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 104. 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 H2V and K2V 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.
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.
Methods: We have solved the three-dimensional, nonlinear, time-dependent hydrodynamic equations for impulsively-generated, upward-propagating acoustic waves, assuming cylindrical symmetry.
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.
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.
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 105 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.
Results: 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.
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.

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.

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 H2v and K2v 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.

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 (∇ z T <0) and violent temperature fluctuations (δ T ∼ 10,000 K); modeling based on the emergent spectrum gives a positive gradient (∇ z T>0,\ z>0.5 Mm) and modest fluctuations (δ T ∼ 300 K). Clearly, these two models are incompatible with one another. The model of the dynamics claims that the traditional temperature structure of the chromosphere (∇ z T>0) is an illusion created by time averaging of the emission. But the dissipation and radiative emission associated with the dynamics make only a minor contribution to chromospheric heating and the emergent radiation. In addition, in a typical supergranulation cell, the dynamics is confined to 10 to 20 regions (grains) with a combined filling factor ranging from 1% in the photosphere to 50% in the upper chromosphere. In the middle chromosphere (z=1 Mm), 90% to 95% of the medium falls outside the calcium grains and thus, according to the dynamical model, has no chromosphere, i.e., ∇ z T <0.

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 & 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 & Stein and shows that it predicts deep absorption lines, none of which are observed; intensity fluctuations in the Lyman continuum that are much larger than observed; and time-averaged emission that falls far short of the observed emission. The paper concludes that the solar chromosphere, while time-dependent, is never cold and dark. The same conclusion applies for stellar chromospheres. A complete, time-dependent model of the nonmagnetic chromosphere must describe two phenomena: (1) dynamics, like that modeled by Carlsson & Stein for chromospheric bright points but corrected for the geometrical properties of shocks propagating in an upward-expanding channel, and (2) the energetically more important general, sustained heating of the chromosphere, as described by current time-independent empirical models but modified in the upper photosphere for the formation of molecular absorption lines of CO in a dynamical medium. This model is always hot and, except for absorption features caused by departures from local thermodynamic equilibrium, shows chromospheric lines only in emission. Title: Acoustic waves in a stratified atmosphere. III. Temperature inhomogeneities Authors: Bodo, G.; Kalkofen, W.; Massaglia, S.; Rossi, P. 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 K2v 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 & 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 K2V 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 K2V bright points in the interior of the network and corresponding magnetic elements. We find that about 60% of the K2V bright points spatially coincide with magnetic elements of flux density > 4 Mx cm-2. About 25% of the K2V bright points with equally enhanced emission lie over bipole elements where the fields are > 4 Mx cm-2 for both polarity elements which merge and presumably cancel and result in low fields. The rest, 15%, of the bright points coincide with areas of fields < 4 Mx cm-2 which is the noise level set by us for the magnetic scans. When magnetic elements of opposite polarity merge and form bipoles, the associated K2V bright points show excess emission. Although such excess emission is a magnetic-field-driven phenomenon, the measured value of the field at the site of the bipole is typically low, and these cases would therefore be excluded in the count of coincidences of excess emission with excess magnetic fields. In our opinion, these cases of excess emission at the sites of the bipoles, as well as at the sites of fields > 4 Mx cm-2, 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 K2V 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-1. 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 & Loeser (1981), which is based on the emergent spectrum of emission lines and continua from the chromosphere, points to a particular heating mechanism; the simulations of Carlsson & Stein (1994) of the dynamics of calcium bright points conclusively settle the question of the nature of the waves that power the bright points; and systematic discrepancies between simulated and observed intensities at maximal H 2v enhancement reveal the geometry of wave propagation in a stratified atmosphere. The power spectrum and the energy flux in the Carlsson & Stein simulations faithfully reproduce bright point dynamics, but the spectrum predicted from their dynamical model does not match other observations. Support by NASA is gratefully acknowledged Title: Acoustic Waves in a Three-Dimensional Stratified Atmosphere Authors: Kalkofen, W.; Massaglia, S.; Bodo, G.; Rossi, P. 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 & Kalkofen 1999, ApJ 519, 899) where it was suggested that impulsively generated MHD kink, or transverse, waves can contribute efficiently to chromospheric heating. On the other hand, it was argued that this scenario for heating the magnetic network would produce "strongly intermittent chromospheric emission consisting of brief, intense flashes superimposed on a very low background" (Hasan, Kalkofen & van Ballegooijen 2000, ApJL, in press). In this paper, we analyse in greater detail the consequences based on the above picture by adopting different forms for the footpoint point velocity. We compute the transverse wave energy flux injected into the chromosphere through (a) impulsive and (b) turbulent footpoint motions. Finally, we point out observational implication of our calculations. Title: Acoustic waves in a stratified atmosphere. II. Three-dimensional hydrodynamics Authors: Bodo, G.; Kalkofen, W.; Massaglia, S.; Rossi, P. 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 H2v bright points in the nonmagnetic chromosphere by Carlsson & Stein gave as a by-product a part-time chromosphere lacking the persistent outward temperature increase of time-average empirical models, which is needed to explain observations of UV emission lines and continua. We discuss the failure of the dynamical model to account for most of the observed chromospheric emission, arguing that their model uses only about 1% of the acoustic energy supplied to the medium. Chromospheric heating requires an additional source of energy in the form of acoustic waves of short period (P<2 minutes), which form shocks and produce the persistent outward temperature increase that can account for the UV emission lines and continua. Title: Excitation of Oscillations in Photospheric Flux Tubes through Buffeting by External Granules Authors: Hasan, S. S.; Kalkofen, W. 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, & 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-1 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 & 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 K2upsilon, bright points are propagating acoustic waves. This firm conclusion declares invalid the model of Leibacher & Stein, which explains the observed period with standing acoustic waves in a chromospheric cavity. On the third question, the heating of the chromosphere in the CI, their model predicts that the temperature in the chromosphere is declining in the outward direction up to a height of at least I Mm most of the time, so even the time-average temperature is dropping monotonically in the outward direction, implying that lines formed in the chromosphere up to a height of at least 1 Mm appear in absorption most of the time and everywhere in the CI. The problem of the CI can be resolved with a two-component model, which combines a model for K2upsilon, 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 & 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 & 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, lmax ~ 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 < 1019-1020 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- 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- and CO opacity is much lower than with H- 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- 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 Teff, 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- 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 τ5000 = 0.1 this difference is small, but near the temperature minimum (τ5000 = 10−4) 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 τ5000 = 10−8 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 < T < 15000 K for log g = 40 and include, in addition to neutral hydrogen, opacity arising from He I, He ii, Si I, Mg I, H-, H3+, and electron and Rayleigh scattering. Opacity from these sources, which are relatively insignificant in this temperature range, is calculated from LTE considerations. In all cases, the non-LTE atmospheres reported here predict a Balmer discontinuity which is smaller than that of an LTE atmosphere of corresponding T,ff. This effect is caused by the underpopulation of level 2. As a consequence of the smaller Balmer discontinuity, the stellar effective temperatures in the range B5 V to A0 V must be lowered by between 500 (at A0 V) to 2000 (at B5 V) with respect to the presently adopted values. The change in the adopted scale is shown to affect significantly the chemical abundances deduced from model atmospheres for the stars Vega and Sirius. Title: Deviations from LTE in stellar atmospheres Authors: Kalkofen, W. 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< T6ff< 15 0000 K. In computing this grid we took into account departures from the LTE population of levels 2 and 3 for hydrogen by assuming detailed balancing for the hydrogen lines and considering no departures for levels higher than n=3. The equations of statistical equilibrium and radiative transfer were solved simultaneously to yield departure coefficients for each level at each optical depth. The departure coefficients converge to consistent values after 10 iterations. In all cases, level 2 is underpopulated whereas level 3 is overpopulated. The other sources of opacity included in these models, H-, H2+, He I, He II, electron and Rayleigh scattering were calculated under the assumption of no departures from LTE. We present as evidence to support our assumption of detailed balancing the monochromatic optical depth at the line centers of the lower Balmer and Lyman lines as a function of Rosseland optical depth, TR. In all cases, monochromatic depth 50 is reached at TR< 5 x 10-~. We conclude that our assumptions are realistic in the region where the continuum and moderately strong lines are formed. The departures from LTE cause the stellar effective temperature scale to be lowered by as much as 20000K at B6V to as little as 5000K at A0V. The choice of model dictated by the non-LTE atmospheres also significantly affects the calculation of stellar abundances as shown by an analysis of Vega and Sirius. 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.