Non-isotropic redistribution effects on spectral line formation

The combined effects of frequency and angular redistribution are examined in slab and semi-infinite static isothermal atmospheres for the cases of pure Doppler damping and Doppler with natural damping using both the dipole and isotropic phase function. The main effect of angle-dependent redistribution is that photons which scatter more coherently in direction are re-emitted more coherently in frequency and this effect is enhanced by the dipole phase function. For the slab atmosphere it was generally found that the source functions, and hence the emergent intensities, for the angle-dependent redistribution were greater in the line core and smaller in the line wings than those obtained for angle-averaged or complete redistribution. For the semi-infinite atmosphere the behaviour of the results was the same as in the slab atmosphere except that in the line core the reverse was true for the emergent intensities and for the source functions at small optical depths.     

A simple quadrature method for the evaluation of the redistribution functions RIII,IV(x′, n′; x, n)

A simple and last method for computing the frequency and angle-dependent redistribution functions $\text{R}{}_{\mathrm{III}}\text{(x′,}\text{n}\text{′x,}\text{n}\text{)}$ and $\text{R}{}_{\mathrm{IV}}\text{(x′;x}\text{n}\text{)}$ is given along with graphs of these functions for various values of the relevant parameters which control their behaviour. These redistribution functions describe photon redistribution when there are deviations from strict frequency coherency in the atom's frame. The redistribution function $\text{R}{}_{\mathrm{III}}\text{(x′,}\text{n}\text{′;x,}\text{n}\text{)}$ assumes collisional broadening of the upper transition states resulting in complete redistribution in the atom's frame, while $\text{R}{}_{\mathrm{IV}}\text{(x′,}\text{n}\text{′;x,}\text{n}\text{)}$ assumes both transition states to be radiation broadened only and thus describes resonance scattering resulting in partial frequency coherency in the atom's frame. A comparison between these angle-dependent redistribution functions and their angle-averaged counterparts is also given.     

Photon escape in model planetary nebulae

The effects of optical thickness, velocity gradients and photon redistribution in frequency and direction, as described by the redistribution function R_II, on emission line profiles from simple slab geometry atmospheres are examined. It is found that the optical thickness and differential expansion are the dominant factors affecting photon escape and hence the characteristics and magnitude of the line emission. The importance of frequency and angular photon redistribution as photon escape mechanisms are found to increase with increasing optical thickness and differential expansion.     

Redistribution effects on line formation in moving stellar atmospheres—II. The non-isotropic redistribution functions RI,II,III(x′,n′; x,n)

The effects of photon frequency and angular redistribution arising from pure Doppler (R_I), Doppler with natural line broadening R_II and from the combined Doppler, natural and collisional line broadening (R_III) are examined for line formation in plane-parallel semi-infinite and slab differentially expanding atmospheres. Line source functions and their corresponding emergent line intensities are obtained using the full angle-dependent redistribution functions. The results are compared with those obtained assuming complete redistribution and also with those using two types of angle-averaged redistribution functions; those angle-averaged in the observer's rest frame and those angle-averaged in the fluid frame. It is found that the redistribution functions angle-averaged in the observer's rest frame can produce spurious effects on line formation in moving media, as pointed out by Magnan.¹ On the other hand, emergent line intensities obtained using the redistribution functions angle-averaged in the fluid frame are found to differ by little from those obtained using the full angle-dependent redistribution functions, for the velocity fields considered here.