P. B. Kunasz

Energy loss by resonance line photons in an absorbing medium

The mean path length of photons undergoing repeated scatterings in media of large optical thickness is calculated from accurate numerical solutions of the transfer equation including the effect of frequency redistribution characteristic of combined Doppler and natural broadening. Energy loss by continuous absorption processes, such as ionization or dust absorption, is discussed, and asymptotic scaling laws for the energy losss, the mean path length, and the mean number of scatterings are inferred from the numerical data.

Solution of the comoving-frame equation of transfer in spherically symmetric flows. IV - Frequency-dependent source functions for scattering by atoms and electrons

A numerical method is presented of solving the radiative transfer equation in the comoving frame of a spherically symmetric expanding atmosphere in which both the line and the electron-scattering source function can depend on frequency (i.e., when there is partial frequency redistribution in the scattering process). This method is used to assess the adequacy of various assumptions regarding frequency redistribution in the comoving frame and to discuss the effects of electron scattering more accurately than previously possible. The methods developed here can be used in realistic model atmospheres to account for the (major) effects of electron scattering upon emergent flux profiles. (AIP)

Solution of the Comoving-Frame Equation of Transfer in Spherically Symmetric Flows. III. Effect of Aberration and Advection Terms

We investigate the importance of the advection and aberration terms, which are of order V/c, in the comoving-frame transfer equation in spherical geometry. Characteristic trajectories are found which reduce the spatial derivatives to a perfect differential, and a generalization of the numerical procedure developed in the earlier papers of this series that permits the integration of the transfer equation on these characteristics is presented. For cases in which V/cvery-much-less-than1, a perturbation solution is developed which reduces the problem to that solved in the first paper in this series. For velocities of the form V (r) approx.r/subn/(n=0,1,2), it is shown that the magnitude of the effects arising from the advection and aberration terms is about 5V/c relative to the solution with these terms omitted. In stellar winds V/capproximately-less-than0.01; hence we conclude that aberration and advection terms may safely be ignored, and that consideration of the Doppler-shift term alone is adequate in the computation of spectra from such expanding atmospheres. (AIP)

Migration of excitation in transfer of spectral-line radiation

A simple mathematical model is developed for the transfer of energy through a gas by the combined effect of radiative transfer and migration of excitation. The “excitation” is carried through the gas by a succession of atoms which experience resonant excitation exchange; it thus appears to random walk through the medium. The theory developed here is valid when the distance traveled by an atom while excited is much larger than the typical distance at which two atoms can exchange excitation (roughly 10-6cm). The model is expressed in terms of a pair of coupled transport equations for the intensity of radiation and the density of excited atoms, which are solved by means of a generalized discrete-ordinate technique. Extensive numerical results are obtained and discussed in terms of characteristics lengths for the various transfer processes. Substantial effects of migration are seen in both the distribution of excited atoms near the cell windows and the line profile of the emergent radiation for typical laboratory conditions.

Resonance-line transfer with partial redistribution. VIII - Solution in the comoving frame for moving atmospheres

An analysis of the effects of partial frequency redistribution in the scattering process for lines formed in moving atmospheres has been performed using a flexible and general method which allows solutions of the transfer equation in the comoving frame of the gas. As a specific example, we consider the same chromospheric and atomic model, with the same velocity field, that was studied by Cannon and Vardavas. We find that the large changes in the profiles obtained by those authors, between the cases of complete and partial redistribution are spurious effects of angle averaging in the observers frame instead of the comoving frame. Our results support fully the conclusion by Magnan that these changes are, in fact, unreal, at least for this particular model and redistribution function. Future work with other redistribution functions and with nonmonotone velocity fields will be possible using the techniques developed in this paper. (AIP)

Solution of the comoving-frame equation of transfer in spherically symmetric flows. II - Picket-fence models

To examine the effect of the radial flow of atmospheric material on the temperature distribution in a stellar atmosphere, a picket-fence model with Gaussian lines is formulated and solved numerically in the comoving frame of the gas, which is assumed to move with a prescribed velocity law. Extensive results have been obtained for both static and dynamical models, with planar and moderately extended spherical geometries. For static models, the effect of lines on the temperature distribution is virtually independent of extension. When a large-scale velocity field is imposed, significant surface heating and additional back-warming are found; the magnitude of these effects increases with the extension of the atmosphere. If a significant flow velocity persists to sufficient depth, the enhanced escape probability can lead to a cooling in the deeper layers, which competes with the back-warming. The results obtained here suggest that the deposition of energy arising from the intrusion of line opacity into the continuum, caused by velocity gradients, could influence the dynamics of the flow. (AIP)