Dissecting the Compton scattering kernel I: Isotropic media. (arXiv:1905.00868v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Sarkar_A/0/1/0/all/0/1">Abir Sarkar</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Chluba_J/0/1/0/all/0/1">Jens Chluba</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Lee_E/0/1/0/all/0/1">Elizabeth Lee</a>
Compton scattering between electrons and photons plays a crucial role in
astrophysical plasmas. Many important aspects of this process can be captured
by using the so-called Compton scattering kernel. For isotropic media, exact
analytic expressions (valid at all electron and photon energies) do exist but
are hampered by numerical issues and often are presented in complicated ways.
In this paper, we summarize, simplify and improve existing analytic expressions
for the Compton scattering kernel. We provide a detailed overview of important
properties of the kernel covering a wide range of energies and highlighting
aspects that have not been appreciated much previously. We discuss analytic
expressions for the moments of the kernel, comparing various approximations and
demonstrating their precision. We also illustrate the properties of the
scattering kernel for thermal electrons at various temperatures and photon
energies. The obtained improved formulae for the kernel and its moments should
prove useful in many astrophysical computations, one of them being the
evolution of spectral distortions of the cosmic microwave background in the
early Universe.
Compton scattering between electrons and photons plays a crucial role in
astrophysical plasmas. Many important aspects of this process can be captured
by using the so-called Compton scattering kernel. For isotropic media, exact
analytic expressions (valid at all electron and photon energies) do exist but
are hampered by numerical issues and often are presented in complicated ways.
In this paper, we summarize, simplify and improve existing analytic expressions
for the Compton scattering kernel. We provide a detailed overview of important
properties of the kernel covering a wide range of energies and highlighting
aspects that have not been appreciated much previously. We discuss analytic
expressions for the moments of the kernel, comparing various approximations and
demonstrating their precision. We also illustrate the properties of the
scattering kernel for thermal electrons at various temperatures and photon
energies. The obtained improved formulae for the kernel and its moments should
prove useful in many astrophysical computations, one of them being the
evolution of spectral distortions of the cosmic microwave background in the
early Universe.
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