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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