Author name code: kalkofen
ADS astronomy entries on 2022-09-14
author:"Kalkofen, Wolfgang" 
------------------------------------------------------------------------  

Title: The Validity of Dynamical Models of the Solar Atmosphere
Authors: Kalkofen, Wolfgang
Bibcode: 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.

Title: Acoustic waves in a stratified
    atmosphere. IV. Three-dimensional nonlinear hydrodynamics
Authors: Kalkofen, W.; Rossi, P.; Bodo, G.; Massaglia, S.
Bibcode: 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.

Title: Numerical Radiative Transfer
Authors: Kalkofen, Wolfgang
Bibcode: 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.

Title: Line Formation in a Time-Dependent Atmospehre
Authors: Kalkofen, W.
Bibcode: 2009nrt..book..111K
Altcode:
  No abstract at ADS

Title: Operator Perturbation for Differential Equations
Authors: Kalkofen, W.
Bibcode: 2009nrt..book..191K
Altcode:
  No abstract at ADS

Title: Survey of Operator Perturbation Methods
Authors: Kalkofen, W.
Bibcode: 2009nrt..book...23K
Altcode:
  No abstract at ADS

Title: Multidimensional Radiation Hydrodynamics
Authors: Kalkofen, Wolfgang
Bibcode: 2009nmmr.conf..247K
Altcode:
  No abstract at ADS

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.
Bibcode: 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.

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.
Bibcode: 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.

Title: Heating and dynamics of the quiet solar chromosphere
Authors: Kalkofen, Wolfgang
Bibcode: 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.

Title: Wave heating of the solar chromosphere
Authors: Kalkofen, Wolfgang
Bibcode: 2008JApA...29..163K
Altcode:
  No abstract at ADS

Title: Is the Solar Chromosphere Heated by Acoustic Waves?
Authors: Kalkofen, Wolfgang
Bibcode: 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.

Title: Advances in radiative transfer
Authors: Wehrse, Rainer; Kalkofen, Wolfgang
Bibcode: 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.

Title: Dynamics of the Solar Magnetic Network: Two-dimensional
    MHD Simulations
Authors: Hasan, S. S.; van Ballegooijen, A. A.; Kalkofen, W.;
   Steiner, O.
Bibcode: 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.

Title: On the Validity of Acoustically Heated Chromosphere Models
Authors: Ulmschneider, P.; Rammacher, W.; Musielak, Z. E.; Kalkofen, W.
Bibcode: 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.

Title: Is the Chromosphere Always Hot, or Mostly Cold?
Authors: Kalkofen, Wolfgang
Bibcode: 2005BASI...33..337K
Altcode:
  No abstract at ADS

Title: Dynamics of the Magnetic Network on the Sun
Authors: Hasan, S.; van Ballegoiijen, A.; Kalkofen, W.; Steiner, O.
Bibcode: 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.

Title: The structure of the quiet solar chromosphere
Authors: Kalkofen, W.
Bibcode: 2005ESASP.560..695K
Altcode: 2005csss...13..695K
  No abstract at ADS

Title: Observations of the Solar Chromosphere with SUMER
Authors: Wilhem, K.; Kalkofen, W.
Bibcode: 2004ESASP.547..137W
Altcode: 2004soho...13..137W
  No abstract at ADS

Title: Dynamics and Heating of Chromospheres
Authors: Kalkofen, W.
Bibcode: 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.

Title: Observations of the upper solar chromosphere with SUMER
Authors: Wilhelm, K.; Kalkofen, W.
Bibcode: 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.

Title: The Filling Factor of Solar Internetwork Grains
Authors: Kalkofen, Wolfgang; Hammer, Reiner
Bibcode: 2003ANS...324..101K
Altcode: 2003ANS...324..P07K
  No abstract at ADS

Title: The Violent Solar Chromosphere
Authors: Kalkofen, W.
Bibcode: 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 &lt;0) and violent temperature fluctuations (δ T ∼ 10,000 K);
  modeling based on the emergent spectrum gives a positive gradient
  (∇ <SUB>z</SUB> T&gt;0,\ z&gt;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&gt;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 &lt;0. <P />This paper discusses observational constraints on the
  temperature structure of the quiet solar chromosphere.

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.
Bibcode: 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.

Title: Near-infrared chromospheric observatory
Authors: Labonte, Barry; Rust, David M.; Bernasconi, Pietro N.;
   Georgoulis, Manolis K.; Fox, Nicola J.; Kalkofen, Wolfgang; Lin,
   Haosheng
Bibcode: 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.

Title: Is the Solar Chromosphere Heated by Oscillations?
Authors: Kalkofen, Wolfgang
Bibcode: 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.

Title: The Temperature Structure of the Chromosphere
Authors: Kalkofen, W.
Bibcode: 2003ASPC..286..443K
Altcode: 2003ctmf.conf..443K
  No abstract at ADS

Title: Wave Propagation in the Nonmagnetic Chromosphere
Authors: Kalkofen, W.
Bibcode: 2003ASPC..286..385K
Altcode: 2003ctmf.conf..385K
  No abstract at ADS

Title: The dynamics of the quiet solar chromosphere
Authors: Kalkofen, W.; Hasan, S. S.; Ulmschneider, P.
Bibcode: 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.

Title: 3D wave propagation in the chromosphere
Authors: Kalkofen, W.
Bibcode: 2003AN....324..409K
Altcode:
  No abstract at ADS

Title: Heating of the solar chromosphere
Authors: Ulmschneider, P.; Kalkofen, W.
Bibcode: 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.

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
Bibcode: 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.

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.
Bibcode: 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.

Title: Structure and Dynamics of the Quiet Solar Chromosphere
Authors: Kalkofen, Wolfgang
Bibcode: 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 &amp; 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
Bibcode: 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 &amp; 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 &amp; 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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 &amp; 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.
Bibcode: 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 &gt; 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 &gt; 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 &lt; 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 &gt;
  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.
Bibcode: 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.
Bibcode: 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 &amp; 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
  &amp; 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 &amp; 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.
Bibcode: 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.
Bibcode: 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 &amp; 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 &amp; 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.
Bibcode: 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
Bibcode: 1999CSci...77.1496K
Altcode:
  No abstract at ADS

Title: MHD Waves in Chromospheric Network Bright Points
Authors: Kalkofen, W.
Bibcode: 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.
Bibcode: 1999ApJ...521L.141K
Altcode:
  The successful modeling of the dynamics of H<SUB>2v</SUB> bright
  points in the nonmagnetic chromosphere by Carlsson &amp; 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&lt;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.
Bibcode: 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, &amp; 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.
Bibcode: 1999AAS...194.9308K
Altcode: 1999BAAS...31..989K
  The dynamical model of the nonmagnetic chromosphere of Carlsson
  &amp; 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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
Bibcode: 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 &amp; 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.
Bibcode: 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.
Bibcode: 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 &amp; 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
Bibcode: 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.
Bibcode: 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.
Bibcode: 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 &amp;
  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
Bibcode: 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.
Bibcode: 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
Bibcode: 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.
Bibcode: 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
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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 &lt; 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1991BAAS...23Q1050R
Altcode:
  No abstract at ADS

Title: The heating of the solar chromosphere.
Authors: Kalkofen, Wolfgang
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1990BAAS...22.1198R
Altcode:
  No abstract at ADS

Title: Wave Heating in Magnetic Flux Tubes
Authors: Kalkofen, W.
Bibcode: 1990IAUS..138..185K
Altcode:
  No abstract at ADS

Title: The Heating of the Quiet Solar Chromosphere
Authors: Kalkofen, Wolfgang
Bibcode: 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
Bibcode: 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
Bibcode: 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.
Bibcode: 1989ASIC..263..571K
Altcode: 1989ssg..conf..571K
  No abstract at ADS

Title: Book-Review - Numerical Radiative Transfer
Authors: Kalkofen, W.; Stahlberg, J.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1988sca..conf...56B
Altcode:
  No abstract at ADS

Title: Numerical Radiative Transfer
Authors: Kalkofen, Wolfgang
Bibcode: 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.
Bibcode: 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.
Bibcode: 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
Bibcode: 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.
Bibcode: 1987nrt..book..111K
Altcode:
  No abstract at ADS

Title: Survey of Operator Perturbation Methods
Authors: Kalkofen, W.
Bibcode: 1987nrt..book...23K
Altcode:
  No abstract at ADS

Title: Operator Perturbation for Differential Equations
Authors: Kalkofen, W.
Bibcode: 1987nrt..book..191K
Altcode:
  No abstract at ADS

Title: Numerical radiative transfer
Authors: Kalkofen, Wolfgang
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1985Obs...105...52K
Altcode:
  No abstract at ADS

Title: Book-Review - Methods in Radiative Transfer
Authors: Kalkofen, W.
Bibcode: 1985Sci...227.1332K
Altcode:
  No abstract at ADS

Title: Book-Review - Methods in Radiative Transfer
Authors: Kalkofen, W.
Bibcode: 1985S&T....69R.132K
Altcode:
  No abstract at ADS

Title: Partial versus complete linearization.
Authors: Kalkofen, W.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1982BAAS...14..938K
Altcode:
  No abstract at ADS

Title: Radiative Transfer - Comparison of Finite Difference Equations
Authors: Kalkofen, W.; Wehrse, R.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1976pmas.conf..103U
Altcode:
  No abstract at ADS

Title: Line radiation with large differential velocity
Authors: Kalkofen, W.
Bibcode: 1976pmas.conf..395K
Altcode:
  No abstract at ADS

Title: The Theoretical Temperature Minimum
Authors: Kalkofen, W.; Ulmschneider, P.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1975MitAG..36..150U
Altcode:
  No abstract at ADS

Title: Complete Linearization of the Integral Equations in Radiative
    Transfer
Authors: Kalkofen, Wolfgang
Bibcode: 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.
Bibcode: 1974JQSRT..14..309K
Altcode:
  No abstract at ADS

Title: The Effect of Mechanical Waves on Empirical Solar Models
Authors: Ulmschneider, Peter; Kalkofen, Wolfgang
Bibcode: 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.
Bibcode: 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.
Bibcode: 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
Bibcode: 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.
Bibcode: 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
Bibcode: 1969BAAS....1R.288N
Altcode:
  No abstract at ADS

Title: The Dependence of Deviations from LTE on Surface Gravity and
    Effective Temperature
Authors: Kalkofen, W.
Bibcode: 1969tons.conf..225K
Altcode:
  No abstract at ADS

Title: Balmer Lines in Early-Type Stars
Authors: Peterson, D. M.; Kalkofen, W.
Bibcode: 1968rla..conf..431P
Altcode:
  No abstract at ADS

Title: The Simultaneous Solution of Strongly Coupled Transfer
    Equations
Authors: Kalkofen, W.
Bibcode: 1968rla..conf....1K
Altcode:
  No abstract at ADS

Title: Mapping Methods in Radiative Transfer
Authors: Kalkofen, W.
Bibcode: 1968rla..conf...65K
Altcode:
  No abstract at ADS

Title: Deviations from LTE in Stellar Photospheres
Authors: Kalkofen, W.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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 &lt;
  T &lt; 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 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.
Bibcode: 1965SAOSR.174..249K
Altcode:
  No abstract at ADS

Title: Radiative Transfer in Lines for Media in Statistical
    Equilibrium
Authors: Kalkofen, W.
Bibcode: 1965SAOSR.174..187K
Altcode:
  No abstract at ADS

Title: The Effect of Departures from LTE on Stellar Continuum Fluxes
    in the Spectral-Type B5-A0.
Authors: Strom, S. E.; Kalkofen, W.
Bibcode: 1965AJ.....70S.693S
Altcode:
  A grid of stellar models has been calculated for the effective
  temperature range 90000&lt; T6ff&lt; 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&lt; 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.

Title: Departures from LTE Implied by Bound-Free and Free-Free
    Transitions
Authors: Kalkofen, W.
Bibcode: 1964SAOSR.167..176K
Altcode:
  No abstract at ADS

Title: Departures from LTE in a Model Atmosphere.
Authors: Kalkofen, W.; Avrett, E. H.
Bibcode: 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.

