Author name code: schwarzschild-martin
ADS astronomy entries on 2022-09-14
author:"Schwarzschild, Martin"
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Title: Jeans and Boltzmann solutions for oblate galaxies with flat
rotation curves
Authors: de Zeeuw, P. T.; Evans, N. W.; Schwarzschild, M.
Bibcode: 1996MNRAS.280..903D
Altcode: 1995astro.ph.12082D
A general solution of the Jeans equations for oblate scale-free
logarithmic potentials is given. This provides all possible second
velocity moments that can hold up a stellar population of flattened
scale-free density against the gravity field. A two-parameter subset
of second moments for the self-consistent density of Binney's model
is examined in detail. These solutions have the desirable property
that the observable dispersions in the radial and proper motions
can be given explicitly. In the spherical limit, the potential of
these models reduces to that of the singular isothermal sphere. The
Jeans solutions for scale-free densities of arbitrary flattening that
can correspond to physical three-integral distribution functions are
identified. The problem of finding distribution functions associated
with the Jeans solutions in flattened scale-free logarithmic potentials
is then investigated for Binney's model. An approximate solution of
the collisionless Boltzmann equation is found which provides a third
(partial) integral of good accuracy for thin and near-thin tube
orbits. It is a modification of the total angular momentum. This
enables the construction of many simple three-integral distribution
functions. The kinematic properties of these approximate DFs are shown
to agree with a subset of the Jeans solutions --- which are thereby
confirmed as good approximations to physical solutions.
Title: Self-consistent Models for Galactic Halos
Authors: Schwarzschild, Martin
Bibcode: 1993ApJ...409..563S
Altcode:
Richstone has pioneered the use of the scale-free logarithmic potential
for the study of the dynamics of galactic halos. Now modern computers
make it practical to exploit that potential in its exact form without
central softening. The orbital structure of the potential, which differs
significantly from that of the separable Stackel potentials, has been
explored systematically with the help of 2-D start spaces. Six triaxial
nonrotating density models representative of various axis ratios have
been selected. For each model 600 orbits have been integrated over
a time interval equivalent to about 55 orbital periods, or 1 Hubble
time. Of these orbits, half are defined in the x-z start space (mostly
S-tubes, O-tubes, and I-tubes) and the other half in the stationary
start space (mostly boxlets such as bananas but also many unstable
stochastic orbits). From these orbits self-consistent equilibrium models
have been constructed by the usual methods, with the help of a 48 cell
grid on the reference sphere and by employing long sequences of Lucy
iterations. The main result of these numerical constructions is that in
all six cases self-consistent solutions exist. For the rounder models
(with density axis ratios c/a >= 0.5) solutions involving only stable
orbits exist, although solutions also involving stochastic orbits may
be preferred by the halo formation processes. For the flatter models
(with density axis ratios c/a ~ 0.3) stochastic orbits have to be
included in the solution-a consequence of the replacement of box orbits
by boxlets in halo potentials. The inclusion of unstable stochastic
orbits in self-consistent equilibrium models raises the question
of the persistence of these models. The rate of such impersistence
has been estimated and found not threatening under the conditions
prevailing in halos where only about 50 orbital periods occur in a
Hubble time. It is concluded that equilibrium considerations alone,
without the consideration of possible instabilities and without the
consideration of halo formation processes, do not suffice to constrain
the overall shape of galaxy halos.
Title: The Orbital Structure of Galactic Halos
Authors: Lees, Joanna F.; Schwarzschild, M.
Bibcode: 1992ApJ...384..491L
Altcode:
Numerical experiments have been carried out to investigate the
restrictions on triaxial models for the halos of galaxies. Some of
the conclusions drawn from the numerical experiments are: (1) the
dominant occurrence of boxlets may be a fairly general phenomenon in
triaxial galactic halos; (2) most of the tube orbits in the halo are
not affected by the higher resonances; and (3) triaxiality truncations
favor the existence of self-consistent equilibria in galactic halos.
Title: The Ring Instability in Radially Cold Oblate Galaxy Models
Authors: de Zeeuw, Tim; Schwarzschild, Martin
Bibcode: 1991ApJ...369...57D
Altcode:
Goodman's indicator has been employed to investigate the stability
of self-consistent perfect oblate spheroids built exclusively with
thin tube orbits. Guided by the results of recent N-body simulations,
we have experimented with a variety of axisymmetric perturbations
which leave the flattening of the model constant, but change the
radial density distribution. Goodman's indicator has been calculated
by combination of the orbital indicators with the exact and unique
phase-space distribution function of the thin-orbit model. This confirms
that strongly flattened thin-orbit models are unstable against a ring
perturbation, in agreement with the classical result for circular disks,
and recent N-body simulations. The transition to stability occurs at
an axis ratio of 0.33 +/- 0.02. Perturbations that are concentrated in
the center are most destabilizing. The limitations of the application
of Goodman's indicator are discussed.
Title: Prolate Galaxy Models with Thin Tube Orbits
Authors: Hunter, C.; de Zeeuw, P. T.; Park, C.; Schwarzschild, M.
Bibcode: 1990ApJ...363..367H
Altcode:
We consider the construction of self-consistent distribution functions
for prolate Stackel models. The orbits are confined by three independent
integrals of motion and form two different families, the inner and
outer long-axis tubes. The models constructed are built exclusively
with infinitesimally thin orbits, and orbits of both families
are needed. Once the density of the model has been split into two
components, one for each family, two phase-space distribution functions
can be found uniquely by solving one-dimensional integral equations
of Abel type. But the models are not unique, because a variety of
splits of the density is possible at all except extreme values of
the axis ratio. Except at these extremes, physical models require
that both families of orbits are populated. We have constructed a
range of models for perfect prolate spheroids of all axis ratios, and
have computed several of their other basic physical properties such as
mean-streaming velocities, dispersions, angular momenta and the relative
masses of their two orbit families. The mean- streaming motions exceed
the circular velocity in the inner regions of these models.
Title: Orbital Contributions to the Stability of Triaxial Galaxies
Authors: de Zeeuw, Tim; Schwarzschild, Martin
Bibcode: 1989ApJ...345...84D
Altcode:
Goodman's indicator is employed to investigate the stability of
perfect ellipsoids, which are prototypical nonrotating triaxial galaxy
models. The contributions of the individual stellar orbits to the
indicator are presented for three specific adiabatic perturbations,
which change the axis ratios of the ellipsoids but leave the density
profile invariant. It is found that for barlike perturbations, in
which one axis is elongated and another is compressed, box orbits
are predominantly destabilizing, while outer long-axis tubes are
invariably stabilizing. Short-axis tubes and inner long-axis tubes
may be both stabilizing and destabilizing. These results for the
contributions by individual orbits have been combined with Statler's
(1987) results for the distribution functions of self-consistent perfect
ellipsoid models. This combination, though still numerically insecure,
permits tentative estimates of Goodman's indicator for these models,
with the following results. The occurrence of a bar instability
appears to be confirmed for triaxial models in which box orbits are
heavily occupied. Nearly prolate models seem to suffer from the same
instability. In strongly elongated triaxial models nearly all orbits
are stabilizing, so that these systems are likely to be stable against
barlike perturbations, in agreement with recent N-body simulations. The
results for an adiabatic perturbation in which all three axes of the
ellipsoid are changed in the same direction indicate--but by no means
prove-- the existence of a possible core instability.
Title: Stability of Selfconsistent Galaxy Models
Authors: de Zeeuw, P. T.; Schwarzschild, M.
Bibcode: 1989BAAS...21.1012D
Altcode:
No abstract at ADS
Title: On the Orbit Structure of the Logarithmic Potential
Authors: Miralda-Escude, Jordi; Schwarzschild, M.
Bibcode: 1989ApJ...339..752M
Altcode:
The consequences of replacing centrophilic box orbits with
centrophobic boxlets in the scale-free logarithmic potential are
examined. Particular attention is given to the possibility that exact
triaxial self-consistent dynamical models do not exist for density
figures corresponding to the logarithmic potential. It is suggested
that the central cusp of the logarithmic potential destroys the
box orbits at high energy and replaces them with boxlets which are
too wide to reproduce the triaxial density figure of the model in a
self-consistent manner.
Title: Nonuniqueness of Self-consistent Equilibrium Solutions for
the Perfect Elliptic Disk
Authors: de Zeeuw, P. T.; Hunter, C.; Schwarzschild, M.
Bibcode: 1987ApJ...317..607D
Altcode:
The uniqueness or nonuniqueness of the physical solution for the
self-consistent dynamical equilibrium of a perfect elliptic disk is
investigated. A physical solution is defined as one that corresponds
to a distribution function in action space that is not only nonnegative
everywhere but also smooth. A specific solution is constructed for the
perfect elliptic disk by using the elliptic closed orbits exclusively
to provide the density of the model along the short axis beyond the
focus. The specific solution, consisting of boxes and elliptic closed
orbits, turns out to have the maximum possible angular momentum. It
is shown that a band of nonclosed tubes provides the same density
as a properly chosen combination of elliptic closed orbits and box
orbits. This result permits a more general solution to be derived from
the specific one. This general solution is found to be not unique.
Title: Galactic Models with Moderate Stochasticity
Authors: Schwarzschild, Martin
Bibcode: 1987NYASA.497...16S
Altcode:
No abstract at ADS
Title: Galactic Models with Moderate Stochasticity
Authors: Schwarzschild, M.
Bibcode: 1987cpa..work...16S
Altcode:
Contents: 1. Separable potentials. 2. Potentials for elliptical
galaxies. 3. Central scatterer. 4. Figure rotation. 5. Galactic systems
with more chaos.
Title: Dynamical Models for Galactic Bars: Truncated Perfect
Elliptic Disk
Authors: Schwarzschild, Martin
Bibcode: 1986ApJ...311..511S
Altcode:
de Zeeuw's perfect ellipsoid has been truncated on a surface of constant
density. This truncation preserves the internal potential. A strongly
triaxial case is considered, and the truncation is placed inside the
bifurcation points (foci of the relevant ellipsoidal coordinates). Then
the ellipsoid is projected into a two-dimensional perfect elliptic
disk. The self-consistent dynamics of such disks involves only one major
orbit family (box orbits) since all tube orbits reach beyond the foci,
i.e., outside the truncation surface. The dynamical models for two
samples of these disks have been derived numerically. The occupation
frequencies are found to be positive everywhere. The dynamical solutions
for these disks appear to be unique, owing to the limitation to one
major orbit family. The limit of the truncated perfect elliptic disks
(for the truncation approaching the center) is Freeman's disk, which
itself is the projection of a uniform ellipsoid. The uniqueness of the
dynamical solution for a highly triaxial truncated perfect elliptic
disk suggests that the dynamics of a thin elongated nonrotating
galactic bar with little density beyond the bifurcation points may
be completely determined by its density figure. The same may well be
true for corresponding bars with nonzero figure rotation, but this
extension is outside the scope of this study.
Title: An analysis of observations of the streaming velocities in
the bulge of M 31.
Authors: Teuben, P.; Turner, E. L.; Schwarzschild, M.
Bibcode: 1985ApJ...289...58T
Altcode:
McElroy (1983) has recently provided an extensive set of radial
velocity measurements for the stellar mean motions in the bulge
of M31. These velocities show a surprisingly bumpy pattern. It is
frequently postulated that the absorption clouds in the bulge are the
cause of these observed velocity bumps. If this postulate is correct,
further improvements of the velocity measurements will be futile and
their use as a dynamical diagnostic minimal. To test this pessimistic
hypothesis, the effects of the observed dust clouds on the velocity
observations have been analyzed. Fortunately the observed clouds cannot
be the main cause of the bumps in the observed velocities. Furthermore,
a statistical analysis of the present velocity observations strongly
suggests the existence of unidentified systematic errors which might
explain the apparent bumps.
Title: An approximate numerical model for a nonrotating galactic bar.
Authors: Schwarzschild, M.
Bibcode: 1984BAAS...16..720S
Altcode:
No abstract at ADS
Title: Stellar orbits in angle variables
Authors: Ratcliff, S. J.; Chang, K. M.; Schwarzschild, M.
Bibcode: 1984ApJ...279..610R
Altcode:
Following recent basic developments by Binney and Spergel, the equations
of motion for a star in a galactic potential have been transformed from
time to angle variables. A numerical procedure has been devised to solve
the transformed equations for two-dimensional box and loop orbits in the
equatorial plane of a triaxial potential. In this procedure an orbit
is specified not by its starting values in phase space, but either by
its frequencies or by its action values. A substantial set of orbits
has been derived by this procedure for one potential. The results
for their physical and geometrical characteristics are displayed in
action diagrams.
Title: Analysis of box orbits in a triaxial galaxy
Authors: Vietri, M.; Schwarzschild, M.
Bibcode: 1983ApJ...269..487V
Altcode:
It is pointed out that box orbits appear to play a key role for triaxial
hot self-consistent stellar systems, just as the near-circular orbits
do for cool fast-rotating disk systems. Since elliptical galaxies and
possibly also the bulges of spiral galaxies may be triaxial in many
cases, the present investigation is concerned with a further study of
box orbits. Binney and Spergel (1982) have suggested a qualitative model
for box orbits, taking into account the basic fact that box orbits are
quasi-periodic with as many independent periods as dimensions. The
current investigation has the objective to derive an approximate,
reasonably simple representation of two-dimensional box orbits. The
considered representation exploits directly the quasi-periodic character
of the box orbits. In the incomplete second order development described,
the coordinates X and Y of a two-dimensional box orbit in a triaxial
potential are each represented by the sum of several terms.
Title: Triaxial equilibrium models for elliptical galaxies with slow
figure rotation
Authors: Schwarzschild, M.
Bibcode: 1982ApJ...263..599S
Altcode:
An earlier numerical construction of a triaxial model for a stellar
system in dynamical equilibrium has been extended, first by adding
a slow figure rotation, and second by adding rotational streaming
on Z-tube orbits. The figure rotation was kept low so that the main
resonances, including the outer edge of Binney's instability strip,
fall outside the model. This figure rotation induces weak rotational
streaming, prograde on box orbits and retrograde on X-tube orbits. The
resulting net streaming has a very low velocity (although substantially
higher than the figure rotation by itself) and a complicated pattern,
prograde in the inner portion and retrograde in the outer portion. The
addition of prograde Z-tube orbits, circling around the short (Z)
rotation axis, introduces strong rotational streaming on these
orbits. The net effect of this streaming is, however, substantially
diluted by the box orbits, which are needed for the support of the
triaxial figure. The maximum net rotational streaming velocity thus
permitted for the figure here used (1:1.25:2) appears sufficient to
model the observed rotation of most giant ellipticals.
Title: Retrograde closed orbits in a rotating triaxial potential
Authors: Heisler, J.; Merritt, D.; Schwarzschild, M.
Bibcode: 1982ApJ...258..490H
Altcode:
Four closed periodic orbit sequences are determined numerically, and
their stability is investigated by the standard Floquet method, for the
case of a specific, triaxial rotating potential. The sequences comprise
(1) stable anomalous orbits that are tipped to the long axis which they
circle, so that they also circle the short rotation axis, (2) unstable,
anomalous orbits circling the intermediate axis, otherwise behaving
like (1), (3) stable, normal retrograde orbits lying in the equatorial
plane, which become unstable against perpendicular perturbations
in Binney's instability strip, and (4) Z-axis orbits lying on the
rotation axis, which, although stable in their inner section, become
unstable to perturbations parallel to the intermediate axis farther
out, and to the long axis farther out still. The entire set contains
one composite sequence which is stable over the entire energy range,
consisting of the outer section of the normal retrograde orbits, the
sequence of the anomalous orbits, and the inner section of the Z-axis
orbits. It is suggested that the composite sequence may be relevant
to the dynamics of gas masses captured by rotating triaxial galaxies.
Title: A model for elliptical radio galaxies with dust lanes.
Authors: van Albada, T. S.; Kotanyi, C. G.; Schwarzschild, M.
Bibcode: 1982MNRAS.198..303V
Altcode:
The stationary states of motion of gas in a triaxial stellar system
which rotates about one of its principal axes are described. It is
noted that four dynamically different situations are possible and that
in two of these the gas layer is warped. The morphology of elliptical
radio galaxies with dust lanes, such as NGC 5128 (Cen A) and M84, can
be understood through this model; transient phenomena are not required.
Title: Semistochastic orbits in a triaxial potential
Authors: Goodman, J.; Schwarzschild, M.
Bibcode: 1981ApJ...245.1087G
Altcode:
The numerical investigation of stellar orbits in a specific triaxial
potential, which was previously described, has been extended. The
local stability has been tested for box orbits for one representative
energy. Of these box orbits, 27% were found to be unstable. The
stationary points of the unstable orbits fall in an area mostly near
the minor axis but also extending to the intermediate axis. This
situation is related to the characteristics of the special periodic
orbits along the principal axes. The orbit along the major axis is
stable, the one along the minor axis is unstable, and the one along
the intermediate axis is unstable in one out of two independent
perturbation directions. These results, which can be interpreted
in terms of resonances between an orbit and its perturbations, may
extend to a wider class of triaxial nonharmonic potentials. Seven
box orbits-three stable ones and four unstable ones-were further
investigated by integrating each orbit over a full Hubble time and
recording the velocity vector each time the orbit crossed through
a small cell at the center of the figure. For each stable orbit
the velocities for all central crossings were identical within the
numerical uncertainty, except for an eightfold multiplicity with the
same reflection symmetries as the potential. This reemphasizes that
the majority of orbits in the chosen potential have three effective
integrals. On the other hand, for each unstable orbit the velocities for
central crossings scatter around a mean value. However, the scatter
is much less than one expects for a truly stochastic orbit. Each
of the four unstable orbits visited only a small subregion of the
total velocity domain visited by all unstable box orbits of the same
energy. Accordingly these orbits are here referred to as semi stochastic
rather than truly stochastic. The cause of this semistochasticity is
not understood. To test whether the gross features of semistochastic
orbits are more sensitive to perturbations than those of orbits
with three effective integrals, three box orbits one stable and two
unstable-were rerun with the application of perturbations at regular
intervals. The perturbation strength varied between runs from the low
level expected from stellar encounters to much stronger levels. Though
strong perturbations increased the velocity dispersion for central
crossings, the semi stochastic orbits proved no more sensitive
than the stable one. It is concluded that in the specific case
investigated no truly stochastic orbits exist and that, for the purpose
of constructing numerical self-consistent equilibrium configurations,
the semistochastic orbits may be considered in much the same way
as regular orbits with three effective integrals. if the absence of
truly stochastic orbits should prove to be a general phenomenon for
potentials relevant to galaxies, the variety of equilibrium figures
for galaxies should be larger than otherwise might be expected.
Title: Shapes of unperturbed galaxies
Authors: Schwarzschild, M.
Bibcode: 1981seng.proc...43S
Altcode:
The shapes of galaxies not perturbed by a nearby important companion
or large-scale spiral structure are considered in order to ascertain
the relative importance of present equilibrium conditions and formation
history in determining galactic shape. The differences between the three
possible levels of symmetry of a galactic shape - spherical, axial
and triaxial - with respect to their implications for the dynamics
of stellar systems are examined, and the existence of nonclassical
effective integrals corresponding to an isolating function of the six
phase-space coordinates which is essentially constant on an orbit
for the relevant time, is demonstrated. A numerical procedure for
the construction of self-consistent equilibrium models is outlined to
illustrate the role played by orbits with three effective integrals,
and the behavior of stochastic orbits, which have no effective
integrals other than the energy integral, is considered. Finally,
the qualitative properties of the major orbit families in a triaxial
potential are reviewed and the probable existence of hot triaxial
equilibrium configurations is noted.
Title: Tri-axial dynamics in the core of normal galaxies.
Authors: Schwarzschild, M.
Bibcode: 1980HiA.....5..205S
Altcode:
No abstract at ADS
Title: On the nonexistence of three-dimensional tube orbits around
the intermediate axis in a triaxial galaxy model.
Authors: Heiligman, G.; Schwarzschild, M.
Bibcode: 1979ApJ...233..872H
Altcode:
A specific triaxial model for a galaxy was previously investigated
by numerical methods. In that investigation tube orbits around the
major axis (X), as well as tube orbits around the minor axis (Z),
had been found, but no tube orbit around the intermediate axis (Y)
had been encountered. The present paper shows, again by numerical
methods, that Y-tube orbits nearly certainly do not exist in the
adopted model. Instead, a new family of 'shell orbits' has been
found. The existence of X- and Z-tube orbits and the replacement of
Y-tube orbits by shell orbits are made understandable by a numerical
determination of the stability or instability, respectively, of the
relevant two-dimensional closed resonance orbits in the three symmetry
planes of the model.
Title: A photometric determination of twists in early-type
galaxies. II.
Authors: Williams, T. B.; Schwarzschild, M.
Bibcode: 1979ApJS...41..209W
Altcode:
In continuation of previous work, detailed photometric data have been
obtained for two elliptical galaxies by using the Mount Lemmon 1.5-m
telescope and a large SEC television camera. As before, the aim of this
photometry is to gain additional information on the occurrence of twists
in such galaxies; i.e., on the change of the position angle of the major
axes of the isophotes from the center outward. No significant twist
was found in NGC 1052. However, NGC 584 was found to have a securely
observed twist of about 10 deg within 10 kpc from its center. These
data strengthen previous indications that many ellipticals contain
twists in their inner, bright portions.
Title: A numerical model for a triaxial stellar system in dynamical
equilibrium.
Authors: Schwarzschild, M.
Bibcode: 1979ApJ...232..236S
Altcode:
A sample numerical model has been computed for a triaxial stellar system
in dynamical equilibrium. A four-step procedure was employed. (1) A
density distribution with a modified Hubble profile - to approximate
elliptical galaxies - and axis ratios of 1:25:2 was chosen. This figure
was further chosen not to rotate. (2) The potential corresponding to the
chosen density distribution was computed. (3) About 1500 orbits were
computed with this potential, one at a time, each covering typically
100 oscillations through the system; i.e., about 1 billion years. These
orbits belong to two families, viz., box orbits and tube orbits around
the long axis of the system. (4) A reproduction of the chosen density
distribution - in terms of its mass in 285 cells in each octant -
was sought by superposition of a subset of the available orbits,
each populated by an appropriate nonnegative number of stars. The
application of linear programming led to a numerical solution. The
main results are: First, the majority of the orbits computed in step
3 turned out to have three effective integrals; i.e., two nonclassical
ones in addition to the energy integral. Second, the existence of the
numerical solution found in step 4 suggests the existence of triaxial
self-consistent systems in dynamical equilibrium with density profiles
fitting elliptical galaxies.
Title: Large area CCD image sensors for space astronomy
Authors: Schwarzschild, M.
Bibcode: 1979puobsrept.....S
Altcode:
The Defense Advanced Research Projects Agency (DARPA) has a substantial
program to develop a 2200 x 2200 pixel CCD (Charge Coupled Device)
mosaic array made up of 400 individual CCD's, 110 x 110 pixels
square. This type of image sensor appeared to have application in space
and ground-based astronomy. Under this grant a CCD television camera
system was built which was capable of operating an array of 4 CCD's to
explore the suitability of the CCD's to explore the suitability of the
CCD for astronomical applications. Two individual packaged CCD's were
received and evaluated. Evaluation of the basic characteristics of the
best individual chips was encouraging, but the manufacturer found that
their yield in manufacturing this design is two low to supply sufficient
CDD's for the DARPA mosaic array. The potential utility of large mosaic
arrays in astronomy is still substantial and continued monitoring of
the manufacturers progress in the coming year is recommended.
Title: A photometric determination of twists in three early-type
galaxies.
Authors: Williams, T. B.; Schwarzschild, M.
Bibcode: 1979ApJ...227...56W
Altcode:
Detailed photometric data have been obtained for three early-type
galaxies by using the Cerro Tololo 1.5-m telescope and an SEC
television camera. The aim of this photometry is to gain further
accurate information on the occurrence of twists in such galaxies; i.e.,
on any variations with radius of the position angle of the major axes
of the isophotes. The results of the photometry are: (1) the finding
of no detectable twist within the bulge of the S0 galaxy NGC 5102;
(2) confirmation of a substantial twist (about 10 deg) in the inner
portion of the E3 galaxy IC 1459; and (3) determination of a moderate
twist (about 5 deg) within the E4 galaxy NGC 4697, possibly too small
to have been previously detected. If such moderate twists should turn
out to be common in elliptical galaxies, the suspicion of triaxiality
for most such galaxies would be enhanced.
Title: Surface Photometry of Two Elliptical Galaxies.
Authors: Williams, T. B.; Schwarzschild, M.
Bibcode: 1978BAAS...10..422W
Altcode:
No abstract at ADS
Title: Conference Summary
Authors: Schwarzschild, M.
Bibcode: 1978sfsn.conf..273S
Altcode:
No abstract at ADS
Title: The study of stellar structure.
Authors: Schwarzschild, M.
Bibcode: 1978tpar.book....1S
Altcode:
The physical principles and processes introduced into the study
of stellar structure during the past 100 years are reviewed,
emphasizing those processes that dominate the simplest stars in
their various evolutionary phases. Attention is given to hydrostatic
equilibrium, stellar energy transport, nuclear and gravitational
energy sources, quiet mass ejection, violent dynamical phases, and
nucleosynthesis. Investigations of radiative and convective energy
transport are discussed along with the derivations of pressure-density
relations for white dwarfs and neutron stars, the Hayashi limit, the
first analyses of hydrogen fusion and inhomogeneous stellar models, the
discovery of evolutionary transitions powered by gravitational-energy
release, and mass loss from the sun, hot giants and supergiants, and
red giants and supergiants. Studies of stellar pulsation, contraction to
the main sequence, violent mass ejection, and stellar nucleosynthesis of
heavy elements are also summarized. The lack of a theory for turbulent
convection and the problem of missing solar neutrinos are identified
as two flagrant deficiencies in the study of stellar structure.
Title: An instability due to the local mixing-length approximation.
Authors: Kruskal, M.; Schwarzschild, M.; Haerm, R.
Bibcode: 1977ApJ...214..498K
Altcode:
The basic equations normally used for the study of dynamical phases in
stellar evolution are shown to lead to short-wavelength instabilities
when they are applied to convective envelopes in which the density
decreases inward. This instability results from the standard local
approximation for the mixing-length theory, which has unphysical
consequences for small-scale perturbations. The instability disappears
when a nonlocal mixing-length approximation is used.
Title: Robert E. Danielson (1931-1976)
Authors: Schwarzschild, Martin; Spitzer, Lyman
Bibcode: 1977Icar...30..601S
Altcode:
No abstract at ADS
Title: SEC TV Surface Photometry of Three Southern Galaxies.
Authors: Williams, T. B.; Schwarzschild, M.
Bibcode: 1977BAAS....9..319W
Altcode:
No abstract at ADS
Title: Mixing between burned core material and surface layer.
Authors: Schwarzschild, M.
Bibcode: 1977saif.conf..205S
Altcode:
No abstract at ADS
Title: An Approximate Dynamical Model for Spheroidal Stellar Systems
Authors: Ruiz, Maria Teresa; Schwarzschild, M.
Bibcode: 1976ApJ...207..376R
Altcode:
A simple dynamical model is derived for axisymmetric stellar systems in
which the density is constant on spheroids with fixed eccentricity. The
model is given as a tool for the analysis of the relations between
the brightness distribution, the rotational velocity, and the
velocity dispersion in the inner portions of an observed spheroidal
system. Subject headings: galaxies: internal motions - galaxies:
structure - stars: stellar dynamics
Title: Transition from a Red Giant to a Blue Nucleus after Ejection
of a Planetary Nebula
Authors: Harm, R.; Schwarzschild, M.
Bibcode: 1975ApJ...200..324H
Altcode:
The evolution of two stars, with 0.65 M0 and 1.00 M0, respectively,
has been computed through the transition phase following the rapid
dynamical ejection of a planetary nebula by a red giant. This ejection
phase was mimicked by a sequence of hydrostatic red-giant models with
steadily decreasing mass. The sequence was terminated at the moment of
rapid decrease of the previously high pulsational instability. With
the starting model thus derived, the constant-mass transition phase
was found to last about 6000 years. This time interval is just short
enough that the star can start providing the ultraviolet radiation
in time to excite the ejected nebula before the nebula completely
disperses. Subject headings: interiors, stellar - late-type stars -
planetary nebulae - stellar evolution
Title: Absolute spectrophotometry in M31 and M32.
Authors: Oke, J. B.; Schwarzschild, M.
Bibcode: 1975ApJ...198...63O
Altcode:
For a number of places in the bulge of M31, and for two places in
M32, photometric scans from lambda = 3300 A to lambda = 10,600 A
have been obtained with the multichannel spectrometer on the 5-m Hale
telescope. The scans show that in both objects the color temperature
(particularly shortward of 5000 A) decreases toward the center,
and that the strength of the CN bands increases toward the center in
both objects, in agreement with other earlier observations. The new
data can all be interpreted in terms of an increase of heavy-element
abundance toward the center in both objects by a factor probably less
than 2, and by an excess of heavy elements in M31 compared with M32
by a factor probably greater than 2, in qualitative agreement with
earlier conclusions of other observers.
Title: Photoelectric speckle interferometry of the solar granulation.
Authors: Harvey, J. W.; Schwarzschild, M.
Bibcode: 1975ApJ...196..221H
Altcode:
Using the Mc Math solar telescope on a morning of average seeing
it has been found possible, with the help of photoelectric speckle
interferometry, to detect securely the existence of details in the
quiet solar granulation up to a wavenumber of 240 x 10-6 km-1, i.e.,
a wavelength of one-third of an arc second. Subject headings: granules
and supergranules, solar - image processing
Title: On the scale of photospheric convection in red giants and
supergiants.
Authors: Schwarzschild, M.
Bibcode: 1975ApJ...195..137S
Altcode:
An attempt is made to estimate the sizes of the convective elements
which dominate the brightness variations on the photospheres of red
giants and supergiants. The data assembled permit the extreme hypothesis
that these dominant convective elements are so large that only a modest
number of them exists at any one time on the entire surface of such
a star - in contrast with two million granules on the sun.
Title: The nucleus of M31.
Authors: Light, E. S.; Danielson, R. E.; Schwarzschild, M.
Bibcode: 1974ApJ...194..257L
Altcode:
The nucleus of M31 was photographed at a resolution of 0.2 sec with the
91-cm balloon-borne Stratoscope II telescope. At the half-intensity
level, the nucleus was observed to be elliptical with its major axis
lying in position angle of 63 (plus or minus 5) deg. The peak surface
brightness was 12.7 plus or minus 0.3 V mag per square second of arc
assuming B - V = 1.0. The nucleus appears to be a separate feature
from the bulge with a scale height of approximately 0.5 pc. The mass
of the nucleus is of the order of 100 million solar masses, and the
apparent visual mass-to-light ratio is of the order of 20.
Title: Concluding Remarks
Authors: Schwarzschild, M.
Bibcode: 1974IAUS...66..256S
Altcode:
No abstract at ADS
Title: Absolute spectrophotometry in M31 and M32
Authors: Oke, J. B.; Schwarzschild, M.
Bibcode: 1974STIN...7510879O
Altcode:
For a number of places in the bulge of M31 and for two places in M32
photometric scans from 3300 A to 10,600 A have been obtained with the
multichannel spectrometer on the 5-meter Hale telescope. The scans show
that in both objects the color temperature (particularly shortwards of
5000 A) decreases towards the center and that the strength of the CN
bands increases towards the center in both objects in agreement with
earlier observations. The new data can all be interpreted in terms
of an increase of heavy element abundance towards the center in both
objects by a factor probably less than 2 and by an excess of heavy
elements in M31 compared to M32 by a factor probably greater than 2,
in qualitative agreement with earlier conclusions.
Title: Stability of the Sun against Spherical Thermal Perturbations
Authors: Schwarzschild, M.; Harm, R.
Bibcode: 1973ApJ...184....5S
Altcode:
In view of the serious solar neutrino discrepancy, the stability of
the Sun against spherical thermal perturbations has been investigated
by detailed computations. It was found that the Sun is stable against
perturbations of this class, thus confirming the usual assessment based
on approximate physical arguments. Subject headings: instabilities -
interiors, solar
Title: An Upper Limit to the Angular Diameter of the Nucleus of
NGC 4151
Authors: Schwarzschild, Martin
Bibcode: 1973ApJ...182..357S
Altcode:
During the seventh flight of Stratoscope II, a 36-inch balloon-borne
telescope, five photographs of the nucleus of the Seyfert galaxy
NGC 4151 as well as four equivalent photographs of a comparison star
were obtained. These photographs show high definition and are well
exposed. From a densitometric analysis a safe upper limit to the
half-intensity diameter of the nucleus of O'!O8 is derived. This
new upper limit is less than half the upper limit previously
determined. Subject headings: galactic nuclei - galaxies individual -
Seyfert galaxies
Title: INVITED PAPER - Convection in Stars.
Authors: Schwarzschild, M.
Bibcode: 1973BAAS....5....1S
Altcode:
No abstract at ADS
Title: Oscillatory Thermal Instabilities at the Onset of Helium
Shell Burning.
Authors: Härm, R.; Schwarzschild, M.
Bibcode: 1972ApJ...172..403H
Altcode:
The onset of thermal instability has been investigated in detail
for globular-cluster stars in the evolutionary phase during which
the helium-burning shell is just forming. The investigation shows
that (a) the main unstable phase ("second red-giant phase" or
"asymptotic branch") is preceded by a short and inconsequential
preliminary unstable phase during which the instability is weak and
of an oscillatory character, (b) the main unstable phase generally
commences not with a simple exponential instability (real eigenvalue),
but with an oscillatory instability (complex eigenvalue), (c) this
oscillatory instability appears to be caused by an interaction between
the driving layer containing the helium shell source and a reacting
layer below the driving layer, and (d) the oscillatory instability
gives way (after a quite limited time span) to a simple exponential
instability which causes the repetitive helium-shell flashes described
in earlier investigations.
Title: High Resolution Photographs of the Nuclei of M31 and M32
Obtained by Stratoscope II.
Authors: Danielson, R. E.; Light, E. S.; Schwarzschild, M.; Tomasko,
M. G.
Bibcode: 1971BAAS....3Q.445D
Altcode:
No abstract at ADS
Title: Points noirs dans la théorie de l'évolution stellaire
Authors: Schwarzschild, M.
Bibcode: 1971LAstr..85..277S
Altcode:
No abstract at ADS
Title: High Resolution Photographs of the Nucleus of NGC 4151.
Authors: Schwarzschild, M.
Bibcode: 1971BAAS....3..243S
Altcode:
No abstract at ADS
Title: High-Resolution Photographs Obtained by Stratoscope II
Authors: Danielson, R. E.; Savage, B. D.; Schwarzschild, M.;
Tomasko, M.
Bibcode: 1970BAAS....2Q.307D
Altcode:
No abstract at ADS
Title: On the Evolutionary Phase of Cepheids in Globular Clusters
Authors: Schwarzschild, M.; Härm, R.
Bibcode: 1970ApJ...160..341S
Altcode:
The beginning of the helium shell burning phase has been computed
through the first flash cycle for each of nine globular-cluster
stars (differing in mass and initial composition). While seven of
thesestarsremained on the red-giant branch throughout the cycle, two
stars did not. The latter passed, after each flash, through a loop in
the H-R diagram reaching well into the strip occupied by Population II
Cepheids. It is suggested that the occurrence of these evolutionary
loops might be the reason for the occurrence of Cepheids in globular
clusters.
Title: Stellar Evolution in Globular Clusters
Authors: Schwarzschild, Martin
Bibcode: 1970QJRAS..11...12S
Altcode:
No abstract at ADS
Title: An Upper Limit to the Angular Diameter of the Nucleus of
NGC 4151
Authors: Danielson, R.; Savage, B. D.; Schwarzschild, M.
Bibcode: 1968ApJ...154L.117D
Altcode:
From an analysis of images of the nucleus of the Seyfert galaxy NGC
4151 obtained during a recent ifight of Stratoscope II, a 36-inch
balloon-borne telescope, we conclude that a safe upper limit to the
half-intensity angular diameter of the nucleus is O~'18. This diameter,
which refers to the non-thermal continuum, is several times as small
as the lower limit to the half-intensity diameter of the region giving
rise to the emission lines
Title: Stratoscope II Integrating Television System.
Authors: Cope, A. D.; Luedicke, E.; Danielson, R.; Schwarzschild, M.
Bibcode: 1968AJS....73....9C
Altcode:
An integrating television system has been developed as part of the
Stratoscope II program, and will be flown in place of photographic
film in later flights. The TV camera, which is capable of operating
with either an image orthicon or an image isocon tube, can integrate
for more than 1 h when cooled to - 200C. The isocon scan is superior to
the orthicon scan because a single setting of the isocon beam current
will suffice to read from threshold to full target while the orthicon
beam current must be carefully adjusted for each level of exposure to
obtain the best signal to noise ratio. The resolution of a diffraction
limited image will not be significantly degraded if the sine wave
response of the imaging device is at least 50% at the spatial frequency
for which the response of the optics becomes zero. The television tube
which has been most fully tested contained an S20 photo- cathode and
a wide spaced MgO target. The sine wave response for first scan read
out of this isocon tube is 50% at 2.5 cycles/mm and 30% at 5 cycles/
mm. The above criterion would require that the tube be operated in
conjunction with optics at f/800, a prohibitively large focal ratio. An
integrating image isocon tube with a close- spaced Elcon glass target
has just been developed by RCA. Preliminary measurements on this
tube indicate that the 50% response for first scan readout occurs at
about 10 cycles/mm. It thus appears that this integrating TV tube,
operated atf/200, is a satisfactory substitute for 103aG film at f/100
as presently used by Stratoscope II. Project Stratoscope of Princeton
University is sponsored by NSF, ONR, and NASA.
Title: On the Blue End of the Horizontal Branch in Globular Clusters
Authors: Hartwick, F. D. A.; Härm, R.; Schwarzschild, M.
Bibcode: 1968ApJ...151..389H
Altcode:
No abstract at ADS
Title: Oscillatory Thermal Instability of Helium-Burning Shells.
Authors: Schwarzschild, Martin; Harm, R.
Bibcode: 1968AJS....73R..35S
Altcode:
All recent investigations on stellar models containing helium- burning
shells have shown these models to be thermally unstable. Thus thermal
instability appears to be a general characteristic of helium-shell
models. In view of this fact the onset of this instability has
been reinvestigated. It was found that in some cases the thermal
instability does not set in as a simple exponential runaway, but as
an oscillatory instability (corresponding to "over- stability" in
dynamical problems). This result runs contrary to the usual experience
in problems of thermal flow in hydrostatic systems. It does not vitiate
the conclusions drawn from detailed computations of evolutionary model
sequences. It does, however, complicate the study of the onset of this
instability since it necessitates the search for complex eigenvalues,
rather than for the simple real eigenvalues usually characteristic
for thermal flow problems.
Title: An Upper Limit to the Angular Diameter of the Nucleus of
NGC 4151.
Authors: Danielson, R.; Savage, B. D.; Schwarzschild, M.
Bibcode: 1968AJS....73Q.173D
Altcode:
The most recent launch of Stratoscope II, a 36-in. balloon-borne
telescope, occurred on 18 May 1968. The telescope operated reliably
during the entire night at an altitude of 80 000 ft, but the diffraction
limited performance of the optics (0'.' 1 limiting resolution)
was degraded by a quasisteady convection pattern set up in the main
telescope tube. The stellar images (X =3800- 5800 A) recorded during
the flight were elongated with angular dimensions generally less than
0'.'3 by 0'.'8. However, in spite of the degraded images, an average
guidance jitter as low as 0 "03 rms was achieved on 6th to 8th magnitude
guide stars. Photoelectric tracings of two weakly exposed images of the
nucleus of the Seyfert galaxy NGC 4151 give a width (at the half maximum
intensity) of 0 "20 for the narrowest dimension. Taking account of the
probable error of this measurement as well as the broadening effects
of the telescope diffraction and the microdensitometer slitwidth, we
conclude that a safe upper limit to the half maximum intensity diameter
of the nucleus of NGC 4151 is 0 `118 (about 9 pc). This upper limit
refers to the nonthermal continuum which, according to Oke and Sargent
(Astrophys. J. 151, 807,1968), comprises most of the energy radiated by
the nucleus. In contrast, the observations of Oke and Sargent indicate
that the volume in which the emission lines arise has a half maximum
intensity diameter of at least 016. Project Stratoscope of Princeton
University is sponsored by NSF, ONK, and NASA.
Title: Hydrogen Mixing by Helium-Shell Flashes
Authors: Schwarzschild, M.; Härm, R.
Bibcode: 1967ApJ...150..961S
Altcode:
Numerical calculations have been carried out which cover the first
4 million years of those evolution phases in which helium burning
occurs in a shell in a star of 1 solar mass and of a Population
II composition. The thermal instability previously found to
occur in these helium-shell-burning phases leads to relaxation
oscillations-just as has already been shown by other authors for
other types of stars. Thirteen consecutive relaxation cycles are
covered by the present computations. In each cycle the main helium-
shell flash causes a convective xone to stretch outward from the helium
shell. In the initial relaxation cycles this convection xone does not
reach the hydrogen-containing layers. However, cycle after cycle the
main helium-shell flash increases in strength and, in consequence,
causes a larger and larger convection xone. Mter about nine cycles
the convection xone finally reaches the hydrogen-containing layers
and from then on, for a short while in each cycle, hydrogen is mixed
into the hot carbon-rich interior. This physical situation with its
likely importance for nucleosynthesis we had searched for originally in
connection with the helium-core flash, with, however, negative results;
while now, in connection with the helium-shell flashes, the results
seem to be encouragingly positive.
Title: The Sun as a Star
Authors: Schwarzschild, M.
Bibcode: 1967easp.book...14S
Altcode:
No abstract at ADS
Title: Red Giants of Population II. IV
Authors: Härm, R.; Schwarzschild, M.
Bibcode: 1966ApJ...145..496H
Altcode:
The evolutionary phases of a Population II star through the helium
flash have been recomputed with improved representations for several
of the relevant physical processes. The new computations show that
the helium flash is less extreme than indicated by the earlier, less
accurate computations; the nuclearenergy release reaches only 1011
LQ at the peak, and the rate of evolutionary changes now appears
to be too slow for major hydrodynamic effects. On the other hand,
the new computations confirm the earlier results indicating that the
convective core at its greatest extent (after the flash) misses the
hydrogen-rich region by about two density scale heights. Accordingly,
in view of the very small overshooting from convective cores found
in a recent separate investigation, it now appears highly likely that
the helium flash does not lead to mixing in the star.
Title: New impetus to astrometry
Authors: Schwarzschild, Martin
Bibcode: 1966VA......8....3S
Altcode:
No abstract at ADS
Title: Overshooting from Stellar Convective Cores.
Authors: Saslaw, W. C.; Schwarzschild, M.
Bibcode: 1965ApJ...142.1468S
Altcode:
The possible extent by which the motions in a convective core might
overshoot into the surrounding stable layers has been investigated by
a fundamental mode analysis as well as by the method of following the
entropy excess of a rising element. The fact that a great number of
convective motions occur consecutively in a relevant evolution time
has also been taken into account. The results indicate that the usual
procedure of neglecting all overshooting from convective cores will
generally be a good approximation.
Title: Thermal Instability in Non-Degenerate Stars.
Authors: Schwarzschild, M.; Härm, R.
Bibcode: 1965ApJ...142..855S
Altcode:
In the numerical investigation of the evolution of a star of 1 Mo
through the phases in which it contains a helium-burning shell as well
as a hydrogen-burning shell, an unexpected type of thermal instability
has been encountered. This instability is somewhat reminiscent of
the helium flash even though degeneracy plays no role in the models
considered. The existence of the instability has been made reasonably
certain both by a physical analysis and by a direct mathematical
derivation. The new instability appears to have the character of
a thermal runaway in a non-degenerate shell containing a highly
temperature-sensitive nuclear-energy source. Such a shell will be
unstable only if it is sufficiently thin not to affect the over-all
hydrostatic structure of the star noticeably. Under this condition the
pressure within the shell cannot greatly increase during the thermal
runaway, and hence cooling by an adiabatic expansion cannot stabilize
the shell. Some speculations are presented regarding whether this
instability could have substantial consequences for a star's evolution.
Title: Structure and evolution of the stars
Authors: Schwarzschild, Martin
Bibcode: 1965ses..book.....S
Altcode: 1965QB801.S35......
No abstract at ADS
Title: Infrared Spectra of Red-Giant Stars.
Authors: Woolf, N. J.; Schwarzschild, M.; Rose, W. K.
Bibcode: 1964ApJ...140..833W
Altcode:
The second flight of Stratoscope II was carried out during the night
of November 26,1963. The telescope was equipped with an infrared
spectrometer with a useful sensitivity range from 1 to 3 M The balloon
operations were carried out without difficulty. The telescope was
operated from 6 P.M to 6 A.M. Spectral tracings were obtained for
ten objects. This paper reports on the observations of six nearby
red- giant stars. The spectra of the hotter objects showed that the
terrestrial atmosphere above the balloon had no disturbing effects
on the measurements. The only terrestrial band weakly indicated in
the spectra is that of carbon dioxide at 2.7 . The spectrum of a Tau
(KS) shows practically no bands but has a clear intensity peak around
1.6 where bound-free and free-free absorption of H- and H2- leaves
a relatively transparent region in the continuous absorption . The
same phenomenon is shown in the spectra of the cooler stars although
complicated by band structure. Water-vapor absorption bands at 1.4
and 1.9 appear distinctly in the spectrum of the supergiant a Ori
(M2). These bands occur with a similar strength in the spectrum of p
Per (M4), but are weaker in M Gem (M3). In the spectrum of R Leo (M8,
m = 7.9) and particularly of o Cet (M9, m = 8.4) the water-vapor bands
at 1.4,1.9, and 2.7 are extremely strong.
Title: SYMPOSIUM ON INSTRUMENTAL ASTRONOMY: Mars observations from
Stratoscope II
Authors: Danielson, R. E.; Gaustad, J. E.; Schwarzschild, M.; Weaver,
H. F.; Woolf, N. J.
Bibcode: 1964AJ.....69..344D
Altcode:
On 1 March 1963 Stratoscope II, a balloon-borne telescope, was flown
for the first time with the aim of investigating the infrared spectrum
of Mars. A series of technical difficulties arose during the flight and
severely restricted the number and quality of the spectrometer scans
that were obtained. Nevertheless, the following results could be deduced
from these scans: (1) It is improbable that the water vapor content
of Mars is greater than 40 (2) If the total pressure at the surface
of Mars is assumed to be 87 mbar, the amount of CO2 in the atmosphere
of Mars amounts to about 6000 cm-atm rather than 3000 cm-atm as pre-
viously estimated.
Title: Red Giants of Population II. III.
Authors: Härm, H.; Schwarzschild, M.
Bibcode: 1964ApJ...139..594H
Altcode:
The question whether the helium flash causes mixing of hydrogen into
the helium core is examin' computing detailed model sequences for
three stars differing in mass and composition. These sequ derived by
the Henyey method, cover the entire helium-flash phases. The numerical
results indicatc the convective core, though greatly extended during the
later cooling phases after the helium misses reaching the hydrogen-rich
layers, but only by a very narrow margin. In view of the narro of this
margin and because of the fact that a number of physical complications
have not yet been 1 into account in these computations, we still cannot
answer the question regarding mixing caused b helium fla .
Title: Variation of the Gravitational Constant and the Evolution of
the Sun.
Authors: Pochoda, P.; Schwarzschild, M.
Bibcode: 1964ApJ...139..587P
Altcode:
Evolutionary model sequences have been computed for the Sun under
various assumptions for the variation of the gravitational constant
G. For these computations G was taken to vary to the reciprocal of the
power n of the time. For the age of the Universe, T, values ranging from
15 billion years were used. It was assumed that 4.5 billion years ago
the Sun was in its initial mainuence state. It was found that a mild
variation of G, corresponding to n = 0.2, produces no difficulty the
representation of the observed Sun as the end product of an evolution
starting with the initial in-sequence state and lasting for 4.5 billion
years. In contrast, a strong variation of G, corresponding =1.0,
permits a satisfactory representation of the present Sun only if the
age of the Universe is ut 15 billion years or more. This limitation
arises from the circumstance that with a shorter age of Universe the
initial main-sequence state of the sun falls relatively earlier in the
history of the Universe a G, under the present assumptions, was still
rather high; this causes so large an initial luminosity .he Sun as to
lead to an exhaustion of the hydrogen in the solar core and an evolution
off the main uence before 4.5 billion years would have elapsed.
Title: New Infrared Observations with Stratoscope II.
Authors: Danielson, R. E.; Rose, W. K.; Schwarzschild, M.; Woolf, N. J.
Bibcode: 1964AJ.....69Q.539D
Altcode:
The second flight of Stratoscope II was carried out during the night
of 26 November 1963. The telescope was again equipped with an infrared
spectrometer, this time employing indium arsenide detectors with a
useful sensitivity range from 1 to 3 P. The balloon operations were
carried out without difficulties from the launch at Palestine, Texas,
to the landing at Kosciusko, Mississippi. The telescope was operated
from the ground station near Ruston, Lousiiana, from 6 p.m. until
6 a.m. Spectral tracings were obtained for ten objects: Jupiter,
the moon, Aldebaran, Mu Cephei, Betelgeuse, Mira, Sirius, R Leonis,
Rho Persei, and Mu Geminorum. The spectra of the moon, Aldebaran,
and Sirius showed that the terrestrial atmosphere above the balloon
(80 000 ft) had no disturbing effects on the measurements; the only
terrestrial band weakly indicated in the spectra is that of carbon
dioxide at 2.7 P. The spectrum of the moon shows an increasing albedo
from 1 to 2 P. Above 2 P the intensity increases rapidly in accordance
with the expected thermal emission of the moon. The spectrum of Jupiter
shows deep methane bands at 0.85, 0.99,1.16,1.37, and 1.7 P and the
ammonia fundamental band at 3.0 P. A very broad feature in Jupiter's
spectrum from 2.0 to 2.5 P is probably caused by combination bands
of methane with the possibility of a contribution from the hydrogen
molecule. The spectrum of Aldebaran (KS) shows practically no bands
but has a clear intensity peak around 1.6 P where the bound-free and
the free-free absorption of Ii- and H2- leave a relatively transparent
region in the continuous absorption coefficient; the same phenomenon
is also shown by the spectra of the cooler giants through complicated
by band structure. Betelgeuse (M2) clearly shows the water vapor
bands at 1.4 and 1.9 P as well as indications of a band at 2.7 P;
also the carbon monoxide band at 2.3 P is fairly strong. The spectra
of R Leonis (M8) and particularly of Mira at minimum (M9) show the
water vapor bands at 1.4 and 1.9 P with extreme strength. Finally,
the spectrum of Mu Cephei permits the determination of an upper limit
for the absorption of interstellar ice grains in the band at 3.1 ~
this upper limit turns out rather smaller than the expected value.
Title: Professor Svein Rosseland
Authors: Randers, Gunnar; Schwarzschild, Martin
Bibcode: 1964ApNr....9....7R
Altcode:
No abstract at ADS
Title: Prepared Statement on the Space Program
Authors: Schwarzschild, M.
Bibcode: 1963PASP...75..527S
Altcode:
No abstract at ADS
Title: Hydrodynamic Oscillations in the Solar Chromosphere.
Authors: Bahng, J.; Schwarzschild, M.
Bibcode: 1963ApJ...137..901B
Altcode:
Compression waves in the chromosphere, with the motions assumed vertical
and of standing-wave character, are studied with the aim of accounting
for the 5-minute oscillations recently discovered. For such waves the
photosphere is found to provide an effectively solid bottom, while the
corona can provide a free, largely reflective surface. The temperatures
and depths in the chromosphere required to fit the observed period are
not in discord with other evidence for the chromospheric temperature
profile.
Title: Book Review: Structure and Evolution of the stars
Authors: Schwarzschild, M.
Bibcode: 1963SvA.....6..600S
Altcode:
No abstract at ADS
Title: Red Giants of Population II. II.
Authors: Schwarzschild, M.; Härm, R.
Bibcode: 1962ApJ...136..158S
Altcode:
In continuation of the work described in Paper I of this series,
a sequence of 70 core models has been constructed for a red giant of
population II, covering the helium flash. This phenomenon occurs when
helium-burning starts in the contracting core. Because of the high
degeneracy in the core, the new energy source causes heating, not an
expansion. The rise of the temperature accelerates the helium-burning,
and thus a thermal runaway occurs, which terminates only when the
core becomes non-degenerate. Subsequent helium-burning causes rapid
expansion and cooling. At the peak of the helium flash the temperature
reaches over 300 million degrees. The rate of energy liberation at this
peak corresponds to about 1012 solar luminosities. Practically none
of this energy penetrates the thermal blanket of the non-degenerate
outer layers of the helium core. The evolution at the peak is so fast
that the time interval between successive numerical models had to be
reduced to as low as 2 seconds.
Title: Hydrodynamic Oscillation of Solar Chromosphere.
Authors: Bahng, J.; Schwarzschild, M.
Bibcode: 1962AJ.....67..267B
Altcode:
Standing compression waves in a plane parallel atmosphere are studied
with the aim of accounting for the oscillations recently discovered by
Leighton (1960, 4th IAU-IAUTAM Symposium on Cosmical Gas Dynamics)
in the solar atmosphere. An idealized model consisting of three
isothermal layers with temperature discontinuities at the interfaces is
considered. The bottom layer, representing the photosphere, is assumed
to be at 60000 K. Because of its steep density gradient, this layer
acts as a reflector and the amplitude of the oscillation in this bottom
layer decreases very rapidly with increasing depth. The top layer,
with a temperature of the order of 10~ 0K or higher, acts also as a
reflector, similar to the action of a free surface. This reflection
is however, not perfect, and some energy leaks out in the form of
progressive waves traveling upwards'. The corresponding energy loss
is small enough to fit the observed oscillation decay rate if the top
temperature is not substantially below 10~ 0K. In the middle layer
the oscillation has essentially the character of a standing wave. The
period of the oscillation is largely determined by the temperature and
depth of the middle layer. To explain the observed 5-min period a depth
between 1200 and 1700 km is required for a temperature between 80000
and 300000K. This depth range is of the right order of magnitude for the
depth of the chromosphere. This work is a part of Project Stratoscope,
which is sponsored by the ONR, NSF, and NASA.
Title: Stellar Evolution Phases with Mass Ejection
Authors: Schwarzschild, M.
Bibcode: 1962dmim.conf..266S
Altcode: 1972dmim.conf..266S
No abstract at ADS
Title: Book Review: Structure and Evolution of the stars
Authors: Schwarzschild, M.
Bibcode: 1962AZh....39..770S
Altcode:
No abstract at ADS
Title: Stellar Evolution
Authors: Schwarzschild, M.
Bibcode: 1962IAUTB..11..137S
Altcode:
No abstract at ADS
Title: The Temperature Fluctuations in the Solar Granulation.
Authors: Bahng, J.; Schwarzschild, M.
Bibcode: 1961ApJ...134..337B
Altcode:
A new measurement of the root-mean-square intensity fluctuation in the
granulation has been made from a photograph obtained on the Stratoscope
flight of September 24, 1959. After correcting this measurement for the
effects of the instrumental profile, the root-mean-square temperature
fluctuation in the granulation is found to be +920 K.
Title: Lifetime of Solar Granules.
Authors: Bahng, J.; Schwarzschild, M.
Bibcode: 1961ApJ...134..312B
Altcode:
A time sequence of high-definition photographs of the solar granulation
was obtained on the Stratoscope flight of August 17,1959 The correlation
function in time for the photospheric intensity variations has been
determined from these photographs. The correlation function was found to
be well represented by a simple exponential decay with a time constant
of 6 27 minutes. If the average lifetime of granules is defined as
twice the time interval in which the correlation drops to hall, then
this lifetime is found to be 8.6 minutes.
Title: Convection in Stars.
Authors: Schwarzschild, Martin
Bibcode: 1961ApJ...134....1S
Altcode:
No abstract at ADS
Title: The Helium Flash in Population II Giants.
Authors: Härm, R.; Schwarzschild, M.
Bibcode: 1961AJ.....66R..45H
Altcode:
The evolution of a star of 1.2 solar masses has been followed through
the phase in which the helium burning begins, with the following
results. The helium burning sets in when the temperature in the
contracting core reaches about 80 million degrees. Owing to the
high degeneracy in the core the new energy source does not cause an
expansion but rather heating. The rise of the temperature further
accelerates the helium burning and thus a thermal runaway occurs,
as predicted by Mestel. This runaway terminates only when the core
becomes nondegenerate. Subsequent helium burning causes rapid expansion
and cooling. At the peak of the helium flash the temperature reaches
approximately 300 million degrees. The energy liberated at this peak
corresponds to about 1012 solar luminosities. Practically none of this
energy penetrates the thermal blanket of the nondegenerate outer layers
of the helium core. The evolution at the peak is so fast that the time
interval between successive numerical models had to be reduced to as
low as 2 sec. It appears uncertain whether the neglect of dynamical
effects remains a reasonable approximation in this phase. In the Hertz
sprung-Russell diagram the star slides down the red-giant branch while
the helium flash goes on,in the interior.
Title: Die Theorie des inneren Aufbaus der Sterne
(Karl-Schwarzschild-Vorlesung)
Authors: Schwarzschild, M.
Bibcode: 1961MitAG..12...15S
Altcode:
No abstract at ADS
Title: On the Spectrum of Turbulent Convection.
Authors: Ledoux, P.; Schwarzschild, M.; Spiegel, E. A.
Bibcode: 1961ApJ...133..184L
Altcode:
A procedure is described by which, under certain assumptions, the
turbulence spectrum can be derived for the motions in a convectively
unstable layer. The energy input from the buoyancy forces is assessed
in this procedure by deriving the growth rates of the laminar modes
obtained from the relevant linearized equations On the other hand,
the exchange of energy between modes is assumed to follow Heisenberg's
elementary theory of turbulence. The procedure is carried through for
an exceptionally simple case for which a closed solution was found for
the spectrum. The results, though not strictly applicable, are applied
to the convection in the solar photosphere for purposes of orientation.
Title: On the Periods of Long-Period Variables in Globular Clusters.
Authors: Stothers, Richard B.; Schwarzschild, M.
Bibcode: 1961ApJ...133..343S
Altcode:
No abstract at ADS
Title: Lifetime of Solar Granules.
Authors: Baling, J. D. R.; Schwarzschild, M.
Bibcode: 1960AJ.....65..481B
Altcode:
A sequence of high-definition photographs of the solar granulation was
obtained on the Stratoscope flight of August 17, 1959. The sequence
covers a time interval of eight minutes. The correlation function in
time for the photospheric intensity variations has been determined
frnm these photographs, with the help of an optical method proposed by
Kovasznay. The resulting correlation function can be closely represented
by an exponential decay: R(At)= exp(-~t/6.3 minutes). If the average
lifetime of granules is defined as twice the time interval in which
the correlation drops to Si one half, then this lifetime is found to be
8.6 minutes with an internal probable error of ~0.2 minutes. This new
value is approximately twice as long as the classical determination
by Ten Bruggencate and Grotrian based on low-definition plates. It
is in general agreement with the more recent approximate estimates by
Macris, Rbsch and Hugon, and Bray and Loughhead. Project Stratoscope
is supported by the Office of Naval Research and by the National
Science Foundation. % CO2, 22- 25% N2, and 0-3% H2O. The additional
assumptions of adiabatic equilibrium below the cloud cover and
isothermal equilibrium above the clouds were made. These conditions
imply an average temperature gradient of 90K/km below the clouds,
a cloud height of 33 km, a scale height of 6.86 km, and a pressure
at the cloud level of 0.038 of the surface pressure. The mechanism of
absorption results from the collision-induced dipole moment in CO2 and
N2 and the rotational lines of H2O. The optical depth at any height
has been computed and the radio brightness calculated from that. A
surface pressure of 30 (terrestrial) atmospheres for 0% H2O or 10 atm
for 3% H2O is needed to match the radio data. Thus, assuming a surface
temperature of 6000K, fairly high surface pressures are indicated
unless an unknown atmospheric constituent is a strong absorber of
microwave energy. Further millimeter measurements are indicated, and
these could be coupled with the possible detection of other molecules
by their radio spectral lines. These include O2 at 5 and 2.53 mm, CO
at 2.6 and 1.3 mm, NO at 1.99 and 1.20 mm, NO2 at 1.13 cm, and N2O at
1.19 cm, 5.97, 2.98, and 2.39 mm.
Title: Note on the brightness fluctuation in the solar granulation
Authors: Gaustad, J.; Schwarzschild, M.
Bibcode: 1960MNRAS.121..260G
Altcode:
On photographs of the solar granulation obtained with a balloon-borne
telescope, Blackwell, Dewhirst and Dollfus (i) measured a
r.m.s. brightness fluctuation of per cent. From this measurement they
deduced a true r.m.s. brightness fluctuation of i8 per cent. This
deduction was based on an accurate measurement of the contrast
transmission function of their instrument, but on an approximate
application of this transmission function to the granulation. This
note alms to show that, using the same observed r.m.s. brightness
fluctuation, the same measured instrumental transmission function, and
the same value of I 4 seconds of arc for the average granule diameter,
a more detailed analysis gives a true r.m.s. brightness fluctuation
not of i8 per cent, but of only about 7 per cent. The overestimate by
Blackwell et al. appears to have resulted from their identifying the
granule diameter with a wave-lenght rather thin half a wave-length.
Title: Photographs of the Solar Granulation Taken from the
Stratosphere.
Authors: Schwarzschild, Martin
Bibcode: 1959ApJ...130..345S
Altcode:
A 12-inch solar telescope equipped with a photoelectric pointing
mechanism and an automatic camera has been flown by unmanned balloons
to an altitude of 80000 feet. A number of photographs of the solar
granulation obtained with this telescope are of very high definition
and show the granulation to have the character of non-stationary
convection. The bright granules, ranging in diameter from about 300
to about 1800 km, are of highly irregular, often polygonal, shape and
are separated from one another by dark, often very narrow, lanes. The
root-mean-square temperature fluctuation, uncorrected for instrumental
smoothing, is found to be only + 60 . The analysis suggests that the
true root-mean-square temperature fluctuation is probably not larger
than * 100 .
Title: Balloon Astronomy
Authors: Schwarzschild, Martin; Schwarzschild, Barbara
Bibcode: 1959SciAm.200e..52S
Altcode: 1959SciAm.200e..52M
No abstract at ADS
Title: On the Maximum Mass of Stable Stars.
Authors: Schwarzschild, M.; Härm, R.
Bibcode: 1959ApJ...129..637S
Altcode:
Following an earlier investigation of Ledoux, the coefficient of
pulsational stability has been recomputed for massive stars on the
basis of the detailed models just published. From the homogeneous models
representing the initial main-sequence state it is found that (assuming
a helium content of 22 per cent) stars are pulsationally stable if
they are lighter than 60 solar masses and unstable if they are heavier
than this critical mass. From the inhomogeneous models representing
subsequent evolution phases it is found that a star gains in pulsational
stability as it evolves. For stars just above the critical mass, in
the range from 60 to 65 solar masses, pulsational stability is gained
so quickly after the initial main-sequence state that the pulsational
instability can hardly have serious consequences. For stars heavier than
65 solar masses, however, the instability is of sufficient duration and
e-folding speed to have probably major effects. As already suggested
by Ledoux, the existence of a critical mass for pulsational stability
of mainsequence stars makes it appear probable that pulsational
instability is indeed the mechanism which determines the upper limit
for stellar masses. To bridge the gap between the theoretical value
of 65 solar masses and the observed limit of about 95 solar masses,
one might assume that in this mass range the pulsational instability,
though not yet strong enough to cause immediate disruption, is already
sufficiently strong to cause continuous shell ejection, as indicated
by the P Cygni phenomenon.
Title: Sunspot photographs from the stratosphere.
Authors: Bahng, J. D. R.; Danielson, J. B.; Rogerson, J. B., Jr.;
Schwarzschild, M.
Bibcode: 1959AJ.....64Q.323B
Altcode:
The i~-inch telescope used during the balloon flights in 1957 has
been modified by adding a television link so that the astronomer
on the ground can see what the telescope is photographing, and by
adding a radio command so that the astronomer can focus the telescope
and direct it to any place on the solar disk during the flight. On
the first flight this season the television and command links worked
satisfactorily but instrumental vibrations and dust on optical surfaces
limited the number and usefulness of the high- definition photographs
obtained. However, before the next flight both these disturbances
were greatly reduced and on the second flight (Aug. 17, 1959) a large
number of high quality photographs was obtained. Time sequences were
taken, both of granulation far from sunspots and of sunspots with their
immediate surroundings. The time variations of the granules as well as
of the penumbral filaments are clearly visible. A highly preliminary
inspection of the photographs suggests that the granulation directly
adjacent to sunspots does not seem to differ strikingly in size or
lifetime from those in undisturbed regions. Project Stratoscope is
sponsored jointly by the Office of Naval Research and the National
Science Foundation. Princeton University Observatory Princeton, N. J.
Title: Theoretical interpretation of the Hertzsprung-Russell diagram
(Introductory paper)
Authors: Schwarzschild, M.
Bibcode: 1959IAUS...10...79S
Altcode: 1959SAnAp...8...79S
No abstract at ADS
Title: Evolution of Very Massive Stars.
Authors: Schwarzschild, M.; Härm, R.
Bibcode: 1958ApJ...128..348S
Altcode:
Models for the initial state and for the early evolution phases of stars
with masses between 30 and 200 solar masses have been constructed It
was found that, as evolution proceeds in these very massive stars,
the convective instability moves outward. This effect is caused by
the low values of produced by the radiation pressure. In consequence,
an intermediate semiconvective zone develops in which the convection
is so slow that it does not contribute to the energy transport but is
fast enough to modify the composition, so that convective neutrality is
maintained in every layer of this zone throughout the early evolution
phases. The resulting models show that these very massive stars will
use up as much as two-thirds of their total initial hydrogen content
before exhaustion in the core occurs. Accordingly, the evolution
proceeds somewhat more slowly for these stars than had previously been
estimated; even a star of 200 solar masses spends over two million
years in the evolutionary phases before its core gets exhausted
Title: Solar photographs from 80,000 feet.
Authors: Schwarzschild, M.; Rogerson, J. B., Jr.; Evans, J. W.
Bibcode: 1958AJ.....63..313S
Altcode:
During the summer of 1957 three unmanned balloon flights have been
carried out with the aim of obtaining direct solar photographs with
high definition, undisturbed by atmospheric seeing. The first flight
had the purpose of testing the pointing mechanism and carried only a
dummy telescope. The full telescope, constructed by Perkin-Elmer Co.,
carried on the second and third flights, consisted of a parabolic
mirror of ~~-inch aperture, f/8, an enlarging lens which produced an
effective focal length of 200 feet, and a 35-mm movie camera taking an
exposure each second with exposure time 0~.00I. The focus was scanned
over a range of 10 to 20 times the focus tolerance. In the pointing
control which was constructed by the Research Service Laboratories
of the University of Colorado, photo- diodes were employed to find
the sun and center on it. Motor-driven magnetic clutches were used
to move the telescope with the motion in azimuth being accomplished
by rotating against a heavy flywheel carrying the batteries. In
the execution of the flights, carried out by General Mills, Inc.,
no serious difficulties were encountered in the launching, tracking
and recovering of the equipment. The cost of repairs for launching
damage averaged for each of the three flights about 5 per cent
of the construction cost. *Presented at the 99th A.A.S. meeting,
Indianapolis, Ind., December 27-30, 1957. Several exposures of very
high definition were obtained, both of the center of the solar disk
and of the limb. These exposures show that the solar granulation has
a cellular though highly irregular character. The bright cells appear
separated from each other by dark, often very sharp lines. The sizes
of the elements seem to range from 2" down to 0'.'3. This project was
sponsored by the Office of Naval Research and the Geophysics Research
Directorate of the Air Force. Princeton University Observatory,
Princeton, N. J., and Sacramento Peak Observatory, Sunspot, N. M.
Title: Theory of Stellar Evolution and the Age Sequence of Stellar
Populations
Authors: Schwarzschild, M.
Bibcode: 1958RA......5..204S
Altcode:
No abstract at ADS
Title: Structure and evolution of the stars.
Authors: Schwarzschild, Martin
Bibcode: 1958ses..book.....S
Altcode:
No abstract at ADS
Title: Inhomogeneous Stellar Models. V. a. Solar Model with Convective
Envelope and Inhomogeneous Interior.
Authors: Schwarzschild, M.; Howard, R.; Härm, R.
Bibcode: 1957ApJ...125..233S
Altcode:
A model for the sun has computed in which account has been taken both
of the deep hydrogen convection zone and of the internal inhomogeneity
in composition caused by the transmutation of hydrogen during the last
five billion years. The model is found to permit good agreement with
the analysis of the solar photosphere as regards chemical composition
and as regards the depth of the hydrogen convection zone. Furthermore,
the model indicates that the sun must have become brighter by nearly
2 mag. during the five billion years.
Title: A Spectroscopic Comparison Between - and Low-Velocity K Giants.
Authors: Schwarzschild, Martin; Schwarzschild, Barbara; Searle, L.;
Meltzer, A.
Bibcode: 1957ApJ...125..123S
Altcode:
High-dispersion spectra of six high-velocity and ten low-velocity
K giants were taken with the coude' spectrograph of the 100-inch
telescope at Mount Wilson. Central depths were measured for 78 lines
and profiles for 3 lines in the region X 4100-4500 The high-velocity
giant # Ori was found to deviate from the low-velocity giants in an
appreciable strengthening of CH relative to Fe I, a slight weakening
of CN relative to Fe I, and a weakening of the Fe 1 lines-all in
agreement with previous estimates. The amounts of these deviations can
be explained by a deficiency of the metals in # Ori by a factor of 4 and
by a deficiency of carbon, nitrogen, and oxygen by a similar amount. The
same type of deviations, though to a lesser degree, were found for the
high-velocity giants 14 And and a Boo, while no significant deviations
were found for HD 39853, HD 154733, and a Sct Regarding the abundance of
barium and the rare earths relative to iron, no significant difference
was observed between any of the high- and low-velocity giants
Title: Stellar Structure and Evolution
Authors: Schwarzschild, M.
Bibcode: 1956SCoA....1..177S
Altcode:
No abstract at ADS
Title: On the Colors of Subdwarfs.
Authors: Schwarzschild, M.; Searle, L.; Howard, R.
Bibcode: 1955ApJ...122..353S
Altcode:
No abstract at ADS
Title: A comparison of stellar populations in the Andromeda galaxy
and its elliptical companion
Authors: Baum, W. A.; Schwarzschild, M.
Bibcode: 1955AJ.....60..247B
Altcode:
. For selected fields in the Andromeda Galaxy, M 31, and in its
elliptical companion, NGC 205, the resolved stars were counted and the
surface brightnesses measured photoelectrically. The count-brightness
ratio thus obtained was found to be significantly higher for the
companion than for the Andromeda Galaxy. The count-brightness ratio
for the companion agrees with that for globular clusters, whereas
the ratio for the Andromeda Galaxy agrees with that for the solar
neighborhood. This indicates that the bulk of the light of the Andmmeda
Galaxy is contributed not by extreme Population II stars but likely
by old Population I stars.
Title: Note on the Mass of M92.
Authors: Schwarzschild, M.; Bernstein, S.
Bibcode: 1955ApJ...122..200S
Altcode:
No abstract at ADS
Title: On the Evolution of Type II Stars.
Authors: Hoyle, F.; Schwarzschild, M.
Bibcode: 1955ApJS....2....1H
Altcode:
The evolution of the stars in globular clusters has been followed from
the main sequence to the top Qf the red giant branch. In the initial
phases the relevant models consist of partially degenerate isothermal
helium cores and radiative hydrogen envelopes. These models show the
well-known turnoff from tile main sequence in the Hertasprung-Russell
diagram of globular clusters. The helium core steadily increases
in mass because of the hydrogen-burning. When the core has reached
approximately 20 per cent of the total stellar mass, tile envelope
has reached an appreciable extent, and it is found necessary to
take into account explicitly the photospheric boundary condition
and the hydrogen convection zone. During the subsequent phases this
convection zone steadily deepens while the luminosity increases; the
star evolves in the Hertxsprung-Russell diagram along the observed red
giant sequence. During these phases the internal temperature steadily
rises so that the carbon cycle can keep in balance with the increasing
luminosity. At the top of the red giant sequence the temperature in the
hydrogen-burning shell at the edge of the core reaches about 40,000,000
, while the helium core reaches approximately 50 per cent of the stellar
mass. The model sequence thus computed appears to be' in satisfactory
agreement with the observations in globular clusters. In addition,
the difference between the red giants of population I and \ II can,
it seems, be explained by the difference in the metal abundance of the
two populations if this abundance difference is taken account of in the
photospheric boundary condition; for the relevant evolution phases,
a larger metal content produces a larger extent of the envelope and
hence later spectral types. It is estimated that near the top of
the red giant sequence the more and more rapid contraction of the
core will heat the center until it reaches the temperature necessary
to start helium-burning. The onset of this process is believed to
terminate the red giant sequence by eliminating the degeneracy in the
core. Preliminary computations suggest that this change in the stellar
model will rather suddenly lower the luminosity and put the star on the
beginning of the horizontal branch in the Hertxsprung-Russell diagram.
Title: On the Evolution of Type II Stars.
Authors: Hoyle, F.; Schwarzschild, M.
Bibcode: 1955ApJ...121..776H
Altcode:
No abstract at ADS
Title: Inhomogeneous Stellar Models. IV. Models with Continuously
Varying Chemical Composition.
Authors: Härm, R.; Schwarzschild, M.
Bibcode: 1955ApJ...121..445H
Altcode:
Nine sample models are constructed in which the mean molecular weight
varies from the center to the surface by a factor of 2.5 and in which
this variation occurs continuously inside an intermediate zone. These
models are compared with simpler models in which the same composition
variation occurs discontinuously at an interface. The comparison shows
that the simpler, discontinuous models may be used to compute the
luminosity with satisfactory accuracy but that they tend to exaggerate
the radii-in certain cases by an order of magnitude.
Title: Additional Data for Turbulence Spectrum of Solar Photosphere
at Long Wave Lengths.
Authors: Frenkiel, F. N.; Schwarzschild, M.
Bibcode: 1955ApJ...121..216F
Altcode:
A plate showing the granulation with exceptional deflnition was
selected from the regular Mount Wilson solar program. On this plate
8000 intensity measurements were made. The measurements were analyzed
in terms of a turbulence spectrum of photospheric intensities. The
spectrum, when corrected for the flnite resolution of the photograph, is
found to be fairly constant in the wave-length band from 2000 to 30,000
km. This result for the turbulence spectrum of photospheric intensities
is similar to the earlier indications found for the turbulence spectrum
of velocities, in showing that the spectrum contains much energy in
the wave-length band around 15,000 km, but disagrees with them in
not showing in the corrected spectrum a large decrease from 15,000 to
4000 km.
Title: Mass distribution and mass-luminosity ratio in galaxies
Authors: Schwarzschild, M.
Bibcode: 1954AJ.....59..273S
Altcode:
. The observational data bearing on the mass distribution and
mass-luminosity ratio in galaxies are rediscussed and assembled. The
observations on the mass distribution indicate, contrary to earlier
suggestions, that the data now available permit the assumption of
identical spacial distribution of mass and luminosity. The results for
the mass-lumi- nosity ratio are summarized in Table 7. In agreement
with earlier investigations, the elliptical galaxies are found to
have a mass4uminosity ratio much larger than that of pure population
I systems. The Andromeda nebula is found to have an intermediate
mass-luminosity ratio, suggesting that the body of the Andromeda nebula
may consist of a mixture of population II and old population I stars.
Title: Inhomogeneous Stellar Models. III. Models with Partially
Degenerate Isothermal Cores.
Authors: Schwarzschild, M.; Rabinowitz, I.; Härm, R.
Bibcode: 1953ApJ...118..326S
Altcode:
A search was made for conditions under which models with partially
degenerate isothermal cores could give radii as large as those of red
giants. Special conditions were found for which detailed computations
gave, indeed, models fitting well the red giants in radius and
luminosity. But it has not been investigated whether the special
conditions are likely to be realized in the evolution of a star.
Title: The Possible Influence of Interstellar Clouds on Stellar
Velocities. II.
Authors: Spitzer, Lyman, Jr.; Schwarzschild, Martin
Bibcode: 1953ApJ...118..106S
Altcode:
The increase with time of random stellar velocities, as a result of
gravitational encounters with interstellar cloud complexes, has been
recomputed, taking into account the presence of differential galactic
rotation. As a result of such nonuniform rotation, the clouds will have
velocities relative to one another even if their random velocities
are zero; the gravitational potential of these clouds will he a
fluctuating function of time; and the stars will gain kinetic energy
from the clouds. To explain the increase of velocity dispersion with
advancing spectral type along the main sequence, the mass of a typical
cloud complex must be in the neighborhood of 106m0, the value found
previously; but the random velocity of a cloud complex, as a whole,
is irrelevant and may be vanishingly small. Since inhomogeneities
of density with the required scale of some 300 parsecs or more seem
indicated by the extinction observations, it seems not unlikely that
star-cloud encounters are, in fact, responsible for the greater velocity
dispersion of the later-type, older stars of population type I.
Title: On the evolution of stars and chemical elements in the early
phases of a galaxy
Authors: Schwarzschild, M.; Spitzer, L.
Bibcode: 1953Obs....73...77S
Altcode:
No abstract at ADS
Title: Inhomogeneous Stellar Models. II. Models with Exhausted Cores
in Gravitational Contraction.
Authors: Sandage, A. R.; Schwarzschild, M.
Bibcode: 1952ApJ...116..463S
Altcode:
Seven shell-source models with exhausted, gravitationally contracting
cores have been computed in detail. The models form an evolutionary
sequence starting from a confignration whose isothermal core
contains the -Chandrasekhar limitating mass. It is found that, as the
cores contract, the envelopes greatly expand. Thus from the initial
confignration, which is near the main sequence, the stars evolve rapidly
to the right in the H-R diagram, amply covering the giant region. In
this evolution the gravitational contraction contributes less than
4 per cent to the total luminosity. A comparison of this theoretical
evolution with the observed H-R diagram for globular clusters appears
to explain the sudden turnoff from the main sequence to the giant
region at about Mb = +3.5.
Title: Preliminary Analysis of the Turbulence Spectrum of the Solar
Photosphere at Long Wave Lengths.
Authors: Frenkiel, F. N.; Schwarzschild, M.
Bibcode: 1952ApJ...116..422F
Altcode:
The available data on the velocities of granules are analyzed according
to the methods of the statistical theory of turbulence. The analysis
indicates that the turbulence spectrum of the solar photosphere may not
be of a simple form but may have-in addition to the suspected primary
maximum at wave lengths of the order of 300 km-a secondary maximum at
long wave lengths of about 15,000 km.
Title: Inhomogeneous Stellar Models. I. Models with a Convective
Core and a Discontinuity in the Chemical Composition.
Authors: Oke, J. B.; Schwarzschild, M.
Bibcode: 1952ApJ...116..317O
Altcode:
A number of stellar models with a discontinuity in chemical composition
have been computed through in detail. An arbitrary, but fixed,
hydrogen-poor composition was used for the interior of all models,
and a fixed hydrogen-rich composition was similarly used for all
envelopes. The position in the star at which the change in chemical
composition occurs was varied over a wide range. The computed models
were found to cover well the observed red giants, as far as radii and
luminosities are concerned. The masses of the theoretical red-giant
models, however, fall systematically somewhat below the standard
massluminosity relation-a circumstance not necessarily in discordance
with observation.
Title: Note on the color-magnitude diagram of Messier 3
Authors: Schopp, John; Schwarzschild, Martin
Bibcode: 1952AJ.....57...61S
Altcode:
No abstract at ADS
Title: Perigalactic and apogalactic distances of high-velocity stars
Authors: Schwarzschild, Martin
Bibcode: 1952AJ.....57...57S
Altcode:
No abstract at ADS
Title: Inherited and acquired characteristics of stars
Authors: Schwarzschild, Martin
Bibcode: 1952AJ.....57....5S
Altcode:
No abstract at ADS
Title: The Possible Influence of Interstellar Clouds on Stellar
Velocities.
Authors: Spitzer, Lyman, Jr.; Schwarzschild, Martin
Bibcode: 1951ApJ...114..385S
Altcode:
Gravitational encounters between stars and interstellar clouds produce
a much shorter relaxation time of the galaxy in the solar neighborhood
than do star-star encounters. This result is caused by much larger
masses of the interstellar clouds as compared with stars. In the
extreme case that the largest cloud complexes acting as gravitational
units should have masses of the order of a million solar masses it is
found that low-velocity stars may have been speeded up appreciably by
star-cloud encounters during 3 X lO years. This speedup of the stars,
which is the same for stars of all masses, arises from the tendency of
the encounters to act toward equipartition of energy between clouds
and stars, though at the present time equipartition must be far from
reached. If the masses of the large cloud complexes are, in fact,
high enough to make the star-cloud encounters sufficiently effective,
one may suppose that all low-velocity population I stars have been
formed from interstellar clouds with initial average velocities equal
to those of the present clouds and that the present differences in the
velocity dispersions of population I stars have been caused entirely
by star-cloud encounters. Under this assumption, the encounters would
have increased the average velocity of older groups (late dwarfs
and red giants) by about a factor of 2, while they would not have
had time to affect the velocities of the younger stars (early main
sequence). Even under extreme assumptions the star-cloud encounters
are found to be incapable of changing noticeably the velocities of
the fast population II stars. This may indicate that all population
II stars were formed from the interstellar matter at an early stage,
when the velocities of the primeval clouds were still high.
Title: On the Difference in Chemical Composition Between - and
Low-Velocity Stars.
Authors: Schwarzschild, M.; Spitzer, L., Jr.; Wildt, R.
Bibcode: 1951ApJ...114..398S
Altcode:
The spectroscopic peculiarities of highwelocity of the CH bands and
weakening of the CN bands and of the metal lines-can tentatively be
explained by a general reduction in the abundance of the heavy elements
and a somewhat lesser reduction in the abundance of the medium-heavy
elements, relative to the abundances for low-velocity stars. As a
working hypoQhesis, it is proposed that such a general difference in
chemical composition between stars of populations I and II stems from
the preferential accumulation of grains in the denser interstellar
clouds from which the star of population I might be formed. The
astrophysical discussion indicates that the dissociation energy of
the molecules N2 and CO should be close to 9.5 e.v.; the considerably
lower or higher values still advocated by some spectroscopists are
not supported by the astronomical evidence.
Title: On the Color-Magnitude Diagram for M 15.
Authors: Johnson, Harold L.; Schwarzschild, Martin
Bibcode: 1951ApJ...113..630J
Altcode:
Magnitudes and colors determined for 251 nonvariable stars in the
globular cluster M 15. The resulting color-magnitude diagram indicates
that the brighter stars in M 15 may belong to two sequences. The first
sequence consists of red giants and supergiants and may possibly be
the bright end of the subdwarf sequence. The second sequence consists
of the horizontal branch characteristic of globular clusters. This
branch appears to bend downward at its blue end and may thus possibly
be the bright continuation of the regular main sequence.
Title: A Spectroscopic Comparison Between - and Low-Velocity F Dwarfs.
Authors: Schwarzschild, Martin; Schwarzschild, Barbara
Bibcode: 1950ApJ...112..248S
Altcode:
High-dispersion spectrograms were obtained with the coud spectrograph
of the l(iO4nch telescope at Mount Wilson for nine F stars, including
three high-velocity and three low-velocity,'dwarfs. On the spectrograms,
depths were measured for seventy-eight lines, equivalent widths for'
thirteen lines, and profiles for four lines. The relative temperatures
and pressures of the nine stars were analyxed with the help of the
photoelectric color indices determined by Dr. Eggen and the degrees of
ionixation derived from the line depths, and the various measurements
were discussed as functions of temperature and pressure. The final data
showed no difference between the high-velocity and the low-velocity
F dwarfs, with the following exceptions: The CH features were found
somewhat stronger relative to the Fe I lines in the highvelocity dwarfs
than in the low-velocity dwarfs, indicating that the abundance ratio of
C to Fe is probably approximately 2.5 times higher in the high-velocity
dwarfs than in the low-velocity dwarfs. A second, though extremely
uncertain, difference appeared in the equivalent widths of the Fe I
lines, which indicated that possibly the abundance ratio of H to Fe
might be larger in the high-velocity dwarfs by about a factor of 2 as
compared with the low-velocity dwarfs.
Title: Zeeman Shifts for Stellar Dipoles and Quadrupoles with
Inclined Axes.
Authors: Schwarzschild, Martin
Bibcode: 1950ApJ...112..222S
Altcode:
No abstract at ADS
Title: On the Turbulent Velocities of Solar Granules.
Authors: Richardson, R. S.; Schwarzschild, M.
Bibcode: 1950ApJ...111..351R
Altcode:
With the 150-foot solar tower of the Mount Wilson Observatory, a
spectrum of the solar granulation was obtained, showing individual
granules with good definition. The Doppler shifts shown by this
plate were measured and the corresponding turbulent velocities
determined. From these data, together with the turbulent velocities
determined from other solar observations, a tentative turbulence
spectrum is derived for the solar photosphere. This spectrum suggests
the possible existence of turbulent elements only 10(Y 200 km in
diameter, with velocities of the order of 2 km/sec and brightness
contrasts much exceeding those of the directly observable larger
granules.
Title: On the Abundance of C13 in the Solar Atmosphere
Authors: Greenstein, J. L.; Richardson, R. S.; Schwarzschild, M.
Bibcode: 1950PASP...62...15G
Altcode:
No abstract at ADS
Title: Book Reviews: The Pulsation Theory of Variable Stars
Authors: Schwarzschild, Martin
Bibcode: 1949Sci...110...21S
Altcode: 1949Sci...110...21R
No abstract at ADS
Title: Anharmonic Pulsations of the Standard Model.
Authors: Schwarzschild, Martin; Savedoff, Malcolm P.
Bibcode: 1949ApJ...109..298S
Altcode:
The anharmonic pulsations of the standard model are investigated. It
is found that for the amplitude of characteristic cepheids, anharmonic
pulsations yield practically the same period as harmonic pulsa- tions
do. Furthermore, the anharmonic pulsations are found to produce an
appreciable skewness in the radial velocity-curve; however, this
skewness is still smaller than that observed
Title: Red-Giant Models with Chemical Inhomogeneities
Authors: Hen, Li; Schwarzschild, M.
Bibcode: 1949MNRAS.109..631H
Altcode:
No abstract at ADS
Title: The Interior of the Sun
Authors: Schwarzschild, Martin
Bibcode: 1949ASPL....5..392S
Altcode: 1949ASPL..248.....S
No abstract at ADS
Title: The Energy Source in the Interior of the Sun
Authors: Schwarzschild, Martin
Bibcode: 1949ASPL....5..400S
Altcode: 1949ASPL..249.....S
No abstract at ADS
Title: Magnetic oscillations of a highly idealized star
Authors: Schwarzschild, Martin
Bibcode: 1949AnAp...12..148S
Altcode:
No abstract at ADS
Title: A Stellar Model for Red Giants of High Central Temperature.
Authors: Richardson, Robert S.; Schwarzschild, Martin
Bibcode: 1948ApJ...108..373R
Altcode:
The assumption is made that the turbulence in the convective core of
a red giant emits acoustical noise of such strength that the entire
energy flux is carried solely by the noise through the layers sur-
rounding the core. According to this assumption, a stellar model is
computed which consists of a con- vective core, an isothermal zone,
and a radiative envelope. It is found that a star built according to
this model may have a central temperature high enough for the carbon
cycle to operate and have simul- taneously a radius as large as that
of the biggest red giant
Title: On the Pulsation in the Atmosphere of η Aquilae.
Authors: Schwarzschild, M.; Schwarzschild, B.; Adams, W. S.
Bibcode: 1948ApJ...108..207S
Altcode:
On twenty spectra of ~ Aquilae, taken with the coudé spectrograph of
the 100-inch telescope with a dispersion of 2.9 A/mm and covering the
entire pulsation cycle, forty-three lines of iron were selected for
measurement. The radial-velocity variations of these lines were found
to indicate that the selected lines of Fe i and Fe ii arise essentially
from the same atmospheric layers. From the depth measurements of these
lines the variations of the excitation temperature and of the electron
pressure were determined. The equivalent widths, determined for a few
iron lines at mid-descending branch, showed that the hydrogen-metal
ratio in ~ Aquilae can differ from that in the sun by only a small
factor. The curve of growth at the same phase gave turbulent velocities
much smaller than the velocities determined from line profiles, which
may possibly indicate the existence of a fast turbulence with very large
elements. From the above data the density variation was computed. The
comparison of this variation with that of the velocity suggests that
possibly in the atmosphere of ~ Aquilae the kinetic temperature in-
creases greatly with height and that in the highest layers the pulsation
has the character of a simple pro- gressive wave. I. INTRODUCTIO
Title: On Noise Arising from the Solar Granulation.
Authors: Schwarzschild, Martin
Bibcode: 1948ApJ...107....1S
Altcode:
It is shown that the mechanism which maintains the high temperature
of the corona may consist of a stream of acoustical noise which is
produced-by the granulation and which transports mechanical energy
into the corona
Title: On Stellar Rotation. II.
Authors: Schwarzschild, M.
Bibcode: 1947ApJ...106..427S
Altcode:
No abstract at ADS
Title: The new photometer of the Rutherfurd Observatory
Authors: Eichner, L. C.; Hett, J. H.; Schilt, J.; Schwarzschild, M.;
Sterling, H. T.
Bibcode: 1947AJ.....53...25E
Altcode:
No abstract at ADS
Title: On the Helium Content of the Sun.
Authors: Schwarzschild, Martin
Bibcode: 1946ApJ...104..203S
Altcode:
Under the assumption that the sun consists of hydrogen, helium, and
Russell mixture, it is shown that the sun contains approximately 40
per cent of helium
Title: Symposium: Intrinsic Stellar Variation. Recent studies of
the pulsation theory
Authors: Schwarzschild, Martin
Bibcode: 1946PAAS...10..117S
Altcode:
No abstract at ADS
Title: On Stellar Rotation.
Authors: Schwarzschild, Martin
Bibcode: 1942ApJ....95..441S
Altcode:
In section I the general problem of stellar rotation is discussed,
and a special formulation, taking ac- count of the viscous forces in a
restricted form, is given. The corresponding equations are set down in
section II, and the first-order perturbation method for their solution
is discussed in section III. For the special case of the standard model
in slow rotation the equations are given in section IV and solved in
sections V and VI. The solution is found to be unique and to correspond
to a solid-body rotation
Title: Note on the ionisation in the hydrogen convection zone
Authors: Schwarzschild, Martin
Bibcode: 1942MNRAS.102..152S
Altcode:
No abstract at ADS
Title: Overtone Pulsations for the Standard Model.
Authors: Schwarzschild, Martin
Bibcode: 1941ApJ....94..245S
Altcode:
No abstract at ADS
Title: On the variables in Messier 3
Authors: Schwarzschild, Martin
Bibcode: 1940HarCi.437....1S
Altcode:
No abstract at ADS
Title: The Harvard Conference on Cepheid Variables
Authors: Gaposchkin, S.; Menzel, Donald H.; Mohr, Jenka; Norman, D.;
Schwarzschild, M.; Shapley, Harlow; Sterne, T. E.; Thorndike, S. L.;
Whipple, Fred L.
Bibcode: 1938PA.....46..378G
Altcode: 1938PA.....46..378.; 1938HarRe.148....1G
No abstract at ADS
Title: On the Light Curves of Cepheids.
Authors: Schwarzschild, Martin
Bibcode: 1938HarCi.429....1S
Altcode:
No abstract at ADS
Title: Zur Pulsationstheorie. (Mitteilung aus dem Institut für
theoretische Astrophysik, Oslo. ) Mit 2 Abbildungen.
Authors: Schwarzschild, M.
Bibcode: 1938ZA.....15...14S
Altcode:
No abstract at ADS
Title: Über die Energieerzeugung in den Sternen.
Authors: Schwarzschild, M.
Bibcode: 1937ZA.....13..126S
Altcode:
No abstract at ADS
Title: Improved elements of BB Centauri
Authors: Schwarzschild, M.
Bibcode: 1936BAN.....7..337S
Altcode:
No abstract at ADS
Title: Zur Pulsationstheorie der δ
Cephei-Sterne. (Veröffentlichungen der Universitäts-Sternwarte
Göttingen, Nr. 45. ) Mit 2 Abbildungen.
Authors: Schwarzschild, Martin
Bibcode: 1936ZA.....11..152S
Altcode:
No abstract at ADS
Title: Die Schwankung der Farbtemperatur von α Ursae
minoris. (Veröffentlichungen der Universitäts-Sternwarte Göttingen,
Nr. 46). Mit 2 Abbildungen.
Authors: Schwarzschild, M.
Bibcode: 1936ZA.....12..171S
Altcode:
No abstract at ADS
Title: Zur Pulsationstheorie der δ Cephei-Sterne Title: Zur
Pulsationstheorie der δ Cephei-Sterne Title: On the pulsation theory
of cepheid stars;
Authors: Schwarzschild, Martin
Bibcode: 1936PhDT........19S
Altcode:
No abstract at ADS