Boltzmann equations for astrophysical Stochastic Gravitational Wave Backgrounds scattering off of massive objects

Abstract

We present a set of coupled Boltzmann equations describing the intensity and polarisation Stokes parameters of the SGWB, including collision terms which account for gravitational Compton scattering off of massive objects. This set resembles that for the CMB Stokes parameters, but the different spin nature of the gravitational radiation and the physics involved in the scattering process determine crucial differences. In the case of gravitational Compton scattering, due to the Rutherford angular dependence of the cross section, all the SGWB intensity multipoles of order are scattered out, therefore producing outgoing intensity anisotropies of any order if they are present in the incoming radiation. SGWB linear polarisation modes can be generated from unpolarised anisotropic radiation only with m = ±4, which requires at least a hexadecapole anisotropy ( ≥ 4) in the incoming intensity. We confirm the contribution of the gravitational Compton scattering to the SGWB anisoptropies is extremely small for collisions with massive compact objects (BH and SMBH) in the frequency range of current and upcoming surveys. However, we stress that the system of coupled Boltzmann equations presented here provides an accurate estimate of the total amount of anisotropies generated by multiple SGWB scattering processes off of massive objects, as well as the interplay between polarisation and intensity, during the GW propagation across the LSS of the universe. These results will be useful for the full treatment of the astrophysical SWGB anisotropies in view of upcoming gravitational waves observatories.

Probing parity-odd bispectra with anisotropies of GW V modes

“…refs. [137][138][139][140][141][142][143][144][145][146][147][148][149][150][151]. Of specific interest is the recent code [152] that compute anisotropies of the AGWB.…”