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Author name code: kalkofen
ADS astronomy entries on 2022-09-14
author:"Kalkofen, Wolfgang"
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Title: The Validity of Dynamical Models of the Solar Atmosphere
Authors: Kalkofen, Wolfgang
2012SoPh..276...75K Altcode:
Important results on the structure and dynamics of the nonmagnetic
solar chromosphere are based on hydrodynamic models that oversimplify
either the geometry of the atmosphere or the interaction of radiation
and matter. Although the observed granulation pattern is well reproduced
by the three-dimensional (3D) models, oversimplification of radiative
relaxation leads to the prediction of temperature fluctuations that are
too high (by a factor of 10 to 100) and result in a monotonic decrease
with height in the chromosphere of the horizontally and temporally
averaged temperature, and hence in the prediction of absorption lines
at wavelengths where only emission lines are observed on the Sun. New
values of solar abundances of oxygen and other metals are based on
3D hydrodynamic models with temporal and spatial fluctuations that
are far greater than those observed. These new abundances destroy the
previous agreement of observed modes with acoustic eigenmodes that had
been predicted for the old abundances from a solar model for which the
sound speed throughout most of the Sun was determined to an accuracy
of a few parts in 10<SUP>4</SUP>. One expects that, when radiative
relaxation is properly accounted for, 3D models will reproduce the
essential characteristics of the solar atmosphere, among them a positive
temperature gradient in the outward direction and hence exclusively
emission lines in the extreme ultraviolet at all times and positions
in the nonmagnetic chromosphere. A minimum characteristic length of
0.1 arcsec is identified for the solar atmosphere, below which there
is no significant structure in the actual Sun, only in wave models of
the Sun. This criticism does not detract from the notable success of
hydrodynamic modeling to explain the mechanism by which chromospheric
H<SUB>2V</SUB> and K<SUB>2V</SUB> bright points are formed.
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Title: Acoustic waves in a stratified
atmosphere. IV. Three-dimensional nonlinear hydrodynamics
Authors: Kalkofen, W.; Rossi, P.; Bodo, G.; Massaglia, S.
2010A&A...520A.100K Altcode:
Context. The quiet solar chromosphere in the interior of
supergranulation cells is believed to be heated by the dissipation of
acoustic waves that originate with a typical period of 3 min in the
photosphere. <BR /> Aims: We investigate how the horizontal expansion
with height of acoustic waves traveling upward into an isothermal,
gravitationally stratified atmosphere depends on the size of the source
region. <BR /> Methods: We have solved the three-dimensional, nonlinear,
time-dependent hydrodynamic equations for impulsively-generated,
upward-propagating acoustic waves, assuming cylindrical symmetry. <BR />
Results: When the diameter of the source of acoustic waves is small,
the pattern of the upward-propagating waves is that of a point source,
for which the energy travels upward in a vertical cone, qualitatively
matching the observed pattern of bright-point expansion with height. For
the largest plausible size of a source region, i.e., with granular size
of 1 Mm, wave propagation in the low chromosphere is approximately that
of plane waves, but in the middle and upper chromosphere it is also
that of a point source. The assumption of plane-wave propagation is not
a good approximation in the solar chromosphere. The upward-directed
energy flux is larger than that of the solar chromosphere, at least
in the middle and upper chromosphere, and probably throughout. <BR
/> Conclusions: Simulations of impulsively generated acoustic waves
emitted from source regions with diameters that are small compared to
the pressure scale height of the atmosphere qualitatively reproduce
the upward expansion observed in chromospheric bright points. The
emission features in the cores of the H and K lines are predicted to be
blueshifted for a pulse and redshifted for the waves in its wake. The
contribution of internal gravity waves to the upward energy flux is
small and decreases with increasing size of the source region.
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Title: Numerical Radiative Transfer
Authors: Kalkofen, Wolfgang
2009nrt..book.....K Altcode:
Preface; Introduction; Part I. Operator Perturbation: 1. Survey
of operator perturbation methods W. Kalkofen; 2. Line formation
in expanding atmospheres: multilevel calculations using approximate
lambda operators W. R. Hamann; 3. Stellar atmospheres in non-LTE: model
construction and line formation calculations using approximate lambda
operators K. Werner; 4. Acceleration of convergence L. H. Auer; 5. Line
formation in a time-dependent atmosphere W. Kalkofen; 6. Iterative
solution of multilevel transfer problems Eugene H. Avrett and Rudolf
Loeser; 7. An algorithm for the simultaneous solution of thousands
of transfer equations under global constraints Lawrence S. Anderson;
8. Operator perturbation for differential equations W. Kalkofen; Part
II. Polarised Radiation: 9. A gentle introduction to polarised radiative
transfer David E. Rees; 10. Non-LTE polarised radiative transfer in
special lines David E. Rees and Graham A. Murphy; 11. Transfer of
polarised radiation using 4x4 matrices E. Landi Degli'Innocenti;
12. Radiative transfer in the presence of strong magnetic fields
A. A. van Ballegooijen; 13. An integral operator technique of radiative
transfer in spherical symmetry A. Peraiah; 14. Discrete ordinate matrix
method M. Schmidt and R. Wehrse.
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Title: Line Formation in a Time-Dependent Atmospehre
Authors: Kalkofen, W.
2009nrt..book..111K Altcode:
No abstract at ADS
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Title: Operator Perturbation for Differential Equations
Authors: Kalkofen, W.
2009nrt..book..191K Altcode:
No abstract at ADS
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Title: Survey of Operator Perturbation Methods
Authors: Kalkofen, W.
2009nrt..book...23K Altcode:
No abstract at ADS
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Title: Multidimensional Radiation Hydrodynamics
Authors: Kalkofen, Wolfgang
2009nmmr.conf..247K Altcode:
No abstract at ADS
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Title: Reversal-free Ca II H Profiles: a Challenge for Solar
Chromosphere Modeling in Quiet Inter-Network
Authors: Rezaei, R.; Bruls, J.; Beck, C.; Schmidt, W.; Kalkofen, W.;
Schlichenmaier, R.
2008ESPM...12.2.13R Altcode:
There is no agreement on the thermal structure of the solar
chromosphere. While results of the CO observations and 3D MHD
simulations suggest very cool structures in the upper atmosphere,
SUMER observations of UV spectral lines is interpreted as signature
of a full-time hot chromosphere. We tried to look for cool structures
in the solar chromosphere. We observed the intensity profile of the
Ca II H line in a quiet Sun region close to the disk center at the
German Vacuum Tower Telescope. We analyze over 10^5 line profiles from
inter-network regions. For comparison with the observed profiles, we
synthesize spectra for a variety of model atmospheres with a non local
thermodynamic equilibrium(NLTE) radiative transfer code. A fraction of
about 25% of the observed Ca II H line profiles do not show a measurable
emission peak in H2v and H2r wavelength bands (reversal-free). All of
the chosen model atmospheres with a temperature rise fail to reproduce
such profiles. On the other hand, the synthetic calcium profile of a
model atmosphere that has a monotonic decline of the temperature with
height shows a reversal-free profile that has much lower intensities
than any observed line profile. The observed reversal-free profiles,
at a spatial resolution of 1 arcs and a temporal resolution of 5 s,
indicate the existence of cool patches in the interior of chromospheric
network cells, at least for short time intervals. Our finding is not
only in conflict with a full-time hot chromosphere (e.g., FALC), but
also with a very cool chromosphere as found in some dynamic simulations.
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Title: Reversal-free Ca II H profiles: a challenge for solar
chromosphere modeling in quiet inter-network
Authors: Rezaei, R.; Bruls, J. H. M. J.; Schmidt, W.; Beck, C.;
Kalkofen, W.; Schlichenmaier, R.
2008A&A...484..503R Altcode: 2008arXiv0804.2325R
Aims: We study chromospheric emission to understand the temperature
stratification in the solar chromosphere. <BR />Methods: We observed
the intensity profile of the Ca II H line in a quiet Sun region close
to the disk center at the German Vacuum Tower Telescope. We analyze
over 10<SUP>5</SUP> line profiles from inter-network regions. For
comparison with the observed profiles, we synthesize spectra for a
variety of model atmospheres with a non local thermodynamic equilibrium
(NLTE) radiative transfer code. <BR />Results: A fraction of about
25% of the observed Ca II H line profiles do not show a measurable
emission peak in H<SUB>2v</SUB> and H<SUB>2r</SUB> wavelength bands
(reversal-free). All of the chosen model atmospheres with a temperature
rise fail to reproduce such profiles. On the other hand, the synthetic
calcium profile of a model atmosphere that has a monotonic decline of
the temperature with height shows a reversal-free profile that has much
lower intensities than any observed line profile. <BR />Conclusions:
The observed reversal-free profiles indicate the existence of cool
patches in the interior of chromospheric network cells, at least
for short time intervals. Our finding is not only in conflict with a
full-time hot chromosphere, but also with a very cool chromosphere as
found in some dynamic simulations.
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Title: Heating and dynamics of the quiet solar chromosphere
Authors: Kalkofen, Wolfgang
2008IAUS..247...93K Altcode: 2007IAUS..247...93K
The quiet solar chromosphere in regions with negligible magnetic
field is believed to be heated by acoustic waves. But their energy
flux, measured in the upper photosphere with the Transition Region And
Coronal Explorer (TRACE), has been found to be insufficient to account
for the radiative emission from the chromosphere. Wedemeyer-Böhm et
al. (2007) and Cuntz et al. (2007), employing a 3D hydrodynamical model
by Wedemeyer et al. (2004), have proposed that the spatial resolution
of TRACE is inadequate to resolve intensity fluctuations that occur
on small spatial scales. This paper accepts the principle of spatial
averaging by TRACE as a qualitative explanation for the low acoustic
flux but finds that the hydrodynamical model is too much simplified in
the treatment of radiative energy exchange to provide a quantitative
measure of the suppression of the fluctuations. The heating mechanism
of the chromosphere thus remains an open question.
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Title: Wave heating of the solar chromosphere
Authors: Kalkofen, Wolfgang
2008JApA...29..163K Altcode:
No abstract at ADS
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Title: Is the Solar Chromosphere Heated by Acoustic Waves?
Authors: Kalkofen, Wolfgang
2007ApJ...671.2154K Altcode:
Space observations with TRACE have measured only 10% of the energy
flux required to heat the nonmagnetic part of the solar chromosphere
and have thereby called into question the theory of chromospheric
heating by acoustic waves. To explain the deficit in the measured flux,
heating by processes related to the magnetic field and the limited
spatial resolution of the space observations have been invoked. This
paper argues that radiation emerging from the nonmagnetic chromosphere
shows that the heating mechanism is dissipation of acoustic waves. The
full energy flux required for acoustic heating of the chromosphere must
therefore pass through the photosphere. The explanation of the missing
flux by the limited spatial resolution of TRACE confirms the principle
of the effect, but the test is preliminary since the hydrodynamic model
on which the test is based has temperature fluctuations that far exceed
those of the Sun. The shape of the acoustic spectrum observed with
TRACE appears to support the theory of wave generation in the solar
convection zone. But the low energy flux and the limited acoustic
frequency range of the observations prevent a definitive conclusion.
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Title: Advances in radiative transfer
Authors: Wehrse, Rainer; Kalkofen, Wolfgang
2006A&ARv..13....3W Altcode:
This review describes advances in radiative transfer theory since
about 1985. We stress fundamental aspects and emphasize modern
methods for the numerical solution of the transfer equation for
spatially multidimensional problems, for both unpolarized and
polarized radiation. We restrict the discussion to two-level atoms
with noninverted populations for given temperature, density and
velocity fields.
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Title: Dynamics of the Solar Magnetic Network: Two-dimensional
MHD Simulations
Authors: Hasan, S. S.; van Ballegooijen, A. A.; Kalkofen, W.;
Steiner, O.
2005ApJ...631.1270H Altcode: 2005astro.ph..3525H
The aim of this work is to identify the physical processes that occur
in the network and contribute to its dynamics and heating. We model the
network as consisting of individual flux tubes, each with a nonpotential
field structure, that are located in intergranular lanes. With a typical
horizontal size of about 150 km at the base of the photosphere, they
expand upward and merge with their neighbors at a height of about 600
km. Above a height of approximately 1000 km the magnetic field starts
to become uniform. Waves are excited in this medium by means of motions
at the lower boundary. We focus on transverse driving, which generates
both fast and slow waves within a flux tube and acoustic waves at
the interface of the tube and the ambient medium. The acoustic waves
at the interface are due to compression of the gas on one side of
the flux tube and expansion on the other. These longitudinal waves
are guided upward along field lines at the two sides of the flux
tube, and their amplitude increases with height due to the density
stratification. Being acoustic in nature, they produce a compression
and significant shock heating of the plasma in the chromospheric part of
the flux tube. For impulsive excitation with a time constant of 120 s,
we find that a dominant feature of our simulations is the creation of
vortical motions that propagate upward. We have identified an efficient
mechanism for the generation of acoustic waves at the tube edge, which
is a consequence of the sharp interface of the flux concentration. We
examine some broad implications of our results.
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Title: On the Validity of Acoustically Heated Chromosphere Models
Authors: Ulmschneider, P.; Rammacher, W.; Musielak, Z. E.; Kalkofen, W.
2005ApJ...631L.155U Altcode:
Theoretical models of solar and stellar chromospheres heated by
acoustic waves have so far been constructed by using time-dependent,
one-dimensional, radiation-hydrodynamic numerical codes that are
based on the approximation of plane-parallel geometry. The approach
seems to be justified by the fact that the chromospheres of most
stars extend over very narrow height ranges compared to the stellar
radius. It is demonstrated that this commonly used assumption may lead
to unrealistic shock mergings, to the artificial formation of unusually
strong shocks and the artificial destruction of high-frequency acoustic
wave power. Comparing one-dimensional calculations with observations may
lead to severe misjudgment about the nature of chromospheric heating.
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Title: Is the Chromosphere Always Hot, or Mostly Cold?
Authors: Kalkofen, Wolfgang
2005BASI...33..337K Altcode:
No abstract at ADS
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Title: Dynamics of the Magnetic Network on the Sun
Authors: Hasan, S.; van Ballegoiijen, A.; Kalkofen, W.; Steiner, O.
2005AGUSMSH13C..08H Altcode:
Observations have revealed the presence of a rich spectrum of waves
with different periods in regions of the solar atmosphere called the
"magnetic network" that are dominated by strong magnetic fields. This
network is believed to be heated by dissipation of magnetohydrodynamic
(MHD) waves, but the MHD processes involved in wave generation,
propagation and dissipation are poorly understood. In this work we
attempt to identify some of the processes that occur in the network and
which contribute to its dynamics and heating. We model the network as
consisting of individual magnetic elements or flux tubes, rooted in
intergranular lanes, with a typical horizontal size of 100 km. They
expand upward and merge with their neighbors at a height of about 600
km. Above this height the magnetic field becomes uniform. An equilibrium
configuration based on the above model is constructed by solving the
magnetostatic equations in 2-D. Waves are generated in this medium
by means of motions at the lower boundary. We focus on transverse
driving which generates fast waves within the flux tubes and acoustic
waves at the interface of the tubes and the field-free medium, but not
otherwise in the field-free gas. The acoustic waves at the interface
are due to compression of the gas on one side of the flux tube and
expansion on the other. These waves travel upward along the two sides
of the (2D) flux tube and enter it, where they become longitudinal
waves. For impulsive excitation with a time constant of 120 s, we
find that a dominant feature is the creation of vortical motions that
propagate upwards. We have identified a new and efficient mechanism
for the generation of longitudinal waves and shock formation in the
chromosphere. We examine the observational implications of our results
and their broad applications to chromospheric heating and activity.
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Title: The structure of the quiet solar chromosphere
Authors: Kalkofen, W.
2005ESASP.560..695K Altcode: 2005csss...13..695K
No abstract at ADS
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Title: Observations of the Solar Chromosphere with SUMER
Authors: Wilhem, K.; Kalkofen, W.
2004ESASP.547..137W Altcode: 2004soho...13..137W
No abstract at ADS
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Title: Dynamics and Heating of Chromospheres
Authors: Kalkofen, W.
2004IAUS..219..115K Altcode:
The chromosphere constitutes the lower part of the transition between
the relatively cool photosphere and the extremely hot corona.Detailed
observations show the chromosphere to be highly dynamic. Its complicated
structure is due to the intricate interaction of the solar plasma with
the pervasive magnetic field. <P />However the solar chromosphere
is difficult to study. It lies just above the photosphere where the
transitions from optically thick to thin occurs so that the convenient
approximation of LTE no longer holds for the calculation of radiative
energy transfer. Secondly it is the region where a transition from high
to low plasma beta (the ration of gas pressure to magnetic pressure)
occurs. In combination these two properties require us to employ
full-blown radiation magneto-hydrodynamic simulations to fathom the
complexities of the chromosphere. <P />A lingering chromospheric
question is the presence of cool material (with temperatures as low
as 3700 K) that seems to be required by dark spectral lines due to
vibration-rotation transitions of the CO molecule. No physical models
at this time can adequately explain the simultaneous presence of this
cool material and the omni-presence of chromospheric UV emission which
requires high temperatures at similar altitude in the chromosphere.
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Title: Observations of the upper solar chromosphere with SUMER
Authors: Wilhelm, K.; Kalkofen, W.
2003A&A...408.1137W Altcode:
The structure and dynamics of the solar chromosphere are still matters
of debate. The chromospheric network reflecting the supergranulation
of the outer convection zone of the Sun is a prominent feature of the
lower solar atmosphere that extends into the transition zone between
chromosphere and corona. In particular, the physics of the so-called
“nonmagnetic” chromosphere in internetwork regions as well as the
physics of the magnetic network are not yet fully understood. Here
we present observations of the H I Lyman continuum obtained in areas
of the undisturbed Sun by the Solar Ultraviolet Measurements of
Emitted Radiation (SUMER) instrument on the Solar and Heliospheric
Observatory (SOHO). The observing sequences are unique in the sense
that they cover the spectral range from 67 nm to 93 nm with the
highest cadence the SUMER spectrometer can achieve operating near the
limit of its mechanism performance, telemetry allocation, and memory
capabilities. In this wavelength range not only the Lyman continuum
but also many extreme-ultraviolet emission lines (N II, N III, S IV,
O II, O III, O IV, O V, Ne VIII, and Mg IX) are prominent, allowing
the investigation of radiation formed at temperatures representative
of regions from the chromosphere to the corona. Brightenings have
been identified that are presumed to be related to the well-known
3 min oscillations as seen, for instance, in Ca II H<SUB>2v</SUB>
and K<SUB>2v</SUB> observations. The relative temporal variations of
the continuum radiance near 77 nm were typically 20% to 40%, whereas
simultaneously recorded transition-region lines varied by about 40%
of their lowest values in phase with the continuum. In the corona,
the Ne VIII and Mg IX lines with formation temperatures of 620 000
K and 950 000 K, respectively, experienced relative changes of ~ 10%
and displayed no phase relationship with the transition-region lines
or the continuum. Radiance variations in the spatial regime across
the solar disk show a higher correlation between the chromosphere
and the corona than between the transition region and the corona. The
observations will be discussed with a view towards providing constraints
for modelling chromospheric structure and dynamics. <P />Part of this
work was carried out while KW was visiting the Harvard-Smithsonian
Center for Astrophysics, Cambridge, MA, USA.
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Title: The Filling Factor of Solar Internetwork Grains
Authors: Kalkofen, Wolfgang; Hammer, Reiner
2003ANS...324..101K Altcode: 2003ANS...324..P07K
No abstract at ADS
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Title: The Violent Solar Chromosphere
Authors: Kalkofen, W.
2003SPD....34.1101K Altcode: 2003BAAS...35..826K
Two different types of models have been proposed to describe
the quiet solar chromosphere: Simulating the dynamics and the
temperature structure resulting from shock waves gives a negative
average temperature gradient with respect to height (∇ <SUB>z</SUB>
T <0) and violent temperature fluctuations (δ T ∼ 10,000 K);
modeling based on the emergent spectrum gives a positive gradient
(∇ <SUB>z</SUB> T>0,\ z>0.5 Mm) and modest fluctuations
(δ T ∼ 300 K). Clearly, these two models are incompatible with
one another. The model of the dynamics claims that the traditional
temperature structure of the chromosphere (∇ <SUB>z</SUB> T>0)
is an illusion created by time averaging of the emission. But the
dissipation and radiative emission associated with the dynamics make
only a minor contribution to chromospheric heating and the emergent
radiation. In addition, in a typical supergranulation cell, the
dynamics is confined to 10 to 20 regions (grains) with a combined
filling factor ranging from 1% in the photosphere to 50% in the
upper chromosphere. In the middle chromosphere (z=1 Mm), 90% to 95%
of the medium falls outside the calcium grains and thus, according
to the dynamical model, has no chromosphere, i.e., ∇ <SUB>z</SUB>
T <0. <P />This paper discusses observational constraints on the
temperature structure of the quiet solar chromosphere.
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Title: Kink and Longitudinal Oscillations in the Magnetic Network
on the Sun: Nonlinear Effects and Mode Transformation
Authors: Hasan, S. S.; Kalkofen, W.; van Ballegooijen, A. A.;
Ulmschneider, P.
2003ApJ...585.1138H Altcode:
We examine the propagation of kink and longitudinal waves in the solar
magnetic network. Previously, we investigated the excitation of network
oscillations in vertical magnetic flux tubes through buffeting by
granules and found that footpoint motions of the tubes can generate
sufficient wave energy for chromospheric heating. We assumed that
the kink and longitudinal waves are decoupled and linear. We overcome
these limitations by treating the nonlinear MHD equations for coupled
kink and longitudinal waves in a thin flux tube. For the parameters
we have chosen, the thin tube approximation is valid up to the layers
of formation of the emission features in the H and K lines of Ca II,
at a height of about 1 Mm. By solving the nonlinear, time-dependent MHD
equations we are able to study the onset of wave coupling, which occurs
when the Mach number of the kink waves is of the order of 0.3. We also
investigate the transfer of energy from the kink to the longitudinal
waves, which is important for the dissipation of the wave energy in
shocks. We find that kink waves excited by footpoint motions of a
flux tube generate longitudinal modes by mode coupling. For subsonic
velocities, the amplitude of a longitudinal wave increases as the square
of the amplitude of the transverse wave, and for amplitudes near Mach
number unity, the coupling saturates and becomes linear when the energy
is nearly evenly divided between the two modes.
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Title: Near-infrared chromospheric observatory
Authors: Labonte, Barry; Rust, David M.; Bernasconi, Pietro N.;
Georgoulis, Manolis K.; Fox, Nicola J.; Kalkofen, Wolfgang; Lin,
Haosheng
2003SPIE.4853..140L Altcode:
NICO, the Near Infrared Chromosphere Observatory, is a platform for
determining the magnetic structure and fources of heating for the
solar chromosphere. NICO, a balloon-borne observatory, will use the
largest solar telescope flying to map the magnetic fields, velocities,
and heating events of the chromosphere and photosphere in detail. NICO
will introduce new technologies to solar flight missions, such as
wavefront sensing for monitoring telescope alignment, real-time
correlation tracking and high-speed image motion compensation, and
wide aperture Fabry-Perot etalons for extended spectral scanning.
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Title: Is the Solar Chromosphere Heated by Oscillations?
Authors: Kalkofen, Wolfgang
2003IAUJD...7E..37K Altcode:
The 3 min oscillations by large-amplitude waves that are observed in
calcium bright points in the quiet Sun are confined to a small fraction
of the internetwork chromosphere. Their contribution to the heating at
the location of the bright points is small and their contribution to
chromospheric heating overall is negligible. This observational evidence
contradicts a recent dynamical model in which the dissipation of the
3~min waves creates the chromosphere. I discuss the topology of the
internetwork chromosphere and why the dynamical model describes only
some aspects of the dynamics but not others and not the overall heating.
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Title: The Temperature Structure of the Chromosphere
Authors: Kalkofen, W.
2003ASPC..286..443K Altcode: 2003ctmf.conf..443K
No abstract at ADS
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Title: Wave Propagation in the Nonmagnetic Chromosphere
Authors: Kalkofen, W.
2003ASPC..286..385K Altcode: 2003ctmf.conf..385K
No abstract at ADS
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Title: The dynamics of the quiet solar chromosphere
Authors: Kalkofen, W.; Hasan, S. S.; Ulmschneider, P.
2003dysu.book..165K Altcode:
Wave propagation in the nonmagnetic chromosphere is described for
plane and spherical waves, and excitation by means of impulses in small
source regions in the photosphere; excitation for flux tube waves in
the magnetic network is described for large, single impulses and for a
fluctuating velocity field. Observational signatures of the various wave
types and their effect on chromospheric heating are considered. It is
concluded that calcium bright points in the nonmagnetic chromosphere
are due to spherical acoustic waves, and that for the oscillations
in the magnetic network, transverse waves are more important than
longitudinal waves; they may penetrate into the corona, giving rise
to some coronal heating.
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Title: 3D wave propagation in the chromosphere
Authors: Kalkofen, W.
2003AN....324..409K Altcode:
No abstract at ADS
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Title: Heating of the solar chromosphere
Authors: Ulmschneider, P.; Kalkofen, W.
2003dysu.book..181U Altcode:
Overlying the photosphere is the chromosphere, a layer that is dominated
by mechanical and magnetic heating. By simulating the chromospheric
line and continuum emission, empirical models can be constructed that
allow the energy balance to be evaluated. Several possible heating
processes are discussed as well as the search is made for the actual
heating mechanisms. It is found that dissipation by acoustic waves is
the basic heating mechanism for nonmagnetic regions of the chromosphere,
and MHD tube waves for magnetic regions.
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Title: The Near-Infrared Chromosphere Observatory
Authors: Rust, David M.; Bernasconi, Pietro N.; Labonte, Barry J.;
Georgoulis, Manolis K.; Fox, Nicola J.; Kalkofen, Wolfgang; Lin,
Haoseng
2002ESASP.505..561R Altcode: 2002IAUCo.188..561R; 2002solm.conf..561R
The Near-Infrared Chromosphere Observatory (NICO) is a proposed
balloon-borne observatory aiming to investigate the magnetic structure
and the sources of heating in the solar chromosphere. NICO will be based
on the successful Flare Genesis Experiment (FGE), a pioneer in applying
novel technologies for the study of the Sun. NICO will map magnetic
fields, velocity fields, and heating events in the chromosphere with
unprecedented quality.
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Title: The Near-Infrared Chromosphere Observatory (NICO)
Authors: Rust, D. M.; Bernasconi, P. N.; LaBonte, B. J.; Georgoulis,
M. K.; Kalkofen, W.; Fox, N. J.; Lin, H.
2002AAS...200.3902R Altcode: 2002BAAS...34..701R
NICO is a proposed cost-effective platform for determining the magnetic
structure and sources of heating for the solar chromosphere. It is a
balloon-borne observatory that will use the largest solar telescope
flying and very high data rates to map the magnetic fields, velocities,
and heating events of the chromosphere and photosphere in unprecedented
detail. NICO is based on the Flare Genesis Experiment (FGE), which
has pioneered in the application of technologies important to NASA's
flight program. NICO will also introduce new technologies, such
as wavefront sensing for monitoring telescope alignment; real-time
correlation tracking and high-speed image motion compensation for
smear-free imaging; and wide aperture Fabry-Perot filters for extended
spectral scanning. The telescope is a classic Cassegrain design with
an 80-cm diameter F/1.5 primary mirror made of Ultra-Low-Expansion
glass. The telescope structure is graphite-epoxy for lightweight,
temperature-insensitive support. The primary and secondary mirror
surfaces are coated with silver to reflect more than 97% of the incident
solar energy. The secondary is made of single-crystal silicon, which
provides excellent thermal conduction from the mirror surface to its
mount, with negligible thermal distortion. A third mirror acts as a
heat dump. It passes the light from a 15-mm diameter aperture in its
center, corresponding to a 322"-diameter circle on the solar surface,
while the rest of the solar radiation is reflected back out of the
front of the telescope. The telescope supplies the selected segment
of the solar image to a polarization and spectral analysis package
that operates with an image cadence 1 filtergram/sec. On-board data
storage is 3.2 Terabytes. Quick-look images will be sent in near real
time to the ground via the TDRSS communications link.
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Title: Structure and Dynamics of the Quiet Solar Chromosphere
Authors: Kalkofen, Wolfgang
2002STIN...0239999K Altcode:
The grant supported research on the structure of the quiet, nonmagnetic
chromosphere and on wave excitation and propagation in both the
nonmagnetic chromosphere and the magnetic network. The work on the
structure of the chromosphere culminated in the recognition that between
two competing views of the solar chromosphere, older models by Avrett
and collaborators (referred to as VAL) and the newer, dynamical model by
Carlsson & Stein (referred to as CS), the clear decision is in favor
of the older models, and this in spite of the evident lack of physics,
which does not include wave motion and oscillations. The contrast
between the static VAL models and the dynamical CS model can be stated
most succinctly by comparing the temperature variation implied by the
VAL models and the temperature fluctuations of the CS model, which are,
respectively, of the order of 10% for the VAL model (at heights where
hydrogen is 50% ionized) and a factor of 10 (at the upper boundary
of their chromospheric model). The huge fluctuations of the CS model
have never been observed, whereas the smaller temperature variations
of the VAL models are consistent with ground-based and space-based
observations. While it should be obvious which model describes the
Sun and which one fails, the case is far from settled in the minds of
solar physicists. Thus, much educational work remains to be done and,
of course, more research to develop arguments that make the case more
convincing. The research on waves and oscillations has been based on
a unified theory of excitation of acoustic waves in the field-free
atmosphere and of transverse and longitudinal waves in magnetic flux
tubes located in the magnetic network by noting, first, that impulsive
excitation of all these waves in gravitationally stratified media leads
to oscillations at the respective cutoff frequencies and, second, that
the observed oscillation frequencies in the nonmagnetic and magnetic
parts of the chromosphere match corresponding cutoff frequencies in
the upper solar photosphere. The dynamical simulations by Carlsson
and Stein have been most instructive and of fundamental importance
for understanding wave propagation in a stratified medium by their
"flaws", the most important of which is an intensity excess at the H2v
emission peak in the H line of Ca II, which is surprising since the
observed intensity should have been an upper limit to the simulated
intensity. The only plausible explanation for a predicted intensity
that is higher than observed is that energy is spread horizontally in
upward propagation in the Sun, but not in the plane-wave modeling of CS
(as well as by almost everyone else). Investigations of the horizontal
size of the region disturbed by the upward-propagating shock in the
acoustic-wave propagation implies that the waves in H2v bright-point
oscillations emanate from a point source with a diameter corresponding
to the width of an intergranular lane, about 100 km, and reach a
size of about 4000 km in the upper layers of the chromosphere. Linear,
analytic modeling of waves emanating from a point source in a stratified
atmosphere shows that the upward-expanding propagation channel does not
have sharp boundaries and that the shape of the wave front depends on
the order of the wave behind the initial pulse. Otherwise, the behavior
of the linear waves resembles that of the nonlinear shock waves observed
in the Sun. Research that needs to be done to firm up the conclusions
reached above concerns the numerical simulations of nonlinear waves
and oscillations in a three-dimensional stratified atmosphere with
impulsive excitation, and observations linking directly the horizontal
size of the disturbed area in upward propagation to individual waves.
---------------------------------------------------------
Title: The Case against Cold, Dark Chromospheres
Authors: Kalkofen, Wolfgang
2001ApJ...557..376K Altcode: 2001astro.ph..6072K
Is the solar chromosphere always hot, with relatively small temperature
variations (δT/T~0.1), or is it cold most of the time, with temperature
fluctuations that reach δT/T~10 at the top of the chromosphere? Or,
equivalently, is the chromosphere heated continually or only for
a few seconds once every 3 minutes? Two types of empirical model,
one essentially time independent and always hot, the other highly
time dependent and mostly cold, come to fundamentally different
conclusions. This paper analyzes the time-dependent model of the
quiet, nonmagnetic chromosphere by Carlsson & Stein and shows
that it predicts deep absorption lines, none of which are observed;
intensity fluctuations in the Lyman continuum that are much larger
than observed; and time-averaged emission that falls far short of the
observed emission. The paper concludes that the solar chromosphere,
while time-dependent, is never cold and dark. The same conclusion
applies for stellar chromospheres. A complete, time-dependent model
of the nonmagnetic chromosphere must describe two phenomena: (1)
dynamics, like that modeled by Carlsson & Stein for chromospheric
bright points but corrected for the geometrical properties of shocks
propagating in an upward-expanding channel, and (2) the energetically
more important general, sustained heating of the chromosphere, as
described by current time-independent empirical models but modified
in the upper photosphere for the formation of molecular absorption
lines of CO in a dynamical medium. This model is always hot and, except
for absorption features caused by departures from local thermodynamic
equilibrium, shows chromospheric lines only in emission.
---------------------------------------------------------
Title: Acoustic waves in a stratified atmosphere. III. Temperature
inhomogeneities
Authors: Bodo, G.; Kalkofen, W.; Massaglia, S.; Rossi, P.
2001A&A...370.1088B Altcode:
In a gravitationally stratified atmosphere, small temperature
variations distort the paths of acoustic waves from the rectilinear
paths in an isothermal atmosphere. For temperature increasing
upward, low-frequency waves near the acoustic cutoff frequency
propagating at a given polar angle are refracted towards the vertical
direction (focused) and high-frequency waves, away from the vertical
(defocused). Similarly, for temperature increasing towards the axis of
a vertical cylinder, low-frequency waves are focused and high-frequency
waves are defocused. This effect of temperature inhomogeneities may
be important for wave propagation in the chromospheric K<SUB>2v</SUB>
bright point phenomenon.
---------------------------------------------------------
Title: Coronal Heating by Kink Waves
Authors: Hasan, S. S.; Kalkofen, W.; Ulmschneider, P.
2001AGUSM..SH41B01H Altcode:
We examine the hypothesis that kink waves contribute to coronal
heating. In earlier work we demonstrated that the excitation of
kink oscillations flux tubes in the magnetic network of the Sun
through their footpoint motions can provide sufficient energy for
chromospheric heating. This calculation assumed that: (a) the waves
could be treated using the linear approximation, and (b) the kink
and longitudinal waves were decoupled. These approximations, although
valid in the lower atmosphere, break down in the upper chromosphere,
where the wave amplitude becomes comparable with the tube speed. We
overcome the earlier limitations by numerically solving the nonlinear
MHD equations for coupled kink and longitudinal waves. Using a specified
form of the footpoint motions, which is compatible with observations,
we solve the nonlinear time-dependent MHD equations for a thin flux
tube extending vertically from the sub-photosphere to the base of the
corona. Our code is able to resolve shocks and also self-consistently
treats mode transformation. We calculate the energy fluxes in vertically
propagating kink waves and show that there is in principle adequate
energy in the waves to heat the corona.
---------------------------------------------------------
Title: The Solar Chromosphere: Observations and Models
Authors: Kalkofen, W.
2001AGUSM..SH21B01K Altcode:
The quiet solar chromosphere shows two characteristic signatures: an
emission spectrum, and oscillations with periods that depend on the
magnetic field. For the general emission spectrum, two fundamentally
different empirical models have been proposed. The first, which is
based on the observed time-average spectrum, has a positive temperature
gradient outward and is always hot. The intensity variations caused by
the dynamics are accounted for by temperature variations of relatively
low amplitude (δ T/T ~ 0.1). The second model, which is based on
the observed dynamics and applies only to the part of the medium
in which magnetic fields are dynamically unimportant, is heated
intermittently by shocks. This model is cool most of the time and
has temperature excursions above the cool background that can be very
large (δ T/T ~10). A complete description of the quiet chromosphere
contains aspects of both models. This time-dependent model is always
hot and has temperature variations of relatively low amplitude on the
background of an atmosphere with a positive temperature gradient in
the outward direction.
---------------------------------------------------------
Title: Intensity Fluctuations in the Solar Chromosphere
Authors: Kalkofen, W.; Warren, H. P.; Winebarger, A. R.; van
Ballegooijen, A.; Avrett, E. H.
2001AGUSM..SP41C05K Altcode:
We examine two very different empirical models of the solar
chromosphere. The first model implies steady heating, is hot at the
top of the chromosphere and has temperature fluctuations of relatively
low amplitude; the second model is heated intermittently, is cold most
of the time and undergoes large temperature variations. Estimates of
intensity fluctuations of chromospheric radiation are very different
for the two models. We compare the model predictions with observations
made by Skylab and by SUMER.
---------------------------------------------------------
Title: The Structure of the Quiet Solar Chromosphere
Authors: Kalkofen, W.
2000AAS...19712802K Altcode: 2001BAAS...33R.710K
Is the temperature in the chromosphere high and increasing outward,
because of heating by shock waves throughout and all the time? Or is
the temperature low and decreasing outward most of the time, because of
heating typically by a single shock, for a few seconds once every three
minutes? Carlsson & Stein (1994) have simulated the oscillations
seen in calcium bright points in the nonmagnetic chromosphere, obtaining
a valid, and valuable, description of the physics of chromospheric
three-minute oscillations. But the temperature structure resulting as
a by-product from the dynamical simulations reflects the intermittent
heating pattern and, as a consequence, predicts deep absorption lines
at some phases of the shock wave. None of these absorption lines has
been observed, either from the ground or from space. In addition,
the total energy emitted by the dynamical model is much less than the
energy emitted by the coolest of the models that reproduce the emergent
chromospheric spectrum. The cause of the failure of the dynamical
model to reproduce the emergent chromospheric spectrum is the limited
acoustic frequency range of the empirical input velocity spectrum,
which drives the oscillations but provides no sustained background
heating. Support by NASA is gratefully acknowledged.
---------------------------------------------------------
Title: Results from a revisit to the K<SUB>2V</SUB> bright points
Authors: Sivaraman, K. R.; Gupta, S. S.; Livingston, W. C.; Damé,
L.; Kalkofen, W.; Keller, C. U.; Smartt, R.; Hasan, S. S.
2000A&A...363..279S Altcode:
We have used pairs of temporally simultaneous CaII K-line
spectroheliograms and magnetic area scans to search for spatial
correlation between the CaII K<SUB>2V</SUB> bright points in the
interior of the network and corresponding magnetic elements. We find
that about 60% of the K<SUB>2V</SUB> bright points spatially coincide
with magnetic elements of flux density > 4 Mx cm<SUP>-2</SUP>. About
25% of the K<SUB>2V</SUB> bright points with equally enhanced emission
lie over bipole elements where the fields are > 4 Mx cm<SUP>-2</SUP>
for both polarity elements which merge and presumably cancel and
result in low fields. The rest, 15%, of the bright points coincide
with areas of fields < 4 Mx cm<SUP>-2</SUP> which is the noise
level set by us for the magnetic scans. When magnetic elements of
opposite polarity merge and form bipoles, the associated K<SUB>2V</SUB>
bright points show excess emission. Although such excess emission is a
magnetic-field-driven phenomenon, the measured value of the field at the
site of the bipole is typically low, and these cases would therefore be
excluded in the count of coincidences of excess emission with excess
magnetic fields. In our opinion, these cases of excess emission at
the sites of the bipoles, as well as at the sites of fields >
4 Mx cm<SUP>-2</SUP>, are both instances of magnetic-field-related
emissions. If the former are not taken into account as coincidences,
the correlation will drop down and this might be interpreted as not an
obvious correlation. Our present results, taking into account the low
fields of merging bipoles, establish the association of K<SUB>2V</SUB>
bright points with magnetic elements.
---------------------------------------------------------
Title: Excitation of Oscillations in the Magnetic Network on the Sun
Authors: Hasan, S. S.; Kalkofen, W.; van Ballegooijen, A. A.
2000ApJ...535L..67H Altcode: 2000astro.ph..4246H
We examine the excitation of oscillations in the magnetic network of
the Sun through the footpoint motion of photospheric magnetic flux
tubes located in intergranular lanes. The motion is derived from a
time series of high-resolution G-band and continuum filtergrams using
an object-tracking technique. We model the response of the flux tube
to the footpoint motion in terms of the Klein-Gordon equation, which
is solved analytically as an initial value problem for transverse
(kink) waves. We compute the wave energy flux in upward-propagating
transverse waves. In general we find that the injection of energy into
the chromosphere occurs in short-duration pulses, which would lead
to a time variability in chromospheric emission that is incompatible
with observations. Therefore, we consider the effects of turbulent
convective flows on flux tubes in intergranular lanes. The turbulent
flows are simulated by adding high-frequency motions (periods 5-50 s)
with an amplitude of 1 km s<SUP>-1</SUP>. The latter are simulated by
adding random velocity fluctuations to the observationally determined
velocities. In this case, we find that the energy flux is much
less intermittent and can in principle carry adequate energy for
chromospheric heating.
---------------------------------------------------------
Title: The Physics of the Chromosphere from Empirical Models
Authors: Kalkofen, W.
2000SPD....31.1103K Altcode: 2000BAAS...32..843K
Models empirically reproducing observed characteristics of the solar
chromosphere give insight into its physics and provide important
constraints for theoretical modeling. Thus, the temperature structure of
the model of Vernazza, Avrett & Loeser (1981), which is based on the
emergent spectrum of emission lines and continua from the chromosphere,
points to a particular heating mechanism; the simulations of Carlsson
& Stein (1994) of the dynamics of calcium bright points conclusively
settle the question of the nature of the waves that power the bright
points; and systematic discrepancies between simulated and observed
intensities at maximal H<SUB></SUB> 2v enhancement reveal the geometry
of wave propagation in a stratified atmosphere. The power spectrum
and the energy flux in the Carlsson & Stein simulations faithfully
reproduce bright point dynamics, but the spectrum predicted from their
dynamical model does not match other observations. Support by NASA is
gratefully acknowledged
---------------------------------------------------------
Title: Acoustic Waves in a Three-Dimensional Stratified Atmosphere
Authors: Kalkofen, W.; Massaglia, S.; Bodo, G.; Rossi, P.
2000SPD....31.0130K Altcode: 2000BAAS...32..806K
We investigate the propagation of acoustic waves in a three-dimensional,
nonmagnetic, isothermal atmosphere stratified in plane-parallel layers
in a study of oscillations in chromospheric calcium bright points. We
present analytic results for the linear and numerical results for the
nonlinear evolution of a disturbance. An impulsively excited acoustic
disturbance emanates from a point source and propagates outward as
a spherical acoustic wave, amplifying exponentially in the upward
direction. A significant wave amplitude is found only in a relatively
narrow cone about the vertical. The amplitude of the wave and the
opening angle of the cone decrease with time. Because of the lateral
spread of the upward-propagating energy, the decay is faster in 2D and
3D simulations than in 1D. We discuss observational consequences of this
scenario, some of which are not anticipated from 1D calculations. We
acknowledge support from NASA, NSF and the Ministero per l'Università
e la Ricerca Scientifica e Tecnologica.
---------------------------------------------------------
Title: The Nature of Wave Excitation in the Magnetic Network
Authors: Hasan, S. S.; Kalkofen, W.
2000SPD....31.0129H Altcode: 2000BAAS...32..806H
We examine the nature of wave excitation in the magnetic network of
the Sun through the footpoint motion of photospheric magnetic flux
tubes located in intergranular lanes. This contribution builds on
earlier work (Hasan & Kalkofen 1999, ApJ 519, 899) where it was
suggested that impulsively generated MHD kink, or transverse, waves can
contribute efficiently to chromospheric heating. On the other hand, it
was argued that this scenario for heating the magnetic network would
produce "strongly intermittent chromospheric emission consisting of
brief, intense flashes superimposed on a very low background" (Hasan,
Kalkofen & van Ballegooijen 2000, ApJL, in press). In this paper,
we analyse in greater detail the consequences based on the above picture
by adopting different forms for the footpoint point velocity. We compute
the transverse wave energy flux injected into the chromosphere through
(a) impulsive and (b) turbulent footpoint motions. Finally, we point
out observational implication of our calculations.
---------------------------------------------------------
Title: Acoustic waves in a stratified
atmosphere. II. Three-dimensional hydrodynamics
Authors: Bodo, G.; Kalkofen, W.; Massaglia, S.; Rossi, P.
2000A&A...354..296B Altcode: 1999astro.ph.11332B
We investigate analytically the propagation of linear waves in a
three-dimensional, nonmagnetic, isothermal atmosphere stratified
in plane-parallel layers. The motivation is to study oscillations
in the nonmagnetic chromosphere and to assess the limitations of
one-dimensional simulations of the K_2v bright point phenomenon. We
consider an impulsively excited acoustic disturbance, emanating from
a point source, and propagating outward as a spherical acoustic wave
accompanied by an internal gravity wave. The waves amplify exponentially
in the upward direction. A significant wave amplitude is therefore found
only in a relatively narrow cone about the vertical. The amplitude
of the wave decreases with time. Because of the lateral spread, the
wave amplitude decays faster in 2D and 3D simulations than in 1D. The
initial pulse, which travels at the sound speed, carries most of the
energy injected into the medium. Subsequent wave crests leave the source
region at ever-increasing phase speed, but slow to the sound speed as
they approach the head of the wave. Important conclusions from the 3D
solution that were not anticipated from the plane-wave solution are:
1. The bulk of the energy is emitted in the upward (and downward)
direction; much less goes into the horizontal direction. 2. The wave
profile narrows from the initial pulse through the amplitude maxima in
the wake of the pulse. As a consequence of both points, the shock-heated
regions in the wake of the initial pulse would weaken in strength and
shrink in size. 3. The height at which a given wave amplitude is reached
spreads outward from the symmetry axis of the disturbance as the wave
propagates upward. Thus the diameter of the shock-heated region would
increase as the acoustic wave travels upward in the atmosphere.
---------------------------------------------------------
Title: The dynamics and heating of the quiet solar chromosphere
Authors: Kalkofen, Wolfgang; Ulmschneider, Peter
1999CSci...77.1496K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: MHD Waves in Chromospheric Network Bright Points
Authors: Kalkofen, W.
1999ASPC..184..227K Altcode:
Transverse and longitudinal waves in magnetic flux tubes are proposed
as the explanation for the dynamics observed in network bright
points. Impulsive excitation in the photosphere generates mainly
transverse (kink) waves. They become nonlinear in the chromosphere
and then couple to longitudinal flux tube waves, which dissipate in
shocks. The oscillation period observed in the chromospheric network
is interpreted as the cutoff period of transverse flux tube waves.
---------------------------------------------------------
Title: Does the Sun Have a Full-Time Chromosphere?
Authors: Kalkofen, Wolfgang; Ulmschneider, Peter; Avrett, Eugene H.
1999ApJ...521L.141K Altcode:
The successful modeling of the dynamics of H<SUB>2v</SUB> bright
points in the nonmagnetic chromosphere by Carlsson & Stein gave as
a by-product a part-time chromosphere lacking the persistent outward
temperature increase of time-average empirical models, which is needed
to explain observations of UV emission lines and continua. We discuss
the failure of the dynamical model to account for most of the observed
chromospheric emission, arguing that their model uses only about 1%
of the acoustic energy supplied to the medium. Chromospheric heating
requires an additional source of energy in the form of acoustic waves
of short period (P<2 minutes), which form shocks and produce the
persistent outward temperature increase that can account for the UV
emission lines and continua.
---------------------------------------------------------
Title: Excitation of Oscillations in Photospheric Flux Tubes through
Buffeting by External Granules
Authors: Hasan, S. S.; Kalkofen, W.
1999ApJ...519..899H Altcode:
We examine the excitation of transverse (kink) and longitudinal
(sausage) waves in magnetic flux tubes by granules in the solar
photosphere. The investigation is motivated by the interpretation
of network oscillations in terms of flux tube waves. We model the
interaction between a granule, with a specified transverse velocity,
and a vertical flux tube in terms of the Klein-Gordon equation, which
we solve analytically as an initial value problem for both wave modes,
assuming the same external impulse. The calculations show that for
magnetic field strengths typical of the network, the energy flux in
transverse waves is higher than in longitudinal waves by an order
of magnitude, in agreement with the chromospheric power spectrum of
network oscillations observed by Lites, Rutten, & Kalkofen. But
for weaker fields, such as those that might be found in internetwork
regions, the energy fluxes in the two modes are comparable. This result
implies that if there are internetwork oscillations in magnetic flux
tubes, they must show the cutoff periods of both longitudinal and
transverse modes at 3 minutes and at 7 minutes or longer. We also find
that granules with speeds of about 2 km s<SUP>-1</SUP> can efficiently
excite transverse oscillations in frequent short-duration (typically
1 minute) bursts that can heat the corona.
---------------------------------------------------------
Title: A Part-Time Solar Chromosphere?
Authors: Kalkofen, W.
1999AAS...194.9308K Altcode: 1999BAAS...31..989K
The dynamical model of the nonmagnetic chromosphere of Carlsson
& Stein (1994) has a time-dependent temperature structure
from shock dissipation of upward-propagating acoustic waves. For
the high-temperature phase of waves due to an observed photospheric
velocity spectrum, the model reproduces to great fidelity the intricate
velocity and intensity variations of the corresponding H line from an
hour-long observing run. But for the low-temperature phase, in which the
temperature drops monotonically in the outward direction up to a height
of at least 1.8 Mm above tau =1, the model predicts UV spectra for
lines and continua that should be observable in absorption everywhere
and almost all the time. However, observations with SUMER show only
emission lines, everywhere and all the time. The dynamical model fails
as a temperature model because it uses less than 5% of the wave energy
entering the chromosphere. The extra energy is hidden in the observed
power spectrum at acoustic frequencies above 10 mHz; it accounts for
a permanent temperature inversion and thus a full-time chromosphere.
---------------------------------------------------------
Title: Excitation of oscillations in the magnetic network on the Sun
Authors: Hasan, S. S.; Kalkofen, W.
1999AAS...194.9309H Altcode: 1999BAAS...31..990H
We examine the excitation of oscillations in the magnetic network of
the Sun through the buffeting action of external granules on vertical
magnetic flux tubes extending through the photosphere. We assume that
the granules motions are turbulent with an extended Kolmogorov energy
spectrum. We model the interaction of the external flow field with
the flux tube in terms of the Klein-Gordon equation, that is solved
analytically as an initial value problem for transverse (kink) and
longitudinal (waves). We compute the wave energy flux in both the modes
for various magnetic field strengths and compare these results with our
previous calculations in which the network oscillations are excited in
short duration pulses by the occasional rapid motions of granules. We
examine the consequences of our results for coronal heating.
---------------------------------------------------------
Title: 2D radiative equilibrium models of magnetic flux tubes
Authors: Hasan, S. S.; Kalkofen, W.; Steiner, O.
1999ASSL..243..409H Altcode: 1999sopo.conf..409H
No abstract at ADS
---------------------------------------------------------
Title: The excitation of oscillations in network bright points.
Authors: Kalkofen, W.; Hasan, S. S.
1999joso.proc..137K Altcode:
The authors study the excitation of flux tube waves in the photosphere
by granular buffeting of magnetic flux tubes and show that for the
strong magnetic fields of the network the emitted energy flux appears
mainly in transverse (kink) waves, and only to a much smaller extent
in longitudinal (sausage) waves.
---------------------------------------------------------
Title: Structure and Dynamics of the Solar Chromosphere
Authors: Kalkofen, Wolfgang
1998sao..rept.....K Altcode:
The problem of chromospheric dynamics and heating consists of two
problems: one, concerning the magnetic network on the boundary of
supergranulation cells (CB), where the oscillation period is seven
minutes, and the other, concerning the cell interior (CI), where the
oscillation period is three minutes. The observational data on the
oscillations and the emission of radiation can be used to determine the
structure and dynamics of the atmosphere provided answers are known to
three critical questions, concerning: the nature of the waves powering
the bright points, the origin of the observed oscillation periods
and the mechanism of chromospheric heating. The recent modeling of
the dynamics of the CI, which combines a sophisticated treatment of
gas dynamics and radiative transfer in a one-dimensional model with
empirical velocity input from the observations, answered the first
of these questions: the waves powering K<SUB>2upsilon</SUB>, bright
points are propagating acoustic waves. This firm conclusion declares
invalid the model of Leibacher & Stein, which explains the observed
period with standing acoustic waves in a chromospheric cavity. On the
third question, the heating of the chromosphere in the CI, their model
predicts that the temperature in the chromosphere is declining in the
outward direction up to a height of at least I Mm most of the time,
so even the time-average temperature is dropping monotonically in the
outward direction, implying that lines formed in the chromosphere up
to a height of at least 1 Mm appear in absorption most of the time
and everywhere in the CI. The problem of the CI can be resolved with a
two-component model, which combines a model for K<SUB>2upsilon</SUB>,
bright points with a model for the background. The bright point model
has the same aims as the CS94 model, except that the empirical driving
from the LRK93 observations is replaced by impulsive excitation,
as suggested by the properties of the Klein-Gordon equation.
---------------------------------------------------------
Title: Spectral line radiation from solar small-scale flux tubes. II
Authors: Hasan, S. S.; Kneer, F.; Kalkofen, W.
1998A&A...332.1064H Altcode:
We examine spectral line radiation from small-scale magnetic flux tubes
in the solar atmosphere. This is a continuation of work by Kneer et
al. (1996). The main difference with the previous investigation is in
the choice of the external atmosphere. Earlier we adopted an atmosphere
resembling the empirical quiet Sun model for the ambient medium. In the
present study, we iteratively adjust the temperature structure of the
external atmosphere to fit the Stokes I and V profiles and the average
continuum intensities with those obtained from observations. Our
models are hotter in the uppermost photospheric layers and cooler
in the deeper layers than the quiet Sun model and agree well with
semi-empirical flux tube models.
---------------------------------------------------------
Title: Excitation of Longitudinal Modes in Solar Magnetic Flux Tubes
by p-Modes
Authors: Hasan, S. S.; Kalkofen, W.
1998ASPC..154..767H Altcode: 1998csss...10..767H
This is a continuation of earlier work by Hasan (1997) on the
interaction of longitudinal (sausage) waves in a slender flux tube
with p-modes in the ambient medium. We use a realistic stratification
for the flux tube and external atmospheres based upon the models of
Hasan & Kalkofen (1994). The MHD equations for a thin flux tube
are solved as an initial value problem incorporating radiative and
convective energy transport. Our calculations confirm the linear
prediction that the interaction is non-resonant. We find that the
response (for a fixed order) increases with mode degree l up to a
maximum and then falls off sharply as l increases. For the f-mode,
l_max ~650. The amplitude of the oscillations tend to become stationary
implying a balance between energy input from p-modes and losses through
radiative damping and leakage from boundaries. Low order p-modes with
degrees of several hundred appear to be most efficient for exciting
longitudinal oscillations in flux tubes. The energy flux in these
oscillations appears to be insufficient for chromospheric heating,
but may contribute partially to the required flux.
---------------------------------------------------------
Title: The Nature of the Waves in the Quiet Solar Chromosphere
Authors: Kalkofen, Wolfgang
1998ASPC..154.1997K Altcode: 1998csss...10.1997K
The waves observed in the chromosphere are interpreted as propagating
acoustic waves in the interior of supergranulation cells, and as
magneto-acoustic waves in the magnetic network on the cell boundary. The
oscillation periods are the cutoff periods, respectively, of acoustic
waves and of transverse magneto-acoustic waves. In addition to the
oscillations of K_2v bright points and network bright points, which
appear to be impulsively excited, there is a general oscillatory field
in the quiet chromosphere, perhaps excited by short-period acoustic
waves, generated by the turbulence of the convection zone. They may
cause the chromospheric temperature rise that is observed in UV emission
lines in the quiet cell interior everywhere and all the time.
---------------------------------------------------------
Title: The Excitation of Oscillations in Network Bright Points
Authors: Kalkofen, W.; Hasan, S. S.
1998joso.proc..137K Altcode:
We study the excitation of flux tube waves in the photosphere by
granular buffeting of magnetic flux tubes and show that for the strong
magnetic fields of the network the emitted energy flux appears mainly
in transverse (kink) waves, and only to a much smaller extent in
longitudinal (sausage) waves.
---------------------------------------------------------
Title: The Influence of Magnetic Flux Tubes on Their Environment
Authors: Hasan, S. S.; Kalkofen, W.
1998ASPC..154..838H Altcode: 1998csss...10..838H
We present new calculations for model atmospheres in magnetic flux
tubes extending vertically through the photosphere and convection zone
of the Sun. This study is a continuation of earlier work by Hasan &
Kalkofen (1994) on the equilibrium structure of intense magnetic flux
tubes. We construct static models of flux tubes by solving the equations
of energy transport and radiative transfer. The most significant aspect
of our study is the inclusion of multidimensional radiative transfer in
cylindrical geometry and the influence of the flux tube on the ambient
medium. Our models satisfy the condition of radiative equilibrium;
the lower boundary intensity includes the effect of convection. We
determine the structure of the thermal boundary layer at the interface
of the flux tube and the ambient medium. We find that the temperature
does not change abruptly from its value on the flux tube axis to the
ambient value far from the tube. Rather, there is a transition layer
at the interface, where there is a significant horizontal temperature
gradient. Detailed calculations have been carried out to examine the
physical conditions in this layer as well as its horizontal extent.
---------------------------------------------------------
Title: Oscillations in Chromospheric Network Bright Points
Authors: Kalkofen, Wolfgang
1997ApJ...486L.145K Altcode:
Intensity oscillations observed in the H and K lines of Ca II in
network bright points in the quiet Sun are interpreted in terms
of transverse and longitudinal magnetoacoustic waves propagating
upward inside magnetic flux tubes. It is supposed that the waves are
generated impulsively in the photosphere as transverse waves. As they
propagate upward, their velocity amplitude increases exponentially
until they become nonlinear in the chromosphere, where they transfer
power to longitudinal waves. The impulsive generation produces waves
at the cutoff frequency of transverse waves. On the assumption that
this frequency signature is transferred to the longitudinal waves,
the magnetic field strength implied by the period observed in the
chromosphere is consistent with the Zeeman effect observed in the
photosphere.
---------------------------------------------------------
Title: Acoustic wave propagation in the solar
atmosphere. V. Observations versus simulations.
Authors: Theurer, J.; Ulmschneider, P.; Kalkofen, W.
1997A&A...324..717T Altcode: 1997astro.ph..4067T
We study the evolution of spectra of acoustic waves that are generated
in the convection zone and propagate upward into the photosphere,
where we compare the simulated acoustic spectra with the spectrum
observed in an Fe I line. Although there is no pronounced 3-min
component in the spectra generated in the convection zone, there
are dominant 3-min features in the theoretical spectra, in agreement
with the observed spectrum. We interpret the occurrence of the 3-min
features as the response of the solar atmosphere to the acoustic waves
which shifts high frequency wave energy to low frequencies. We also
find qualitative agreement for the acoustic power between the wave
simulations and the observations.
---------------------------------------------------------
Title: The Nature of the Waves in the Solar Chromosphere
Authors: Kalkofen, Wolfgang
1997SPD....28.0107K Altcode: 1997BAAS...29..880K
Several models have been proposed for waves and oscillations in
the solar chromosphere. In the magnetic network on the boundary
of supergranulation cells the waves are assumed to be internal
gravity waves or trapped magneto-gravity waves with energy flowing
downward in magnetic flux tubes, or transverse and longitudinal
magneto-acoustic waves traveling upward in flux tubes; and in the
interior of supergranulation cells they are assumed to be standing
acoustic waves in a chromospheric cavity or upward-propagating acoustic
waves. The paper examines these models critically.
---------------------------------------------------------
Title: Excitation of longitudinal modes in Magnetic Flux Tubes by
external p-modes
Authors: Hasan, S. S.; Kalkofen, W.
1997SPD....28.0237H Altcode: 1997BAAS...29R.899H
This is a continuation of earlier work by Hasan (1997, ApJ 480,
in press) on the interaction of sausage waves in a slender flux
tube with p-modes in the ambient medium. In the above paper, the
time-asymptotic response of a vertical tube in the solar photosphere
due to the buffeting action by external p-modes was examined using
linear theory. For mathematical tractability an isothermal atmosphere
was assumed, which allowed the problem to be solved exactly. This
study provided insight into the behavior of the tube response and
its dependence on various parameters. The previous analysis has
now been extended in three important respects; firstly, a realistic
stratification for the flux tube and external atmospheres has been
used based upon the models of Hasan and Kalkofen (1994, ApJ 436,
355). Secondly, the interaction has been treated as an initial value
problem, which enables the gradual buildup of energy in flux tube
oscillations to be studied. Thirdly, non-adiabatic effects involving
radiative transport have been taken into account. Our calculations
confirm the linear prediction that the interaction is non-resonant. We
find that the response does not exhibit a monotonic variation with the
p-mode degree l (for a fixed order), but increases to a maximum and
then falls off sharply as l increases. For the f- mode, l<SUB>max</SUB>
~ 700. The amplitude of the oscillations tend to become stationary
(i.e. constant in time) implying a balance between energy input
from p-modes and losses through radiative damping and leakage from
boundaries. The dominant contribution to the energy flux in the upper
photosphere comes from the enthalpy flux. This flux by itself appears to
be insufficient for chromospheric heating, but may contribute partially
to the required flux. P-modes of low order and degree appear to be
most efficient for exciting longitudinal oscillations in flux tubes.
---------------------------------------------------------
Title: Chromospheric Oscillations in K 2v Bright Points
Authors: Kalkofen, Wolfgang
1996ApJ...468L..69K Altcode:
The 3 minute waves observed in K2 v emission from bright points in
the quiet solar chromosphere are shown to be oscillations of the
atmosphere at the cutoff period of acoustic waves, implying impulsive
excitation. Other interpretations of the period are shown not to be
viable since they fail the dual requirement of spatial intermittence,
in which most of the supergranulation cell interior is inert over the
course of an hour, and temporal intermittence, in which the active
locations in the cell interior are active at most half the time. It
is speculated that the episodic excitation of the K2 v oscillations is
due to collisions of granules with magnetic elements of mixed polarity
with a field strength of at least 0.5 kG.
---------------------------------------------------------
Title: NASA solar missions
Authors: Kalkofen, W.
1996AdSpR..17d.363K Altcode: 1996AdSpR..17..363K
The paper lists US solar missions, both those planned and funded by
NASA alone as well as those carried out in collaboration with other
space agencies. Some of the missions are now in operation, the others
are either planned and approved or under active discussion. The paper
also describes the principal scientific objectives of the missions
and gives some orbital characteristics.
---------------------------------------------------------
Title: Wave heating in the solar chromosphere
Authors: Kalkofen, W.
1996ASPC..109..137K Altcode: 1996csss....9..137K
No abstract at ADS
---------------------------------------------------------
Title: Spectral line radiation from solar small-scale magnetic
flux tubes.
Authors: Kneer, F.; Hasan, S. S.; Kalkofen, W.
1996A&A...305..660K Altcode:
We consider spectral line radiation from small-scale magnetic model flux
tubes in the solar atmosphere. The structure of the tube is determined
from the magnetostatic equations in the thin flux tube approximation. We
assume that the tube is in energy equilibrium and pressure balance
with the ambient medium. For the latter, we construct a quiet sun model
with an artificial heating term in order to reproduce the VAL C model,
treating the medium as a plane-parallel atmosphere. The flux tube models
are parameterized by the plasma β_0_ (the ratio of gas the pressure
to the magnetic pressure), the convective efficiency parameter α,
and the radius R_0_ at height z=0 (τ_5000_=1) in the quiet sun. The
Stokes I and V profiles emerging from the models and averaged over
areas that include the neighbourhood of the flux tube are calculated
for various spectral lines with different sensitivity for magnetic
field strength and temperature. The profiles are compared with high
spatial resolution observations of plages near disc centre that have
been obtained with the Gregory Coude Telescope at the Observatorio del
Teide/Tenerife. The information contained in both I and V profiles is
found to be very useful in constraining the theoretical models. The
best match of models with observations is achieved for values of β_0_
between 0.3 and 0.5. For a sufficiently wide separation of the V extrema
of the strongly split lines, a broadening mechanism is required. Pure
velocity (microturbulent) broadening compatible with observations
of strongly split lines gives too much broadening for weakly split
lines. A broadening that is proportional to the Lande factor, i.e.,
magnetic broadening, appears to be more appropriate. This suggests
dynamic models with temporary enhancement of the magnetic field
strength. The continuum intensity of our models is higher and the
absorption and V amplitude in the FeII 6149A line are stronger than
observed. An improvement in the match between model predictions and
observations is likely to come from models in which the ambient gas
has a lower temperature as well as a lower temperature gradient than
are found in the quiet, field-free sun. Such models are currently
under development for cylindrical flux tubes.
---------------------------------------------------------
Title: Constraints on Wave Heating in Chromospheric Bright Points
Authors: Kalkofen, W.; Höflich, P.; Ulmschneider, P.
1995SPD....26..706K Altcode: 1995BAAS...27R.966K
No abstract at ADS
---------------------------------------------------------
Title: Equilibrium Structure of Solar Magnetic Flux Tubes: Energy
Transport with Multistream Radiative Transfer
Authors: Hasan, S. S.; Kalkofen, W.
1994ApJ...436..355H Altcode:
We examine the equilibrium structure of vertical intense magnetic
flux tubes on the Sun. Assuming cylindrical geometry, we solve the
magnetohydrostatic equations in the thin flux-tube approximation,
allowing for energy transport by radiation and convection. The radiative
transfer equation is solved in the six-stream approximation, assuming
gray opacity and local thermodynamic equilibrium. This constitutes
a significant improvement over a previous study, in which the
transfer was solved using the multidimensional generalization of the
Eddington approximation. Convection in the flux tube is treated using
mixing-length theory, with an additional parameter alpha, characterizing
the suppression of convective energy transport in the tube by the
strong magnetic field. The equations are solved using the method of
partial linearization. We present results for tubes with different
values of the magnetic field strength and radius at a fixed depth in
the atmosphere. In general, we find that, at equal geometric heights,
the temperature on the tube axis, compared to the ambient medium,
is higher in the photosphere and lower in the convection zone, with
the difference becoming larger for thicker tubes. At equal optical
depths the tubes are generally hotter than their surroundings. The
results are comparatively insensitive to alpha but depend upon whether
radiative and convective energy transport operate simultaneously or
in separate layers. A comparison of our results with semiempirical
models shows that the temperature and intensity contrast are in broad
agreement. However, the field strengths of the flux-tube models are
somewhat lower than the values inferred from observations.
---------------------------------------------------------
Title: Propagation of acoustic waves in a stratified atmosphere I.
Authors: Kalkofen, W.; Rossi, P.; Bodo, G.; Massaglia, S.
1994A&A...284..976K Altcode:
This work is motivated by the chromospheric 3 minute oscillations
observed in the K_2v_ bright points. We study acoustic gravity
waves in a one-dimensional, gravitationally stratified, isothermal
atmosphere. The oscillations are excited either by a velocity pulse
imparted to a layer in an atmosphere of infinite vertical extent, or
by a piston forming the lower boundary of a semi-infinite medium. We
consider both linear and nonlinear waves.
---------------------------------------------------------
Title: Solar Variability and its Terrestrial Effects
Authors: Withbroe, G. L.; Kalkofen, W.
1994svsp.coll...11W Altcode: 1994IAUCo.143P..11W
No abstract at ADS
---------------------------------------------------------
Title: Thin flux tube models with multistream radiative transfer
Authors: Hasan, S. S.; Kalkofen, W.
1994smf..conf..334H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Report of IAU Commission 36: Theory of stellar atmospheres
(Théorie des atmosphères stellaires).
Authors: Kalkofen, W.
1994IAUTA..22..409K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Dynamics of the Solar Chromosphere. I. Long-Period Network
Oscillations
Authors: Lites, B. W.; Rutten, R. J.; Kalkofen, W.
1993ApJ...414..345L Altcode:
We analyze differences in solar oscillations between the chromospheric
network and internetwork regions from a 1 hr sequence of spectrograms
of a quiet region near disk center. The spectrograms contain Ca II
H, Ca I 422.7 nm, and various Fe I blends in the Ca II H wing. They
permit vertical tracing of oscillations throughout the photosphere
and into the low chromosphere. We find that the rms amplitude of
Ca II H line center Doppler fluctuations is about 1.5 km/s for both
network and internetwork, but that the character of the oscillations
differs markedly in these two regions. Within internetwork areas the
chromospheric velocity power spectrum is dominated by oscillations
with frequencies at and above the acoustic cutoff frequency. They are
well correlated with the oscillations in the underlying photosphere,
but they are much reduced in the network. In contrast, the network Ca
II H line center velocity and intensity power spectra are dominated by
low-frequency oscillations with periods of 5-20 min. Their signature
is much clearer in our Ca II H line center measurements than in
previously used diagnostics which are contaminated by signals from
deeper layers. We find that these long-period oscillations are not
correlated with underlying photospheric disturbances, and we discuss
their nature.
---------------------------------------------------------
Title: On the interchange instability of solar magnetic flux
tubes. II. The influence of energy transport effects
Authors: Bunte, M.; Hasan, S.; Kalkofen, W.
1993A&A...273..287B Altcode:
We examine the interchange instability of thin photo spheric magnetic
flux tube models which satisfy both force and energy balance with
their surroundings. The stability of the tubes is independent of the
efficiency of internal convective energy transport and shows only a
weak dependence on the plasma beta. The structures are susceptible
to the instability in a layer 200 - 300 km deep immediately below
optical depth unity in the quiet photosphere. The presence of an
internal atmosphere reduces the magnetic field strength in comparison
with that of an evacuated tube. While this has a stabilizing effect
on the tube surface, temperature differences between interior and
exterior are usually destabilizing. We find that the two effects
approximately cancel each other for tubes with radii R ≲ 200 km for
which the stability properties are very similar to those of completely
evacuated structures. For larger tubes, the temperature contrast with
respect to the surroundings begins to dominate and destabilizes the
tubes. Thus, despite the inclusion of energy transport effects on the
tube structure, the stability problem of small tubes (with magnetic
fluxes Φ < 10<SUP>19</SUP>-10<SUP>20</SUP> Mx) remains. Consequences
for photospheric magnetic fields are discussed.
---------------------------------------------------------
Title: Oscillations of the Magnetic Network
Authors: Lites, B. W.; Rutten, R. J.; Kalkofen, W.
1993ASPC...46..530L Altcode: 1993mvfs.conf..530L; 1993IAUCo.141..530L
No abstract at ADS
---------------------------------------------------------
Title: Oscillations in a Stratified Atmosphere
Authors: Rossi, P.; Kalkofen, W.; Bodo, G.; Massaglia, S.
1992ASPC...26..546R Altcode: 1992csss....7..546R
No abstract at ADS
---------------------------------------------------------
Title: The 3 min Oscillations in Chromospheric Bright Points
Authors: Kalkofen, W.; Rossi, P.; Bodo, G.; Massaglia, M.
1992ASPC...26..543K Altcode: 1992csss....7..543K
No abstract at ADS
---------------------------------------------------------
Title: Long-Period Oscillations of the Chromospheric Network
Authors: Lites, B. W.; Kalkofen, W.; Rutten, R. J.
1991BAAS...23.1050L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Generation of the Chromospheric 3 min Oscillation
Authors: Kalkofen, W.; Rossi, P.; Bodo, G.; Massaglia, S.
1991BAAS...23Q1033K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The K Line of Ca II in Chromospheric Bright Points
Authors: Rossi, P.; Kalkofen, W.; Uitenbroek, H.; Bodo, G.;
Massaglia, S.
1991BAAS...23Q1050R Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The heating of the solar chromosphere.
Authors: Kalkofen, Wolfgang
1991sia..book..911K Altcode:
The chromospheric layers in the quiet Sun show three distinct
regions. The chromosphere can be largely identified with the atmosphere
inside magnetic elements (flux tubes). This chapter discusses the
heating mainly of the bright points that are associated with the
intranetwork magnetic fields. It reviews the relevant observations in
line and continuum radiation and concludes that the energy dissipated
by the 3-min waves is probably sufficient to heat the low and middle
chromosphere in the bright points to the observed temperatures.
---------------------------------------------------------
Title: Wave Heating in Chromospheric Bright Points
Authors: Kalkofen, W.
1991mcch.conf...54K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Nonlinear Pulse Propagation in a Stratified Atmosphere (With
1 Figure)
Authors: Bodo, G.; Kalkofen, W.; Massaglia, S.; Rossi, P.
1991mcch.conf..353B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On Wave Heating in Chromospheric Bright Points
Authors: Rossi, P.; Kalkofen, W.; Bodo, G.; Massaglia, S.
1990BAAS...22.1198R Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Wave Heating in Magnetic Flux Tubes
Authors: Kalkofen, W.
1990IAUS..138..185K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Heating of the Quiet Solar Chromosphere
Authors: Kalkofen, Wolfgang
1990IAUS..142..197K Altcode:
The quiet solar chromosphere shows three distinct regions. Ordered
according to the strength of the emission from the low and middle
chromosphere they are (1) the magnetic elements on the boundary of
supergranulation cells, (2) the bright points in the cell interior,
and (3) the truly quiet chromosphere, also in the cell interior. The
magnetic elements on the cell boundary are associated with intense
magnetic fields and are heated by waves with very long periods, ranging
from six to twelve minutes; the bright points are associated with
magnetic elements of low field strength and are heated by (long-period)
waves with periods near the acoustic cutoff period of three minutes;
and the quiet cell interior, which is free of magnetic field, may
be heated by short-period acoustic waves, with periods below one
minute. This paper reviews mainly the heating of the bright points
and concludes that the large-amplitude, long-period waves heating the
bright points dissipate enough energy to account for their chromospheric
temperature structure.
---------------------------------------------------------
Title: Wave Heating in Magnetic Flux Tubes
Authors: Kalkofen, Wolfgang
1990ASPC....9...48K Altcode: 1990csss....6...48K
The bright chromosphere in the quiet sun is confined to magnetic
elements (flux tubes), which are located in the interior of the
supergranulation cells and within the network that surrounds the
cells. The paper discusses the heating of the gas in the magnetic
elements of the cell interior. These intranetwork flux tubes are closely
associated with bright points, which are heated by large-amplitude
compressive waves with periods near the acoustic cutoff that travel
outward from the photosphere and dissipate their energy in the
chromosphere. The energy flux of these long-period waves appears to
be sufficient for the heating of the low and middle chromosphere in
the bright points.
---------------------------------------------------------
Title: Chromospheric Heating
Authors: Kalkofen, Wolfgang
1989ApJ...346L..37K Altcode:
The solar chromosphere is identified with the atmosphere inside magnetic
flux tubes. Between the temperature minimum and the 7000 K level,
the chromosphere in the bright points of the quiet sun is heated by
large-amplitude, long-period, compressive waves with periods mainly
between 2 and 4 minutes. These waves do not observe the cutoff condition
according to which acoustic waves with periods longer than 3 minutes do
not propagate vertically in the upper solar photosphere. It is concluded
that the long-period waves probably supply all the energy required
for the heating of the bright points in the quiet solar chromosphere.
---------------------------------------------------------
Title: 2-D Flux Tube in Radiative Equilibrium
Authors: Kalkofen, W.; Bodo, G.; Massaglia, S.; Rossi, P.
1989ASIC..263..571K Altcode: 1989ssg..conf..571K
No abstract at ADS
---------------------------------------------------------
Title: Book-Review - Numerical Radiative Transfer
Authors: Kalkofen, W.; Stahlberg, J.
1989AN....310..272K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Equilibrium Structure of a Thin Magnetic Flux
Tube. III. The Effects of Molecular CO Absorption
Authors: Massaglia, S.; Bodo, G.; Kalkofen, W.; Rosner, R.
1988ApJ...333..925M Altcode:
The authors determine the structure of a stellar atmosphere and
of a thin magnetic flux tube embedded in it, taking the opacity by
H<SUP>-</SUP> and carbon monoxide into account. It is found that CO
has a strong cooling effect on the external atmosphere. For effective
temperatures below ≡5900K, the surface temperature of the atmosphere
with H<SUP>-</SUP> and CO opacity is much lower than with H<SUP>-</SUP>
alone. In the interior of the flux tube the equations can have multiple
solutions. Thus hot flux tubes can exist in a cool atmosphere even in
the absence of nonradiative heating.
---------------------------------------------------------
Title: Book-Review - Numerical Radiative Transfer
Authors: Kalkofen, W.
1988Sci...241R.991K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Methods for 2-D Radiative Transfer in Magnetic Flux Tubes
Authors: Bodo, G.; Kalkofen, W.; Massaglia, S.
1988sca..conf...56B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Numerical Radiative Transfer
Authors: Kalkofen, Wolfgang
1988nrt..book.....K Altcode:
Preface; Introduction; Part I. Operator Perturbation: 1. Survey
of operator perturbation methods W. Kalkofen; 2. Line formation
in expanding atmospheres: multilevel calculations using approximate
lambda operators W. R. Hamann; 3. Stellar atmospheres in non-LTE: model
construction and line formation calculations using approximate lambda
operators K. Werner; 4. Acceleration of convergence L. H. Auer; 5. Line
formation in a time-dependent atmosphere W. Kalkofen; 6. Iterative
solution of multilevel transfer problems Eugene H. Avrett and Rudolf
Loeser; 7. An algorithm for the simultaneous solution of thousands
of transfer equations under global constraints Lawrence S. Anderson;
8. Operator perturbation for differential equations W. Kalkofen; Part
II. Polarised Radiation: 9. A gentle introduction to polarised radiative
transfer David E. Rees; 10. Non-LTE polarised radiative transfer in
special lines David E. Rees and Graham A. Murphy; 11. Transfer of
polarised radiation using 4x4 matrices E. Landi Degli'Innocenti;
12. Radiative transfer in the presence of strong magnetic fields
A. A. van Ballegooijen; 13. An integral operator technique of radiative
transfer in spherical symmetry A. Peraiah; 14. Discrete ordinate matrix
method M. Schmidt and R. Wehrse.
---------------------------------------------------------
Title: The Influence of a Magnetic Flux Tube on its Environment
Authors: Kalkofen, W.; Rosner, R.; Bodo, G.; Massaglia, S.
1987BAAS...19..939K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Acoustic tube waves in the solar atmosphere. I - Magnesium
and calcium line emission with complete redistribution
Authors: Ulmschneider, P.; Muchmore, D.; Kalkofen, W.
1987A&A...177..292U Altcode:
The propagation of acoustic waves through vertical magnetic flux tubes
in the solar atmosphere was computed with radiation damping by (non-LTE)
emission from H(-) and the Mg II k line. Waves of various amplitudes and
periods were investigated in flux tubes with three different spreading
rates characterized by the radius as a: (1) constant, (2) linear or
(3) exponential function of height. The geometry of the flux tubes
greatly influences the behavior of the waves. Large wave amplitudes
and intense postshock radiative relaxation zones are found in constant
tubes while small amplitudes and weak radiation zones were found in
exponential tubes. In all calculations following Mg II ionization,
transition-layer-like rapid temperature rises formed and transient
mass flows were initiated. In constant tubes the rapid temperature
rises occurred at low heights while in exponential tubes these layers
were found much higher. Waves with longer periods produced steep
temperature rises at lower height and led to more mass motion. The
heights of the rapid temperature rises did not depend much on the
initial wave energy flux.
---------------------------------------------------------
Title: Numerical radiative transfer
Authors: Kalkofen, Wolfgang
1987cup..bookR....K Altcode:
Numerical techniques for the analysis of radiative transfer
(RT) in optically thick radiating atmospheres are presented
in papers contributed by leading experts. The emphases are on
operator-perturbation methods and the treatment of polarized radiation
in astrophysical applications. Topics examined include multilevel
calculations with approximate lambda operators for line formation in
expanding atmospheres, non-LTE stellar atmospheres, acceleration of
convergence, time-dependent atmospheres, the iterative solution of
multilevel RT problems, and operator perturbation for differential
equations. Consideration is given to non-LTE polarized RT in special
lines, RT in strong magnetic fields, an integral-operator technique
for RT in spherical symmetry, and discrete ordinate matrix methods.
---------------------------------------------------------
Title: Line Formation in a Time-Dependent Atmosphere
Authors: Kalkofen, W.
1987nrt..book..111K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Survey of Operator Perturbation Methods
Authors: Kalkofen, W.
1987nrt..book...23K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Operator Perturbation for Differential Equations
Authors: Kalkofen, W.
1987nrt..book..191K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Numerical radiative transfer
Authors: Kalkofen, Wolfgang
1987nrt..book.....K Altcode: 1987QB809.N86......
No abstract at ADS
---------------------------------------------------------
Title: The Equilibrium Structure of Thin Magnetic Flux Tubes. II.
Authors: Kalkofen, W.; Rosner, R.; Ferrari, A.; Massaglia, S.
1986ApJ...304..519K Altcode:
The thermal structure of the medium inside thin, vertical magnetic flux
tubes embedded in a given external atmosphere is investigated, assuming
cylindrical symmetry and a depth-independent plasma beta. The variation
with tube radius of the temperature on the tube axis is computed and the
temperature on the tube wall is estimated. The temperature variation
across the flux tube is found to be due to the depth variation of the
intensity and to the density stratification of the atmosphere. Since
the temperature difference between the axis and the wall is small in
thin flux tubes (of the order of 10 percent), the horizontal temperature
gradient may often be neglected and the temperature in a tube of given
radius may be described by a single function of depth. Thus, a more
detailed numerical treatment of the radiative transfer within thin
flux tubes can be substantially simplified by neglecting horizontal
temperature differences within the flux tube proper.
---------------------------------------------------------
Title: Book-Review - Methods in Radiative Transfer
Authors: Kalkofen, W.; Domke, H.
1986AN....307..254K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On magnetohydrodynamic thermal instabilities in magnetic
flux tubes
Authors: Massaglia, S.; Ferrari, A.; Bodo, G.; Kalkofen, W.; Rosner, R.
1985ApJ...299..769M Altcode:
The authors discuss the stability of current-driven filamentary modes
in magnetic flux tubes embedded in a plane-parallel atmosphere in LTE
and in hydrostatic equilibrium. Within the tube only energy transport
by radiation is considered. The dominant contribution to the opacity is
due to H<SUP>-</SUP> ions and H atoms (in the Paschen continuum). The
authors delimit a region in the parameter space of the equilibrium
configuration in which the instability is effective, and they discuss
the relevance of this process for the formation of structured coronae
in late-type stars and accretion disks.
---------------------------------------------------------
Title: The equilibrium structure of thin magnetic flux tubes. I
Authors: Ferrari, A.; Massaglia, S.; Kalkofen, W.; Rosner, R.; Bodo, G.
1985ApJ...298..181F Altcode:
A model atmosphere within a thin magnetic flux tube that is embedded in
an arbitrarily stratified medium is presently constructed by solving the
radiative transfer equation in the two-stream approximation for gray
opacity, under the assumption that the magnetic field is sufficiently
strong to warrant the neglect of both thermal conduction and convective
diffusion; energy inside the flux tube therefore being transported
solely by radiation. The structure of the internal atmosphere is
determined on the basis of the hydrostatic and radiative equilibrium
conditions of the tube embedded in an external atmosphere. The gas
temperature along the axis of the tube is computed, and the geometry of
the flux tube is determined on the basis of magnetic flux conservation
and total pressure equilibrium.
---------------------------------------------------------
Title: Book-Review - Methods in Radiative Transfer
Authors: Kalkofen, W.; Hubeny, I.
1985Ap&SS.115..199K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Atmosphere in a Thin Magnetic Flux Tube
Authors: Bodo, G.; Ferrari, A.; Kalkofen, W.; Massaglia, S.; Rosner, R.
1985tphr.conf..192B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Acoustic waves in the solar atmosphere. VII - Non-grey,
non-LTE H(-) models
Authors: Schmitz, F.; Ulmschneider, P.; Kalkofen, W.
1985A&A...148..217S Altcode:
The propagation and shock formation of radiatively damped acoustic waves
in the solar chromosphere are studied under the assumption that H(-)
is the only absorber; the opacity is non-grey. Deviations from local
thermodynamic equilibrium (LTE) are permitted. The results of numerical
simulations show the depth dependence of the heating by the acoustic
waves to be insensitive to the mean state of the atmosphere. After the
waves have developed into shocks, their energy flux decays exponentially
with a constant damping length of about 1.4 times the pressure scale
height, independent of initial flux and wave period. Departures from
LTE have a strong influence on the mean temperature structure in
dynamical chromosphere models; this is even more pronounced in models
with reduced particle density - simulating conditions in magnetic flux
tubes - which show significantly increased temperatures in response
to mechanical heating. When the energy dissipation of the waves is
sufficiently large to dissociate most of the H(-) ions, a strong
temperature rise is found that is reminiscent of the temperature
structure in the transition zone between chromosphere and corona;
the energy flux remaining in the waves then drives mass motions.
---------------------------------------------------------
Title: Resonance lines in dusty gaseous nebulae
Authors: Wehrse, R.; Kalkofen, W.
1985A&A...147...71W Altcode:
Under the assumption that dust is either homogeneously mixed throughout
or confined to either 1/2 or 1/4 of the space in question, the effect of
absorption and scattering by dust grains on resonance lines that were
formed in static gaseous nebulae with plane-parallel stratification is
studied and a comparison is made between the total emergent flux in the
line from the dust-filled nebula and the emergent flux from a dust-free
medium. Many line optical thickness values, and several combinations
of the opacity ratio of dust and gas, dust albedo, and collision
parameter, are compared. A novel method is used to analytically solve
the transfer equation for a spectral line in the presence of scattering
and absorbing dust. It is noted that dust distribution can have large
effects on the value of the total emergent flux.
---------------------------------------------------------
Title: Book-Review - Methods in Radiative Transfer
Authors: Kalkofen, W.; Mihalas, D.
1985Obs...105...52K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Book-Review - Methods in Radiative Transfer
Authors: Kalkofen, W.
1985Sci...227.1332K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Book-Review - Methods in Radiative Transfer
Authors: Kalkofen, W.
1985S&T....69R.132K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Partial versus complete linearization.
Authors: Kalkofen, W.
1985ASIC..152..169K Altcode: 1985pssl.proc..169K
The convergence properties of the partially or completely linearized
equations for a grey model atmosphere in radiative equilibrium are
compared. The completely linearized equations show the quadratic
convergence properties of Newton-Raphson equations. When the opacity
depends strongly on temperature, the convergence of the partially
linearized equations is very slow initially but improves once the
maximal error has moved to the lower boundary.
---------------------------------------------------------
Title: The atmosphere in a thin magnetic flux tube.
Authors: Bodo, G.; Ferrari, A.; Kalkofen, W.; Massaglia, S.; Rosner, R.
1985MPARp.212..192B Altcode:
The authors construct the equilibrium atmosphere inside a thin, vertical
magnetic flux tube embedded in a grey external atmosphere in radiative
and convective equilibrium.
---------------------------------------------------------
Title: Numerical methods in radiative transfer.
Authors: Kalkofen, W.
1985ASIC..152..153K Altcode: 1985pssl.proc..153K
The author discusses the operator perturbation method for the solution
of radiative transfer problems in the integral equation formulation. The
example given is that of line transfer in complete redistribution for
a two-level atom in statistical equilibrium. The essence of the method
is the separation of the calculation into two parts: the calculation
of corrections to a solution with the aid of an approximate integral
operator; and the calculation of the error with which the solution
satisfies the conservation equation.
---------------------------------------------------------
Title: Ayres' bifurcated solar model.
Authors: Kalkofen, W.
1985cdm..proc..272K Altcode:
The assumptions of Ayres' model of the upper solar atmosphere are
examined. It is found that the bistable character of his model is
postulated - through the assumptions concerning the opacity sources
and the effect of mechanical waves, which are allowed to destroy the
CO molecules but not to heat the gas. The neglect of cooling by metal
lines is based on their reduced local cooling rate, but it ignores the
increased depth over which this cooling occurs. Thus the bifurcated
model of the upper solar atmosphere consists of two models, one cold
at the temperature minimum, with a kinetic temperature of 2900K,
and the other hot, with a temperature of 4900K.
---------------------------------------------------------
Title: Pannel discussion on radiative transfer methods.
Authors: Kalkofen, W.; Linsky, J.; Rybicki, G.; Scharmer, G.;
Weherse, R.
1985ASIC..152..233K Altcode: 1985pssl.proc..233K
No abstract at ADS
---------------------------------------------------------
Title: Apparent solar temperature enhancement due to large-amplitude
waves
Authors: Kalkofen, W.; Ulmschneider, P.; Schmitz, F.
1984ApJ...287..952K Altcode:
The effect of slow-mode acoustic-type MHD waves propagating outward
in the solar atmosphere on the temperature structures predicted by
empirical models is investigated analytically. A model is constructed,
and numerical results are presented for wing intensities, line profiles,
temperature enhancements, waves with higher energy flux, temperature
depression, and the Si continuum. The flux in the MgII and CaII UV
resonance lines is found to be increased relative to that in the IR
continuum, leading to model temperatures which depend systematically
on which observations are used in the computation. It is suggested
that mechanical heating may take place in smaller regions such as flux
tubes rather than uniformly over the surface.
---------------------------------------------------------
Title: Time dependent effects at the foot of the chromosphere
Authors: Kalkofen, W.
1984sao..reptQ....K Altcode:
A dynamical model was proposed which is in agreement with
the observations that suggest the solar chromosphere is heated
preferentially in magnetic regions. The dynamical model requires an
energy flux that is large enough to lead to amplitudes for which the
apparent temperatures match the empirical line temperatures in the UTV
lines. Consistency with the observations of chromospheric emission
then requires that the emission take place not uniformly over the
solar surface but in smaller spatial regions.
---------------------------------------------------------
Title: Equilibrium Model of Thin Magnetic Flux Tubes
Authors: Bodo, G.; Ferrari, A.; Massaglia, S.; Kalkofen, W.; Rosner, R.
1984ESASP.207..277B Altcode: 1984plap.rept..277B
The existence of a physically realizable domain in which approximations
that lead to a self consistent solution for flux tube stratification
in the solar atmosphere, without ad hoc hypotheses, is proved. The
transfer equation is solved assuming that no energy transport other
than radiative is present. Convective motions inside the tube are
assumed to be suppressed by magnetic forces. Only one parameter, the
plasma beta at tau = 0, must be specified, and this can be estimated
from observations of spatially resolved flux tubes.
---------------------------------------------------------
Title: Radiative Transfer in an Expanding Spherical Medium
Authors: Kalkofen, W.; Wehrse, R.
1984LNP...193..306K Altcode: 1984csss....3..306K
We describe a method for solving the transfer equation of a spectral
line in statistical equilibrium with a background continuum; the
atmosphere may be static or expanding and have plane or spherical
symmetry. The method permits the rapid and accurate solution of
line transfer problems in media with given gross structure. The
basic approach is to separate the calculation into two parts:
the accurate determination of the error with which an assumed,
or an iterated, solution satisfies the conservation equations of
statistical equilibrium; and the calculation of corrections by means
of an approximate operator. The method combines differential as well
as integral equations.
---------------------------------------------------------
Title: Radiative transfer in spherical atmospheres.
Authors: Kalkofen, W.; Wehrse, R.
1984mrt..book..307K Altcode: 1984mrt..conf..307K
The authors discuss the construction of extended model atmospheres in
radiative-convective and hydrostatic equilibrium for given luminosity
and mass of the star and for prescribed net flux, of T<SUB>eff</SUB>,
at a standard monochromatic optical depth. The transfer equation is in
the form of a first-order partial integro-differential equation for the
specific intensity. For the solution of the corresponding difference
equation the authors use the finite-difference matrix to develop
"integral operators" in curvilinear coordinates that are analogous to
the integral operator of the formal solution of the transfer equation
in plane geometry.
---------------------------------------------------------
Title: Core saturation in a moving medium.
Authors: Kalkofen, W.; Ulmschneider, P.
1984mrt..book..131K Altcode: 1984mrt..conf..131K
The authors discuss a method of solving line transfer problems in
moving media with plane symmetry. The method is an adaptation of the
core saturation method of Rybicki (1972) to a medium with internal
structure, such as shocks. Its speed follows from two simplifications:
the neglect of detailed transfer in the line core, and the neglect
of atmospheric regions that contribute negligibly to the formation of
the emergent spectrum of interest. The method has been tested with the
calculation of a line source function in a static, isothermal medium
and in a model solar atmosphere traversed by multiple shocks.
---------------------------------------------------------
Title: Operator perturbation methods: a synthesis.
Authors: Kalkofen, W.
1984mrt..book..427K Altcode: 1984mrt..conf..427K
This paper shows the equivalence of the perturbation methods decribed
by Cannon, Scharmer, and Nordlund with a method based on the expansion
of an inverse operator, discusses the treatment of non-linearities in
the transfer equation, sketches an integral equation method for solving
partial redistribution problems, and shows how the source function
equation in a moving medium is modified. It also considers the impact
of operator perturbation on methods for building model atmospheres
and discusses the properties and construction of approximate integral
operators.
---------------------------------------------------------
Title: Methods in Radiative Transfer.
Authors: Kalkofen, W.
1984mrt..book.....K Altcode:
Numerical methods for solving radiative transfer problems in optically
thick, radiating media are explored in depth. Attention is focused on
astrophysical plasmas, especially stellar atmospheres. Fast methods
are considered for solving the transfer equations, including escape
probability methods, probabilistic radiative transfer, and perturbation
techniques. Consideration is also given to core saturation in a moving
media, approximate lambda operators for nonlinear energy transfer
problems, and a single-ray approximation iterative method. Spherical
radiative transfer is approached with difference equations and
linearization methods, a discrete space theory, from data on line
blanketing, using operator perturbation methods, and with integral
equations.
---------------------------------------------------------
Title: Apparent Photospheric Temperature Enhancement Due to Large
Amplitude Waves
Authors: Kalkofen, W.; Ulmschneider, P.
1982BAAS...14..938K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Radiative Transfer - Comparison of Finite Difference Equations
Authors: Kalkofen, W.; Wehrse, R.
1982A&A...110...18K Altcode:
The one-dimensional radiative transfer equation in several finite
difference approximations is studied with respect to stability and
accuracy. For some differencing schemes the solutions are unstable
or show damped oscillations on a wide mesh; for others, such as the
differencing on interleaved grids of the coupled equations for the
symmetric and antisymmetric parts of the radiation field, j and H, the
solutions are stable and as accurate as those of the Feautrier equation,
provided the mesh points for H are in the middle of the intervals for
j, the latter being differenced without restriction. The treatment of
the transfer in other geometries and physical situations by means of
the finite difference equations is considered.
---------------------------------------------------------
Title: Radiative transfer - Analytic solution of difference equations
Authors: Kalkofen, W.; Wehrse, R.
1982A&A...108...42K Altcode:
The calculus of finite differences is used to determine analytic
solutions of the discretized equation of radiative transfer for
coherent scattering in a medium with plane parallel geometry. The
absorption fraction is assumed constant but the run of the Planck
function is arbitrary. In an actual calculation only integration
constants have to be determined from the boundary conditions. The
method is applied to the calculation of the radiation field in a
one-dimensional medium with absorption, conservative scattering, or
non-conservative scattering. For infinitesimal step size the solution
to the differential equation of transfer is recovered. The character of
the solutions and the implications for numerical methods are discussed,
and the extension of the method to noncoherent scattering with partial
redistribution is indicated.
---------------------------------------------------------
Title: Is energy conserved at the foot of the solar chromosphere?
Authors: Kalkofen, W.
1982SAOSR.392A..59K Altcode: 1982csss....2...59K
The current empirical models of the solar atmosphere which have kinetic
temperatures that are too low at the temperature minimum to balance
radiative heating and cooling are examined. It was noted that when there
is additional energy input from the dissipation of hydrodynamic waves
the apparent imbalance is aggravated. It is suggested that the problem
lies in the assumption of a static upper photosphere. It is proposed
that the mechanical waves, which further out cause the chromospheric
temperature rise, traverse the temperature minimum region with large
amplitude and produce the apparent nonconservation of energy as well
as other difficulties of the empirical models through nonlinear,
time dependent effects.
---------------------------------------------------------
Title: Stellar atmosphere in statistical equilibrium.
Authors: Kalkofen, W.; Klein, R. I.
1979ApJ...234..200K Altcode:
A static atmosphere with only Lyman continuum radiation in radiative
equilibrium is studied for the effects of radiative and collisional
ionization on deviations from local thermodynamic equilibrium
(LTE). Large increases and decreases of the kinetic temperature
(range in T of about factor 2) and, correspondingly, very large over-
and underpopulation of the bound state (range in b of about factor
1,000,000) are found, depending on the frequency dependence of the
photoionization cross section. Despite these large deviations from
LTE, which strongly modify the emergent spectrum, there is almost no
effect on the particle densities, the degree of ionization, and the
basic structure of the atmosphere.
---------------------------------------------------------
Title: Deviations from LTE in a stellar atmosphere.
Authors: Kalkofen, W.; Klein, R. I.; Stein, R. F.
1979JQSRT..21..355K Altcode:
Deviations for LTE are investigated in an atmosphere of hydrogen
atoms with one bound level, satisfying the equations of radiative,
hydrostatic, and statistical equilibrium. The departure coefficient and
the kinetic temperature as functions of the frequency dependence of the
radiative cross section are studied analytically and numerically. Near
the outer boundary of the atmosphere, the departure coefficient
is smaller than unity when the radiative cross section grows with
frequency faster than with the square of frequency; it exceeds unity
otherwise. Far from the boundary the departure coefficient tends
to exceed unity for any frequency dependence of the radiative cross
section. Overpopulation always implies that the kinetic temperature in
the statistical-equilibrium atmosphere is higher than the temperature
in the corresponding LTE atmosphere. Upper and lower bounds on the
kinetic temperature are given for an atmosphere with deviations from
LTE only in the optically shallow layers when the emergent intensity
can be described by a radiation temperature.
---------------------------------------------------------
Title: Acoustic dissipation and H<SUP>-</SUP> radiation in the solar
chromosphere. II.
Authors: Kalkofen, W.; Ulmschneider, P.
1979ApJ...227..655K Altcode:
The relation between mechanical heating and radiative cooling in
the solar chromosphere is investigated, and the dependence of the
temperature rise on the mechanical dissipation rate and on the
microscopic state of H(-) ions at the foot of the chromosphere is
studied. It is found that H(-) is very nearly in local thermodynamic
equilibrium (LTE) at the temperature minimum; but near the upper end of
the range where H(-) dominates the opacity, deviations from LTE should
be taken into account in estimating the mechanical energy input from
the empirical temperature distribution. The use of empirical models
for calculating the mechanical energy input into the chromosphere is
considered. The estimate of mechanical heating implied by the recent
work of Pradeire and Thomas (1976) is found to be too low by about an
order of magnitude.
---------------------------------------------------------
Title: Acoustic Waves in the Solar Atmosphere. V. On the Chromospheric
Temperature Rise
Authors: Ulmschneider, R.; Schmitz, F.; Kalkofen, W.; Bohn, H. U.
1978A&A....70..487U Altcode:
Summary. In this fifth of a series of papers studying large amplitude
acoustic waves we use methods developed in previous papers to
compute the propagation of acoustic waves into the chromosphere. The
temperature minimum is found close to the point of shock formation
and the chromospheric temperature rise is determined after the mean
quantities reach a steady state. The position of the chromospheric
rise depends primarily on the initial acoustic flux. Photo spheric
temperature enhancement and the temperature depression of 200 to 500
K at the temperature minimum region caused by the nonlinearity of both
Planck function and opacity are discussed. The large amplitude of our
waves causes mass loss. Amplification of the acoustic flux due to the -
mechanism is found in the region near unity optical depth. Key words:
solar chromosphere - acoustic heating - mass loss - -mechanism
---------------------------------------------------------
Title: Acoustic Dissipation and H Radiation in the Solar Chromosphere
I
Authors: Ulmschneider, P.; Kalkofen, W.
1978A&A....69..407U Altcode:
Summary. The radiative energy loss of the solar chromosphere due to H -
transitions in statistical equilibrium is estimated from the empirical
model of Vernazza et al. (1976), and the energy input due to dissipation
of acoustic sawtooth type shock waves is computed for various energy
fluxes and wave periods. The two energy rates show similar dependence
on height for waves with periods near 20 s only. This suggests that
the chromosphere is heated mainly by short period acoustic waves. Key
words: chromosphere - acoustic heating - H - radiation loss
---------------------------------------------------------
Title: Radiative shock dynamics. II. Hydrogen continua.
Authors: Klein, R. I.; Stein, R. F.; Kalkofen, W.
1978ApJ...220.1024K Altcode:
The interaction between radiation and a shock wave propagating
through a stellar atmosphere is investigated. Departures from local
thermodynamic equilibrium (LTE) are permitted in the first two levels
of a 10-level hydrogen atom; levels 3-10 are in LTE. A piston moving
at constant velocity into the bottom of the atmosphere drives a shock
wave. This shock produces precursor radiation that diffuses through
the gas well ahead of the shock and causes a mild luminosity flash
in the emergent Balmer and free-free radiation when it reaches the
surface. The precursor wave deposits a large amount of radiative energy
in the outer layers of the atmosphere, initiating a radiation-induced
pressure wave. The process of energy transfer from the radiation field
to the compression wave is similar to the Eddington valve mechanism
which drives stellar pulsations. Material is accelerated outward by
the radiation-induced wave; eventually it free-falls inward, hits the
quasistationary atmosphere, and forms an accretion shock. The piston
driven shock is weakened by radiative energy losses. When it reaches
the surface, the shock is invisible in the continuum radiation.
---------------------------------------------------------
Title: Theoretical stellar chromospheres of late type
stars. II. Temperature minima.
Authors: Ulmschneider, P.; Schmitz, F.; Renzini, A.; Cacciari, C.;
Kalkofen, W.; Kurucz, R.
1977A&A....61..515U Altcode:
The theory of heating by short period acoustic waves is applied to
predict the height of shock formation and the acoustic flux at the
base of the chromosphere for stars with effective temperatures of
4000 to 6500 K and log g of 2 to 4. These predictions are compared
with heights of temperature minima and with chromospheric radiation
losses computed from semiempirical models.
---------------------------------------------------------
Title: Cooling by Line Radiation Deep in an Atmosphere.
Authors: Kalkofen, W.
1977BAAS....9..635K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Acoustic Waves in the Solar Atmosphere. Ill. A Theoretical Tem-
perature Minimum
Authors: Ulmschneider, P.; Kalkofen, W.
1977A&A....57..199U Altcode:
Summary. In this third of a series ofpapers studying large amplitude
acoustic waves we use the methods developed in previous papers to
compute the propagation of acoustic waves until shock formation. A
perturbation approach is used to let the waves travel on top of
a prescribed atmosphere. From estimates of the fluxes and periods
of acoustic waves generated in the convection zone we predict the
position ofthe temperature minimum and the energy flux transferred to
the chromosphere. The agreement between predictions and observations
gives strong support to the short period acoustic heating theory of the
chromosphere. A scaling law was found for radiatively damped acoustic
waves. This law is used to compute acoustic frequency spectra at the
base of the chromosphere. Key words: acoustic waves shocks radiation
damping temperature minimum chromospheric heating
---------------------------------------------------------
Title: Acoustic waves in the solar atmosphere. II. Radiative damping.
Authors: Kalkofen, W.; Ulmschneider, P.
1977A&A....57..193K Altcode:
A method is described for calculating radiative damping of
large-amplitude acoustic waves propagating in the solar photosphere
and low chromosphere. The basic radiation expressions to be used with
the time-dependent hydrodynamic equations are derived, the equation
of radiative transfer is solved numerically for an atmosphere in
which shock discontinuities may arise, and approximations valid in
different limiting cases are considered. The numerical solution is
tested against an exact solution, and the transfer equation is combined
with the hydrodynamic equations to construct a model atmosphere in
radiative equilibrium. The methods developed are then employed to
determine theoretically the location of the temperature minimum and
to investigate the validity of the short-period acoustic-heating
theory for the solar atmosphere. A perturbation approach is adopted
to compute radiative damping of the acoustic waves, and the time
behavior of acoustic waves with various periods is evaluated. The
results are taken as convincing evidence that short-period acoustic
waves constitute the main chromospheric heating mechanism.
---------------------------------------------------------
Title: The Solar Temperature Minimum.
Authors: Kalkofen, W.
1977BAAS....9..324K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Acoustic waves in the solar atmosphere. I. The hydrodynamic
code.
Authors: Ulmschneider, P.; Kalkofen, W.; Nowak, T.; Bohn, U.
1977A&A....54...61U Altcode:
This paper studies large-amplitude radiatively damped acoustic waves in
the solar atmosphere. A modified method of characteristics is described
for the solution of the time-dependent hydrodynamic equations in a
gravitational atmosphere. A procedure for the detection of shocks is
outlined. Several tests of the accuracy of the method are described. The
evolution of the wave and the height of shock formation are computed
for several values of the period and the initial acoustic flux in
isothermal atmospheres with temperatures of 4000 and 5000 K as well
as in a model solar atmosphere.
---------------------------------------------------------
Title: Radiative shock dynamics. I. The Lyman continuum.
Authors: Klein, R. I.; Stein, R. F.; Kalkofen, W.
1976ApJ...205..499K Altcode:
The paper investigates coupled non-LTE radiative transfer and nonlinear
hydrodynamics by considering a shock propagating outward through an
atmosphere of pure hydrogen in which the hydrogen atoms have one bound
level and a continuum. Self-consistent numerical solutions are obtained
for the nonlinear hydrodynamic equations, the transfer equation for
Lyman continuum radiation, and the time-dependent population equation
for atoms with one bound level plus continuum. Results are discussed
for a piston-driven shock propagating through a static atmosphere
in radiative and statistical equilibrium, with attention given
to the formation of the ionization front, the ionization contour,
and the radiation intensity at the Lyman edge. The structure of the
temperature spike developed by the shock is compared for the three
cases of adiabatic, collisional, and radiating shocks. It is shown
that the escape of recombination radiation narrows the temperature
spike at small optical depth and that low postshock densities in the
upper atmosphere reduce the three-body recombination rate and produce
a large plateau of nearly constant ionization behind the shock.
---------------------------------------------------------
Title: Theoretical temperature minimum for the Sun
Authors: Ulmschneider, P.; Kalkofen, W.
1976pmas.conf..103U Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Line radiation with large differential velocity
Authors: Kalkofen, W.
1976pmas.conf..395K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Theoretical Temperature Minimum
Authors: Kalkofen, W.; Ulmschneider, P.
1975BAAS....7..363K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Analysis of OSO data to determine the structure and energy
balance of the solar chromosphere
Authors: Avrett, E. H.; Kalkofen, W.
1975STIN...7520190A Altcode:
A detailed reexamination of the temperature-density structure of the
photosphere and low chromosphere shows that the middle and upper
chromosphere, which directly emits most of the OSO spectrum, is
sensitive to conditions in this underlying region of the atmosphere. A
model of this region is based on a unified compilation of all recently
published broadband flux and central intensity observations of the
solar spectrum from 500 microns in the far infrared to 1220 A in the
far ultraviolet. This extensive compilation includes the OSO 4 and
6 observations in the wavelength range 1400 to 1220 A. A model is
presented of the quiet solar atmosphere in the height range between
the temperature minimum and the upper part of the chromosphere-corona
transition region. This model is based on statistical equilibrium
calculations of H, He 1, He 2, Si 1, C 1, and other ions.
---------------------------------------------------------
Title: Theoretisches Temperaturminimum der Sonne auf Grund der
Ausbreitung von strahlungsgedämpften akustischen Wellen
Authors: Ulmschneider, P.; Kalkofen, W.
1975MitAG..36..150U Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Complete Linearization of the Integral Equations in Radiative
Transfer
Authors: Kalkofen, Wolfgang
1974ApJ...188..105K Altcode:
The transfer equation is linearized and a procedure presented for
constructing integral operators that give the effect of density
perturbations on the specific intensity, the mean intensity,
the net rate of photoexcitation, and the equations of statistical
equilibrium. An iteration method based on the linearized integral
equation is applied to the solution of the equations of radiative
transfer and of statistical equilibrium for atomic models with two
levels (one line) and three levels (three lines). The method is very
much faster than the usual iteration method, which solves equations
for equivalent two-level atoms, and it converges rapidly even when
begun with extremely poor initial solutions. The features of this
method are compared with those of the complete linearization methods
of Auer and Mihalas and of Skumanich and Domenico. Subject heading:
radiative transfer
---------------------------------------------------------
Title: A comparison of differential and integral equations of
radiative transfer.
Authors: Kalkofen, W.
1974JQSRT..14..309K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Effect of Mechanical Waves on Empirical Solar Models
Authors: Ulmschneider, Peter; Kalkofen, Wolfgang
1973SoPh...28....3U Altcode:
Empirical solar models contain the effect of heating due to radiative
energy loss from acoustic waves. We estimate here the temperature
difference between the radiative equilibrium model and the empirical
model. At optical depth τ<SUB>5000</SUB> = 0.1 this difference
is small, but near the temperature minimum (τ<SUB>5000</SUB> =
10<SUP>−4</SUP>) it reaches between 53 and 83 K. The temperature
difference between the equator and the poles caused by a hypothetical
difference in the heating is estimated.
---------------------------------------------------------
Title: The Harvard-Smithsonian reference atmosphere
Authors: Gingerich, O.; Noyes, R. W.; Kalkofen, W.; Cuny, Y.
1971SoPh...18..347G Altcode:
We present a model of the solar atmosphere in the optical depth
range from τ<SUB>5000</SUB> = 10<SUP>−8</SUP> to 25. It combines
an improved model of the photosphere that incorporates recent EUV
observations with a new model of the quiet lower chromosphere. The
latter is based on OSO 4 observations of the Lyman continuum, on
infrared observations, and on eclipse electron densities.
---------------------------------------------------------
Title: Line formation in pulsating stars.
Authors: Kalkofen, W.; Whitney, C. A.
1971JQSRT..11..531K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Solar Lyman Continuum and the Structure of the Solar
Chromosphere
Authors: Noyes, Robert W.; Kalkofen, Wolfgang
1970SoPh...15..120N Altcode:
Data on the spectrum and center-to-limb variation of the solar Lyman
continuum have been analyzed. They show: (a) The brightness temperature
of the Lyman continuum is about 6500 K, but the kinetic temperature,
as deduced from the slope of the continuum, lies between 8000 and
9000 K. The difference between the kinetic temperature and the
brightness temperature requires that the source function be smaller
than the Planck function by a factor of several hundred. (b) The
Lyman continuum exhibits slight limb darkening longward of 825 Å,
and slight limb brightening shortward of 750 Å. The crossover point
varies from equator to pole and with solar activity. (c) The slope d ln
I(λ)/dλ of the Lyman continuum decreases toward the limb, implying
that the kinetic temperature increases outward in the region of Lyman
continuum formation.
---------------------------------------------------------
Title: Line Formation in Moving Atmospheres
Authors: Kalkofen, W.
1970sfss.coll..120K Altcode: 1970IAUCo...2..120K
No abstract at ADS
---------------------------------------------------------
Title: Observations and Interpretation of the Solar Lyman Continuum
Authors: Noyes, Robert W.; Kalkofen, Wolfgang
1969BAAS....1R.288N Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Dependence of Deviations from LTE on Surface Gravity and
Effective Temperature
Authors: Kalkofen, W.
1969tons.conf..225K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Balmer Lines in Early-Type Stars
Authors: Peterson, D. M.; Kalkofen, W.
1968rla..conf..431P Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Simultaneous Solution of Strongly Coupled Transfer
Equations
Authors: Kalkofen, W.
1968rla..conf....1K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Mapping Methods in Radiative Transfer
Authors: Kalkofen, W.
1968rla..conf...65K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Deviations from LTE in Stellar Photospheres
Authors: Kalkofen, W.
1968ApJ...151..317K Altcode:
The equations of statistical equilibrium are considered for the case
of detailed balancing in the strong lines, an assumption that is valid
in the photosphere. The equations are specialized to low particle
density and applied to stars in the spectral class range from B to
K. The direction in which the populations in the bound state of H and in
atomic hydrogen deviate from their LTE values is predicted essentially
from the temperature increase into the star and the concomitant change,
with depth, in the spectral dis- tribution of the continuous flux. It
is found that the H state is overpopulated; the lower hydrogen levels
are underpopulated, and the higher levels overpopulated relative to the
LTE values. The effects of the departures on the emergent continuous
spectrum are such that, for given effective temperature, giants tend
to be classified earlier than dwarfs, if the continuous flux of LTE
models is used; also, in A and F stars the surface gravity that is
determined from the color tends to be overestimated. The influence of
line blanketing and convection on the departures from LTE is briefly
discussed
---------------------------------------------------------
Title: An Observational Test for Departures from LTE in the Spectral
Range b5 to A0
Authors: Strom, S. E.; Kalkofen, W.
1967ApJ...149..191S Altcode:
The ratio of observed Paschen to Balmer discontinuities is found to be
a sensitive indicator, independent of stellar rotation, of departures
from LTE in the spectral range B5 to A0. The ratio computed from model
atmospheres that are not based on the assumption of LTE agrees better
with existing photographic observations than does the ratio computed
from LTE models. A program of the photoelectric observations necessary
to verify this conclusion is suggested.
---------------------------------------------------------
Title: The Effect of Departures from LTE on the Stellar Continuum
Fluxes in the Spectral-Type Range B5-A0
Authors: Strom, S. E.; Kalkofen, W.
1966ApJ...144...76S Altcode:
The details are presented for a set of model stellar atmospheres in
which departures from LTE in levels 2 and 3 for neutral hydrogen have
been considered. These models cover the temperature range 9000 <
T < 15000 K for log g = 40 and include, in addition to neutral
hydrogen, opacity arising from He I, He ii, Si I, Mg I, H-, H3+, and
electron and Rayleigh scattering. Opacity from these sources, which
are relatively insignificant in this temperature range, is calculated
from LTE considerations. In all cases, the non-LTE atmospheres reported
here predict a Balmer discontinuity which is smaller than that of an
LTE atmosphere of corresponding T,ff. This effect is caused by the
underpopulation of level 2. As a consequence of the smaller Balmer
discontinuity, the stellar effective temperatures in the range B5
V to A0 V must be lowered by between 500 (at A0 V) to 2000 (at B5 V)
with respect to the presently adopted values. The change in the adopted
scale is shown to affect significantly the chemical abundances deduced
from model atmospheres for the stars Vega and Sirius.
---------------------------------------------------------
Title: Deviations from LTE in stellar atmospheres
Authors: Kalkofen, W.
1966JQSRT...6..633K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Deviations from LTE and their effect on stellar spectra in
the range B5 to F0
Authors: Strom, S. E.; Kalkofen, W.
1966AJ.....71T.873S Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The effects of deviations from LTE and line blanketing on
stellar atmospheres in the range B5 to A5
Authors: Kalkofen, W.
1966JQSRT...6..653K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solution of the Line and Continuum Transfer Problem for a
Three-Level Atom
Authors: Kalkofen, W.; Avrett, E. H.
1965SAOSR.174..249K Altcode:
No abstract at ADS
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Title: Radiative Transfer in Lines for Media in Statistical
Equilibrium
Authors: Kalkofen, W.
1965SAOSR.174..187K Altcode:
No abstract at ADS
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Title: The Effect of Departures from LTE on Stellar Continuum Fluxes
in the Spectral-Type B5-A0.
Authors: Strom, S. E.; Kalkofen, W.
1965AJ.....70S.693S Altcode:
A grid of stellar models has been calculated for the effective
temperature range 90000< T6ff< 15 0000 K. In computing this grid
we took into account departures from the LTE population of levels 2
and 3 for hydrogen by assuming detailed balancing for the hydrogen
lines and considering no departures for levels higher than n=3. The
equations of statistical equilibrium and radiative transfer were solved
simultaneously to yield departure coefficients for each level at each
optical depth. The departure coefficients converge to consistent values
after 10 iterations. In all cases, level 2 is underpopulated whereas
level 3 is overpopulated. The other sources of opacity included in
these models, H-, H2+, He I, He II, electron and Rayleigh scattering
were calculated under the assumption of no departures from LTE. We
present as evidence to support our assumption of detailed balancing the
monochromatic optical depth at the line centers of the lower Balmer and
Lyman lines as a function of Rosseland optical depth, TR. In all cases,
monochromatic depth 50 is reached at TR< 5 x 10-~. We conclude that
our assumptions are realistic in the region where the continuum and
moderately strong lines are formed. The departures from LTE cause the
stellar effective temperature scale to be lowered by as much as 20000K
at B6V to as little as 5000K at A0V. The choice of model dictated by
the non-LTE atmospheres also significantly affects the calculation of
stellar abundances as shown by an analysis of Vega and Sirius.
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Title: Departures from LTE Implied by Bound-Free and Free-Free
Transitions
Authors: Kalkofen, W.
1964SAOSR.167..176K Altcode:
No abstract at ADS
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Title: Departures from LTE in a Model Atmosphere.
Authors: Kalkofen, W.; Avrett, E. H.
1964AJ.....69Q.546K Altcode:
The assumption of LTE is investigated in a model atmosphere composed
of atomic hydrogen, with an effective temperature of 10 0000K and
a surface gravity of g=104. Model atmospheres are constructed (a)
under the assumption of local thermodynamic equilibrium and (b) with
departures from LTE permitted in the populations of the two lowest
bound levels. We illustrate the influence of Lyman-a radiation on the
populations of these two levels and, hence, on the continuous flux. The
following models are compared: (1) LTE, no lines; (2) Non-LTE in the
two lowest levels, no lines; (3) LTE, with Lyman-a line; (4) Non-LTE
in the two lowest levels, with Lyman-a line. The models (1), (2), and
(4) have approximately the same boundary temperature, whereas the LTE
model (3) with the Lyman-a line has a very low boundary temperature. The
two LTE models (1) and (3) have the same emergent continuous flux. The
flux of the two non-LTE models is depressed in the Lyman con- tinuum
relative to the LTE models by a factor of approximately 4, and the
ratio of the monochromatic emergent fluxes on the red and blue sides
of the Balmer absorption edge is reduced by approximately 15%. Thus
on the basis of the LTE model, the effective temperature of a star
would tend to be overestimated. The two non-LTE models (2) and (4)
differ in the pop~lation of the ground state which in case (2) is in
LTE at TiOOO 10-6; in case (4), where the Lyman-a line is included,
the ground state is underpopulated by approximately 10% r5000 = 0.1.
