A model for the penetration of Lyman alpha in the solar chromosphere

Abstract

A multilevel calculation of the hydrogen spectrum by Skumanich and Lites, followed by a two-level representation of each transition, shows that all the solar Lya photons are created in an optically thick layer in the high chromosphere above t 0 ae 10 2 (t 0 denotes the optical depth at line center). Below this depth they conjecture that the Lya line is fed only by multiple scatterings of photons which have penetrated down from the creation region. Here the source function decreases inward, first very slowly and then as the inverse of the line optical depth until it thermalizes to the Planck function at t 0 ä 10 7 . The change in slope occurs at t 0 « 10 5 .We give a simplified model that demonstrates the penetration of Lya into the lower chromosphere below the creation region, i.e., for t 0 > 10 2 . The hydrogen atom is treated as a two-level atom and the lower chromosphere as a .semi-infinite medium free of primary sources but illuminated by an isotropic and frequency independent radiation field at its "boundary," i.e., at t 0 « 10 2 . A second-order escape probability approximation yields a simple analytical expression which accurately reproduces the behavior of the Lya source function for 10 2 < t 0 < 5 x 10 6 provided the destruction probability, e is set close to 10 ~6. This value agrees quite well with that obtained by Skumanich and Lites for the Lya destruction probability in the middle and low chromosphere. We indicate how the simplified model can be used to estimate the behavior of Lya for other situations.

Spectral line polarization with angle-dependent partial frequency redistribution

“…The atmospheric model is the same as in Fig. 6b except for the value of r. When r increases, one can observe a significant decrease in amplitude of the near wing peak, an effect already investigated in Faurobert (1988), and a gradual disappearance of the differences between the angle-averaged and angle-dependent Q/I profiles. For r = 10 −2 (result not shown here), the differences become essentially zero.…”

“…In this approximation, frequency redistribution is independent of the scattering angle and also of the polarization phase matrix. This so-called "hybrid" approximation has been employed in works by Rees & Saliba (1982), McKenna (1985), Faurobert (1987Faurobert ( , 1988, Nagendra (1988Nagendra ( , 1994, Faurobert-Scholl (1991), Nagendra et al (1999), Fluri et al (2003), Sampoorna et al (2008b), Sampoorna & Trujillo Bueno (2010), among others. For the Rayleigh scattering, the use of an angle-averaged PRD function is not unjustified as the quantitative differences between the Q/I profiles calculated with angle-dependent (AD) and angle-averaged (AA) frequency redistribution remain around 15% or less as shown by Faurobert (1987) and Nagendra et al (2002).…”

“…They differ rather strongly from previous methods used for angle-dependent PRD. In Dumont et al (1977), Faurobert (1987Faurobert ( , 1988, Nagendra et al (2002), Sampoorna et al (2008a), the radiation field is described by the two Stokes parameters I and Q and the transfer equations for I and Q are solved by Feautrier-type methods, sometimes associated with a perturbation method, or fully perturbative methods, which is based on the linear polarization created by resonance scattering being a few percent only. In McKenna (1985), the radiation field is also described by I and Q, but the radiative transfer equations are solved by a moment equation method.…”

Hanle effect with angle-dependent partial redistribution

“…For a microturbulent magnetic field, the redistribution matrix can be averaged over the random orientations of the magnetic field and one is left with a resonance scattering problem with a renormalized de-polarization parameter which incorporates the effect of the magnetic field (Stenflo 1994). For resonance scattering, as shown in Faurobert (1987Faurobert ( , 1988, the effects of angular dependence in the frequency redistribution function are quite small. corresponds to circular polarization which is not considered in this paper.…”

Spectral line polarization with angle-dependent partial frequency redistribution

“…Comparisons between Q/I profiles calculated with angledependent and angle-averaged PRD can be found in Faurobert (1987Faurobert ( , 1988 and in Nagendra et al (2002). For strong lines (total optical thickness at line center around 10 4 ) differences shown in Faurobert (1988) for the ratio Q/I appear to be large enough to be measurable, but in Nagendra et al (2002) they are essentially negligible. These two articles use a rather different numerical approach.…”