Dimitri Mihalas

On the Solution of the Time-Dependent inertial-Frame Equation of radiative Transfer in Moving Media to O(vc)☆

Abstract A stable and efficient mixed-frame method has been formulated for the solution of the time-dependent equation of radiative transfer with full retention of all velocity dependent terms to O ( v c ) . The method retains the simplicity of the differential operator found in the inertial frame while transforming the absorption and emission coefficients to the comoving frame keeping them isotropic. The method is ideally suited to continuum calculations. To correctly treat the time dependence of the radiation field over fluid-flow time increments, the velocity-dependent terms on the right-hand side of both the transfer and moment equations must be retained for consistency. Both explicit and two- and three-level implicit schemes have been explored for a variety of time-dependent problems and it has been concluded that an implicit-backward Euler scheme works best for propagating a radiation front, but that these schemes are essentially first-order accurate in the space derivative. A second order scheme was formulated with the method of lines which should provide higher spatial accuracy. The formulation naturally couples to hydrodynamics in both the Eulerian and Lagrangian formulations for application to astrophysical flows. It is shown that for uniform flow between the fixed and comoving frames, the solution of the Lorentz transformation of the integrated moments provides a powerful check on the formulation and solution.

Adaptive-mesh radiation hydrodynamics—I. The radiation transport equation in a completely adaptive coordinate system

Abstract We formulate the radiation transport equation in a completely adaptive coordinate system, which we define as a system in which the mesh in spacetime, angles and frequency adapts automatically to the dynamical evolution of the radiation field and fluid flow.

Adaptive-mesh radiation hydrodynamics—II. The radiation and fluid equations in relativistic flows

Abstract We derive the radiation and fluid equations for relativistic flows in conservative from in a completely adaptive coordinate system.

The computation of radiation transport using Feautrier variables. II. Spectrum line formation in moving media

Abstract This paper contains a review of methods for solving line transport problems in moving media in terms of the symmetric/antisymmetric radiation-field averages introduced by P. Feautrier. These techniques have proven to be popular and effective in a wide range of astrophysical applications, and may be useful in other areas of computational physics. We outline the physical motivation, formulation, and algorithms for both observer-frame and comoving-frame methods, each of which has distinctive advantages and disadvantages. We cite basic references to provide easy access to the astrophysical literature for workers in other fields.

The H− equilibrium using coupled rate equations for H−, H, H+, H2, and H2+

We formulate rate equations for the reaction network coupling H, H−, H+, H2, and H2+. We attempt to systematize the notation, and to write the equations in a form suitable for modern computational methods of handling the coupled rate equations and radiative transfer equations, for both dynamical and static atmospheres. We have accounted for more processes than are generally considered in most current work; some of these may have an impact on the equilibrium of H− (hence its opacity) and on charge conservation (hence the proton density) in the atmospheres of solar-type stars.

An archetype hydrogen atmosphere problem

AbstractPopulations for the first three bound states and the continuum of hydrogen are determined for an isothermal, hydrostatic atmosphere at 20 000 K. The atmosphere is treated as being optically thin in the Balmer and Paschen continua and illuminated by continuum radiation at these wavelengths with prescribed radiation temperatures. The atmosphere is optically thick in the 2-1, 3-1, 3-2 and c-1 transitions. Three stages of approximation are treated:(1)radiative detailed balance in the 2-1, 3-1 and 3-2 transitions,(2)radiative detailed balance in the 3-1 and 3-2 transitions, and(3)all transitions out of detailed balance. The solution of this problem is non-trivial, and presents sufficient difficulty to have caused failure of at least one rather standard technique. The problem is thus a good archetype against which new methods, or new implementations of old methods may be tested.

Calculation of the solar chromospheric Lα profile allowing for partial redistribution effects

Recent work by Vernazza (1972) and by Vernazza et al (1973) showed that the assumption of complete redistribution of the emitted photons over the entire line profile fails badly to match observation. With complete redistribution, the predicted line wing is too bright by a factor of 5 or 6. Methods for treating the partial redistribution problem have now been developed (Milkey and Mihalas, 1973), and are applied to a schematic L alpha calculation to assess whether the effects of partial redistribution explains the discrepancy. (WDM)