Relativistic corrections to the multiple scattering effect on the Sunyaev–Zel'dovich effect in the isotropic approximation

We extend the formalism for the calculation of the relativistic corrections to the Sunyaev–Zel'dovich effect for clusters of galaxies and include the multiple scattering effects in the isotropic approximation. We present the results of the calculations by the Fokker–Planck expansion method as well as by the direct numerical integration of the collision term of the Boltzmann equation. The multiple scattering contribution is found to be very small compared with the single scattering contribution. For high-temperature galaxy clusters of     the ratio of both the contributions is −0.2 per cent in the Wien region. In the Rayleigh–Jeans region the ratio is −0.03 per cent. Therefore the multiple scattering contribution is safely neglected for the observed galaxy clusters.     

Weakening of the solar extreme-ultraviolet line emission by lyman continuum absorption as derived from line ratios

The intensity ratios of Niii, Oiii, Oiv, and Ov lines observed by the HCO experiment on Skylab are compared with the results of recent multilevel calculations. It is found that solar transition-region spectra require Lyman continuum absorption. The equivalent optical thickness of the absorbers causing the weakening is found to be 1.6–1.7 for a quiet area, 1.4–1.9 for a coronal hole, and 2.4–2.5 for active regions. These values are consistent with previous estimates from different methods.