Relativistic corrections to the Sunyaev-Zeldovich effect for extremely hot clusters of galaxies

Abstract

We present an accurate numerical table for the relativistic corrections to the thermal Sunyaev-Zeldovich effect for clusters of galaxies. The numerical results for the relativistic corrections have been obtained by numerical integration of the collision term of the Boltzmann equation. The numerical table is provided for the ranges 0.002 ≤, θe, ≤0.100 and 0 ≤ X ≤ 20, where θe, = kBTe/m ec2, X ξ hℏωkBT0, Te is the electron temperature, ω is the angular frequency of the photon and T0 is the temperature of the cosmic microwave background radiation. We also present an accurate analytic fitting formula that reproduces the numerical results with high precision.