Boltzmann equations for astrophysical stochastic gravitational wave backgrounds scattering off of massive objects. (arXiv:2208.02800v1 [astro-ph.CO])

<a href="http://arxiv.org/find/astro-ph/1/au:+Pizzuti_L/0/1/0/all/0/1">Lorenzo Pizzuti</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Tomella_A/0/1/0/all/0/1">Alessandro Tomella</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Carbone_C/0/1/0/all/0/1">Carmelita Carbone</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Calabrese_M/0/1/0/all/0/1">Matteo Calabrese</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Baccigalupi_C/0/1/0/all/0/1">Carlo Baccigalupi</a>

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,

all the SGWB intensity multipoles $ell$ (with $m=0$ in the case of scalar

metric perturbations alone) are scattered out, therefore producing outgoing

intensity anisotropies of any order $ell$ if they are present in the incoming

radiation. SGWB linear polarisation can be generated from unpolarised

anisotropic radiation only with $m=pm 4$, which requires at least an

hexadecapole anisotropy ($ellge 4$) 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

detectors.

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,

all the SGWB intensity multipoles $ell$ (with $m=0$ in the case of scalar

metric perturbations alone) are scattered out, therefore producing outgoing

intensity anisotropies of any order $ell$ if they are present in the incoming

radiation. SGWB linear polarisation can be generated from unpolarised

anisotropic radiation only with $m=pm 4$, which requires at least an

hexadecapole anisotropy ($ellge 4$) 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

detectors.

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