Abstract
We evaluate an adaptive Gaussian quadrature integration scheme suitable for the numerical evaluation of generalized redistribution in frequency functions. The latter are indispensable ingredients for “full non-LTE” radiation transfer computations, assuming potential deviations of the velocity distribution of massive particles from the usual Maxwell–Boltzmann distribution. A first validation is made with computations of the usual Voigt profile.
Highlights
Radiation transfer is, by essence, a difficult problem (e.g., Rutily & Chevallier 2006), as well as a question of very large relevance in astrophysics
Results obtained using our double adaptive Gaussian quadrature scheme (AGQ) quadrature scheme are displayed in Fig. 4, for different values of a ranging from 0.001 to 10−6, that is more likely regimes expected for our computations
That should our procedure be used for Voigt profile computations and radiative modeling, such small and very local discontinuities will not impair further computations of these scattering integrals entering the equations of the statistical equilibrium. This new numerical scheme is efficient for small values of a, typically lower than 0.01, where other schemes may fail. First of all, it is certainly suitable for our applications of such a numerical integration scheme, and for physical conditions leading to very sharp Lorentzian peaks
Summary
By essence, a difficult problem (e.g., Rutily & Chevallier 2006), as well as a question of very large relevance in astrophysics. It relies on complex nonlinear light-matter interactions (see e.g., Hubeny & Mihalas 2014; Rutten 2003). The vast majority of astrophysical problems are solved, still, within the frame of CRD, for which further simplifications are the equality of emission and absorption profiles – the latter usually known a priori – which leads to the independence of the so-called source function vs frequency
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