Comptonization of an isotropic distribution in moving media: higher-order effects

We consider the Comptonization of an isotropic radiation field by a thermal distribution of electrons with non-vanishing bulk velocity. We include all relativistic effects, including induced scattering and electron recoil, in the derivation of a kinetic equation which is correct to O(theta^2, beta theta^2, beta^2 theta), where beta is the bulk velocity (in units of c) and theta is the ratio of the electron temperature to mass. The result given here manifestly conserves photon number, and easily yields the energy transfer rate between the radiation and electrons. We also confirm recent calculations of the relativistic corrections to the thermal and kinematic Sunyaev-Zel'dovich effect.Comment: Minor revisions. To appear in the Astrophysical Journa

Thermal and kinematic corrections to the microwave background polarization induced by galaxy clusters along the line of sight

We derive analytic expressions for the leading-order corrections to the polarization induced in the cosmic microwave background (CMB) due to scattering off hot electrons in galaxy clusters along the line of sight. For a thermal distribution of electrons with a kinetic temperature of 10 keV and a bulk peculiar velocity of 1000 km/s, the dominant corrections to the polarization induced by the primordial CMB quadrupole and the cluster peculiar velocity arise from electron thermal motion and are at the level of 10 per cent in each case, near the peak of the polarization signal. When more sensitive measurements become feasible, these effects will be significant for the determination of transverse peculiar velocities, and the value of the CMB quadrupole at the cluster redshift, via the cluster polarization route.Comment: 7 pages, 2 figures. Version accepted for MNRAS. Minor expansion of text in some section

Geometric Algebra, Gravity and Gravitational Waves

Abstract: We discuss an approach to gravitational waves based on Geometric Algebra and Gauge Theory Gravity. After a brief introduction to Geometric Algebra (GA), we consider Gauge Theory Gravity, which uses symmetries expressed within the GA of flat spacetime to derive gravitational forces as the gauge forces corresponding to making these symmetries local. We then consider solutions for black holes and plane gravitational waves in this approach, noting the simplicity that GA affords in both writing the solutions, and checking some of their properties. We then go on to show that a preferred gauge emerges for gravitational plane waves, in which a ‘memory effect’ corresponding to non-zero velocities left after the passage of the waves becomes clear, and the physical nature of this effect is demonstrated. In a final section we present the mathematical details of the gravitational wave treatment in GA, and link it with other approaches to exact waves in the literature. Even for those not reaching it via Geometric Algebra, we recommend that the general relativity metric-based version of the preferred gauge, the Brinkmann metric, be considered for use more widely by astrophysicists and others for the study of gravitational plane waves. These advantages are shown to extend to a treatment of joint gravitational and electromagnetic plane waves, and in a final subsection, we use the exact solutions found for particle motion in exact impulsive gravitational waves to discuss whether backward in time motion can be induced by strongly non-linear waves