A comparison of mean number of scatterings and escape probabilities has been made in isotropic scattering and dipole scattering by using the angle-averaged partial frequency redistribution functionR_I. We have solved the equations of radiative transfer and statistical equilibrium simultaneously in a spherically symmetric expanding atmosphere. Two cases of atmospheric extension (i.e.)B/A=3 and 10 (whereB andA are the outer and inner radii of the atmosphere) have been treated.

We find that the partial frequency redistribution gives a larger mean number of scatterings compared to that given by complete redistribution. Velocities tend to reduce the mean number of scatterings and in crease the mean escape probabilities.

The partial frequency redistribution function for zero natural line width with dipole scattering (R_I) has been considered in obtaining the simultaneous solution of the statistical equilibrium and line transfer equations in the comoving frame of the expanding gas. We have considered a non-LTE two level atom in an expanding spherical medium whose outer radii are 3, 10 and 20 times the stellar radius with a total optical depthT ≃ 2 × 10³. In all the cases, we have calculated the population ratio of the two levels N₂/N₁ and compared these results with those obtained by using different expansion velocities and geometrical extensions. Initially, the upper level population (N₂) is set equal to zero. The converged simultaneous solution shows that the upper level population is enhanced considerably from the initial value. Variation in velocity gradients seem to have little effect on the ratio N₂/N₁ when the geometrical thickness of the medium is 3 or 10 times the stellar radius. However, when the thickness is increased to 20 times the central radius, the velocity gradients change the ratio N₂/N₁ considerably in the region where log T ≤ 2. The effect of variation of geometrical thickness is to reduce the N₂/N₁ ratio atτ = 0.

The effects of partial frequency redistribution on the formation of spectral lines have been studied. We considered the angle-averaged R_II, R_III andR_v types of redistribution with isotropic phase function, Transfer equation with plane-parallel geometry is solved in isothermal atmospheres. For an atmosphere with constant thermal sources, the frequency-dependent source function S_L (R_v) lies below S_L (R_III) but above S_L(R_III) in the line wings.

Analysis of spectropolarimetric observations of two circular sunspots located close to disk centre in H$\alpha$ (6562.8 Å) and Fe i (6569.22 Å) is presented in this paper. The corresponding active region numbers areNOAA 10940 and NOAA 10941 referred to as AR1 and AR2, respectively. The vector magnetic field at the photosphere is derived through inversion of Stokes profiles of Fe I under Milne–Eddington atmospheric model. The chromospheric vector magnetic field is derived from H$\alpha$ Stokes profiles under weak-field approximation. Azimuthally averaged magnetic field as a function of radial distance from the centre of sunspot at the photosphere and chromosphere are studied. At the photosphere, the radial variation shows a well known behaviour that the total field and the line-of-sight (LOS) component monotonically decrease from centre to the edge of the sunspot and the transverse component initially increases, reaches a maximum close to half the sunspot radius and thendecreases. LOS and the transverse components become equal close to half the sunspot radius consistent with the earlier findings. At the chromosphere, all the components of the magnetic field decrease with the sunspot radius. However, the LOS component decreases monotonically whereas the transverse component decreases monotonically up to about 0.6 times the sunspot radius after which it reaches a constant value. Azimuthally averaged magnetic field gradient from photosphere to chromosphere is also presented here.