SPECTRAL DISTORTIONS OF THE COSMIC MICROWAVE BACKGROUND-RADIATION DUETO INTERACTION WITH THE HOT GAS IN A MOVING CLUSTER - INCLUSION OF RELATIVISTIC EFFECTS

A relativistic treatment of the spectral effects that arise during the passage of the cosmic microwave background (CMB) radiation through in tergalactic gas due to chaotic motion of electrons (thermal effect) an d due to the motion of a galaxy cluster as a: whole (kinematic effect) is given. The Monte Carlo simulations which were performed by two dif ferent methods (i) confirm the existence of the previously proposed re lativistic corrections to the thermal effect of the form (kT(e)/m(e)c( 2))(n), where T-e is the gas temperature, and (ii) provide evidence fo r the presence of additional corrections related to the cluster peculi ar motion; the most important correction is proportional to V-r/c x kT (e)/m(e)c(2), where V-r is the radial component of the cluster velocit y (V). The kinematic effect to an accuracy of (V/c)(4) and the ''cross '' effect (proportional to V-r/c x kT(e)/m(e)c(2)) are derived analyti cally. All of the effects under consideration are small and, therefore , additive. The relativistic effects are shown to cause the submillime ter flux from galaxy clusters to increase appreciably. This may facili tate searches for clusters at large redshifts.