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Atmospheres of cool stars a thesis submitted for the degree of Doctor of Philosophy in the faculty of science, Bangalore University, Bangalore P. Singh [Ph.D Thesis]

By: Contributor(s): Material type: TextTextPublication details: Bangalore Indian Institute of Astrophysics 1995Description: 90pSubject(s): Online resources: Dissertation note: Doctor of Philosophy Indian Institute of Astrophysics, Bangalore 1995 Summary: In this study I use partial frequency redistribution (PRD) functions to examine their effects on spectral line formation in spherically symmetric and expanding atmospheres of cool giant and supergiant stars. Primary aim of this investigation is to bring out the differences between the emergent spectral line profiles resulting from PRD and complete redistribution (CRD) under the influence of various physical parameters characterizing the atmospheres of cool giants and supergiants. The appreciation of this aspect will be important for quantitative analysis of stellar spectra and for computing model atmospheres of such stars. In a scattering process, both the direction and the frequency of a photon may change. These changes are described by partial frequency redistribution functions. There a.re following four categories of redistribution functions: Case I, zero line width, denoted by RI. It does not apply to any real line; demonstrates the effects of Doppler redistribution alone to an observer in the laboratory frame. Case ll, radiation, damping in the upper state and coherence in the atom's rest frame, denoted by RII. It applies to resonance lines in low density media. Case III, complete redistribution in the atom's frame, denoted by R lll. Case IV, subordinate line redistribution between two broadened states, denoted by Rv. It applies to non-coherent subordinate line scattering. Complete redistribution is a limiting approximation which implies that there is a complete reshuffling of atoms in their excited state in such a way that there is no correlation between the frequencies of the incoming and the scattered photons. The assumption of CRD has been widely used in earlier works on line transfer because it not only simplifies the numerical. solution of the transfer equation but also provides a good approximation to reality in those media which are dense enough to support high collision rates. However, in the extended and tenuous atmospheres of cool giants and supergiants where low densities (and hence low collision rates) prevail, CRD is not expected to yield accurate emergent spectral line profiles. Moreover, in the wings of strong resonance lines, the scattering is nearly coherent. This leads to a deviation of the line profiles from those calculated in accordance with the assumption of CRD. Therefore, a natural recourse to the application of partial frequency redistribution can lead to more accurate line profiles. Over the last two decades, considerable progress has been made in using partial frequency redistribution functions to study the spectral line formation in idealized stellar atmospheres. Most of these studies are limited to the assumption of plane-parallel geometry and/or the absence of velocity fields. These assumptions a.re unrealistic because the real atmospheres of cool giants and supergiants expand and are geometrically extended. There are only few papers in literature which have taken into account both the spherical geometry and the expansion effects to study PRD effects on emergent line profiles in idealized atmospheres. These studies employ either RI or R II. R III has usually been represented by CRD. Some studies have been done to model the spectral lines formed in the expanding chromospheres of red giants using R II. So far, the combined effects of sphericity and velocity fields on the differences between the solutions resulting from Rv and the CRD have not been explored. As an important feature of the present work I make a detailed comparative study of the PRD effects of R II, R III and Rv on the spectral line formation in the atmospheres of cool giants and supergiants taking into account both the sphericity and the expansion effects.
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Thesis Supervisor A. Peraiah

Doctor of Philosophy Indian Institute of Astrophysics, Bangalore 1995

In this study I use partial frequency redistribution (PRD) functions to examine their effects on spectral line formation in spherically symmetric and expanding atmospheres of cool giant and supergiant stars. Primary aim of this investigation is to bring out the differences between the emergent spectral line profiles resulting from PRD and complete redistribution (CRD) under the influence of various physical parameters characterizing the atmospheres of cool giants and supergiants. The appreciation of this aspect will be important for quantitative analysis of stellar spectra and for computing model atmospheres of such stars.
In a scattering process, both the direction and the frequency of a photon may change. These changes are described by partial frequency redistribution functions. There a.re following four categories of redistribution functions: Case I, zero line width, denoted by RI. It does not apply to any real line; demonstrates the effects of Doppler redistribution alone to an observer in the laboratory frame. Case ll, radiation, damping in the upper state and coherence in the atom's rest frame, denoted by RII. It applies to resonance lines in low density media. Case III, complete redistribution in the atom's frame, denoted by R lll. Case IV, subordinate line redistribution between two broadened states, denoted by Rv. It applies to non-coherent subordinate line scattering. Complete redistribution is a limiting approximation which implies that there is a complete reshuffling of atoms in their excited state in such a way that there is no correlation between the frequencies of the incoming and the scattered photons.
The assumption of CRD has been widely used in earlier works on line transfer because it not only simplifies the numerical. solution of the transfer equation but also provides a good approximation to reality in those media which are dense enough to support high collision rates. However, in the extended and tenuous atmospheres of cool giants and supergiants where low densities (and hence low collision rates) prevail, CRD is not expected to yield accurate emergent spectral line profiles. Moreover, in the wings of strong resonance lines, the scattering is nearly coherent. This leads to a deviation of the line profiles from those calculated in accordance with the assumption of CRD. Therefore, a natural recourse to the application of partial frequency redistribution can lead to more accurate line profiles.
Over the last two decades, considerable progress has been made in using partial frequency redistribution functions to study the spectral line formation in idealized stellar atmospheres. Most of these studies are limited to the assumption of plane-parallel geometry and/or the absence of velocity fields. These assumptions a.re unrealistic because the real atmospheres of cool giants and supergiants expand and are geometrically extended. There are only few papers in literature which have taken into account both the spherical geometry and the expansion effects to study PRD effects on emergent line profiles in idealized atmospheres. These studies employ either RI or R II. R III has usually been represented by CRD. Some studies have been done to model the spectral lines formed in the expanding chromospheres of red giants using R II. So far, the combined effects of sphericity and velocity fields on the differences between the solutions resulting from Rv and the CRD have not been explored. As an important feature of the present work I make a detailed comparative study of the PRD effects of R II, R III and Rv on the spectral line formation in the atmospheres of cool giants and supergiants taking into account both the sphericity and the expansion effects.

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