..2462G
At least several percent of solar-type stars possess giant
planets. Surprisingly, most move on orbits of substantial
eccentricity. We investigate the hypothesis that interactions
between a giant planet and the disk from which it forms promote
eccentricity growth. These interactions are concentrated at discrete
Lindblad and corotation resonances. Interactions at principal
Lindblad resonances cause the planet's orbit to migrate and open
a gap in the disk if the planet is sufficiently massive. Those at
first-order Lindblad and corotation resonances change the planet's
orbital eccentricity. Eccentricity is excited by interactions at
external Lindblad resonances that are located on the opposite side
of corotation from the planet, and damped by co-orbital Lindblad
resonances that overlap the planet's orbit. If the planet clears
a gap in the disk, the rate of eccentricity damping by co-orbital
Lindblad resonances is reduced. Density gradients associated with the
gap activate eccentricity damping by corotation resonances at a rate
that initially marginally exceeds that of eccentricity excitation
by external Lindblad resonances. But the corotation torque may be
reduced as the result of the trapping of fluid in libration around
potential maxima. This nonlinear saturation can tip the balance in
favor of eccentricity excitation. A minimal initial eccentricity
of the order of 1% is required to overcome viscous diffusion,
which acts to unsaturate corotation resonances by reestablishing
the large-scale density gradient. Thus, eccentricity growth is a
finite-amplitude instability. Formally, the apsidal resonance,
which is a special kind of co-orbital Lindblad resonance that
exists in pressure-dominated disks, appears to damp eccentricity
faster than external Lindblad resonances can excite it. However,
the wavelength of the apsidal wave in a pressure-dominated disk
is so long that it does not propagate. A self-gravity-dominated
disk does not have an apsidal resonance. Nevertheless, apsidal
waves are excited at gap edges. Although these propagate, their long
wavelengths suggest that they are likely to be reflected at disk edges
to form standing waves. Viscous damping of standing waves results in
eccentricity damping, but at level far below that which traveling
waves would produce. Although the level of eccentricity damping
due to apsidal waves is reduced to a modest level in both pressure-
and self-gravity-dominated disks, whether it drops well below that
of Lindblad resonances depends sensitively on the disk's thickness
and planet's mass. However, our analysis shows that with reasonable
parameters, planet-disk interactions can promote eccentricity growth.

---------------------------------------------------------
Title: Imbalanced Weak Magnetohydrodynamic Turbulence
Authors: Lithwick, Yoram; Goldreich, Peter
2003ApJ...582.1220L Altcode: 2002astro.ph..8046L
Weak MHD turbulence consists of waves that propagate along magnetic
field lines, in both directions. When two oppositely directed
waves collide, they distort each other, without changing their
respective energies. Each wave suffers many collisions before
cascading; by contrast, in strong MHD turbulence, waves cascade on
the same timescale at which they collide. “Imbalance” means that
more energy is going in one direction than the other. In general,
MHD turbulence is imbalanced. Yet imbalanced MHD cascades are not
understood. For example, turbulence in the solar wind is observed
to be imbalanced, so solar wind turbulence will not be understood
until a theory of the imbalanced cascade is developed. We solve
weak MHD turbulence that is imbalanced. Of crucial importance is
that the energies going in both directions are forced to equalize
at the dissipation scale. This “pinning” of the energy spectra was
discovered by Grappin and coworkers. It affects the entire inertial
range. Weak MHD turbulence is particularly interesting because
perturbation theory is applicable. Hence, it can be described with a
simple kinetic equation. Galtier and coworkers derived this kinetic
equation. We present a simpler, more physical derivation, based on
the picture of colliding wavepackets. In the process, we clarify the
role of the zero-frequency mode. We also explain why Goldreich &amp;
Sridhar claimed that perturbation theory is inapplicable, and why
this claim is wrong. (Our “weak” is equivalent to Goldreich &amp;
Sridhar's “intermediate.”) We perform numerical simulations of the
kinetic equation to verify our claims. We construct simplified model
equations that illustrate the main effects. Finally, we show that
a large magnetic Prandtl number does not have a significant effect,
and that hyperviscosity leads to a pronounced bottleneck effect.

---------------------------------------------------------
Title: Formation of Kuiper-belt binaries by dynamical friction and
three-body encounters
Authors: Goldreich, Peter; Lithwick, Yoram; Sari, Re'em
2002Natur.420..643G Altcode: 2002astro.ph..8490G
The Kuiper belt is a disk of icy bodies that orbit the Sun beyond
Neptune; the largest known members are Pluto and its companion
Charon. A few per cent of Kuiper-belt bodies have recently been found
to be binaries with wide separations and mass ratios of the order of
unity. Collisions were too infrequent to account for the observed number
of binaries, implying that these binaries formed through collisionless
interactions mediated by gravity. These interactions are likely to
have been most effective during the period of runaway accretion,
early in the Solar System's history. Here we show that a transient
binary forms when two large bodies penetrate one another's Hill sphere
(the region where their mutual forces are larger than the tidal force
of the Sun). The loss of energy needed to stabilize the binary orbit
can then occur either through dynamical friction from surrounding
small bodies, or through the gravitational scattering of a third large
body. Our estimates slightly favour the former mechanism. We predict
that five per cent of Kuiper-belt objects are binaries with apparent
separations greater than 0.2arcsec, and that most are in tighter
binaries or systems of higher multiplicity.

---------------------------------------------------------
Title: The Chaotic Dynamics of Prometheus and Pandora
Authors: Rappaport, N. J.; Goldreich, P.
2002DPS....34.2401R Altcode: 2002BAAS...34..883R
The longitudes of the F-ring shepherd satellites Prometheus and Pandora
measured in recent HST images are different from predictions based on
Voyager images. The discrepancies are of order 20 degrees. In a paper
submitted to Icarus (Goldreich, P., and N. Rappaport 2002: Chaotic
Motions of F-Ring Shepherds), we showed that these discrepancies are
fully accounted for by the gravitational interactions between these
satellites. These peak every 24.8 days at conjunctions and excite
chaotic perturbations. Interactions are strongest when the orbits
come close together. This happens at intervals of 6.2 years when the
apses are anti-aligned. We found that the sudden changes of opposite
changes in the mean motions of Prometheus and Pandora at the end of
2000 occurred shortly after their apsidal line was anti-aligned. The
Lyapunov exponent for the Prometheus-Pandora system is of order 0.35
year-1 for satellite masses based on a nominal density of 1.3
g/cm3. In this presentation we will characterize the chaos
as a function of the parameters and discuss new results pertaining
to the understanding of the mechanism giving rise to it. Rappaport
acknowldeges funding by NASA Planetary Geology and Geophysics Program,
Grant 344-30-53-02. Goldreich acknowledges NSF Grant AST-0098301 and
NASA Grant NAG5-12037.

---------------------------------------------------------
Title: Chaotic Motions of F-Ring Shepherds
Authors: Goldreich, Peter; Rappaport, Nicole
2002astro.ph..5330G Altcode:
Recent HST images of the Saturnian satellites Prometheus and Pandora
show that their longitudes deviate from predictions of ephemerides
based on Voyager images. Currently Prometheus is lagging and Pandora
leading these predictions by somewhat more than 20 degrees. We show
that these discrepancies are fully accounted for by gravitational
interactions between the two satellites. These peak every 24.8 days at
conjunctions and excite chaotic perturbations. The Lyapunov exponent
for the Prometheus-Pandora system is of order 0.35 inverse years for
satellite masses based on a nominal density of 1.3 gm/cm^3. Interactions
are strongest when the orbits come closest together. This happens at
intervals of 6.2 years when their apses are anti-aligned. In this
context we note the sudden changes of opposite signs in the mean
motions of Prometheus and Pandora at the end of 2000 occured shortly
after their apsidal lines were anti-aligned.

---------------------------------------------------------
Title: Fundamental Models Of MHD Turbulence
Authors: Goldreich, Peter
2002APS..APR.J2001G Altcode:
The inertial range of incompressible MHD turbulence is most conveniently
described in terms of counter propagating waves. Shear Alfvén waves
control the cascade dynamics. Slow waves play a passive role and
adopt the spectrum set by the shear Alfvén waves. Cascades composed
entirely of shear Alfvén waves do not generate a significant measure
of slow waves. MHD turbulence is anisotropic with energy cascading
more rapidly along k_⊥ than along k_allel. Anisotropy increases
with k_⊥ such that the excited modes are confined inside a cone
bounded by k_allel∝ k_⊥^2/3. The opening angle of the cone,
θ(k_⊥)∝ k_⊥-1/3, defines the scale dependent
anisotropy. MHD turbulence is generically strong in the sense that
the waves which comprise it are critically damped. Nevertheless,
deep inside the inertial range, turbulent fluctuations are
small. Their energy density is less than that of the background
field by a factor θ^2(k_⊥)&lt;&lt; 1. MHD cascades are best
understood geometrically. Wave packets suffer distortions as they
move along magnetic field lines perturbed by counter propagating
wave packets. Field lines perturbed by unidirectional waves map
planes perpendicular to the local field into each other. Shear
Alfvén waves are responsible for the mapping's shear and
slow waves for its dilatation. The former exceeds the latter by
θ-1(k_⊥)&gt;&gt; 1 which accounts for dominance of the
shear Alfvén waves in controlling the cascade dynamics.

---------------------------------------------------------
Title: Tidal Evolution of the Planetary System around HD 83443
Authors: Wu, Yanqin; Goldreich, Peter
2002ApJ...564.1024W Altcode: 2001astro.ph..8499W
Two planets with an orbital period ratio of approximately 10:1 have
been discovered around the star HD 83443. The inner and more massive
planet, HD 83443b, has the smallest semimajor axis among all currently
known exoplanets. Unlike other short-period exoplanets, it maintains
a substantial orbital eccentricity, e1=0.079+/-0.008,
in spite of efficient tidal damping. This is a consequence of its
secular interactions with HD 83443c, whose orbital eccentricity
e2=0.42+/-0.06. Dissipation, associated with tides the star
raises in the inner planet, removes energy but not angular momentum
from its orbit, while secular interactions transfer angular momentum
but not energy from the inner to the outer planet's orbit. The outward
transfer of angular momentum decreases the tidal decay rate of the
inner planet's orbital eccentricity while increasing that of the
outer planet. The alignment of the apsides of the planets' orbits is
another consequence of tidal and secular interactions. In this state
the ratio of their orbital eccentricities, e1/e2,
depends on the secular perturbations the planets exert on each other
and on additional perturbations that enhance the inner planet's
precession rate. Tidal and rotational distortions of the inner
planet along with general relativity provide the most important
of these extra precessional perturbations, each of which acts to
reduce e1/e2. Provided the planets' orbits are
coplanar, the observed eccentricity ratio uniquely relates sini and
C≡(k2/k2J)(R1/RJ)5,
where the tidal Love number, k2, and radius, R1,
of the inner planet are scaled by their Jovian equivalents.

---------------------------------------------------------
Title: Compressible Magnetohydrodynamic Turbulence in Interstellar
Plasmas
Authors: Lithwick, Yoram; Goldreich, Peter
2001ApJ...562..279L Altcode: 2001astro.ph..6425L
Radio wave scintillation observations reveal a nearly Kolmogorov
spectrum of density fluctuations in the ionized interstellar
medium. Although this density spectrum is suggestive of turbulence,
no theory relevant to its interpretation exists. We calculate the
density spectrum in turbulent magnetized plasmas by extending the
theory of incompressible magnetohydrodynamic (MHD) turbulence given by
Goldreich &amp; Sridhar to include the effects of compressibility and
particle transport. Our most important results are as follows:1. Density
fluctuations are due to the slow mode and the entropy mode. Both modes
are passively mixed by the cascade of shear Alfvén waves. Since the
shear Alfvén waves have a Kolmogorov spectrum, so do the density
fluctuations.2. Observed density fluctuation amplitudes constrain
the nature of MHD turbulence in the interstellar medium. Slow mode
density fluctuations are suppressed when the magnetic pressure is
less than the gas pressure. Entropy mode density fluctuations are
suppressed by cooling when the cascade timescale is longer than
the cooling timescale. These constraints imply either that the
magnetic and gas pressures are comparable or that the outer scale
of the turbulence is very small.3. A high degree of ionization is
required for the cascade to survive damping by neutrals and thereby
to extend to small length scales. Regions that are insufficiently
ionized produce density fluctuations only on length scales larger than
the neutral damping scale. These regions may account for the excess
of power that is found on large scales.4. Provided that the thermal
pressure exceeds the magnetic pressure, both the entropy mode and the
slow mode are damped on length scales below that at which protons can
diffuse across an eddy during the eddy's turnover time. Consequently,
eddies whose extents along the magnetic field are smaller than the
proton collisional mean free path do not contribute to the density
spectrum. However, in MHD turbulence eddies are highly elongated along
the magnetic field. From an observational perspective, the relevant
length scale is that transverse to the magnetic field. Thus, the cutoff
length scale for density fluctuations is significantly smaller than
the proton mean free path.5. The Alfvén mode is critically damped at
the transverse length scale of the proton gyroradius and thus cascades
to smaller length scales than either the slow mode or the entropy mode.

---------------------------------------------------------
Title: Incompressible MHD Turbulence
Authors: Goldreich, Peter
2001Ap&SS.278...17G Altcode:
The inertial range of incompressible MHD turbulence is most conveniently
described in terms of counter propagating waves. Shear Alfvén waves
control the cascade dynamics. Slow waves play a passive role and
adopt the spectrum set by the shear Alfvén waves. Cascades composed
entirely of shear Alfvén waves do not generate a significant measure
of slow waves. MHD turbulence is anisotropic with energy cascading more
rapidly along k ⊥ than along k ∥. Anisotropy
increases with k ⊥ such that the excited modes are
confined inside a cone bounded by k ∥∝ k perp
2/3. The opening angle of the cone, θ( k ⊥)∝
k ⊥ -1/3, defines the scale dependent
anisotropy. MHD turbulence is generically strong in the sense that
the waves which comprise it are critically damped. Nevertheless, deep
inside the inertial range, turbulent fluctuations are small. Their
energy density is less than that of the background field by a
factor θ2( k ⊥)≪. MHD cascades are best
understood geometrically. Wave packets suffer distortions as they
move along magnetic field lines perturbed by counter propagating wave
packets. Field lines perturbed by unidirectional waves map planes
perpendicular to the local field into each other. Shear Alfvén
waves are responsible for the mapping's shear and slow waves for
its dilatation. The former exceeds the latter by θ-1(
k ⊥)≫ 1 which accounts for dominance of the shear
Alfvén waves in controlling the cascade dynamics.

---------------------------------------------------------
Title: Simulations of Incompressible Magnetohydrodynamic Turbulence
Authors: Maron, Jason; Goldreich, Peter
2001ApJ...554.1175M Altcode: 2000astro.ph.12491M
We simulate incompressible MHD turbulence using a pseudospectral
code. Our major conclusions are: (1) MHD turbulence is most conveniently
described in terms of counterpropagating shear Alfvén and slow
waves. Shear Alfvén waves control the cascade dynamics. Slow waves
play a passive role and adopt the spectrum set by the shear Alfvén
waves. Cascades composed entirely of shear Alfvén waves do not
generate a significant measure of slow waves. (2) MHD turbulence is
anisotropic, with energy cascading more rapidly along k⊥
than along k∥, where k⊥ and k∥
refer to wavevector components perpendicular and parallel to the local
magnetic field, respectively. Anisotropy increases with increasing
k⊥ such that excited modes are confined inside a
cone bounded by k∥~kγ⊥,
where γ&lt;1. The opening angle of the cone,
Θ(k⊥)~k-(1-γ)⊥,
defines the scale-dependent anisotropy. (3) The one-dimensional
inertial range energy spectrum is well fitted by a power law,
E(k⊥)~k-α⊥, with α&gt;1. (4)
MHD turbulence is generically strong in the sense that the waves that
comprise it suffer order unity distortions on timescales comparable
to their periods. Nevertheless, turbulent fluctuations are small deep
inside the inertial range. Their energy density is less than that of the
background field by a factor of Θ(α-1)/(1-γ)&lt;&lt;1. (5)
MHD cascades are best understood geometrically. Wave packets suffer
distortions as they move along magnetic field lines perturbed by
counterpropagating waves. Field lines perturbed by unidirectional waves
map planes perpendicular to the local field into each other. Shear
Alfvén waves are responsible for the mapping's shear and slow waves
for its dilatation. The amplitude of the former exceeds that of the
latter by 1/Θ(k⊥), which accounts for dominance of the
shear Alfvén waves in controlling the cascade dynamics. (6) Passive
scalars mixed by MHD turbulence adopt the same power spectrum as the
velocity and magnetic field perturbations. (7) Decaying MHD turbulence
is unstable to an increase of the imbalance between the fluxes of waves
propagating in opposite directions along the magnetic field. Forced
MHD turbulence displays order unity fluctuations with respect to the
balanced state if excited at low k⊥ by δ(t)-correlated
forcing. It appears to be statistically stable to the unlimited growth
of imbalance. (8) Gradients of the dynamic variables are focused into
sheets aligned with the magnetic field whose thickness is comparable to
the dissipation scale. Sheets formed by oppositely directed waves are
uncorrelated. We suspect that these are vortex sheets, which the mean
magnetic field prevents from rolling up. (9) Items 1-6 lend support
to the model of strong MHD turbulence put forth by Goldreich &amp;
Sridhar (GS). Results from our simulations are also consistent with
the GS prediction γ=2/3, as are those obtained previously by Cho &amp;
Vishniac. The sole notable discrepancy is that one-dimensional energy
spectra determined from our simulations exhibit α~3/2, whereas the
GS model predicts α=5/3. Further investigation is needed to resolve
this issue.

---------------------------------------------------------
Title: Compressible Turbulence in Interstellar Plasmas
Authors: Lithwick, Yoram; Goldreich, P.
2001AAS...198.9003L Altcode: 2001BAAS...33..919L
Radio-wave scintillation observations reveal a nearly Kolmogorov
spectrum of interstellar electron density fluctuations. Although this
spectrum is suggestive of turbulence, there is little theoretical
understanding of compressible turbulence in magnetized plasmas. We
calculate the spectrum of density fluctuations by extending the
theory of incompressible magnetohydrodynamic (MHD) turbulence given by
Goldreich &amp; Sridhar (1995) to include the effects of compressibility
and particle transport. Our most important results are as follows. (1)
Density fluctuations are due to the slow mode and the entropy mode. Both
modes are passively mixed by the cascade of shear Alfvén waves. Since
the shear Alfvén waves have a Kolmogorov spectrum, so do the density
fluctuations. (2) Density fluctuation amplitudes constrain the nature
of MHD turbulence in the interstellar medium. Slow mode density
fluctuations are inversely proportional to β , the ratio of the gas
pressure to the magnetic pressure. Entropy mode density fluctuations
are suppressed by cooling when the cascade timescale is longer than
the cooling timescale. These constraints suggest that either β is of
order unity or the outer scale of the turbulence is very small. (3)
A high degree of ionization is required for the cascade to survive
damping by neutrals and extend to small lengthscales. Regions that are
insufficiently ionized only produce density fluctuations on lengthscales
larger than the neutral damping scale. They may account for the excess
of power that is found on large scales. (4) Both the entropy mode and
the slow mode are damped on lengthscales below that at which protons can
diffuse across an eddy during the eddy's turnover time. Consequently,
eddies whose extents along the magnetic field are smaller than the
proton collisional mean free path do not contribute to the density
spectrum. However, in MHD turbulence eddies are highly elongated along
the magnetic field. From an observational perspective, the relevant
lengthscale is that transverse to the magnetic field. Thus the cut-off
lengthscale for density fluctuations is significantly smaller than the
proton mean free path. (5) The Alfvén mode is critically damped at
the transverse lengthscale of the proton gyroradius, and thus cascades
to smaller lengthscales than either the slow mode or the entropy mode.

---------------------------------------------------------
Title: Gravity Modes in ZZ Ceti Stars. IV. Amplitude Saturation by
Parametric Instability
Authors: Wu, Yanqin; Goldreich, Peter
2001ApJ...546..469W Altcode: 2000astro.ph..3163W
ZZ Ceti stars (also known as DAV stars) exhibit small-amplitude
photometric pulsations in multiple gravity modes. As the stars cool,
their dominant modes shift to longer periods. We demonstrate that
parametric instability limits overstable modes to amplitudes
similar to those observed. In particular, it reproduces the
trend that longer period modes have larger amplitudes. Parametric
instability is a form of resonant three-mode coupling. It involves the
destabilization of a pair of stable daughter modes by an overstable
parent mode. The three modes must satisfy exact angular selection
rules and approximate frequency resonance. The lowest instability
threshold for each parent mode is provided by the daughter pair
that minimizes (δω2+γ2d)/
κ2, where κ is the nonlinear coupling constant,
δω is the frequency mismatch, and γd is the energy
damping rate of the daughter modes. Parametric instability leads to
a steady state if |δω|&gt;γd and to limit cycles if
|δω|&lt;γd. The former behavior characterizes low radial
order (n&lt;=3) parent modes, and the latter those with n&gt;=5. In
either case, the overstable mode's amplitude is maintained at close
to the instability threshold value. Although parametric instability
defines an upper envelope for the amplitudes of overstable modes in
ZZ Ceti stars, other nonlinear mechanisms are required to account
for the irregular distribution of amplitudes of similar modes and
the nondetection of modes with periods longer than 1200 s. Resonant
three-mode interactions involving more than one excited mode may account
for the former and Kelvin-Helmholtz instability of the mode-driven
shear layer below the convection zone for the latter.

---------------------------------------------------------
Title: Apse Alignment of Narrow Eccentric Planetary Rings
Authors: Chiang, E. I.; Goldreich, P.
2000ApJ...540.1084C Altcode: 2000astro.ph..4193C
The boundaries of the Uranian ɛ, α, and β rings can be fitted by
Keplerian ellipses. The pair of ellipses that outline a given ring
share a common line of apsides. Apse alignment is surprising because
the quadrupole moment of Uranus induces differential precession. We
propose that rigid precession is maintained by a balance of forces
due to ring self-gravity, planetary oblateness, and interparticle
collisions. Collisional impulses play an especially dramatic
role near ring edges. Pressure-induced accelerations are maximal
near edges because there (1) velocity dispersions are enhanced by
resonant satellite perturbations and (2) the surface density declines
steeply. Remarkably, collisional forces felt by material in the last
~100 m of a ~10 km wide ring can increase equilibrium masses up to a
factor of ~100. New ring surface densities are derived that accord
with Voyager radio measurements. In contrast to previous models,
collisionally modified self-gravity appears to allow for both negative
and positive eccentricity gradients; why all narrow planetary rings
exhibit positive eccentricity gradients remains an open question.

---------------------------------------------------------
Title: Interstellar Scintillation and the Inertial Range of MHD
Turbulence
Authors: Goldreich, Peter
2000astu.progE...8G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Growth of Perturbations in Gravitational Collapse and Accretion
Authors: Lai, Dong; Goldreich, Peter
2000ApJ...535..402L Altcode: 1999astro.ph..6400L
When a self-gravitating spherical gas cloud collapses or accretes onto a
central mass, the inner region of the cloud develops a density profile
ρ~r-3/2 and the velocity approaches free fall. We show
that in this region nonspherical perturbations grow with decreasing
radius. In the linear regime, the tangential velocity perturbation
increases as r-1, while the Lagrangian density perturbation,
Δρ/ρ, grows as r-1/2. Faster growth occurs if the central
collapsed object maintains a finite multiple moment, in which case
Δρ/ρ increases as r-l, where l specifies the angular
degree of the perturbation. These scaling relations are different from
those obtained for the collapse of a homogeneous cloud. Our numerical
calculations indicate that nonspherical perturbations are damped in the
subsonic region and that they grow and approach the asymptotic scalings
in the supersonic region. The implications of our results to asymmetric
supernova collapse and to black hole accretion are briefly discussed.

---------------------------------------------------------
Title: Discovery of Solar Atmospheric Motions
Authors: Goldreich, Peter
1999ApJ...525C.962G Altcode: 1999ApJC..525..962G
No abstract at ADS

---------------------------------------------------------
Title: Gravity Modes in ZZ Ceti Stars. III. Effects of Turbulent
Dissipation
Authors: Goldreich, Peter; Wu, Yanqin
1999ApJ...523..805G Altcode: 1998astro.ph.10038G
We investigate dynamical interactions between turbulent convection
and g-mode pulsations in ZZ Ceti variables. Since our understanding
of turbulence is rudimentary, we are compelled to settle for
order-of-magnitude results. A key feature of these interactions is that
convective response times are much shorter than pulsation periods. Thus
the dynamical interactions enforce near uniform horizontal velocity
inside the convection zone. They also give rise to a narrow shear
layer in the region of convective overshoot at the top of the radiative
interior. Turbulent damping inside the convection zone is negligible
for all modes, but that in the region of convective overshoot may
be significant for a few long-period modes near the red edge of the
instability strip. These conclusions are in accord with those reached
earlier by Brickhill. Our major new result concerns nonlinear damping
arising from the Kelvin-Helmholtz instability of the aforementioned
shear layer. Amplitudes of overstable modes saturate where dissipation
due to this instability balances excitation by convective driving. This
mechanism of amplitude saturation is most effective for long-period
modes, and it may play an important role in defining the red edge of
the instability strip.

---------------------------------------------------------
Title: Spectral Energy Distributions of Passive T Tauri Disks:
Inclination
Authors: Chiang, E. I.; Goldreich, P.
1999ApJ...519..279C Altcode: 1998astro.ph.12194C
We compute spectral energy distributions (SEDs) for passive T Tauri
disks viewed at arbitrary inclinations. Semianalytic models of disks
in radiative and hydrostatic equilibrium are employed. Over viewing
angles for which the flared disk does not occult the central star,
the SED varies negligibly with inclination. For such aspects, the SED
shortward of ~80 μm is particularly insensitive to orientation, since
short wavelength disk emission is dominated by superheated surface
layers, which are optically thin. The SED of a nearly edge-on disk is
that of a class I source. The outer disk occults inner disk regions, and
emission shortward of ~30 μm is dramatically extinguished. Spectral
features from dust grains may appear in absorption. However,
millimeter-wavelength fluxes decrease by at most a factor of 2 from
face-on to edge-on orientations. We present illustrative applications
of our SED models. The class I source 04108+2803B is considered a T
Tauri star hidden from view by an inclined circumstellar disk. Fits
to its observed SED yield model-dependent values for the disk mass
of ~0.015 Msolar and a disk inclination of ~65° relative
to face-on. The class II source GM Aur represents a T Tauri star only
slightly obscured by its circumstellar disk. Fitted parameters include
a disk mass of ~0.050 Msolar and an inclination of ~60°,
where the viewing angle is chosen to reproduce the observed visual
extinction of AV=0.5 mag.

---------------------------------------------------------
Title: Gravity Modes in ZZ Ceti Stars. II. Eigenvalues and
Eigenfunctions
Authors: Wu, Yanqin; Goldreich, Peter
1999ApJ...519..783W Altcode:
We report on numerical calculations of nonadiabatic eigenvalues
and eigenfunctions for g-modes in ZZ Ceti variables. The spectrum
of overstable l=1 modes delineates the instability strip. Its blue
edge occurs where ωτc~1 for the n=1 mode. Here ω is
radian frequency and τc is about 4 times the thermal time
at the bottom of the surface convection zone. As a ZZ Ceti cools,
its convection zone deepens, longer period modes become overstable,
but the critical value of ωτc separating overstable and
damped modes rises. The latter is a consequence of enhanced radiative
damping for modes that propagate immediately below the convection
zone. The critical value of ωτc is of observational
significance, because modes with the smallest value of ωτc
are most observable photometrically. Maximum periods for overstable
modes predicted for our cooler model envelopes are about a factor
of 2 longer than the observational upper limit of 1200 s. We assess
a number of plausible resolutions for this discrepancy among which
convective overshoot and nonlinear saturation look promising. The
nonadiabatic eigenfunctions enable us to predict relative amplitudes
and phases of photospheric variations of flux and velocity, quantities
made accessible by recent observations. We also present asymptotic
formula for damping rates of high-order modes, a result of consequence
for future investigations of nonlinear saturation of the amplitudes
of overstable modes.

---------------------------------------------------------
Title: The infrared excess - age relationship: debris, a NASA
key project
Authors: Spangler, C.; Silverstone, M. D.; Becklin, E. E.; Hare, J.;
Zuckerman, B.; Sargent, A. I.; Goldreich, P.
1999ESASP.427..405S Altcode: 1999usis.conf..405S
The DEBRIS project is primarily a survey of infrared radiation from
nearby solar-like stars to establish how many display infrared emission
in excess of that from the stellar photosphere and the timescale over
which the excess persists. Such excess infrared emission indicates
associated circumstellar material that could be the debris of planet
formation. This survey used the ISOPHOT C100 detector ( te{lem96})
and the 60 and 90 μm filters to search for infrared flux around
approximately 300 stellar targets with a variety of ages, masses
and multiplicities. Here we present a summary of our results. The
preliminary description of a drop of infrared excess as a function
of age reported earlier by te*{bec98} is substantiated. Using a
larger data set, better reduced data, and new age estimates, we find
τpropto{age}-2. Several main sequence stars with newly
discovered excesses are also discussed.

---------------------------------------------------------
Title: Gravity Modes in ZZ Ceti Stars. I. Quasi-adiabatic Analysis
of Overstability
Authors: Goldreich, Peter; Wu, Yanqin
1999ApJ...511..904G Altcode: 1998astro.ph..4305G
We analyze the stability of g-modes in white dwarfs with hydrogen
envelopes. All relevant physical processes take place in the outer
layer of hydrogen-rich material, which consists of a radiative layer
overlaid by a convective envelope. The radiative layer contributes to
mode damping, because its opacity decreases upon compression and the
amplitude of the Lagrangian pressure perturbation increases outward. The
convective envelope is the seat of mode excitation, because it acts as
an insulating blanket with respect to the perturbed flux that enters
it from below. A crucial point is that the convective motions respond
to the instantaneous pulsational state. Driving exceeds damping by
as much as a factor of 2 provided ωτc&gt;=1, where ω is
the radian frequency of the mode and τc~4τth,
with τth being the thermal time constant evaluated at the
base of the convective envelope. As a white dwarf cools, its convection
zone deepens, and lower frequency modes become overstable. However,
the deeper convection zone impedes the passage of flux perturbations
from the base of the convection zone to the photosphere. Thus the
photometric variation of a mode with constant velocity amplitude
decreases. These factors account for the observed trend that longer
period modes are found in cooler DA variables. Overstable modes have
growth rates of order γ~1/(nτω), where n is the mode's
radial order and τω is the thermal timescale evaluated
at the top of the mode's cavity. The growth time, γ-1,
ranges from hours for the longest period observed modes (P~20 minutes)
to thousands of years for those of shortest period (P~2 minutes). The
linear growth time probably sets the timescale for variations of mode
amplitude and phase. This is consistent with observations showing that
longer period modes are more variable than shorter period ones. Our
investigation confirms many results obtained by Brickhill in his
pioneering studies of ZZ Cetis. However, it suffers from two serious
shortcomings. It is based on the quasiadiabatic approximation that
strictly applies only in the limit ωτc&gt;&gt;1, and it
ignores damping associated with turbulent viscosity in the convection
zone. We will remove these shortcomings in future papers.

---------------------------------------------------------
Title: Gravity-Modes in ZZ Ceti Stars III. Eigenvalues and
Eigenfuctions
Authors: Wu, Yanqin; Goldreich, Peter
1998astro.ph.12085W Altcode:
We report on numerical calculations of nonadiabatic eigenvalues and
eigenfunctions for g-modes in ZZ Ceti variables. The spectrum of
overstable $l=1$ modes delineates the instability strip. Its blue
edge occurs where $\omega \tau_c \approx 1$ for the $n=1$ mode. Here
$\omega$ is radian frequency and $\tau_c$ is about four times the
thermal timescale at the bottom of the surface convection zone. As
a ZZ Ceti cools, its convection zone deepens, longer period modes
become overstable, but the critical value of $\omega\tau_c$ separating
overstable and damped modes rises. The latter is a consequence of
enhanced radiative damping for modes which propagate immediately
below the convection zone. The critical value of $\omega\tau_c$ is of
observational significance because modes with the smallest value of
$\omega\tau_c$ are most observable photometrically. Maximum periods for
overstable modes predicted for our cooler model envelopes are about a
factor two longer than the observational upper limit of $1,200\s$. We
assess a number of plausible resolutions for this discrepancy among
which convective overshoot and nonlinear saturation look promising. The
nonadiabatic eigenfunctions enable us to predict relative amplitudes
and phases of photospheric variations of flux and velocity, quantities
made accessible by recent observations. We also present asymptotic
formula for damping rates of high order modes, a result of consequence
for future investigations of nonlinear saturation of the amplidues of
overstable modes.

---------------------------------------------------------
Title: Sources of ISS
Authors: Goldreich, Peter
1998AAS...192.4603G Altcode: 1998BAAS...30..878G
Interstellar scintillations (ISS) of small angular diameter radio
sources have been studied for 30 years. They arise from fluctuations
of the interstellar electron density. These exhibit an anisotropic
Kolmogorov spectrum over scales ranging from about 10(9) cm to
10(15) cm, with the power in these fluctuations varying by orders of
magnitude from place to place. The optics of this phenomenon is fairly
well understood. The same cannot be said for the physical process
responsible for producing the electron density fluctuations. In recent
work, Goldreich and Sridhar argue that incompressible MHD turbulence
will produce a power law velocity spectrum of shear Alfven waves that
matches the ISS electron density spectrum. The velocity spectrum arises
from a critical balance between the linear wave periods and nonlinear
wave interactions. Its connection to the electron density spectrum
remains a puzzle. One might speculate that the turbulent velocity field
mixes specific entropy as a passive contaminant thereby giving rise to
isobaric temperature and density fluctuations whose spectra mimic that
of the velocity field. This is the manner in which the atmospheric
scintillations of optical stars arise. However, as a consequence of
its rapid of cooling, specific entropy is not conserved in large scale
motions of ionized interstellar gas. This severely limits the outer
scale of the electron density spectrum. Implications of this limitation
to potential sources and sites of ISS will be explored in this lecture.

---------------------------------------------------------
Title: Oscillating White Dwarfs
Authors: Goldreich, Peter
1998AAS...192.7501G Altcode: 1998BAAS...30Q.931G
As a hydrogen (DA) white dwarf cools, it passes through an instability
strip centered at T_eff ~ 12,000 K having width Delta T_eff ~
1,000 K. Within this temperature range it exhibits photometric
variations associated with excited g-modes of low angular degree. The
pulsations undergo a pronounced evolution as the star travels across
the instability strip. The periods of the dominant modes increase,
and the modes display larger photometric amplitudes and greater
temporal variability. These trends are consequences of the mechanism
of linear overstability which excites the modes together with the
nonlinear interactions that saturate their amplitudes. Linear
overstability is due to convective driving, a novel mechanism
proposed by Brickhill. Convective driving relies on the ability of
the convective motions to respond to the instantaneous pulsational
state. It destabilizes modes whose periods are comparable to or
shorter than the thermal timescale at the base of the star's surface
convection zone. As a white dwarf cools, its convection zone deepens
and modes of longer period become overstable. Longer period modes
have smaller effective mass and thus faster growth and decay rates
than modes of shorter period. This accounts for their increased
variability. Amplitude saturation is due to parametric instability
which involves the destabilization of pairs of linearly damped daughter
modes by an overstable parent mode. The frequencies and angular degrees
of parent and daughter modes satisfy resonance relations. Parametric
instability requires the amplitude of the parent mode to exceed a
critical threshold. It thereby sets the envelope for the amplitudes of
overstable modes. However, it cannot account for the uneven distribution
of energy among modes which have similar linear growth rates. This
feature is due to nonlinear interactions such as parametric up and
down conversion which couple two excited modes to one damped mode.

---------------------------------------------------------
Title: Spectral Energy Distributions of T Tauri Stars with Passive
Circumstellar Disks
Authors: Chiang, E. I.; Goldreich, P.
1997ApJ...490..368C Altcode: 1997astro.ph..6042C
We derive hydrostatic, radiative equilibrium models for passive disks
surrounding T Tauri stars. Each disk is encased by an optically thin
layer of superheated dust grains. This layer reemits directly to space
about half the stellar energy it absorbs. The other half is emitted
inward and regulates the interior temperature of the disk. The heated
disk flares. As a consequence, it absorbs more stellar radiation,
especially at large radii, than a flat disk would. The portion of the
spectral energy distribution contributed by the disk is fairly flat
throughout the thermal infrared. At fixed frequency, the contribution
from the surface layer exceeds that from the interior by about a
factor 3 and is emitted at more than an order of magnitude greater
radius. Spectral features from dust grains in the superheated layer
appear in emission if the disk is viewed nearly face-on.

---------------------------------------------------------
Title: Magnetohydrodynamic Turbulence Revisited
Authors: Goldreich, P.; Sridhar, S.
1997ApJ...485..680G Altcode: 1996astro.ph.12243G
In 1965, Kraichnan proposed that MHD turbulence occurs as a result of
collisions between oppositely directed Alfvén wave packets. Recent work
has generated some controversy over the nature of nonlinear couplings
between colliding Alfvén waves. We find that the resolution to much
of the confusion lies in the existence of a new type of turbulence,
intermediate turbulence, in which the cascade of energy in the inertial
range exhibits properties intermediate between those of weak and strong
turbulent cascades. Some properties of intermediate MHD turbulence
are the following: (1) in common with weak turbulent cascades, wave
packets belonging to the inertial range are long-lived (2) however,
components of the strain tensor are so large that, similar to the
situation in strong turbulence, perturbation theory is not applicable;
(3) the breakdown of perturbation theory results from the divergence
of neighboring field lines due to wave packets whose perturbations in
velocity and magnetic fields are localized, but whose perturbations in
displacement are not; (4) three-wave interactions dominate individual
collisions between wave packets, but interactions of all orders n &gt;=
3 make comparable contributions to the intermediate turbulent energy
cascade; (5) successive collisions are correlated since wave packets
are distorted as they follow diverging field lines; (6) in common with
the weak MHD cascade, there is no parallel cascade of energy, and the
cascade to small perpendicular scales strengthens as it reaches higher
wavenumbers; (7) for an appropriate weak excitation, there is a natural
progression from a weak, through an intermediate, to a strong cascade.

---------------------------------------------------------
Title: Globally asymmetric supernova.
Authors: Goldreich, P.; Lai, D.; Sahrling, M.
1997upa..conf..269G Altcode:
Asymmetries in type II supernova explosions are the most plausible
cause of the high space velocities of radio pulsars. The origin of
these asymmetries is unknown. Recent work has stressed the potential
importance of local instabilities which occur subsequent to the collapse
of the stellar core. By contrast, relatively little attention has
been paid to the possibility that substantial asymmetry might already
be present during core collapse. The presupernova star supports
g-modes in which the core oscillates with respect to the stellar
envelope. These modes gain excitation by modulating the release of
nuclear energy. Asymmetries associated with these modes could then
be amplified during core collapse. The most likely place for this to
occur is in the supersonically collapsing outer core.

---------------------------------------------------------
Title: The Debris ISO Key Project: Early Release Observations
Authors: Becklin, E. E.; Silverstone, M.; Zuckerman, B.; Spangler,
C.; Sargent, A.; Goldreich, P.; Mannings, V.
1996AAS...188.5207B Altcode: 1996BAAS...28..902B
The ISO Dust Debris key project is a collaboration between UCLA and
Caltech to study the physical nature and evolutionary history of dust
debris clouds around solar mass stars. The sample objects include F
and G stars within 20 pc of the Sun, as well as members of nearby
open clusters and weak-line T Tauri stars. The 60 and 100 micron
observations, made with ISOPHOT, consist of broadband single- element
photometry plus far-infrared imaging with a small array. Approximately
15 nearby and cluster stars were released during February 1996 for early
observations to assess the performance of ISO. The results of these
early release observations, and their effect upon the Debris program,
will be discussed. Issues concerning signal-to-noise and calibration
will be addressed.

---------------------------------------------------------
Title: Single sided shepherding.
Authors: Goldreich, Peter; Rappaport, Nicole; Sicardy, Bruno
1995Icar..118..414G Altcode:
Narrow ringlets are observed to form at isolated Lindblad resonances
in recent simulations (J. Hänninen and H. Salo, Icarus 108, 325-346
(1994) and 117, 435-438 (1995)). Our remarks are directed toward the
interpretation of this phenomenon. Ringlet formation is a consequence
of the negative angular momentum luminosity promoted by satellite
perturbations of the streamlines of particle flow. Contraction halts
once the surface density reaches a value such that the angular momentum
luminosity vanishes. Our estimate for the formation time, tf
∼ (Mp/Ms)1/2Ω,-1, for low
order resonances in optically thin rings is consistent with the results
of the simulations. Ringlets drift across the width of resonance, W
∼ (Ms/Mp)1/2a, as a result of the
unbalanced satellite torque. This occurs on the much longer timescale
td ∼ (Mp/Ms)Ω-1 and
cannot be observed in current simulations.

---------------------------------------------------------
Title: Ringlet Formation at Isolated Lindblad Resonance
Authors: Rappaport, N.; Goldreich, P.; Sicardy, B.
1995DPS....27.2903R Altcode: 1995BAAS...27.1136R
No abstract at ADS

---------------------------------------------------------
Title: Toward a Theory of Interstellar Turbulence. II. Strong
Alfvenic Turbulence
Authors: Goldreich, P.; Sridhar, S.
1995ApJ...438..763G Altcode:
We continue to investigate the possibility that interstellar turbulence
is caused by nonlinear interactions among shear Alfven waves. Here,
we restrict attention to the symmetric case where the oppositely
directed waves carry equal energy fluxes. This precludes application
to the solar wind in which the outward flux significantly exceeds
the ingoing one. All our detailed calculations are carried out for an
incompressible magnetized fluid. In incompressible magnetohydrodynamics
(MHD), nonlinear interactions only occur between oppositely direct
waves. We present a theory for the strong turbulence of shear Alfven
waves. It has the following main characteristics. (1) The inertial-stage
energy spectrum exhibits a critical balance between linear wave periods
and nonlinear turnover timescales. (2) The 'eddies' are elongated
in the direction of the field on small spatial scales; the parallel
and perpendicular components of the wave vector, kz and
k(perpendicular) are related by kz approximately equals
kperpendicular to2/3 L-1/3, where L
is the outer scale of the turbulence. (3) The 'one-dimensional' energy
spectrum is proportional to kperpendicular-5/3-an
anisotropic Kolmogorov energy spectrum. Shear Alfvenic turbulence
mixes specific entropy as a passive contaminant. This gives rise to an
electron density power spectrum whose form mimics the energy spectrum
of the turbulence. Radio wave scattering by these electron density
fluctuations produces anisotropic scatter-broadened images. Damping by
ion-neutral collisions restricts Alfvenic turbulence to highly ionized
regions of the interstellar medium.

---------------------------------------------------------
Title: Toward a Theory of Interstellar Turbulence. I. Weak Alfvenic
Turbulence
Authors: Sridhar, S.; Goldreich, P.
1994ApJ...432..612S Altcode:
We study weak Alfvenic turbulence of an incompressible, magnetized fluid
in some detail, with a view to developing a firm theoretical basis for
the dynamics of small-scale turbulence in the interstellar medium. We
prove that resonant 3-wave interactions are absent. We also show that
the Iroshnikov-Kraichnan theory of incompressible, magnetohydrodynamic
turbulence -- which is widely accepted -- describes weak 3-wave
turbulence; consequently, it is incorrect. Physical arguments, as
well as detailed calculations of the coupling coefficients are used
to demonstrate that these interactions are empty. We then examine
resonant 4-wave interactions, and show that the resonance relations
forbid energy transport to small spatial scales along the direction of
the mean magnetic field, for both the shear Alfven wave and the pseudo
Alfven wave. The three-dimensional inertial-range energy spectrum
of 4-wave shear Alfven turbulence guessed from physical arguments
reads E(kz, kperpendicular) approximately
VAvLL-1/3kperpendicular-10/3,
where VA is the Alfven speed, and vL
is the velocity difference across the outer scale
L. Given this spectrum, the velocity difference across
lambdaperpendicular approximately kperpendicular exp
-1 is vlambda (sub perpendicular) is approximately
vL(lambdaperpendicular/L)2/3. We derive
a kinetic equation, and prove that this energy spectrum is a stationary
solution and that it implies a positive flux of energy in k-space, along
directions perpendicular to the mean magnetic field. Using this energy
spectrum, we deduce that 4-wave interactions strengthen as the energy
cascades to small, perpendicular spatial scales; beyond an upper bound
in perpendicular wavenumber, kperpendicularL is approximately
(VA/vL)3/2, weak turbulence theory
ceases to be valid. Energy excitation amplitudes must be very small
for the 4-wave inertial-range to be substantial. When the excitation
is strong, the width of the 4-wave inertial-range shrinks to zero. This
seems likely to be the case in the interstellar medium.

---------------------------------------------------------
Title: Excitation of Neutron Star Normal Modes during Binary Inspiral
Authors: Reisenegger, Andreas; Goldreich, Peter
1994ApJ...426..688R Altcode:
As a compact binary inspirals due to the emission of gravitational
waves, its orbital period decreases continuously down to approximately
1 ms, its value at coalescence. During the last part of the inspiral,
the two stars are close together, and their tidal interactions become
strong. Neutron stars have many normal modes (core g-modes, crustal
discontinuity modes, shear modes, etc.) whose periods lie in the range
(approximately several ms) swept by the orbital period. Some of these
modes are resonantly excited by the tidal force. The amount of energy
a mode absorbs is proportional to the square of the overlap integral
between its displacement field and the tidal force field. For all
modes of interest, this overlap is poor, resulting in relatively weak
excitation. For the best case, the absorbed energy is only a small
fraction (approximately 10-6) of the orbital energy, so the
orbital phase shift is too weak to be detected by observations of the
gravitational wave signal emitted by the inspiraling binary. However,
with displacement amplitudes of excited quadrupole modes ranging
up to 0.5% of the stellar radius, the possibility of a detectable
electromagnetic signature cannot be dismissed. Both the periods of
the modes and the energy they absorb depend quite strongly on the
internal structure of the star. Their observation could shed light on
the correct high-density equation of state.

---------------------------------------------------------
Title: Effect of Nonlinear Interactions on p-Mode Frequencies and
Line Widths
Authors: Kumar, Pawan; Goldreich, Peter; Kerswell, Richard
1994ApJ...427..483K Altcode:
We calculate the effect of nonlinear interactions among solar acoustic
modes upon the modal frequencies and energy loss rates (or line
widths). The frequency shift for a radial p-mode of frequency 3 mHz is
found to be about -0.5 microHz. The magnitude of nonlinear frequency
shift increases more rapidly with frequency than the inverse mode mass
(mode mass is defined as the ratio of energy in the mode to its surface
velocity amplitude squared). This frequency shift is primarily due to
nonresonant three-mode interactions and is dominated by high l surface
gravity waves (f-modes) and p-modes. The line width of a radial p-mode
of frequency 3 mHz, due to resonant nonlinear interactions, is about
0.3 microHz. This result is consistent with that of Kumar and Goldreich
(1989). We also find, in agreement with these authors, that the most
important nonlinear interactions of trapped p-modes involve f-modes
and high-frequency p-modes (frequency greater than about 5 mHz) which
propagate in the solar photosphere. Thus, using the arguments advanced
by Kumar &amp; Goldreich (1989), we conclude that nonlinear couplings
cannot saturate the overstable solar p-modes at their small observed
amplitudes. Both the nonlinear frequency shifts and line widths,
at a fixed frequency, are proportional to the inverse of mode mass
which for modes of degree greater than about 100 is approximately
l0.8. Therefore, the frequency of an f-mode of l = 1000,
due to nonlinear interactions, is decreased by approximately 0.4%.

---------------------------------------------------------
Title: The Effects of Scattering on Solar Oscillations
Authors: Goldreich, Peter; Murray, Norman
1994ApJ...424..480G Altcode:
Acoustic modes are scattered by turbulent velocity fluctuations
in the solar convection zone. The strongest scattering occurs
near the top of the acoustic cavity where the mode changes
character from propagating to evanescent. This layer is located
at depth z1 approximately g/omega2 below the
photosphere. The scattering optical depth taus is of order
M12, where M1 is the Mach number
of the energy-bearing eddies at z1. The corresponding
contribution to the line width is gammas is approximately
(omega) M12/(pi)(n+1), where n is the mode's
radial order. At the top of the acoustic cavity the correlation time
of energy-bearing eddies is much longer than omega-1. Also,
the pressure scale height H and the eddy correlation length Lambda
are comparable to omega/c, where c is the sound speed. Thus scattering
couples modes of similar omega and all l and has little effect on the
sum of their energies. Observations show that mode energies decline with
decreasing n (increasing l) at fixed omega. Consequently, scattering
damps p-modes and excites f-modes.

---------------------------------------------------------
Title: Excitation of Solar p-Modes
Authors: Goldreich, Peter; Murray, Norman; Kumar, Pawan
1994ApJ...424..466G Altcode:
We investigate the rates at which energy is supplied to individual
p-modes as a function of their frequencies nu and angular degrees l. The
observationally determined rates are compared with those calculated on
the hypothesis that the modes are stochastically excited by turbulent
convection. The observationally determined excitation rate is assumed
to be equal to the product of the mode's energy E and its (radian)
line width Gamma. We obtain E from the mode's mean square surface
velocity with the aid of its velocity eigenfuction. We assume that
Gamma measures the mode's energy decay rate, even though quasi-elastic
scattering may dominate true absorption. At fixed l, E(Gamma) arises as
nu7 at low nu, reaches a peak at nu approximately equal 3.5
mHz, and then declines as nu4.4 at higher nu . At fixed nu,
E(Gamma) exhibits a slow decline with increasing l. To calculate energy
input rates, Palpha, we rely on the mixing-length model
of turbulent convection. We find entropy fluctuations to be about an
order of magnitude more effective than the Reynolds stress in exciting
p-modes . The calculated Palpha mimic the nu7
dependence of E(Gamma) at low nu and the nu-4.4 dependence
at high nu. The break of 11.4 powers in the nu-dependence of E(Gamma)
across its peak is attributed to a combination of (1) the reflection
of high-frequency acoustic waves just below the photosphere where the
scale height drops precipitously and (2) the absence of energy-bearing
eddies with short enough correlation times to excite high-frequency
modes. Two parameters associated with the eddy correlation time are
required to match the location and shape of the break. The appropriate
values of these parameters, while not unnatural, are poorly constrained
by theory. The calculated Palpha can also be made to fit
the magnitude of E(Gamma) with a reasonable value for the eddy aspect
ratio. Our resutls suggest a possible explanation for the decline of
mode energy with increasing l at fixed nu. Entropy fluctuations couple
to changes in volume associated with the oscillation mode. These
decrease with decreasing n at fixed nu, becoming almost zero for
the f-mode.

---------------------------------------------------------
Title: Excitation of Neutron Star Oscillation Modes During Binary
Inspiral
Authors: Reisenegger, A.; Goldreich, P.
1994AIPC..308..311R Altcode: 1994exrb.conf..311R
As a compact binary inspirals due to the emission of gravitational
waves, its orbital period decreases continuously down to ∼1 ms,
its value at coalescence. During the last part of the inspiral,
the two stars are close together and their tidal interactions become
strong. Neutron stars have many normal modes whose periods lie in the
range swept by the orbital period. Some of these modes are resonantly
excited by the tidal force. The amount of energy a mode absorbs
is proportional to the square of the overlap integral between its
displacement field and the tidal force field. For all modes of interest,
this overlap is poor, resulting in relatively weak excitation. The
absorbed energy is only a small fraction (≲10-6) of the
orbital energy, so the orbital phase shift is too weak to be detected
by observations of the gravitational wave signal emitted by the
inspiraling binary. However, with displacement amplitudes of excited
quadrupole modes ranging up to 0.5% (or more) of the stellar radius,
the possibility of a detectable electromagnetic signature cannot be
dismissed. Both the periods of the modes and the energy they absorb
depend quite strongly on the internal structure of the star. Their
observation could shed light on the correct high-density equation
of state.

---------------------------------------------------------
Title: Interactions among convection, magnetic fields and p-mode
oscillations in the sun
Authors: Goldreich, Peter
1993STIN...9414479G Altcode:
Two papers on different aspects of the excitation and damping of
solar oscillations were accepted for publication in the Astrophysical
Journal. The first paper evaluates the rate at which turbulent
convection feeds energy into individual p-modes. It is shown that
stochastic excitation by turbulent convection provides a satisfactory
fit to the product of the mode energies and linewidths. A somewhat
surprising conclusion is that entropy fluctuations are about an order
of magnitude more significant than are fluctuations of the Reynolds
stress in exciting p-modes. However, entropy fluctuations cannot
excite f-modes. This may account for the relatively low energies
of the f-modes compared to those of the p-modes. The second paper
explores the role of scattering of acoustic modes by turbulent velocity
fluctuations. Scattering of a mode is concentrated near the top of
its acoustic cavity. Because the turbulence has low Mach number,
scattering couples modes having similar frequencies. Its net effects
are to increase the linewidths of all modes and to transfer energy
from p-modes to f-modes. Scattering is likely to be the dominant
source for the linewidths of p-modes. In particular, it may account
for the unexpectedly large linewidths measured for low frequency
modes. Copies of preprints of the two papers referred to above are
attached. The remainder of the report is devoted to a description of
unpublished results.

---------------------------------------------------------
Title: Magnetic Field Decay in Isolated Neutron Stars
Authors: Goldreich, Peter; Reisenegger, Andreas
1992ApJ...395..250G Altcode:
Three mechanisms that promote the loss of magnetic flux from an isolated
neutron star - Ohmic decay, ambipolar diffusion, and Hall drift - are
investigated. Equations of motions are solved for charged particles in
the presence of a magnetic field and a fixed background of neutrons,
while allowing for the creation and destruction of particles by weak
interactions. Although these equations apply to normal neutrons and
protons, the present interpretations of their solutions are extended to
cover cases of neutron superfluidity and proton superconductivity. The
equations are manipulated to prove that, in the presence of a magnetic
force, the charged particles cannot be simultaneously in magnetostatic
equilibrium and chemical equilibrium with the neutrons. The application
of the results to real neutron stars is discussed.

---------------------------------------------------------
Title: A New Class of g-Modes in Neutron Stars
Authors: Reisenegger, Andreas; Goldreich, Peter
1992ApJ...395..240R Altcode:
Because a neutron star is born hot, its internal composition is close
to chemical equilibrium. In the fluid core, this implies that the ratio
of the number densities of charged particles (protons and electrons) to
neutrons is an increasing function of the mass density. This composition
gradient stably stratifies the matter giving rise to a Brunt-Vaisala
frequency N of about 500/s. Consequently, a neutron star core provides a
cavity that supports gravity modes (g-modes). These g-modes are distinct
from those previously identified with the thermal stratification of
the surface layers and the chemical stratification of the crust. We
compute the lowest-order, quadrupolar, g-modes for cold, Newtonian,
neutron star models with M/solar M = 0.581 and M/solar M = 1.405, and
show that the crustal and core g-modes have similar periods. We also
discuss damping mechanisms and estimate damping rates for the core
g-modes. Particular attention is paid to damping due to the emission
of gravitational radiation.

---------------------------------------------------------
Title: Constraints on Gravity Waves in Upper Planetary Atmospheres
from Occultation Observations
Authors: Sicardy, B.; Goldreich, P.; Roques, F.
1992DPS....24.1607S Altcode: 1992BAAS...24..963S
No abstract at ADS

---------------------------------------------------------
Title: Solar Phonons
Authors: Goldreich, P.
1992DPS....24.3301G Altcode: 1992BAAS...24.1004G
No abstract at ADS

---------------------------------------------------------
Title: Puzzles and Prospects in Planetary Ring Dynamics (lecture)
Authors: Goldreich, P.
1992IAUS..152...65G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Thermal and Mechanical Damping of Solar p-Modes
Authors: Goldreich, Peter; Kumar, Pawan
1991ApJ...374..366G Altcode:
Nonadiabatic effects associated with the transfer of energy and with
turbulent stresses add small imaginary parts, omega-i(1) and omega-i(2),
to solar p-mode eigenfrequencies. Numerical calculations have shown that
these quite different processes make comparable contributions to omega-i
at frequencies well below the acoustic cutoff at omega-ac. Analytic
expressions are derived which reveal the connection between omega-i(1)
and omega-i(2). The estimates yield omega-i proportional to omega exp 8
for omega much less than omega-ac in good agreement with the numerical
calculations. However, the observed line width is proportional to
omega exp 4.2 at low frequencies. It is suspected that there is an
unmodeled component of perturbed convective energy transport or of
turbulent viscosity that makes an important contribution to omega-i
at omega much less than omega-ac.

---------------------------------------------------------
Title: Implications of Solar p-Mode Frequency Shifts
Authors: Goldreich, Peter; Murray, Norman; Willette, Gregory; Kumar,
Pawan
1991ApJ...370..752G Altcode:
An expression is derived that relates solar p-mode frequency shifts to
changes in the entropy and magnetic field of the sun. The frequency
variations result from changes in path length and propagation
speed. Path length changes dominate for entropy perturbations, and
propagation speed changes dominate for most types of magnetic field
peturbations. The p-mode frequencies increased along with solar activity
between 1986 and 1989; these frequency shifts exhibited a rapid rise
with increasing frequency followed by a precipitous drop. The positive
component of the shifts can be accounted for by variations of the mean
square magnetic field strength in the vicinity of the photosphere. The
magnetic stress perturbation decays above the top of the convection
zone on a length scale comparable to the pressure scale height and
grows gradually with depth below. The presence of a resonance in the
chromospheric cavity means that the transition layer maintains enough
coherence to partially reflect acoustic waves even near cycle maximum.

---------------------------------------------------------
Title: Wave Generation by Turbulent Convection
Authors: Goldreich, Peter; Kumar, Pawan
1990ApJ...363..694G Altcode:
Wave generation by turbulent convection in a plane parallel,
stratified atmosphere lying in a gravitational field is studied. The
turbulent spectrum is related to the convective energy flux via the
Kolmogorov scaling and the mixing length hypothesis. Efficiencies for
the conversion of the convective energy flux into both trapped and
propagating waves are estimated.

---------------------------------------------------------
Title: The Dominant Local Instabilities in an Einstein--de Sitter
Universe
Authors: Blaes, O. M.; Goldreich, P. M.; Villumsen, J. V.
1990ApJ...361..331B Altcode:
The evolution of compensated aspherical perturbations in an Einstein-de
Sitter universe with cold collisionless matter is investigated using
both N-body simulations and quasi-analytic similarity solutions to treat
the evolution of compensated axisymmetric structures. The solutions
consist of a central void surrounded by an inhomogeneous shell. It
is assumed that the structures are much smaller than the horizon
scale so that Newtonian gravity is a good approximation. The results
obtained from the two approaches are compared, and the implications
are discussed.

---------------------------------------------------------
Title: Neutron Starquake Models for Gamma-Ray Bursts
Authors: Blaes, O.; Blandford, R.; Goldreich, P.; Madau, P.
1989ApJ...343..839B Altcode:
The component parts of gamma-ray burst models based on neutron
starquakes are assessed. The requirements for, and the properties of,
neutron starquakes are reviewed. The coupling of seismic waves to
Alfven waves is evaluated and the behavior of Alfven waves in the
magnetosphere is investigated. An attempt is made to identify the
principal sources of free energy in the interiors of old neutron stars.

---------------------------------------------------------
Title: Neptune's Story
Authors: Goldreich, P.; Murray, N.; Longaretti, P. Y.; Banfield, D.
1989Sci...245..500G Altcode:
It is conjectured that Triton was captured from a helio-centric orbit
as the result of a collision with what was then one of Neptune's
regular satellites. The immediate post-capture orbit was highly
eccentric with a semimajor axis a ~ 103RN
and a periapse distance rp that oscillated periodically
above a minimum value of about 5RN. Dissipation due to
tides raised by Neptune in Triton caused Triton's orbit to evolve to
its present state in lesssim 109 years. For much of this
time Triton was almost entirely molten. While its orbit was evolving,
Triton cannibalized most of the regular satellites of Neptune and
also perturbed Nereid, thus accounting for that satellite's highly
eccentric and inclined orbit. The only regular satellites of Neptune
that survived were those that formed well within 5RN and they
move on inclined orbits as the result of chaotic perturbations forced
by Triton. Neptune's arcs are confined around the corotation resonances
of one of these inner satellites. The widths and lengths of the arcs
imply that the satellite's radius is at least 30/(sin i)2/3
kilometers for i lesssim 1, where i is the angle of inclination.

---------------------------------------------------------
Title: The formation of sharp edges in planetary rings by nearby
satellites
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1989Icar...80..344B Altcode:
Sharp edges, boundaries between regions of high and low optical depth in
planetary rings, are maintained by shepherd satellites which transfer
angular momentum to and from the ring particles. We derive equations
that govern the shapes of the perturbed streamlines near such a
boundary. These equations are solved for a simple numerical model
whose parameters are chosen to resemble those of the Encke division
and its associated satellite. The results of our calculation faithfully
reproduce the sharp edges which bound the division and imply that the
ring thickness in the unperturbed regions far from the edges is of
order 10 m. In particular, the angle-averaged surface density is found
to vary on a much shorter radial length scale than that over which
the satellite torque is applied. We demonstrate that this striking
feature is related to the local reversal of the viscous transport of
angular momentum in the most strongly perturbed regions.

---------------------------------------------------------
Title: Tides in Rotating Fluids
Authors: Goldreich, Peter; Nicholson, Philip D.
1989ApJ...342.1075G Altcode:
The tidal disturbance forced in a differentially rotating fluid by a
rigidly rotating external potential is investigated. In the study, the
fluid is assumed to be inviscid, insulated, and self-gravitating, and to
have laminar unperturbed and perturbed velocity fields. Under the steady
torque of second-order strength exerted by the external potential, no
secular changes in the angular momenta of fluid particles are observed,
except possibly at corotation where the angular velocity is equal to
the pattern speed of the potential. Except at corotation, all of the
angular momentum is found to be transported away by internal stresses.

---------------------------------------------------------
Title: Nonlinear Interactions among Solar Acoustic Modes
Authors: Kumar, Pawan; Goldreich, Peter
1989ApJ...342..558K Altcode:
The rates at which nonlinear interactions transfer energy among
the normal modes of a plane-parallel, stratified atmosphere are
evaluated. It is shown that every p-mode in the 5-minute band is
involved in many near-resonant triplets, and, as a consequence, the
energy transfer rates are independent of the mode line widths. It is
also found that nonlinear mode coupling cannot limit the growth of
overstable p-modes, which favors the hypothesis that the sun's p-modes
are stochastically excited by turbulent convection.

---------------------------------------------------------
Title: Tidal Friction in Early-Type Stars
Authors: Goldreich, Peter; Nicholson, Philip D.
1989ApJ...342.1079G Altcode:
Theoretical and observational results related to tides in early-type
stars are summarized. The results suggest that the tidal torque on an
early-type star is concentrated near the boundary between the convective
core and the radiative envelope, and that a train of gravity waves
which is excited at this boundary outwardly transports the angular
momentum removed from the fluid by the torque. Tidal despinning to
synchronous rotation is shown to proceed from the outside to the
inside of the star. The present model can account for the previous
finding that Zahn's (1975, 1977) theory for tidal evolution in
early-type close binaries is compatible with the observed rates of
orbit circularization, while significantly underestimating the observed
rates of spin synchronization.

---------------------------------------------------------
Title: Neptune's Satellite System, Theory and Observations
Authors: Banfield, D.; Goldreich, P.; Murray, N.; Longaretti, P. Y.
1989BAAS...21Q.911B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Neutron starquakes and the nature of gamma-ray bursts.
Authors: Madau, P.; Blaes, O.; Blandford, R. D.; Goldreich, P.
1989plap.work..247M Altcode:
The authors investigate the possibility that gamma-ray bursts originate
from quakes deep in the solid crust of a neutron star. Seismic waves
are radiated if shear stress is relieved by brittle fracture. However
they cannot propagate directly to the surface but are temporarily
trapped below a reflecting layer. The shaking of the stellar surface
couples the seismic waves to Alfvén waves which propagate out into the
magnetosphere. The crust-magnetosphere transmission coefficient strongly
increases with wave frequency and magnetic field strength. Alfvén
wave luminosities sufficient to power galactic gamma-ray bursts are
possible if magnetic fields ⪆1011G cover at least part
of the stellar surface. As the Alfvén waves propagate out into the
low density magnetosphere, they become increasingly charge starved,
thereby accelerating particles to relativistic energies.

---------------------------------------------------------
Title: Neutron Starquake Models of Gamma-Ray Bursts
Authors: Blaes, O.; Blandford, R.; Goldreich, P.; Madau, P.
1988BAAS...20.1054B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Nonlinear Calculations of 3-mode Coupling in One Dimension
Authors: Kochanek, C. S.; Blaes, O. M.; Goldreich, P. M.
1988BAAS...20.1010K Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Research at Palomar Observatory in planetary astronomy
Authors: Soifer, B. T.; Goldreich, P.
1988plas.rept..119S Altcode:
A wide range of observational studies are carried out to improve
our understanding of the bodies of the outer solar system. Using
the 200-inch Hale telescope, near-infrared observations are made of
Uranus, Neptune, and the Pluto-Charon system. High time resolution
occultation observations of the Uranus Ring system are used to study
in detail the dynamics of this system. Occultation studies of Neptune
are probing this intriguing ring-arc system. Occulation observations of
the Pluto-Charon system probe the surface properties of these distant
bodies. In addition, the plate material of the PSSII servey is being
used to search for new comets and asteroids. Researchers observed one
Neptune stellar occultation in July 1987 and completed the analysis
of a series of seven separate Neptune occultation observations in
conjunction with Nicholson et al., of Cornell. The analysis has
shown that minimum of three ring arcs, at radii ranging from 54,000
km - 67,000 km are required to account for the high quality ring
events. Current theoretical models can account for these data. Of two
observations scheduled of Pluto-Charon mutual occulations scheduled
for the 200-inch, the Charon eclipse event was successfully observed
(the other was clouded out).

---------------------------------------------------------
Title: Lunar and planetary studies
Authors: Muhleman, Duane O.; Goldreich, P.; Ingersoll, A. P.; Westphal,
J. A.
1988plas.rept...95M Altcode:
This grant supports the core program in planetary astronomy at
Caltech. The research includes observations in the IR, sub-mm, mm and
cm wavelengths at national and Caltech observatories with a strong
emphasis on integrating the observations with spacecraft data and with
models of atmospheric structure, dynamics and chemistry. Muhleman's
group made extensive observations of Saturn, Uranus and Neptune which
are being interpreted in terms of deep atmospheric structures which
are obvious in the 2 and 6 cm maps of Saturn and Uranus. The microwave
measurements are one of the few sources of information below the 2 bar
level. Goldreich is investigating the dynamics of narrow rings with
postdoctoral fellow, Pierre-Yves Longaretti. Their work has focused
on the role of collisional stresses on the precession of the rings,
since the Voyager radio science results imply that the previous model
based on the ring's self-gravity is not the entire story. In addition
Borderies, Goldreich and Tremaine have completed an investigation of
the dynamics of the Encke division in Saturn's A ring.

---------------------------------------------------------
Title: Distribution Functions for the Time-averaged Energies of
Stochastically Excited Solar p-Modes
Authors: Kumar, Pawan; Franklin, Joel; Goldreich, Peter
1988ApJ...328..879K Altcode:
The excitation of a damped harmonic oscillator by a random force is
studied as a model for the stochastic excitation of a solar p-mode
by turbulent convection. An extended sequence of observations is
required to separate different p-modes and thus determine the energies
of individual modes. Therefore, the observations yield time-averaged
values of the energy. The theory of random differential equations is
applied to calculate distribution functions for the time-averaged
energy of the oscillator. The instantaneous energy satisfies a
Boltzmann distribution. With increasing averaging time, the distribution
function narrows and its peak shifts toward the mean energy. Numerical
integrations are performed to generate finite sequences of time-averaged
energies. These are treated as simulated data from which approximate
probability distributions for the time-averaged energy are obtained.

---------------------------------------------------------
Title: The Interaction of Acoustic Radiation with Turbulence
Authors: Goldreich, Peter; Kumar, Pawan
1988ApJ...326..462G Altcode:
The authors derive expressions for the spectral emissivity and
absorptivity of acoustic radiation by low Mach number turbulent
fluids. They consider three types of turbulence. The first is free
turbulence, that is, turbulence which is not subject to external
forces. The second and third examples are special cases of forced
turbulence, turbulence maintained by stirring with spoons and turbulent
pseudoconvection. The resulting formulae are used to estimate the
equilibrium energies and quality factors of the acoustic modes in a box
which contains turbulent fluid. The scattering of acoustic radiation
by the turbulent velocity and pressure fluctuations is treated and
the rate at which nonlinear interactions transfer energy among the
acoustic modes is evaluated. This work is a first step in the attempt
to relate the excitation of the Sun's acoustic modes to the turbulence
in the solar convection zone.

---------------------------------------------------------
Title: Waves and normal modes in spiral galaxies.
Authors: Goldreich, Peter
1988oseg.proc..127G Altcode:
This lecture is an elementary introduction to some properties of linear
waves in rotating fluids, with special attention paid to spiral waves
in disk galaxies. To keep the lecture simple and self-contained, the
author quotes results obtained for gaseous disks with the aid of the
WKBJ approximation, wherever reasonable. Also, he makes many other
oversimplifying assumptions. He also restricts attention to rotation
laws for which Ω(r) &gt; 0 and dΩ(r)/dr &lt; 0.

---------------------------------------------------------
Title: The Interaction of Acoustic Radiation with Turbulence
Authors: Goldreich, Peter
1988amfm.conf..399G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Physics of modes in a differentially rotating system -
Analysis of the shearing sheet
Authors: Narayan, Ramesh; Goldreich, Peter; Goodman, Jeremy
1987MNRAS.228....1N Altcode:
A model compressible two-dimensional fluid system with constant density,
constant shear, and Coriolis force is investigated to study the linear
nonvortical modes of the shearing sheet. The analysis leads to an
eigenvalue problem based on the Parabolic Cylinder differential
equation. Each mode has an associated corotation radius, and a
particular conserved action is identified that is positive for fluid on
one side of corotation and negative on the other side. In the shearing
sheet, no instability is possible unless there is positive feedback
introduced into the amplifier at the boundaries. When tunneling is
small, most of the modes are neutral, while when tunneling is large,
both neutral and unstable modes are common. Slight perturbation of
the equilibrium shearing sheet by the introduction of density and/or
velocity perturbations results in a corotation resonance.

---------------------------------------------------------
Title: Self-Similar Quadrupole Perturbations in an Expanding Universe
Authors: Blaes, O. M.; Villumsen, J. V.; Goldreich, P.
1987BAAS...19Q1115B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The stability of accretion tori. II - Non-linear evolution
to discrete planets
Authors: Goodman, J.; Narayan, R.; Goldreich, P.
1987MNRAS.225..695G Altcode:
Hawley has shown through two-dimensional computer simulations that a
slender torus in which a linear Papaloizou-Pringle (PP) instability
with azimuthal wavenumber m, is excited evolves non-linearly to
a configuration with m nearly disconnected "planets". The authors
present an analytical fluid equilibrium that they believe represents
his numerical planets. They analyse the linear modes of the analytical
planet and find that there are numerous instabilities, though they are
not as violent as the PP instability in the torus. The authors also
discuss the energy and vorticity of neutral modes, and they argue that
when the torus breaks up into planets, neutral modes with negative
energy and non-zero vorticity are excited in order to conserve total
energy and specific vorticity. The authors speculate that the fluid
in Hawley's simulations may be approaching two-dimensional turbulence.

---------------------------------------------------------
Title: Shepherding of the Uranian Rings. II. Dynamics
Authors: Goldreich, Peter; Porco, Carolyn C.
1987AJ.....93..730G Altcode:
We explore the dynamical significance of the orbital resonances,
identified in Paper I (Porco and Goldreich 1987), involving the
satellites l986U7 and 1986U8, and the ɛ, δ, and γ rings. We
demonstrate that these satellites are capable of exerting torques
on the ɛ ring which supply at the inner edge, and remove at the
outer edge, the unperturbed angular-momentum luminosity transported
by viscous stresses outward across the ring, provided that the ring
has a mass which is comparable to the predicted value Mɛ
= 6.1 x 1018 g, and that it is not more than a few meters
thick. Thus there is no compelling reason to question the applicability
of the standard theory of shepherding to the ɛ ring. However, the
standard theory does place rather stringent requirements on the ring's
properties, suggesting that confinement might be due to the reduction
of the angular-momentum luminosity by flux reversal. Flux reversal
could be associated either with the ring's eccentricity gradient or
with nonlinear density waves in its interior. The drag due to the
planet's extended neutral hydrogen atmosphere probably has only a
minor effect on the dynamics of the ɛ, δ, and γ rings. However,
it poses a severe problem for the shepherding of the α and β rings
unless their masses have been seriously underestimated. This problem,
and the large s-band optical depths of these rings, lead us to question
the proposal that self-gravity is responsible for enforcing rigid
precession in narrow rings.

---------------------------------------------------------
Title: Shepherding of the Uranian Rings. I. Kinematics
Authors: Porco, C. C.; Goldreich, P.
1987AJ.....93..724P Altcode:
The possible kinematical relationships between the Uranian rings and all
ten newly discovered satellites of Uranus are examined. Observational
evidence is presented for interactions between 1986U7 and 1986U8 and
the epsilon, delta, and gamma rings. The likelihood that these two
satellites are shepherding the epsilon ring and are responsible for
some of its internal structure is assessed, and the results are used
to propose a reduction in the ring radius scale. It is also proposed
that 1986U7 and 1986U8 are the inner and outer shepherds for the
epsilon ring, that 1986U7 is the outer shepherd for the delta ring,
and that 1986U8 is an outer shepherd for the gamma ring. The results
of theoretical investigations of planetary ring dynamics are then
applied to these associations, and their dynamical significance is
evaluated. The resonant torques which the satellites exert on each
ring are calculated and compared to the viscous torque which transports
angular momentum outward through the ring and to the atmospheric-drag
torque which causes the ring's orbit to decay.

---------------------------------------------------------
Title: Nonlinear density waves in planetary rings
Authors: Borderies, Nicole; Goldreich, Peter; Tremaine, Scott
1986Icar...68..522B Altcode:
We discuss the steady-state structure of the nonlinear density
waves generated in a planetary ring at the Lindblad resonances of a
satellite. We show that strong density waves lead to an enhancement
of the background surface density in the wave zone.

---------------------------------------------------------
Title: The Interaction of Particles and Bending Waves in Disks of
Finite Thickness
Authors: Goldreich, P.; Chakrabarti, S. K.
1986BAAS...18Q1017G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Excitation and Damping of Solar p-modes
Authors: Kumar, P.; Goldreich, P.
1986BAAS...18.1011K Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Research in planetary astronomy at Palomar Observatory
Authors: Soifer, B. T.; Goldreich, P.
1986plas.rept...60S Altcode:
The goals of this program are three fold. The ring systems in the outer
solar system were studied. New comets and asteroids in the solar system
were surveyed. The volatile surface coverings of the primitive bodies
in the outer solar system were studied via infrared spectroscopy.

---------------------------------------------------------
Title: Towards a theory for Neptune's arc rings
Authors: Goldreich, P.; Tremaine, S.; Borderies, N.
1986AJ.....92..490G Altcode:
It is proposed that the incomplete rings of Neptune consist of a
number of short arcs centered on the corotation resonances of a single
satellite. The satellite must have a radius of the order of 100 km or
more and move on an inclined orbit. Corotation resonances are located at
potential maxima. Thus, mechanical energy dissipated by interparticle
collisions must be continually replenished to prevent the arcs from
spreading. It is shown that each corotation resonance is associated
with a nearby Lindblad resonance, which excites the ring particles'
orbital eccentricity, thus supplying the energy required to maintain
the arc. The ultimate energy reservoir is the satellite's orbital
energy. Therefore, interaction with the arcs damps the satellite's
orbital inclination. The self-gravity of the arcs limits their
contraction and enforces a relation between arc length and mass. The
estimated arc masses are so small, of the order of 10 to the 16th g,
that the satellite's orbital inclination suffers negligible decay over
the age of the solar system. The inferred surface mass densities are
comparable to those found in the major rings of Saturn and Uranus.

---------------------------------------------------------
Title: The stability of accretion tori. I - Long-wavelength modes
of slender tori
Authors: Goldreich, P.; Goodman, J.; Narayan, R.
1986MNRAS.221..339G Altcode:
The principal branch of the dispersion relation of a slender torus
is considered, and it is shown that the long-wavelength unstable
modes of the two-dimensionally incompressible ribbon are coupled
edge waves. Height-averaged fluid equations are used to estimate
the growth rate as a function of q, n, and beta, and the governing
equation for linear modes is reduced from a partial to an ordinary
differential equation. Two-dimensional modes when n = 1/2 are solved,
and the underlying physical mechanism of the instability modes of
Papaloizou and Pringle (1985) is identified. The presence of corotation
resonance is reflected by a singularity in the differential equation
of the height-integrated system whenever there is a nonzero gradient of
vorticity per unit surface density, and regions of parameter space are
identified where both principal modes decay. For the special case q =
2, n = 0, the system is found to be unstable.

---------------------------------------------------------
Title: An Explanation for Neptune's Arc Rings
Authors: Borderies, N.; Goldreich, P.; Tremaine, S. D.
1986BAAS...18R.778B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Dirk Brouwer Memorial Lecture "Planetary Rings"
Authors: Goldreich, Peter
1986BAAS...18R.838G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: New Ideas on the Confinement of Narrow Rings
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1986ESASP.242...95B Altcode: 1986sbos.conf...95B
The confinement of narrow rings by shepherd satellite has been
predicted by Goldreich and Tremaine in 1979. Detailed studies of how
the confinement is achieved revealed new important phenomena. They
are presented in this paper.

---------------------------------------------------------
Title: Initial Results on Ring/Satellite Dynamics from the Voyager
Uranus Encounter
Authors: Porco, C. C.; Goldreich, P.
1986BAAS...18..769P Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Evolution of the Janus-Epimetheus coorbital resonance due to
torques from Saturn's ring
Authors: Lissauer, J. J.; Goldreich, P.; Tremaine, S.
1985Icar...64..425L Altcode:
We analyze the interactions between Saturn's coorbital satellites, Janus
and Epimetheus, and the outer edge of the A ring, which is presumably
maintained by these moons at their 7:6 resonance. Using two distinct
but conceptually related methods, we show that ring torques are driving
these satellites into a tighter lock. Unless there is a counterbalancing
force which we have neglected, their orbital configuration will evolve
from the current horseshoe-type lock to one of tadpole orbits around
a single Lagrange point in ∼20 myr. This finding adds an additional
member to the list of short time scale problems associated with the
interactions between Saturn's rings and its inner moons

---------------------------------------------------------
Title: A granular flow model for dense planetary rings
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1985Icar...63..406B Altcode:
We study the viscosity of a differentially rotating particle disk
in the limiting case where the particles are densely packed and
their collective behavior resembles that of a liquid. The pressure
tensor is derived from the equations of hydrodynamics and from a
simple kinetic model of collisions described by Haff (1983). We find
that density waves and narrow circular rings are unstable if the
liquid approximation applies. The resulting development of nonlinear
perturbations may give rise to "splashing" of the ring material in the
vertical direction. These results may help in understanding the origin
of the ellipticities of ringlets, the nonaxisymmetric features near
the outer edge of the Saturnian B ring, and the unexplained residuals
in kinematic models of the Saturnian and Uranian rings.

---------------------------------------------------------
Title: Concluding Remarks
Authors: Goldreich, P.
1985ASSL..117..313G Altcode: 1985mlrg.proc..313G
No abstract at ADS

---------------------------------------------------------
Title: Non-axisymmetric instability in thin discs
Authors: Goldreich, P.; Narayan, R.
1985MNRAS.213P...7G Altcode:
Theoretical evidence is presented for the inevitability of
the appearance of instability in dynamically rotating thin
disks. The disk is treated as a parallel shear flow of a thin,
compressible, uniform density gas sheet with a constant velocity
gradient. A parabolic-cylinder differential equation is used to
express the perturbations, which include corotation and Lindblad
resonances. Eigenmodes are found to arise in forbidden regions between
the resonant turning points. A maximum growth rate is characterized
for the eigenmodes (WKB modes). A reflecting boundary is determined
necessary for formation of a self-sustained oscillation, and will
appear if the density at the inner or outer edge of the disk cuts off
on a scale shorter than the radial eigenmode wavelength.

---------------------------------------------------------
Title: Erratum: "Saturn's nonaxisymmetric ring edges at 1.95
Rs and 2.27 Rs" [Icarus, Vol. 60, No. 1,
p. 17 - 28 (1984)].
Authors: Porco, C.; Danielson, G. E.; Goldreich, P.; Holberg, J. B.;
Lane, A. L.
1985Icar...61..173P Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The eccentric Saturnian ringlets at 1.29 Rs and
1.45 Rs
Authors: Porco, C.; Nicholson, P. D.; Borderies, N.; Danielson, G. E.;
Goldreich, P.; Holberg, J. B.; Lane, A. L.
1984Icar...60....1P Altcode:
The shapes and kinematics of the two major eccentric ringlets
in Saturn's C ring are studied in data acquired by four Voyager
experiments: imaging science (ISS), radio science (RSS), ultraviolet
spectrometer (UVS), and photopolarimeter (PPS). It is found that the
ringlets have mean widths of ∼25 km (Titan, 1.29 Rs)
and ∼64 km (Maxwell, 1.45 Rs), eccentricities of order
10 -4, sharp edges on a scale of ∼1 km, normal optical
depths τ ∼ 1-2, and are embedded in essentially empty gaps ( τ &lt;
0.05). In addition, they exhibit positive linear width-radius relations,
suggesting that differential precession across the ringlets is being
prevented by the self-gravity of the ring particles. The kinematics
of the Maxwell ringlet are determined solely by Saturn's nonspherical
gravity field; the kinematics of the Titan ringlet are apparently
determined by its interaction with Titan. Masses, mean surface mass
densities, and mass extinction coefficients have been calculated. The
comparatively large optical depths and mass extinction coefficients in
these features suggest an environment and particle size distribution
different from the remainder of the C ring and presumably caused by
the mechanism responsible for ring confinement.

---------------------------------------------------------
Title: Saturn's nonaxisymmetric ring edges at 1.95 Rs
and 2.27 Rs
Authors: Porco, C.; Danielson, G. E.; Goldreich, P.; Holberg, J. B.;
Lane, A. L.
1984Icar...60...17P Altcode:
The outer edges of Saturn's A and B rings, at 2.27 Rs and
1.95 Rs, have been examined using data acquired by four
Voyager experiments. The shapes and kinematics of these features
are influenced by their proximity to strong low-order Lindblad
resonances. The data for the A-ring edge are consistent with a
seven-loded radial distortion of amplitude 6.7 ± 1.5 km which rotates
with the mass-weighted mean angular velocity of the coorbital satellite
system. The B-ring edge has essentially a double-lobed figure of radial
amplitude 74 ± 9 km which rotates with the mean motion of Mimas,
though there is an indication that it is not completely described withe
a simple Saturn-centered ellipse. An upper limit of 10 m has been placed
on the vertical thickness in the unperturbed region of the B ring.

---------------------------------------------------------
Title: Excitation of inclinations in ring-satellite systems
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1984ApJ...284..429B Altcode:
Resonant gravitational interactions between a ring and a satellite
produce secular variations of their orbital inclinations. Interactions
at vertical resonances, analogous to Lindblad resonances but involving
inclinations instead of eccentricities, excite inclinations. There is
no inclination analog of the corotation resonance. An equatorial ring
changes the inclination of a nearby satellite in qualitatively the same
way that a satellite in an equatorial orbit changes the inclination of
a nearby ring. Viscous dissipation in a ring leads to an equilibrium
value of its inclination. These results provide a basis for discussing
the origins of the inclinations of planetary rings.

---------------------------------------------------------
Title: Self-similar gravitational collapse in an expanding universe
Authors: Fillmore, J. A.; Goldreich, P.
1984ApJ...281....1F Altcode:
The authors derive similarity solutions which describe the collapse
of cold, collisionless matter in a perturbed Einstein-de Sitter
universe. They obtain three classes of solutions, one each with planar,
cylindrical, and spherical symmetry. The solutions can be computed to
arbitrary accuracy, and they follow the development of structure in
both the linear and nonlinear regimes.

---------------------------------------------------------
Title: Erratum - the Dynamics of Elliptical Rings
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1984AJ.....89..727B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Shepherding of Narrow Rings Revisited
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1984BAAS...16Q.676B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Self-similar spherical voids in an expanding universe
Authors: Fillmore, J. A.; Goldreich, P.
1984ApJ...281....9F Altcode:
The authors derive similarity solutions which describe the evolution of
spherically symmetric voids in a perturbed Einstein-de Sitter universe
filled with cold, collisionless matter. The character of a solution
depends upon the profile of the initial density deficit. Gradual
perturbations give rise to holes within which the density rises smoothly
to the background value. Steep perturbations result in voids bounded
by overdense shells with sharp edges, i.e. collisionless gravitational
shocks.

---------------------------------------------------------
Title: A Simple Derivation of Capture Probabilities for the J+1:J
and J+2:J Orbit-Orbit Resonance Problems
Authors: Borderies, N.; Goldreich, P.
1984CeMec..32..127B Altcode:
We present a simplified analytic derivation of the capture probabilities
for the j+1∶j and j+2∶j orbital resonances. We apply Henrard's
method which is based on an extension of the theory of adiabatic
invariants and recover the results originally obtained by Yoder.

---------------------------------------------------------
Title: Perturbed Particle Disks
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1984plri.coll..339B Altcode: 1984prin.conf..339B; 1984IAUCo..75..339B
No abstract at ADS

---------------------------------------------------------
Title: Spoke Electrodynamics
Authors: Acterberg, A.; Blandford, R.; Goldreich, P.
1984plri.coll..549A Altcode: 1984prin.conf..549A; 1984IAUCo..75..549A
No abstract at ADS

---------------------------------------------------------
Title: Sharp Edges of Planetary Rings
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1984plri.coll..345B Altcode: 1984prin.conf..345B; 1984IAUCo..75..345B
The ring systems of Saturn and Uranus exhibit a number of sharp
edges across which the optical depth drops from order unity to near
zero. At least two and perhaps all of these features are associated
with the location of orbital resonances between a satellite and a
ring particle. The authors illustrate with qualitative argument the
results of a numerical simulation concerning the outer edge of the B
ring of Saturn.

---------------------------------------------------------
Title: Solved and Unsolved Problems in Planetary Ring Dynamics
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1984plri.coll..327B Altcode: 1984prin.conf..327B; 1984IAUCo..75..327B
The authors discuss a number of new ideas related to planetary ring
dynamics and apply them to Saturn's rings. For simplicity, the ring
particles are taken to be identical, smooth, spheres composed of dense
and chemically pure ice.

---------------------------------------------------------
Title: The Eccentric Ringlet at 1.29 RS
Authors: Porco, C.; Borderies, N.; Danielson, G. E.; Goldreich, P.;
Holberg, J. B.; Lane, A. L.; Nicholson, P. D.
1984plri.coll..259P Altcode: 1984IAUCo..75..259P; 1984prin.conf..259P
The authors present preliminary results of an examination of the
eccentric ringlet near 1.29 Rs in Saturn's inner C
ring. Situated near the Titan 1:0 apsidal resonance, this feature
provides an opportunity to study the behavior of a ring under the
influence of both the gravity field of a major planet and the potential
of an external satellite.

---------------------------------------------------------
Title: Dynamics of Eccentric and Inclined Ringlets
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1984plri.coll..341B Altcode: 1984IAUCo..75..341B; 1984prin.conf..341B
No abstract at ADS

---------------------------------------------------------
Title: Unsolved problems in planetary ring dynamics
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1984prin.conf..713B Altcode:
Voyager photographic data are used for microscopic and macroscopic
analyses of the dynamics of the Saturn rings. Attention is given to
particle collisions, local velocity dispersion, the particle size
distribution, mechanisms governing the ring structure and interactive
effects with Saturn satellite orbits. The mechanical properties and
collision dynamics of the particles are discussed, along with models
for perturbed and unperturbed disks. The forces involved and true scale
of particle erosion are considered, as are instabilities in the rings,
satellite torques, resonances, and the time scale for the evolution of
the satellite orbits. Finally, the possibility that angular momentum
exchanges are occurring between individual rings and satellite orbits
is examined.

---------------------------------------------------------
Title: The dynamics of elliptical rings.
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1983AJ.....88.1560B Altcode:
The paper investigates the evolution of eccentric rings under the
influence of (1) differential precession due to the planetary quadrupole
moment; (2) self-gravity; (3) viscous forces due to interparticle
collisions; and (4) eccentricity excitation by shepherd satellites. The
principal conclusions are that: (1) uniform precession can be enforced
by self-gravity; the resulting configuration is both dynamically and
secularly stable. (2) due to viscous forces the line of apsides at
the inner ring edge is not exactly aligned with the line of apsides
at the outer edge; the apse shift may be detectable in the alpha
and beta rings of Uranus; (3) the mean eccentricity is determined
by a balance between viscous damping and excitation by shepherds;
(4) and the dimensionless eccentricity gradient is expected to be
positive and of order unity in most eccentric rings, as observed.

---------------------------------------------------------
Title: Eccentric Ringlet in the Maxwell Gap at 1.45 Saturn Radii:
Multi-Instrument Voyager Observations
Authors: Esposito, L. W.; Borderies, N.; Goldreich, P.; Cuzzi, J. N.;
Holberg, J. B.; Lane, A. L.; Pomphrey, R. B.; Terrile, R. J.; Lissauer,
J. J.; Marouf, E. A.; Tyler, G. L.
1983Sci...222...57E Altcode:
The Voyager spacecraft observed a narrow, eccentric ringlet in the
Maxwell gap (1.45 Saturn radii) in Saturn's rings. Intercomparison of
the Voyager imaging, photopolarimeter, ultraviolet spectrometer, and
radio science observations yields results not available from individual
observations. The width of the ringlet varies from about 30 to about
100 kilometers, its edges are sharp on a radial scale &lt; 1 kilometer,
and its opacity exhibits a double peak near the center. The shape and
width of the ringlet are consistent with a set of uniformly precessing,
confocal ellipses with foci at Saturn's center of mass. The ringlet
precesses as a unit at a rate consistent with the known dynamical
oblateness of Saturn; the lack of differential precession across
the ringlet yields a ringlet mass of about 5 × 1018
grams. The ratio of surface mass density to particle cross-sectional
area is about five times smaller than values obtained elsewhere in
the Saturn ring system, indicating a relatively larger fraction of
small particles. Also, comparison of the measured transmission of the
ringlet at radio, visible, and ultraviolet wavelengths indicates that
about half of the total extinction is due to particles smaller than 1
centimeter in radius, in contrast even with nearby regions of the C
ring. However, the color and brightness of the ringlet material are
not measurably different from those of nearby C ring particles. We
find this ringlet is similar to several of the rings of Uranus.

---------------------------------------------------------
Title: Erratum - Precession of Inclined Rings
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1983AJ.....88.1074B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Magnetic focusing in the Sco X-1 radio source
Authors: Achterberg, A.; Blandford, R. D.; Goldreich, P.
1983Natur.304..607A Altcode:
There has been much theoretical discussion of the confinement
of the radio jets associated with extragalactic radio
sources1. There are now several examples of sources where the
minimum pressure inferred in the jets appears to exceed the external
gas pressure, which suggests that magnetic pinching may be playing an
important part in the confinement2-4. This issue has been
highlighted by recent remarkable observations, using the Very Large
Array, of the radio lobes associated with the galactic X-ray source Sco
X-1 by Fomalont et al.5. We argue here that these results
necessitate magnetic focusing and that this also strengthens the case
for magnetic focusing in the extragalactic sources. We show that a
sufficient overpressure with respect to the ambient interstellar medium
can be achieved if the radius of the jet is reduced by a factor 10-100,
and the converging flow becomes dissipative. The radio lobes which
form at that point quickly die out again due to electron expansion
losses in the now rapidly diverging jet. On the basis of this model it
is predicted that the Faraday rotation changes sign across the radio
lobes, and that the shape of the lobes should be conical with the apex
pointing towards Sco X-1.

---------------------------------------------------------
Title: Perturbed particle disks
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1983Icar...55..124B Altcode:
The Boltzmann moment equations are solved to determine the velocity
ellipsoid in a particle disk near an isolated satellite resonance. In
a coordinate frame which rotates with the pattern speed of the
perturbation potential, the solutions are stationary functions of
the azimuthal angle. From the velocity ellipsoid we obtain the stress
tensor due to particle collisions and consequently, the viscous angular
momentum flux. We show that the magnitude of the rate of deformation
tensor in a perturbed particle disk is bounded from above by KΩ(1 + τ
2) 1/2, where Ω is the orbital angular velocity,
τ is the optical depth, and K is a dimensionless constant of order
unity. It is also found that in sufficiently perturbed regions there
are ranges of azimuthal angle within which the radial component of
the angular momentum flux is negative. It is even possible for the
angular momentum luminosity, the radial flux integrated over azimuth,
to be negative. These results are important for understanding sharp
edges and the decay of density waves in planetary rings. They are also
relevant to the damping of differential precession and eccentricity
in narrow ringlets.

---------------------------------------------------------
Title: Precession of inclined rings
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1983AJ.....88..226B Altcode:
It is proposed that node alignment across an inclined ring is maintained
by the self-gravity of the ring, which cancels the tendency for
differential node precession due to the planet's multiple moments. The
analysis is confined to circular rings, which is a self-consistent
approximation because the interactions among circular and inclined
ringlets do not generate secular perturbations of eccentricity.

---------------------------------------------------------
Title: The variations in eccentricity and apse precession rate of
a narrow ring perturbed by a close satellite
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1983Icar...53...84B Altcode:
We derive a Hamiltonian which describes the first-order perturbations of
orbital eccentricity and apse precession rate of a narrow ring due to
a close satellite whose orbit is also eccentric. Our treatment covers
cases in which the satellite crosses the ring. The level curves of
the Hamiltonian are displayed for several values of the parameters. We
apply our results to the interaction of Saturn's F ring with its inner
shepherd satellite.

---------------------------------------------------------
Title: Sharp edges of planetary rings
Authors: Borderies, N.; Goldreich, P.; Tremaine, S.
1982Natur.299..209B Altcode:
The ring systems of Saturn and Uranus exhibit several sharp edges,
across which the optical depth drops from order unity to essentially
zero. At least two and perhaps all of these features are associated
with the location of orbital resonances between a satellite and the ring
particles. It is remarkable that the optical depth varies on a distance
scale which is much finer than that over which angular momentum can be
transferred between a satellite and the ring material. The important
features of this phenomenon are: (1) a perturbed band of width
Delta a/a of about (satellite mass/planetary mass) to the 1/2 power
adjacent to the edge within which the angular momentum transfer occurs,
(2) streamlines perturbed such that the angular momentum luminosity
decreases smoothly across the band to zero at the edge even though the
optical depth remains constant, and (3) dynamical equilibrium requires
a relation between the random velocity, the rate of deformation and
the optical depth.

---------------------------------------------------------
Title: Radial widths, optical depths, and eccentricities of the
Uranian rings
Authors: Nicholson, P. D.; Matthews, K.; Goldreich, P.
1982AJ.....87..433N Altcode:
Observations of the stellar occultation by the Uranian rings of 15/16
August 1980 are used to estimate radial widths and normal optical
depths for segments of rings 6, 5, 4, alpha, beta, eta, gamma,
and delta. Synthetic occultation profiles are generated to match the
observed light curves. A review of published data confirms the existence
of width-radius relations for rings alpha and beta, and indicates that
the optical depths of these two rings vary inversely with their radial
widths. Masses are obtained for rings alpha and beta, on the assumption
that differential precession is prevented by their self-gravity. A
quantitative comparison of seven epsilon-ring occultation profiles
obtained over a period of 3.4 yr reveals a consistent structure,
which may reflect the presence of unresolved gaps and subrings.

---------------------------------------------------------
Title: Linear polarization of radio frequency lines in molecular
clouds and circumstellar envelopes
Authors: Goldreich, P.; Kylafis, N. D.
1982ApJ...253..606G Altcode:
It is predicted that interstellar lines possess a few percent linear
polarization provided that the optical depth in the source region is
both anisotropic and of order unity and the radiative rates are at
least comparable to the collision rates. These conditions are expected
to be met in many sources which emit radio and far-infrared line
radiation. Under circumstances in which the Zeeman splitting exceeds
both the radiative and collisional rates the linear polarization is
aligned either parallel or perpendicular to the projection of the
magnetic field on the plane of the sky. This 'strong magnetic field'
limit is expected to apply to all radio frequency lines and to many
of those far infrared lines which form between levels whose magnetic
moments are comparable to the Bohr magneton. The 'weak magnetic field'
limit is relevant to most far-infrared lines formed between levels
with magnetic moments of order the nuclear magneton. In this limit
the polarization direction is determined by the orientation of the
propagation direction with respect to the anisotropic optical depth.

---------------------------------------------------------
Title: The dynamics of planetary rings
Authors: Goldreich, P.; Tremaine, S.
1982ARA&A..20..249G Altcode:
The physical processes that occur in planetary rings are discussed. The
theoretical arguments leading to the conclusion that Saturn's rings are
solid particles in nonuniform rotation are summarized, and the optical
depth, thickness, and particle size of the rings are discussed. The
influence of nearby satellites on the rings is analyzed, and asymmetries
in the rings are briefly discussed. What is known of the rings of Uranus
and of Jupiter's ring is summarized. Some of the dynamical processes
and influences that are expected to be incorporated in more advanced
theories of planetary rings are reviewed in detail, including radiation
drag, plasma drag, interparticle collisions and viscosity, resonances
with external satellites, shepherd satellites and moonlets. Finally,
the orbital evolution of the shepherd satellites caused by the rings
is estimated.

---------------------------------------------------------
Title: Resonances and rings in the solar system
Authors: Goldreich, P.
1982coas.conf..121G Altcode:
Observations of the structure and dynamics of planetary ring systems
are examined for the effects of satellite resonances. The evidence
that indicates the presence of solar system resonances includes the
preferences for low order commensurabilities in the orbital periods
of Jovian and Saturn satellites, the resonant state of Mercury's
spin, and the Kirkwood gaps in the number density versus semi-major
axis distribution of the asteroids. The influences of collisions and
resonance torques in ring systems are discussed. The morphology of
planetary rings is determined by satellites exerting torques on the ring
material at positions of low order resonances. The actions of Mimas on
the Cassini division in Saturn's rings is described, and the existence
of small, undiscovered satellites within the ring is predicted.

---------------------------------------------------------
Title: The dynamics of planetary rings
Authors: Goldreich, P.
1982asme.proc...41G Altcode:
Recent ground observations, and high-resolution photographs and
occultation profiles derived from Voyager radio, photopolarimeter,
and ultraviolet spectrometer instruments, have provided information
about the dynamics of planetary ring systems. Saturn's rings are found
to contain particles ranging in size from centimeters to tens of meters
and are thought to be composed primarily of ice. Groundbased occulation
profiles have revealed nine rings with an eccentric orbit. Circular
velocities of Saturnian ring particles were measured at 20 km/s, and
random velocities on the order of 0.1 to 1mm/s. The orbital resonances
of satellites were found to drive density waves in Saturn's and to
account for the observed abrupt ring boundraries. It is proposed
that a pair of 'shepherding satellites' accompanies each ring of
one side, and that gravitational forces between the satellites keep
ring material in an equilibrium orbit. The effect of the rings' own
self-gravity is shown to cancel the differential precession observed
in the rings. Explanations are offered as to why Saturnian rings reveal
structure down to 300 m, but it is conceded that more work is necessary.

---------------------------------------------------------
Title: The Uranus occultation of 10 June 1979. I - The rings
Authors: Nicholson, P. D.; Matthews, K.; Goldreich, P.
1981AJ.....86..596N Altcode:
Observations and analysis of a stellar occultation by the rings of
Uranus on 10 June 1979 are presented. Occultations by rings 4, α,
β, γ, δ, and ɛ are identified, and radii and azimuths of the
occulting segments in the plane of the rings calculated. Results for
rings γ and δ are consistent with the hypothesis (Elliot et al. 1978;
Nicholson et al. 1978) that these two rings are circular and coplanar,
and an approximate upper limit of 8 × 10-5 is placed
on the eccentricity of either ring. Coplanar elliptical models are
presented for rings α and β with eccentricities of (6.0±0.3) ×
l0-4 and (4.9±0.5) × 10-4, respectively. For
ring 4 two possible elliptical models are obtained, with eccentricities
of (1.2±0.4) × 10-3 and (6.0±0.3) × 10-4, the
former being preferred. The width-radius relation established previously
for the E ring is confirmed, and the elliptical model for this ring
is slightly revised. An improved estimate for Uranus's J2
of (3.390±0.005) × l0-4, based on the apsidal precession
of the ɛ ring, and an upper limit for |J4| of ∼1 ×
10-4, based on the precession of rings 4 and β are obtained.

---------------------------------------------------------
Title: INVITED TALK - Planetary Rings
Authors: Goldreich, Peter
1981BAAS...13..525G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The origin of the eccentricities of the rings of Uranus
Authors: Goldreich, P.; Tremaine, S.
1981ApJ...243.1062G Altcode:
The effect of gravitational perturbations from a nearby satellite on
the eccentricity e of a narrow particulate ring is considered. The
perturbations near a resonance in an eccentric ring may be divided into
corotation and Lindblad terms. For small e, the corotation terms damp
e, whereas the Lindblad terms excite e. In the absence of saturation
the corotation terms win by a small margin, and e damps. However,
if the perturbations open gaps at the strongest resonances, then the
Lindblad terms win, and e grows. This result offers an explanation for
the existence of both circular and eccentric rings around Uranus. It
is also shown that eccentricity changes induced by circular rings on
eccentric satellite orbits are similar to those induced by satellites
with circular orbits on eccentric rings.

---------------------------------------------------------
Title: On mapping the magnetic field direction in molecular clouds
by polarization measurements
Authors: Goldreich, P.; Kylafis, N. D.
1981ApJ...243L..75G Altcode:
It is predicted that interstellar radio-frequency lines possess a
few percent linear polarization, provided that (1) the radiative
transition rate is at least comparable to the collision rate, (2)
the optical depth is moderate and anisotropic, and (3) the number of
extrema of the velocity component along the line of sight through the
source is small. If the Zeeman splitting exceeds both the collisional
frequency and the radiative transition rate, then the polarization is
aligned either perpendicular to or parallel to the projection of the
magnetic field on the plane of the sky.

---------------------------------------------------------
Title: Disk-satellite interactions.
Authors: Goldreich, P.; Tremaine, S.
1980ApJ...241..425G Altcode:
The rate at which angular momentum and energy are transferred between
a disk and a satellite which orbit a central mass is calculated. It
is shown that the angular momentum and energy transfer at Lindblad
resonances tends to increase the satellite's orbit to lowest order
in eccentricity, whereas the transfer at corotation resonances tends
to decrease it. The results are applied to the interaction between
Jupiter and the protoplanetary disk. The angular momentum transfer is
shown to be so rapid that substantial changes in both the structure
of the disk and the orbit of Jupiter must have taken place on a time
scale of a few thousand years.

---------------------------------------------------------
Title: Theoretical studies of solar oscillations
Authors: Goldreich, P.
1980cait.rept.....G Altcode:
Possible sources for the excitation of the solar 5 minute oscillations
were investigated and a linear non-adiabatic stability code was
applied to a preliminary study of the solar g-modes with periods
near 160 minutes. Although no definitive conclusions concerning
the excitation of these modes were reached, the excitation of the
5 minute oscillations by turbulent stresses in the convection zone
remains a viable possibility. Theoretical calculations do not offer
much support for the identification of the 160 minute global solar
oscillation (reported by several independent observers) as a solar
g-mode. A significant advance was made in attempting to reconcile
mixing-length theory with the results of the calculations of linearly
unstable normal modes. Calculations show that in a convective envelope
prepared according to mixing length theory, the only linearly unstable
modes are those which correspond to the turbulent eddies which are
the basic element of the heuristic mixing length theory.

---------------------------------------------------------
Title: Homologously collapsing stellar cores
Authors: Goldreich, P.; Weber, S. V.
1980ApJ...238..991G Altcode:
The paper investigates the collapse of nonrotating gas spheres with
a polytropic equation of state for n = 3, corresponding to gamma =
4/3. Such polytropes provide a reasonable approximation to collapsing
stellar cores during the early phase before nuclear density is
reached. A family of exact homologously collapsing configurations
is found. Homologous collapse of the entire core is possible if the
pressure at a given density is reduced by up to 3% from the value for
a marginally stable static core. For a greater pressure reduction,
an inner core can collapse homologously, the mass of which varies as
the 3/2 power of the reduced pressure at the onset of the collapse.

---------------------------------------------------------
Title: Interpretation of circumstellar masers
Authors: Goldreich, P.
1980IAUS...87..551G Altcode:
Consideration is given to problems in the theoretical interpretation of
masers operating in the circumstellar envelopes about oxygen-rich Mira
variables and supergiants. Following a brief review of the dynamics,
thermodynamics and chemistry of circumstellar envelopes, current
knowledge of the location, directionality, input energy, saturation
state and nature of the pumping of circumstellar SiO, H2O and OH
masers is indicated. Specific theoretical models of 1612-MHz OH masers,
main line OH masers, H2O masers and SiO masers are then considered.

---------------------------------------------------------
Title: The excitation of density waves at the Lindblad and corotation
resonances by an external potential.
Authors: Goldreich, P.; Tremaine, S.
1979ApJ...233..857G Altcode:
The linear response of a differentially rotating two-dimensional gas
disk, both with and without self-gravity, to a rigidly rotating external
potential is calculated on the assumptions that the speed of sound is
much smaller that the orbital velocity and that the external potential
varies on the scale of the disk radius. The results show that: (1)
the external potential exerts torques on the disk only at the Lindblad
and corotation resonances; (2) the torque is positive at the outer
Lindblad resonance and negative at the inner Lindblad resonance; (3)
the torque at corotation has the sign of the radial vorticity gradient;
and (4) the torques are of the same order of magnitude at both types of
resonance and independent of the speed of sound in the disk. It is found
that the external potential also excites density waves in the vicinity
of the Lindblad and corotation resonances, that the long trailing wave
is excited at a Lindblad resonance, and that short trailing waves are
excited at the corotation resonance. The behavior of particle disks
is briefly discussed, and the external torques on particle disks are
proven to be identical to those on gas disks

---------------------------------------------------------
Title: Precession of the epsilon ring of Uranus.
Authors: Goldreich, P.; Tremaine, S.
1979AJ.....84.1638G Altcode:
It is noted that the outer and inner boundaries of the epsilon ring
of Uranus can be fitted by aligned Keplerian ellipses. Four possible
mechanisms for maintaining uniform precession in the epsilon ring are
considered: the ring's self-gravity, precession due to a satellite,
smooth pressure gradients, and shocklike phenomena. It is proposed
that apse alignment is maintained by the self-gravity of the ring. In
this case, a ring mass of approximately 5 x 10 to the 18th g and a
mean surface density at quadrature of about 25 g/sq cm are estimated.

---------------------------------------------------------
Title: The rings of Saturn and Uranus.
Authors: Goldreich, P.; Tremaine, S.
1979ASIC...47..129G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Rings of Saturn and Uranus
Authors: Goldreich, P.
1979IAUS...81..191G Altcode:
Saturn has bright, broad rings separated by narrow gaps, while the
rings of Uranus are dark, narrow and widely spaced. Presumably,
both sets of rings lie inside the Roche limit, which is why the ring
material has not condensed into satellites. This paper briefly reviews
what is known about each ring system, with emphasis on properties of
significance to dynamical astronomy.

---------------------------------------------------------
Title: The Absorption of Trapped Line Photons by Dust
Authors: Goldreich, Peter.; Kwan, John
1979ApJ...227..150G Altcode:
We derive the rate at which photons in an optically thick line
are absorbed by cold dust. This rate is approximately equal to the
dust optical depth to the cloud center times the rate at which the
photons escape from the cloud. Our derivation is in response to a
recent article by Strel'nitskii in which he incorrectly criticized
our previous application of this result to models for the pumping
of cosmic masers. Strel'nitskii now agrees that his criticism was
unjustified. Subject headings: masers - nebulae: general - radiative
transfer

---------------------------------------------------------
Title: Solar System Studies - Jupiter Imaging at 5-MICRONS - Jupiter
Magnetosphere - Infrared Observations of Planets - Diameter of Pluto
Authors: Kowal, C.; Goldreich, P.; Terrile, R. J.; Westphal, J.;
Trauger, J.; Munch, G.; Roesler, F. L.; Soifer, B. T.; Matthews, K.;
Neugebauer, G.; Sargent, W. L. W.; Boksenberg, A.; Arnold, S. J.
1979haob.rept..721K Altcode:
No abstract at ADS

---------------------------------------------------------
Title: HII Regions in Galaxies - Luminosity Classification -
Nonequilibrium Companions of Spiral Galaxies - Dwarf Irregular
Galaxies in Nearby Groups
Authors: Kennicutt, R.; Sulentic, J. W.; Arp, H. C.; di Tullio, G.;
Lo, K. Y.; Sargent, W. L. W.; Sancisi, R.; Goldreich, P.; Kowal, C.;
Thuan, T. X.
1979haob.rept..752K Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Towards a theory for the Uranian rings
Authors: Goldreich, P.; Tremaine, S.
1979Natur.277...97G Altcode:
Interparticle collisions, radiation drag, and differential precession
all tend to disrupt the rings of Uranus. The first two effects lead
to radial spreading which would disrupt a free ring in less than or
approximately 100,000,000 yr. It is proposed that the rings are confined
in radius by gravitational torques from a series of small satellites
that orbit with the ring system. Differential precession tends to
destroy the apse alignment of the elliptical epsilon ring. It is
suggested that apse alignment is maintained by the self-gravity of the
ring. The resulting mass of the epsilon ring is approximately 5 times
10 to the 18th power g. Its radial confinement requires (for example)
a pair of satellites of mass approximately 10 to the 19th power g,
in circular orbits roughly 500 km away on either side of the ring

---------------------------------------------------------
Title: The rings of Uranus: results of the 10 April 1978 occultation.
Authors: Nicholson, P. D.; Persson, S. E.; Matthews, K.; Goldreich,
P.; Neugebauer, G.
1978AJ.....83.1240N Altcode:
Observations of the April 10, 1978, stellar occultation by the rings
of Uranus are presented. Nine rings were observed, and their radii and
widths are calculated. Rings eta, gamma, and delta are found to be most
likely circular and coplanar, in agreement with previous analyses; the
remaining rings are either noncircular or slightly inclined. The width
of the epsilon ring is a linear function of its radius from the center
of Uranus, projected onto the satellites' orbital plane; this suggests
that it forms one continuous noncircular ring. The optical-depth profile
of the epsilon ring has not changed significantly since March 1977. A
model of this ring which fits all available observations adequately
is that of a uniformly precessing Keplerian ellipse coplanar with the
satellites' orbits. This model permits predictions of the radius and
width of the epsilon ring for future occultations. The precession rate
is used to determine J2 for Uranus, on the assumption that precession
is caused solely by the planetary oblateness and not by satellite-ring
interactions.

---------------------------------------------------------
Title: The excitation and evolution of density waves.
Authors: Goldreich, P.; Tremaine, S.
1978ApJ...222..850G Altcode:
The behavior of density waves in a simple analog of a rotating disk is
analyzed. The model considered is a thin gas sheet whose unperturbed
velocity field is a parallel shear flow; the effects of rotation are
simulated by introducing a Coriolis acceleration; the model exhibits
Lindblad resonances and includes both long- and short-wavelength
density waves among its linear perturbations. The linear perturbation
equations are set up in a form appropriate to the model and rewritten
in terms of the comoving coordinates of the unperturbed flow. The
resulting equations are Fourier transformed and then solved in the
tight-winding limit. The excitation of a wave packet by an external
potential is calculated along with the packet's subsequent propagation,
and analytical solutions are obtained which are valid everywhere,
including the Lindblad and corotation resonances. It is found that a
barlike potential excites long-wavelength trailing density waves at
the Lindblad resonances. The amplification of a density wave incident
on the forbidden zone surrounding corotation is also examined.

---------------------------------------------------------
Title: The Rings of Uranus (invited).
Authors: Goldreich, P.
1978BAAS...10..581G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The formation of the Cassini division in Saturn's rings
Authors: Goldreich, P.; Tremaine, S. D.
1978Icar...34..240G Altcode:
The satellite Mimas excites a trailing spiral density wave in Saturn's
rings at the position of the 2:1 resonance. The density wave carries
negative angular momentum and propagates outward. The wave is damped
by a combination of nonlinear and viscous effects, and its negative
angular momentum is transferred to the ring particles. Consequently,
the particles just outside the 2:1 resonance spiral inward, opening
a gap. The inner edge of the gap is close to the resonance position
in agreement with the location of the inner edge of the Cassini
division. Despite its tiny mass, Minas is able to clear a gap as wide as
the Cassini division. We estimate the ability of Saturn's satellites to
open other gaps in the rings. The upper limit to the width of Encke's
division implies that the velocity dispersion of the ring particles
is &lt;10 -2 cm sec -1.

---------------------------------------------------------
Title: The velocity dispersion in Saturn's rings
Authors: Goldreich, P.; Tremaine, S. D.
1978Icar...34..227G Altcode:
The velocity dispersion in a differentially rotating disk of particles
such as Saturn's rings is determined by the details of the collision
process. Collisions give rise to a viscous stress that converts
orbital energy into random motions. Since the collisions are not
perfectly elastic, the energy in random motions is dissipated as
heat. With increasing velocity dispersion the latter process becomes
more important relative to the former because the collisions become
less elastic. The velocity dispersion adjusts so that the effects of
these two processes balance. The condition for this balance fixes the
coefficient of restitution ɛ of the colliding particles as a function
of the disk's optical depth τ. We solve the Boltzmann moment equations
to determine ɛ(τ). If the rings are about as old as the solar system
then their radial width implies that the velocity dispersion of the
ring particles is less than 0.2 cm sec -1. The corresponding
vertical thickness is then less than 10 m. We discuss the effects of
collisions on the particles in Saturn's rings. If the particles are
made of ice they are eroded by collisions and accrete the collisional
debris. The time scale for erosion and accretion is probably shorter
than the age of the solar system. Furthermore, for ice particles ɛ is
likely to be substantially less than unity even at impact velocities
as low as 10 -3 cm sec -1. Thus, a ring of ice
particles would be a monolayer thick.

---------------------------------------------------------
Title: Occultations by Uranian Rings
Authors: To, J.; Persson, E.; Nicholson, P.; Matthews, K.; Goldreich,
P.; Neugebauer, G.; Elliot, L.; Churms, J.; Marsden, B. G.
1978IAUC.3215....3T Altcode:
Further analysis, by the undersigned, of the occultation of SAO 158687
on 1977 Mar. 10 yields the following radii for the rings, assumed to
lie in Uranus' equatorial plane (cf. IAUC 3051, 3061): Ring Distance
Ring Distance alpha 44 835 km delta 48 408 km beta 45 788 epsilon1
51 697 gamma 47 732 epsilon2 51 030 These results (uncertainty
+/- 30 km) are very similar to those by Wasserman et al. (1977,
Bull. Am. Astron. Soc. 9, 498). As the result of observations of another
predicted occultation on 1977 Dec. 23 (IAUC 3108; Astron. J. 1977,
82, 849, 929, 1036), Millis and Wasserman (1978, Astron. J. to be
published) confirm the existence of the gamma, delta and epsilon rings
and possibly also of the alpha ring; these measurements, obtained at a
wavelength of 0.88 um at Cabezon Observatory, Tenerife, were difficult
to make in the dawn sky. E. Persson, Hale Observatories; P. Nicholson,
K. Matthews, P. Goldreich and G. Neugebauer, California Institute of
Technology, report that successful observations at a wavelength of
2.2 um were made with the 250-cm du Pont telescope at the Las Campanas
Observatory on 1978 Apr. 10 of a third occultation by the Uranian rings
(only the occultation by Uranus itself could be detected in the case
of a fainter star on 1978 Apr. 4). All five 'original' rings were
detected, and assuming the above values for the alpha, beta, gamma
and delta rings the radii of further rings were determined as follows:
Ring Distance Ring Distance kappa1 42 029 km kappa2 42 148 km iota1 42
394 iota2 42 304 theta1 42 660 theta2 42 696 eta1 47 290 eta2 47 289
epsilon1 50 848 epsilon2 51 402 As before (IAUC 3051, 3061), subscripts
refer to the western and eastern edges of the rings, respectively. The
kappa ring is uncertain. The iota1 and theta1 events are undoubtedly
identical with the alpha3 and beta3 events previously described by
Millis et al. (IAUC 3051). The eta events were also subsequently
reported by L. Elliot (unpublished) in the case of the SAO 158687
occultation. The more recent results for epsilon suggest that this is
indeed a complete ring but that its width is relatively substantial,
its shape non-circular and its structure complex. The possible zeta
ring of J. Churms (IAUC 3051) has not been confirmed, and there appear
to be no confirmed rings of any consequence outside epsilon.

---------------------------------------------------------
Title: On the radiative acceleration of quasar absorption line clouds.
Authors: Goldreich, P.
1978PhyS...17..225G Altcode:
Radiation may expel dense gas clouds from quasar emission line
regions. Small clouds can be accelerated to velocities approaching
c if they are confined so as to maintain high densities. The kinetic
energies, inferred from the spectra, of low to medium excitation quasar
absorption clouds are too large for radiation pressure to have played
a dominant role in their acceleration. If these clouds are physically
associated with the quasars, they are probably accelerated by the
same stresses that are responsible for their confinement. Models
for absorption clouds based on radiatively driven instabilities in
expanding quasar envelopes predict column densities that are much
larger than those deduced from observation.

---------------------------------------------------------
Title: Revenge of tiny Miranda
Authors: Goldreich, P.; Nicholson, P.
1977Natur.269..783G Altcode:
DERMOTT and Gold1 have proposed a resonance model for the
rings of Uranus. They assume the rings are, in fact, arcs composed of
small particles librating about stable resonances determined by pairs
of satellites, either Ariel and Titania or Ariel and Oberon. Dermott
and Gold dismiss as insignificant resonances involving tiny Miranda. We
report here that, by a wide margin, the strongest resonances are all
associated with Miranda. Furthermore, we show that the hypothesis
that the rings are made up of librating particles, while original and
ingenious, is incorrect.

---------------------------------------------------------
Title: The Azimuthal Asymmetry in the Brightness of Saturn's Rings
Authors: Alcock, C.; Goldreich, P.
1977BAAS....9..462A Altcode:
No abstract at ADS

---------------------------------------------------------
Title: A Dynamical Explanation for the Azimuthal Brightness Asymmetry
of Saturn's A Ring
Authors: Colombo, G.; Goldreich, P.; Harris, A. W.
1977BAAS....9Q.462C Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Turbulent Viscosity and Jupiter's Tidal Q.
Authors: Goldreich, P.; Nicholson, P. D.
1977BAAS....9..474G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Solar seismology. I. The stability of the solar p-modes.
Authors: Goldreich, P.; Keeley, D. A.
1977ApJ...211..934G Altcode:
The stability of the radial p-modes of the sun is investigated by
computing nonadiabatic eigenvalues and eigenfunctions for a solar
envelope model which extends from an inner radius of about 0.3 solar
radius out to an optical depth of about 0.0003. The calculations take
into account in a crude fashion the response of the convective flux to
the oscillation. The dynamical effect of turbulence in the convection
zone is parametrized in terms of a turbulent shear viscosity. The
results show that if damping by turbulent viscosity is neglected, all
modes with periods longer than 6 minutes are unstable. The familiar
kappa-mechanism, which operates in the H ionization-H(-) opacity region,
is the dominant source of driving of the oscillations. Modes with
periods shorter than 6 minutes are stabilized by radiative damping in
the solar atmosphere. When turbulent dissipation of pulsational energy
is included, all modes are predicted to be stable. However, the margin
of stability is very small. In view of the large uncertainty that must
be assigned to the estimate of turbulent damping, it is concluded that
theoretical calculations cannot unequivocally resolve the question of
the stability of the solar p-modes.

---------------------------------------------------------
Title: Solar seismology. II. The stochastic excitation of the solar
p-modes by turbulent convection.
Authors: Goldreich, P.; Keeley, D. A.
1977ApJ...212..243G Altcode:
We test the hypothesis that the solar p-modes are stabilized by damping
due to turbulent viscosity in the convective zone. Starting from
the assumption that the modes are stable, we calculate expectation
values for the modal energies. We find that the interaction between
a p-mode and the turbulent convection is such that the modal energy
tends toward equipartition with the kinetic energy of turbulent
eddies whose lifetimes are comparable to the modal period. From
the calculated values of the modal energies, we compute rms surface
velocity amplitudes. Our predicted rms surface velocities range from
0.01 cm/sec for the fundamental radial mode to 0.6 cm/sec for the
radial mode whose period is approximately 5 minutes. The predicted
surface velocities for the low order p-modes are much smaller than
the velocities inferred from recent observations.

---------------------------------------------------------
Title: Turbulent Viscosity and Jupiter's Tidal Q
Authors: Goldreich, P.; Nicholson, P. D.
1977Icar...30..301G Altcode:
A recent estimate of tidal dissipation by turbulent viscosity in
Jupiter's convective interior predicts that the current value of the
planet's tidal Q ∼ 5 × 106. We point out a fundamental
error in this calculation, and show that turbulent dissipation
alone implies that at present Q ∼ 5 × 1013. Our reduced
estimat for the rate of tidal dissipation shows conclusively that tidal
torques have produced only negligible modifications of the orbits of
the Galilean satellites over the age of the solar system.

---------------------------------------------------------
Title: Solar oscillations
Authors: Goldreich, P.; Keeley, D. A.
1977ComAp...7...35G Altcode:
The main observational results and related theoretical investigations
concerning solar oscillations are reviewed. The normal modes of
oscillation of the sun are classified according to their angular
eigenvalues and the number of their radial nodes. Observations
of excited normal modes are discussed, particularly in relation
to five-minute oscillations, nonlinearly coupled unstable g-modes,
oscillations of the sun's apparent diameter, and reported oscillations
of the solar surface with a period of 2 hr 40 min. Linear stability
calculations are briefly examined, and stochastic excitation of p-modes
by turbulent convection is considered. The five-minute oscillations
are described as the superposition of many excited nonradial p-modes.

---------------------------------------------------------
Title: A perspective of physics. Volume 1. Selections from 1976
Comments on Modern Physics.
Authors: Peierls, R.; Okun, L. B.; Zel'dovich, Ya. B.; Lee, B. W.;
Quigg, C.; Harari, H.; Jacob, M.; Cline, D.; Mann, A. K.; Lewin
Keller, Q.; Negele, J. W.; Stephens, F. S.; Leggett, A. J.; Keyes,
R. W.; Tauc, J.; Nagel, S. R.; Lovesey, S. W.; Thompson, A. H.;
Paczynski, B.; Goldreich, P.; Sargent, W.; Larson, R. B.; Grindlay,
J. E.; Spitzer, L.; Brodsky, S. J.; Karl, G.; Picqué, J. L.; Stroke,
H. H.; Dose, V.; Ambartzumian, R. V.; Letokhov, V. S.; Harris, F. M.;
Bekefi, G.; Deutsch, C.; Furth, H. P.; Tsytovich, V. N.; Callen, J. D.
1977ppv..book.....P Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The evolution of the universe.
Authors: Goldreich, P.
1977fost.conf..215G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Spiral structure as an explanation for the asymmetric
brightness of Saturn's A ring
Authors: Colombo, G.; Goldreich, P.; Harris, A. W.
1976Natur.264..344C Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Quasar Absorption Lines
Authors: Goldreich, P.; Sargent, W.
1976ComAp...6..133G Altcode:
Observations of quasar absorption lines are reviewed, noting that
systems of lines in some objects have been convincingly identified
with absorption redshifts that are different from the emission
redshifts. Evidence for and against line locking between the emission
and absorption redshifts in the same object is discussed, and it is
suggested that the hypothesis of intervening objects cannot be dismissed
on the basis of existing statistical redshift data. Physical properties
of absorbing clouds are considered, the role of radiation pressure
at the present location of the absorbing clouds is examined, and it
is inferred that the clouds should have the form of thin sheets. A
direct observational test for the location of the absorbing material
is outlined.

---------------------------------------------------------
Title: OH-IR stars. II. A model for the 1612 MHz masers.
Authors: Elitzur, M.; Goldreich, P.; Scoville, N.
1976ApJ...205..384E Altcode:
A model is presented for the 1612 MHz OH masers associated with
infrared stars. Its principal conclusions are as follows. The central
stars are losing 3 x l0- M0 yr -1, and the masers operate in the outer
regions (r &gt; 1016 cm) of the circumstellar envelopes. The maser
radiation is narrowly beamed in the radial direction, both inward and
outward. Thus the two maser emission features originate in the near
and the far sides of the expanding circumstellar gas. The 1612 MHz
maser is powered by the absorption of 35 photons which excite the OH
molecules from the 211312, J = 312 ground state to the 211112, J = 512
state. The excited OH molecules return to the ground state by a series
of radiative decays. In most cases, the radiative cascade proceeds
directly down the 211112 ladder. The final and the most important
step in the pump cycle is the radiative decay from the 211112, J =
112 state to the 211312, J = 3/2 state. If the transitions which link
these two states are optically thick, a strong inversion of the F =
1 F = 2 1612 MHz transition is produced. Subject headings: infrared:
sources - masers - stars: circumstellar shells

---------------------------------------------------------
Title: OH-IR stars. I. Physical properties of circumstellar envelopes.
Authors: Goldreich, P.; Scoville, N.
1976ApJ...205..144G Altcode:
A theoretical model of the circumstellar envelope which surrounds a
OH-IR star is developed. The circumstellar gas is ejected by radiation
pressure which acts on dust grains that condense in the atmosphere
of the central star. The dust grains transfer momentum to the gas
by collisions with the gas molecules. These collisions are the
dominant source of heat input to the circumstellar gas. The major
sources of cooling are the emission of radiation by H20 molecules
and adiabatic expansion. The gas temperature decreases from T 2 x l0
K near the stellar surface at r 6 x 1013 cm, to T 8 x 102 K at r =
1015 cm and to T 102 K at r = 1016 cm. The OH molecule abundance in the
circumstellar envelope is controlled by chemical exchange reactions and
by the dissociation of H20 molecules. The reaction OH + H2 H20 + H +
0.69 eV, which has an activation energy of 0.3 eV, rapidly converts
OH molecules into H20 molecules in the warm (T &gt; 5 x 102 K) inner
(r &lt;% 2 x 1015 cm) region of the circumstellar envelope. Beyond r 2
x 1015 cm, T is so low that the exchange reaction is very slow and the
mean lifetime of an OH molecule is greater than the expansion time scale
for the circumstellar envelope. In the outer region of the circumstellar
envelope, OH molecules are produced from the photodissociation of
H20 molecules by the interstellar ultraviolet radiation and from the
dissociation of H20 molecules by collisions with dust grains. These
processes are capable of producing OH number densities greater than 1
at r 1016 cm. The predicted values of the gas temperature, T, and the OH
abundance, o , depend upon the rate of mass loss from the central star,
(t) The results quoted above are based on a calculation with = 3 x l0-
M0 yr-1. In general, T varies inversely and o varies directly with
(I). Subject headings: infrared: sources - stars: circumstellar shells

---------------------------------------------------------
Title: Interstellar masers.
Authors: Goldreich, P.
1975ampi.proc..409G Altcode: 1975ampi.conf..409G
Observations of interstellar OH, H2O, and SiO masers are
discussed along with some theoretical topics related to their
interpretation. Energy-level diagrams are presented for all three
molecules, regions associated with the masers are identified,
and estimates are given for the luminosities, angular sizes,
spatial arrangements, brightness temperatures, time variations, and
polarization of the strongest OH and H2O masers. Physical conditions
in the masers are analyzed on the assumptions that the interaction
between maser radiation and active molecules can be described by the
ordinary equation of radiative transfer and that simple rate equations
determine the populations of the maser levels. A simple pump mechanism
is outlined for a three-level scalar molecule, and determination of
the actual sizes of interstellar masers is considered. Thermodynamic
constraints on strong H2O maser pumps are examined along with a model
for 1612-MHz OH masers associated with M-type Mira variables and some
effects due to the trapping of IR line radiation between the maser
levels and other rotational levels. The problem of polarization of the
OH maser lines from sources associated with H II regions is discussed.

---------------------------------------------------------
Title: Astrophysical Masers. V. Pump Mechanism for H2O Masers
Authors: Goldreich, Peter; Kwan, John
1974ApJ...191...93G Altcode:
The problem of determining the pump mechanism for strong H2O masers
is considered. It is shown that for every class of pump models, very
general constraints may be placed on the maser size and luminosity. A
careful evaluation of these constraints indicates that collisional
pumps and external radiative pumps are unlikely to account for the
strong H2O masers associated with HII regions. It is proposed that
these sources are powered by a hot-dust, cool-gas, internal radiative
pump. Specifically, the pump mechanism involves the absorption by
the H2O molecules of 6.3- photons which are emitted by the hot dust
grains. These absorptions produce transitions from the rotational
levels of the ground vibrational state to the rotational levels of
the first-excited vibrational state. The pump action results because
there are more absorptions per degenerate sublevel from the 523
level than from the 616 level. The heat sink in this pump model is
provided by the cool H2 molecules which collisionally de-excite the
H2O molecules from the first-excited vibrational state to the ground
vibrational state. The hot-dust, cool-gas, pump model can operate only
in the vicinity of a highly luminous, variable star. The variation
in temperature of the dust grains which are heated by the radiation
from the star is essential to prevent the dust and gas from coming
into thermal equilibrium. One feature of this pump model is that at
any point the dust temperature must vary from below to above the gas
temperature. Thus, the strong intensity variations observed in H2O
masers find a natural explanation in the model.

---------------------------------------------------------
Title: Molecular Clouds
Authors: Goldreich, Peter; Kwan, John
1974ApJ...189..441G Altcode:
It is proposed that molecular clouds are in a state of gravitational
collapse. The coupled equations of statistical equilibrium and radiative
transfer from diatomic molecules in a collapsing cloud are solved for
arbitrary optical depths in the rotational lines. It is shown that
most of the observed CS and SiO lines and the stronger CO lines are
optically thick. In this limit the emitted intensities are independent
of the molecular dipole moments. The rate at which energy is radiated
in the CO lines is found to exceed the rate at which work is done by
the adiabatic compression of the collapsing gas. This result implies
the existence of an energy source which maintains the temperature
of the gas against the cooling due to radiative energy losses. It is
suggested that collisions between gas molecules and warm dust grains
transfer energy to the gas. The dust grains are heated by radiation from
H ii regions and protostars in the center of the molecular cloud. This
picture is supported by the detection of copious far infrared fluxes
from many molecular clouds. The rate of energy transfer from the
dust to the gas is calculated to be sufficient to maintain the gas
at temperatures deduced from observations of CO lines if NH2 &gt;
10 . Subject headings: molecules, interstellar - nebulae

---------------------------------------------------------
Title: Astrophysical Masers.IV. Line Widths
Authors: Goldreich, Peter; Kwan, John
1974ApJ...190...27G Altcode:
The standard theory of maser line widths predicts line narrowing during
unsaturated amplification and rebroadening to the full Doppler width
during saturated amplification. These predictions conflict with the
observations of narrow maser lines from sources which appear to be
saturated. in an attempt to resolve this conflict, a new theory of
maser line widths is developed which takes into account effects arising
from infrared line radiation trapped between the molecular levels. it
is shown that if a series of infrared lines connects the upper and
lower maser levels, line rebroadening during saturated amplification
does not occur provided that each infrared transition satisfies A![exp
(hv/kT) - 1] R, where A and v are respectively the spontaneous emission
rate and transition frequency of the infrared line, T is the kinetic
temperature, and R is the stimulated emission rate across the maser
levels. in fact, under these conditions, the maser line continues to
narrow during saturated amplification since the gain profile is not
affected by saturation. Subject headings: line profiles masers

---------------------------------------------------------
Title: A model for the 1612_MHz masers in OH-IR stars.
Authors: Elitzur, M.; Goldreich, P.; Scoville, N.
1974mode.book.....E Altcode: 1974STIN...7520184E
Shklovsky (1966) first suggested that OH masers might be pumped by the
absorption of infrared radiation. Subsequently, the physics of the pump
process was investigated by Litvak (1969) and by Litvak and Dickenson
(1972). The present paper attempts to bring into sharper focus the
essential features responsible for the inversion of the 1612 MHz
transition in OH-IR stars.

---------------------------------------------------------
Title: The Formation of Planetesimals
Authors: Goldreich, Peter; Ward, William R.
1973ApJ...183.1051G Altcode:
Four stages in the accretion of planetesimals are described. The
initial stage is the condensation of dust particles from the gaseous
solar nebula as it cools. These dust particles settle into a thin disk
which is gravitationally unstable. A first generation of planetesimals,
whose radii range up to 10-1 km, form from the dust disk by direct
gravitational collapse to solid densities on a time scale of the
order of 1 year. The resulting disk, composed of first-generation
planetesimals, is still gravitationally unstable, and the planetesimals
are grouped into clusters containing approximately 10 members. The
contraction of these clusters is controlled by the rate at which gas
drag damps their internal rotational and random kinetic energies. On
a time scale of a few thousand years, the clusters contract to form
a second generation of planetesimals having radii of the order of 5
km. Further coalescence of planetesimals proceeds by direct collisions
which seem capable of producing growth at a rate of the order of
15 cm per year at 1 a.u. The final stage of accretion during which
planet-sized objects form is not considered here. Subject headings:
planets - solar system

---------------------------------------------------------
Title: Astrophysical Masers. 111. Trapped Infrared Lines and
Cross-Relaxation
Authors: Goldreich, Peter; Keeley, Douglas A.; Kwan, John Y.
1973ApJ...182...55G Altcode:
Infrared line radiation trapped between a maser level and other
rotational levels produces a rapid relaxation among the degenerate
substates of the maser level. The rate of this relaxation is comparable
to the spontaneous decay rates of the infrared transitions. This
cross-relaxation has important effects on the apparent source sizes and
the polarization properties of interstellar masers. It also affects
the relative amplification of the components of a hyperfine-split
maser line. The effect on apparent source size is pronounced when the
cross-relaxation rate y exceeds the decay rate of the maser levels. In
this limit, cross-relaxation enables maser radiation directed in a
narrow solid angle to saturate the population excess in all magnetic
sublevels. This property is essential to the arguments which suggest
that the apparent sizes of interstellar OH and H2O masers are much
smaller than their physical sizes. Cross-relaxation has an important
effect on the polarization of radiation emitted by saturated masers
if the relaxation rate y is greater than the stimulated emission rate
R. For cases in which the Zeeman splitting g is greater than the maser
line width Aw the maser amplifies the Zeeman pattern. In the presence of
rapid cross-relaxation (y &gt; R), the rates of amplification of the a-
and n-components of the Zeeman pattern are unequal and depend upon the
angle between the propagation direction and the magnetic field. For
R &lt; g &lt; Aw, the limiting maser polarization is linear. However,
cross-relaxation suppresses the growth of linear polarization until and
unless the stimulated emission rate becomes as large as the relaxation
rate. Subject headings: masers - molecules, interstellar - polarization
- Zeeman effect

---------------------------------------------------------
Title: Astrophysical Masers. 11. Polarization Properties
Authors: Goldreich, Peter; Keeley, Douglas A.; Kwan, John Y.
1973ApJ...179..111G Altcode:
The equations governing the transfer of polarized radiation in
astrophysical masers are derived. It is found that the magnetic field
and the plasma in maser sources play a central role in determining the
polarization of the emitted radiation. The character of the polarization
depends upon the relative sizes of the decay constant of the maser
levels, F; the stimulated-emission rate R; the Zeeman splitting, g and
the bandwidth of the amplified radiation, Aw. Unsaturated masers (R
&lt; F) emit unpolarized radiation unless g &gt; Aw. For g &gt; A they
amplify the Zeeman pattern if the Faraday rotation per gain length in
the source is small. If the Faraday rotation per gain length is large,
then the a components of the Zeeman pattern are 100 percent circularly
polarized and the n component is unpolarized. Saturated masers (R &gt;
F) emit unpolarized radiation unless g &gt; (RF)"2. If the Faraday
rotation across the region of saturated amplification is small, the
emitted radiation is partially linearly polarized for (RF)"2 &lt; g
Aw whereas for g &gt; Aw it is just the amplified Zeeman pattern. If
the Faraday rotation across the saturated region is large, all linear
polarization is destroyed. For g &gt; Aw, the a components of the Zeeman
pattern are again 100 percent circularly polarized. Subject headings:
masers - polarization - radiative transfer - Zeeman effect

---------------------------------------------------------
Title: The Case Against Planet X
Authors: Goldreich, Peter; Ward, William R.
1972PASP...84..737G Altcode:
The dynamical consequences of the hypothetical trans-Plutonian planet
suggested by Brady (1972) are considered. It is concluded that the
combination of large mass (9 x ) and unusual orbital inclination (120
) would have two serious effects on the solar system: (a) the angle
between the solar axis and the normal to the ecliptic would suffer large
variations ( 2ir) with a period of a few times 1O years, and (b) the
coplanar configuration of the outer solar system would be disrupted on
a time scale of 106 years. The large residuals in the orbit of Halley's
comet which prompted the suggestion of a trans-Plutonian planet can
be explained in terms of nongravitational forces and the weak orbital
binding energy of this object. Key words: comet - Halley's comet -
celestial mechanics - trans-Plutonian planet

---------------------------------------------------------
Title: On Parametric Down-Conversion in Astrophysical Masers
Authors: Goldreich, Peter; Kwan, John Y.
1972ApJ...176..345G Altcode:
The mechanism of parametric down-conversion proposed by Litvak cannot
explain the observed preference for circular polarization in OH maser
emission because the nonlinear interaction between oppositely circularly
polarized microwaves is too weak.

---------------------------------------------------------
Title: Astrophysical Masers. I. Source Size and Saturation
Authors: Goldreich, Peter; Keeley, Douglas A.
1972ApJ...174..517G Altcode:
The relation between the apparent and actual sizes of maser sources
is important in determining their internal physical conditions. This
relation is investigated for models of homogeneous maser clouds having
spherical and tube-shape geometries. It is found that the apparent
linear size of a spherical OH or H2O maser may be as much as two orders
of magnitude smaller than the physical extent of the emitting cloud. On
the other hand, the observed size of a maser having the shape of a
thick tube is given by its transverse dimensions. The treatment of
maser radiation uses rate equations for the level populations and the
ordinary equation of transfer. Approximate analytic calculations are
presented for all degrees of saturation. The theory is developed in
terms of a multilevel scalar atom in which only two levels are coupled
by the maser radiation. Thus, the effects of hyperfine splitting and
polarization are ignored.

---------------------------------------------------------
Title: Tides and the Earth-Moon System
Authors: Goldreich, Peter
1972SciAm.226d..42G Altcode: 1972SciAm.226...42G
No abstract at ADS

---------------------------------------------------------
Title: Magnetosphere Theory of Pulsar Electrodynamics
Authors: Goldreich, P.
1972phpu.conf..151G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Pulsar Theory II. Radiation Mechanisms
Authors: Goldreich, P.; Pacini, F.; Rees, M. J.
1972CoASP...4...23G Altcode: 1972ComAp...4...23G
No abstract at ADS

---------------------------------------------------------
Title: History of the Lunar Orbit
Authors: Goldreich, P.
1972NASSP.300..485G Altcode: 1972poss.conf..485G; 1972pss..conf..485G
No abstract at ADS

---------------------------------------------------------
Title: Coherent Synchrotron Radiation
Authors: Goldreich, Peter; Keeley, D. A.
1971ApJ...170..463G Altcode:
A simple model consisting of a distribution of charges constrained
to move on a ring is the basis of an investigation of coherent
synchrotron radiation. The radiation produced as a result of a
nonrandom particle distribution on the ring is examined from the
viewpoint of the interaction of individual particles with the total
electric field of the system A linear stability analysis shows that,
under reasonable conditions, a uniform distribution of particles is
unstable to clumping. The model is applied to pulsars, in which the high
brightness temperatures suggest that a cooperative emission mechanism
is responsible for the radiofrequency radiation. The application to
circular accelerators and storage rings is discussed briefly.

---------------------------------------------------------
Title: Pulsar Theory I. Dynamics and Electrodynamics
Authors: Goldreich, P.; Pacini, F.; Rees, M. J.
1971CoASP...3..185G Altcode: 1971ComAp...3..185G
No abstract at ADS

---------------------------------------------------------
Title: Charged Particle Motion Near Pulsars
Authors: Goldreich, Peter
1971PASP...83..599G Altcode:
Key words: pulsar models - charge bunching - synchrotron radiation

---------------------------------------------------------
Title: Cooling effects on interstellar shock waves from supernovae.
Authors: Straka, W. C.; Goldreich, Peter; Sargent, W. L. W.
1971BAAS....3..451S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: History of the Lunar Orbit
Authors: Goldreich, P.
1970pss..conf..491G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Stellar Winds
Authors: Goldreich, Peter; Julian, William H.
1970ApJ...160..971G Altcode:
We present relativistic analytic solutions for the model stellar-wind
problem posed by Weber and Davis. These solutions are consistent with
the hypothesis of minimum torque proposed by Michel, but do not require
it as an additional assumption. The equation of radial momentum has
three critical points which occur where the radial flow velocity
is equal to the propagation speed of infinitesimal disturbances. A
unique continuous solution is determined by the requirement that it
pass through all these critical points.

---------------------------------------------------------
Title: The Obliquity of Venus
Authors: Goldreich, P.; Peale, S. J.
1970AJ.....75..273G Altcode:
Solar gravitational tides tend to reduce the obliquity of Venus from its
present value near 1800 whether or not Venus is locked in the synodic
spin resonance with the Earth. Both a thermally driven atmospheric
tidal torque and dissipation of energy at the boundary between a
rigid mantle and a differentially rotating liquid core are possible
mechanisms for maintaining the retrograde spin. The latter mechanism,
where precession of the spin vector about the orbit normal induces
the differential rotation, is almost certaintly capable of driving
the obliquity to 1800 from values greater than 900 for a wide range
of reasonable core viscosities and spin angular velocities.

---------------------------------------------------------
Title: Neutron Star Crusts and Alignment of Magnetic Axes in Pulsars
Authors: Goldreich, Peter
1970ApJ...160L..11G Altcode:
The electromagnetic torque which brakes the rotation of a magnetic
neutron star also tends to align the magnetic axis with the rotation
axis. For fluid stars the time scale for alignment is comparable to
the time scale for rotational braking. However, the presence of a
crystalline mantle impedes the alignment of the magnetic axis with
the rotation axis. Actual rates of alignment are probably determined
by creeping or cracking of the solid mantle.

---------------------------------------------------------
Title: Pulsar Electrodynamics
Authors: Goldreich, Peter; Julian, William H.
1969ApJ...157..869G Altcode:
Gold has suggested that pulsars are rotating magnetic neutron stars
which formed in supernova explo- sions. We have investigated the
simplest such model, one in which the magnetic dipole moment is
aligned with the rotation axis. Our conclusions are as follows: In
spite of its intense surface gravity, the star must possess a dense
magnetosphere. The particles in the region threaded by those field
lines which close within the light cylinder (of radius 5 X 1O~ p cm,
where P sec is the stellar rotation period) rotate with the star. In
the corotating zone the space-charge den- sity is 7 X 102 BZ/P
electronic charges per cm3, where B~ (in gauss) is the component of
magnetic field parallel to the rotation axis. The field lines which
extend beyond the light cylinder close in a boundary zone near the
supernova shell. Charged particles escape along these lines and are
electrostatically accelerated up to energies of 3 X 1O'~ ZR63 B12 p-2
eV in the boundary zone. (Here, the stellar radius is R6 X 106 cm, and
the magnetic field at the polar surface is B12 X 1012 gauss) Beyond the
light cylinder the magnetic field becomes pre- dominantly toroidal. Its
strength is 6 X 1O~ R63 B12 P~ ~ gauss at a distance of r~0 parsecs from
the central star. The magnetic torque on the star causes its rotation
period to lengthen at the rate P~ dP/dt = 10-8 B122 R64 p-2 M-' yr1
for an 211 solar-mass star. The rotational energy lost by the star is
trans- ported out by the electromagnetic field and is then transmitted
to the particles in the boundary zone. We compare our model with the
observed properties of the Crab pulsar (NP 0332) and CP 1919

---------------------------------------------------------
Title: Pulsar Electrodynamics
Authors: Goldreich, Peter; Julian, William H.
1969BAAS....1R.242G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Some remarks on polar wandering.
Authors: Goldreich, P.; Toomre, A.
1969JGR....74.2555G Altcode:
This paper lends fresh support to the hypothesis that large angular
displacements of the earth's rotation axis relative to the entire
mantle have occurred on a geological time scale, owing to the gradual
redistribution (or decay or manufacture) of density inhomogeneities
within the earth by the same convective processes that are responsible
for continental drift. The first of our three contributions is
a pedagogic theorem that rigorously illustrates this mechanism of
polar wandering for a `quasi-rigid body'. That theorem states that
any slow changes in shape of such a body preserve as an adiabatic
invariant the solid angle traced out by its angular momentum vector
as viewed from its principal axes. Thus, if the body were once set
spinning about the axis with the greatest moment of inertia, it would
always continue to spin almost exactly about the same principal axis
no matter how that axis moves through the deforming body. The second
and main contribution is our refutation of the widely accepted notion
that the earth's figure shows unmistakable signs of the faster spin
rate of the past. If correct, the degree of permanence of the rotation
bulge so inferred by G. J. F. MacDonald (1963, 1965) and D. P. McKenzie
(1966) would have been an effective impediment against any significant
polar wandering of the earth as a whole. However, we show here that,
after subtraction of the hydrostatic flattening, the remaining or
nonhydrostatic part of the earth's inertia ellipsoid is distinctly
triaxial. Such a triaxial shape, as well as the coincidence of the
present rotation axis with the principal axis having the largest
of the nonhydrostatic moments of inertia, is indeed to be expected
of any randomly evolving, nearly spherical object without too much
`memory' for its past axis of rotation. Finally, we discuss briefly
some statistical aspects of polar wandering on the assumption that
the earth is such an object.

---------------------------------------------------------
Title: Io, a jovian unipolar inductor
Authors: Goldreich, P.; Lynden-Bell, D.
1969ApJ...156...59G Altcode:
We show that To may be considered to be a unipolar generator which
develops an emf of 7 X 1O~ volts across its radial diameter (as seen
from a coordinate frame fixed to Jupiter). This voltage difference
is transmitted along the magnetic flux tube which passes through
Jo. The induced charge separation on the surface of the flux tube
causes the plasma within it to rotate with Jo's orbital angular
velocity. A current of about 106 amp is driven across each foot of
the flux tube in the Jovian ionosphere. The current flows up along the
half-surface of the flux tube which faces Jupiter, crosses the magnetic
field in Jo, and then flows down along the opposite half of the flux
tube's surface. Because the number density of charge carriers in the
magnetosphere is low (we use fi = 0.5 cm3 in our calculations) the
current must be carried by keV electrons which are electrostatically
accelerated at lo and at the top of Jupiter's ionosphere. We argue
that beam instabilities in the current sheets are responsible for
the Jo-induced decametric bursts. The geometry of the beaming of the
bursts strongly suggests coherent cyclotron radiation as the emission
mechanism. In addition, we are led to predict that Europa should
modulate decametric bursts whose max- imum frequencies are below 8
Mc/s. Bigg was the first to demonstrate that the position of lo in its
orbit was strongly correlated with the reception of Jovian decametric
bursts. Previously it had been established that the detection of the
bursts was influenced by the position of Jupiter's magnetic dipole. Our
aim is to explain the origin of To's great influence. I. THE INTERACTION
OF 10 WITH JUPITER'S MAGNETOSPHER

---------------------------------------------------------
Title: The physics of rotating magnetic neutron stars
Authors: Goldreich, P.
1969PASA....1..227G Altcode: 1969PASAu...1..227G
No abstract at ADS

---------------------------------------------------------
Title: A Theoretical Upper Bound to the Solar Oblateness
Authors: Goldreich, Peter; Schubert, Gerald
1968ApJ...154.1005G Altcode:
In an earlier paper we investigated the stability of differentially
rotating solar models. We concluded that in regions of constant
mean molecular weight the angular momentum per unit mass could not
significantly decrease away from the rotation axis (in the absence
of toroidal magnetic fields). In the current investigation we show
that it is conceivable for sufficiently large gradients of rotational
angular velocity to exist in the Sun's core to account for the solar
oblateness which Dicke and Goldenberg claim to have measured. However,
we argue that it is more likely that turbulent mixing destroyed the
gradients of mean molecular weight during the time when most of the
Sun's angular momentum was lost and that, in reality, only very little
angular momentum remains hidden in the solar interior

---------------------------------------------------------
Title: Stimulated Inverse Compton Scattering in Radio Sources
Authors: Goldreich, Peter; McCary, Richard; Rees, Martin J.
1968Natur.217..931G Altcode:
OSTER1 has claimed that energy losses due to the inverse
Compton effect can be considerably larger than was previously thought,
when stimulated scattering is taken into account. If true, this would
seriously hinder the understanding of compact radio sources. We wish to
point out that Oster's discussion is erroneous and grossly exaggerates
the importance of stimulated inverse Compton scattering.

---------------------------------------------------------
Title: The Dynamics of Planetary Rotations
Authors: Goldreich, Peter; Peale, Stanton J.
1968ARA&A...6..287G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: On the controversy over the effect of tidal friction upon the
history of the Earth-Moon system a reply to comments by H. Gerstenkorn
Authors: Goldreich, Peter
1968Icar....9..391G Altcode:
In a recent paper Gerstenkorn claims that discrepancies between the
results of his integrations and those of Goldreich are due to an error
in the latter's calculations. We show, contrary to this claim, that the
source of these discrepancies is a fundamental error in Gerstenkorn's
technique of averaging his equations over a processional period of
the Earth-Moon system. As a result, Gerstenkorn's calculations are
not quantitatively correct. However, the qualitative conclusions of
his pioneering work on the past history of the Earth-Moon system are
not affected by the error.

---------------------------------------------------------
Title: Differential Rotation in Stars
Authors: Goldreich, Peter; Schubert, Gerald
1967ApJ...150..571G Altcode:
The stability of differential rotation in the radiative zones of
stars is investigated. For sufficiently large x/ (x is the thermal
diffusivity and the kinematic viscosity),it is shown that a necessary
condition for stability in regions of homogeneous chemical composition
is that the angular momentum per unit mass be an increasing function
of distance from the rotation axis. In cylindrical coordinates (i:',
`o,z), this condition is given by a( 2 )/a &gt; 0 and 3 /az = 0, where
is the angular velocity. The condition is also a sufficient one when
applied to axisymmetric perturbations. The stable thermal stratification
which exists in the radiative zone cannot prevent the instability since,
in stars, the thermal diffusivity is much greater than the kinematic
viscosity. The turbulent diffusion of angnlar momentum, which arises
when the stability condition is violated, is so rapid that it would
appear to preclude the fast rotation of the Sun's interior which has
been proposed by Dicke * In the absence of the instability associated
with thermal diffusion, i.e,if x = 0, Dicke's solar model is found to
be stable. Another means whereby angular momentum might be brought up
from the solar interior is by the mechanism of spin-down associated
with the formation of an Ekman boundary layer just below the solar
convective envelope. The transport of angular momentum, either by
spin-down or by turbulent diffusion, would result in the mixing of
material below the convective zone of solar type stars if an external
torque were applied to the stellar surface. Thus, the depletion of
lithium and beryllium would be an inevitable consequence of the loss
of a significant fraction of the star's initial angular momentum.

---------------------------------------------------------
Title: Spin-orbit coupling in the solar system. II. The resonant
rotation of Venus
Authors: Goldreich, Peter; Peale, Stanton
1967AJ.....72..662G Altcode:
In earlier papers we examined the stability of a resonant rotation
rate for Venus. In the resonant rotation state the planet presents
the same face to the earth at each inferior conjunction. The present
investigation is concerned with the capture probability at this
resonance. It is shown that trapping at the resonance can be understood
if Venus possesses a fluid core similar to the earth's. Maximum capture
probability occurs if the core responds to changes in angular velocity
of the mantle with a time lag of about 3 X 10 yr. If Venus is in the
resonant rotation state, then mapping of its gravitational field will
determine the direction of its primordial rotation and may also permit
an estimate of its magnitude.

---------------------------------------------------------
Title: Precession of the Moon's Core
Authors: Goldreich, Peter
1967JGR....72.3135G Altcode:
The coupling between an assumed lunar liquid core and the moon's mantle
is investigated. It is found that a core of low viscosity would not
share the observed 18.6-year precession of the mantle. The possibility
of detecting such a core is briefly discussed.

---------------------------------------------------------
Title: Rotation of the Sun
Authors: Goldreich, Peter; Schubert, Gerald
1967Sci...156.1101G Altcode:
Dicke has interpreted his recent measurement of the sun's oblateness
as implying a fast (1.8-day period) rotation of the solar radiative
interior. We find that differentially rotating solar models, such
as the one proposed by Dicke, are unstable. The rate of turbulent
diffusion in the unstable regions of these models is so rapid that
it appears to preclude a fast-spinning solar interior. As a corollary
of the stability analysis, we conclude that the loss of a significant
fraction of a star's angular momentum must be accompanied by the mixing
of material below its convective zone. Such mixing inevitably leads
to the depletion of lithium in the star's photosphere.

---------------------------------------------------------
Title: The Interaction of Supernova Remnants with the Interstellar
Medium
Authors: Goldreich, P.; Sargent, W. L. W.
1967LIACo..14..289G Altcode: 1967LIACo...6..289G; 1967MSRSL..15..289G
No abstract at ADS

---------------------------------------------------------
Title: The history of the lunar orbit
Authors: Goldreich, P.
1967metp.conf..221G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Spin-orbit coupling in the solar system
Authors: Goldreich, P.; Peale, S.
1967metp.conf..219G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Spin-orbit coupling in the solar system
Authors: Goldreich, Peter; Peale, Stanton
1966AJ.....71..425G Altcode:
Two possible types of resonant spin rates for planets and satellites
are investigated. The first occurs in eccentric orbits at rotation
rates which are commensurate with the orbital mean motion. A resonant
spin state exists at each half-integer multiple of the mean motion,
the simplest case being the well-known syn- chronous rotation. The
second class of resonant spins involves the presence of another planet
or satellite. A planet (or satellite) with such a resonant spin always
aligns the same axis toward the second planet (or satellite) at each
conjunction. Averaged equations of motion are derived, and stability
criteria are formulated for both types of resonance. Probabilities
of capturing a planet (or satellite) into one of the commensurate
rotation states as it is being despun by tidal friction are
calculated. Application ot the results to Mercury reveals that the very
small value of (B-A)/ -0 would suffice to stabilize Mercury's rotation
period at -22 of its orbital period. The probability that Mercury would
be cap- tured at this resonance is calculated for several assumed forms
of tidal torques. Venus may be in a resonant spin state of the second
kind. A sidereal rotation period of 243.16 days retrograde would be
commensurate with its synodic motion. However, a large value of (B-A)/C(
&gt; 10- ) seems to be required to stabilize this rotation. In addition,
the capture probability at this resonance appears to be small.

---------------------------------------------------------
Title: On the Origin of Planetary Nebulae
Authors: Abell, G. O.; Goldreich, P.
1966PASP...78..232A Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Resonant Rotation for Venus?
Authors: Goldreich, Peter; Peale, Stanton J.
1966Natur.209.1117G Altcode:
CAN the rotation period of Venus be commensurate with its synodic
period? If the rotation period is 243.16 days retrograde, the axis of
Venus which points toward the Earth at one inferior conjunction will
point toward the Earth at all subsequent inferior conjunctions. This
value for the rotation period of Venus lies within the errors of the
measured rotation period1-3. If the moment of inertia of
Venus about this axis is minimal, it is possible that the planet is
locked into this synodic commensurability with its permanent bulge or
longest axis pointed toward the Earth at each inferior conjunction. In
other words, the presence of the Earth may have stabilized the sidereal
rotation period of Venus at the value of 243.16 days retrograde. To
investigate the stability of such a commensurate spin angular velocity
for Venus, we shall use a method similar to that used to determine
the stability of the spin angular velocities of Mercury which are
commensurate with its orbital angular velocity4.

---------------------------------------------------------
Title: Final spin states of planets and satellites
Authors: Goldreich, Peter
1966AJ.....71....1G Altcode:
The spin of a planet or satellite which is losing angular momentum
through tidal friction may approach one of at least two distinct
final states. We derive a criterion which determines whether or not
the final state will be one of synchronous rotation. If the tidal
phase lag is independent of the amplitude and frequency of the tide,
then synchronous rotation will result when [3 (B - A )/C] &gt;1 (9
Sire2). If this inequality is not satisfied, the body will end up
spinning with a mean angular velocity which is somewhat larger than
its orbital mean motion. This criterion is only slightly altered if
the phase lag varies with amplitude and/or fre- quency. It is easily
seen that the moon fails to satisfy the condition for synchronous
rotation with the present value of its orbital eccentricity. However,
the moon could have attained synchronous rotation if its mean orbital
eccentricity was less than 0.041 at some time in the past. No analytical
treatment of commensurate spin states other than synchronous rotation
is included in the present investigation. However, the results of a
separate study of these commensurate spins are briefly described.

---------------------------------------------------------
Title: Interaction of Supernova Remnants with the Interstellar Medium.
Authors: Goldreich, Peter; Sargent, Wallace L. W.
1966AJ.....71Q.162G Altcode:
We investigate the way in which the shock-wave produced in the
interstellar medium by a supernova explosion slows. The shock path
and the motion of the gas behind the shock are computed numerically
using von Neumann and Richtmyer's method of artificial viscosity. We
take into account the effects of radiative cooling behind the shock
front. The cooling has an important effect on the motion for old
remnants and leads to thermal instabilities in obj ects as old as
the Cygnus Loop. We conclude that the visible filaments in the Loop
are regions of thermal instability where the density rises and the
temperature falls by large factors from their values immediately
behind the shock front in a distance of the order of 0.01 PC. A shell
of cool gas having a density about 102 times that in the undisturbed
interstellar medium must lie behind the filaments in the Cygnus
Loop. The mass in this shell should be greater than 100 M0 and is
perhaps as great as 1000 M0. We also investigate the motion taking
into account the interstellar magnetic field. In this case, as has
been shown by van der Laan, the compression of the magnetic field
limits the density rise in the thermal instability behind the shod~.

---------------------------------------------------------
Title: More on spin-orbit coupling in the solar system
Authors: Goldreich, P.; Peale, S. J.
1966AJ.....71R.856G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Near-commensurate satellite orbits in the solar system
Authors: Goldreich, P.
1966IAUS...25..268G Altcode:
No abstract at ADS

---------------------------------------------------------
Title: History of the Lunar Orbit
Authors: Goldreich, Peter
1966RvGSP...4..411G Altcode: 1966RvGeo...4..411G
No abstract at ADS

---------------------------------------------------------
Title: Q in the Solar System
Authors: Goldreich, Peter; Soter, Steven
1966Icar....5..375G Altcode:
Secular changes brought about by tidal friction in the solar system are
reviewed. The presence or absence of specific changes is used to bound
the values of Q (the specific dissipation function) appropriate for
the planets and satellites. It is shown that the values of Q separate
sharply into two groups. Values in the range from 10 to 500 are found
for the terrestrial planets and satellites of the major planets. On
the other hand, Q for the major planets is always larger than 6 ×
10 4. Estimates of tidal dissipation in the atmospheres of
the Jovian planets lead to values of Q which are consistent with those
we have calculated on the basis of secular changes in the satellites'
orbits. However, it is difficult to reconcile these large Q's with the
much smaller values obtained in laboratory tests of solids. Lyttleton's
hypothesis that Pluto is an escaped satellite of Neptune is critically
examined. Using the Q's we obtain for the major planets and their
satellites, we show that any eccentricity that Triton's orbit may have
possessed after a near encounter with Pluto would have been subsequently
damped, thus accounting for its present near-circular orbit.

---------------------------------------------------------
Title: Tidal De-spin of Planets and Satellites
Authors: Goldreich, Peter
1965Natur.208..375G Altcode:
RECENTLY, Peale and Gold1 have shown that the
non-synchronous rotation of Mercury is likely to be a consequence of
tidal friction. They point out that in an eccentric orbit the spin of
an axially symmetric planet will not relax to the orbital mean motion,
but instead will approach a final value which is somewhat larger. The
final spin rate will be somewhere between the mean orbital angular
velocity and the orbital angular velocity at perihelion. The precise
value for the final spin is determined by the condition that the net
tidal torque on the planet around each orbit be equal to zero. The
spin rate at which this condition is satisfied is determined by the
frequency and amplitude dependence of the planet's `Q' (1/Q is the
specific dissipation function2). According to Peale and Gold:
“The condition discussed here is based on the supposition that the
solar torque exerted on the tidal bulge exceeds that exerted on any
permanent deformation from axial symmetry. In the converse case a period
of 88 days for the rotation would indeed result.” This last statement,
if true, would imply that Mercury's principal moments of inertia,
in the plane perpendicular to its spin axis, differ by less than a
few parts in 107. This value is very small when compared
with the values known for the Moon-another solid, slowly rotating body.

---------------------------------------------------------
Title: Inclination of satellite orbits about an oblate precessing
planet
Authors: Goldreich, Peter
1965AJ.....70....5G Altcode:
Equations are derived which govern the rate of change of the inclination
of a satellite orbit to the equator of an oblate precessing planet. It
is shown that if the motion of the satellite's ascending node on
the equator plane has a period which is short when compared with the
planet's precession period then the satellite's orbit will maintain
a constant inclination to the planet's equator. This criterion
is satisfied by many satel- lite orbits in the solar system. These
include all satellites whose orbit planes lie in their planets' equator
planes. In addition, it is shown that changes in the planet's obliquity,
which are slow when compared with the satellite's nodal period, will
also not affect a satellite's inclination to the equator plane of
its planet. Finally a theory of the origin of natural satellites is
proposed which accounts for their inclinations at the present time.

---------------------------------------------------------
Title: I. Gravitational stability of uniformly rotating disks
Authors: Goldreich, P.; Lynden-Bell, D.
1965MNRAS.130...97G Altcode:
The stability of a stratified self-gravitating rotating medium is
discussed. It is found that in all cases pressure effects stabilize
short waves while long waves are stabilized by rotation. when is
greater than a number between i 8 and (depending on the polytropic
index) there is an intermediate range of unstable wave-lengths centred
at several times the thickness of the sheet. These instabilities would
lead to the break-up of the sheet into masses of definite size. This
paper serves as an introduction to the following one on the stability
of differentially rotating media and the formation of spiral arms.

---------------------------------------------------------
Title: II. Spiral arms as sheared gravitational instabilities
Authors: Goldreich, P.; Lynden-Bell, D.
1965MNRAS.130..125G Altcode:
This paper treats examples of gravitational instability in
differentially rotating media. The particular cases dealt with
include polytropic, stratified sheets of gas, as well as the infinite
homogeneous media. Application of the results is made to the formation
of spiral arms in a differentially rotating disk galaxy. Relations
are derived which connect the thickness of the galactic disk, its
density, and the velocity dispersion perpendicular to the galactic
plane with Oort's differential rotation parameters A and B. Sections
1 and 2 discuss requirements of any theory of spiral arms. Sections 3
to 8 give a mathematical treatment of gravitational instability in a
sheared rotating stratified medium. Section 9 discusses these results
qualitatively and proposes a theory of spiral arm formation based
on them. Section 10 gives the observational tests and consequences
of the theory. Finally Section Ii gives a very brief discussion of
barred spirals and points to the many problems left unsolved by the
present work.

---------------------------------------------------------
Title: An explanation of the frequent occurrence of commensurable
mean motions in the solar system
Authors: Goldreich, P.
1965MNRAS.130..159G Altcode:
In this paper a tidal origin of commensurable satellite mean motions is
proposed. It is shown that special cases of commensurate mean motions
are not disrupted by tidal forces. Furthermore, at least four, and
probably seven, 9f the best examples of commensurabilities have this
stability. The significance of these stable configurations to the
evolution of satellite systems is discussed and some inferences are
drawn about tidal dissipation in Jupiter and Saturn.

---------------------------------------------------------
Title: On the eccentricity of satellite orbits in the solar system
Authors: Goldreich, P.
1963MNRAS.126..257G Altcode:
In this paper the secular changes in the eccentricities of satellite
orbits in the solar system are investigated. Two mechanisms which
affect the eccentricities are considered. One of them is the tide
raised on the planet by the satellite, which has been the subject of
discussion in the past; the other is the tide raised on the satellite
by the planet. It is seen that cases arise in the solar system in
which each of these tide's effect on eccentricity is dominant.