Boltzmann Equation with Cutoff Rutherford Scattering Cross Section Near Maxwellian

He, Lingbing; Zhou, Yulong

doi:10.1007/s00205-021-01713-9

Cited by 7 publications

(4 citation statements)

References 19 publications

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“…Ref. [69] and references therein). The cutoff scale comes from the observation that wave-like effects are non-negligible only within a region whose size is given by the square root of the Kretschmann scalar, K, associated to the metric generated by the scattering object.…”

Section: Density Matrix and Stokes Parameters For Gravitational Radia...mentioning

confidence: 99%

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

Pizzuti¹,

Alessandro²,

Carbone³

et al. 2022

Preprint

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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.

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Section: Density Matrix and Stokes Parameters For Gravitational Radia...mentioning

confidence: 99%

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

Pizzuti¹,

Alessandro²,

Carbone³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…ref. [70] and references therein). The cutoff scale comes from the observation that wavelike effects are non-negligible only within a region whose size is given by the square root of the Kretschmann scalar, K, associated to the metric generated by the scattering object.…”

Section: Jcap02(2023)054mentioning

confidence: 99%

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

Pizzuti

Alessandro

Carbone

et al. 2023

J. Cosmol. Astropart. Phys.

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The goal of this work is to present a set of coupled Boltzmann equations describing the intensity and polarisation Stokes parameters of the SGWB. Collision terms (as discussed e.g. in ref. [1]) which account for gravitational Compton scattering off of massive objects, are also included. 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 ℓ are scattered out, therefore producing outgoing intensity anisotropies of any order ℓ if they are present in the incoming radiation. On the other hand, as already outlined in [1], SGWB linear polarisation modes can be expanded in a basis of spherical harmonics with m = ±4 and ℓ ≥ 4. This means that SGWB polarisation modes can be generated from unpolarised anisotropic radiation only with m = ±4, therefore requiring at least a hexadecapole anisotropy (ℓ ≥ 4) in the incoming intensity. Assuming a simplified toy model where scattering targets are localised in a small redshift range, we solve analytically the set of coupled Boltzmann equations to get explicit expressions for the intensity and polarisation angular power spectra. 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. The system of coupled Boltzmann equations presented here provides a way to accurate estimate 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.

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“…For the global well-posedness around the global equilibrium, we refer readers to Guo [24] on the cutoff Boltzmann equation and Grassman-Strain [22] and Alexandre-Morimoto-Ukai-Xu-Yang [3,4,5] on noncutoff Boltzmann equation. See also [17,18,16,30,31] and references therein for recent development. One may also check [25,26] in the case of bounded domains.…”

Section: Introductionmentioning

confidence: 99%

Propagation of moments and sharp convergence rate for inhomogeneous non-cutoff Boltzmann equation with soft potentials

Cao¹,

He²,

Ji³

2022

Preprint

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We prove the well-posedness for the non-cutoff Boltzmann equation with soft potentials when the initial datum is close to the global Maxwellian and has only polynomial decay at the large velocities in L 2 space. As a result, we get the propagation of the exponential moments and the sharp rates of the convergence to the global Maxwellian which seems the first results for the original equation with soft potentials. The new ingredients of the proof lie in localized techniques, the semigroup method as well as the propagation of the polynomial and exponential moments in L 2 space. Contents 1. Introduction 1 2. Analysis of the collision operator 8 3. Global well-posedness, propagation of moments and sharp convergence rate 26 4. Appendix: Toolbox and Proof of Theorem 1.2 43 References 70

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Boltzmann Equation with Cutoff Rutherford Scattering Cross Section Near Maxwellian

Cited by 7 publications

References 19 publications

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

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

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

Propagation of moments and sharp convergence rate for inhomogeneous non-cutoff Boltzmann equation with soft potentials

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