Evolution of low-frequency features in the CMB spectrum due to stimulated Compton scattering and Doppler-broadening

TL;DR

This paper presents a new analytical solution to the Kompaneets equation accounting for stimulated Compton scattering in a near-equilibrium blackbody environment, impacting CMB spectral distortion calculations and radio line observations.

Contribution

It introduces a novel solution to the Kompaneets equation that incorporates stimulated scattering effects, enhancing the modeling of low-frequency photon behavior in cosmic and astrophysical contexts.

Findings

Stimulated scattering slows photon frequency shift by a factor of 3.

New solutions improve understanding of CMB spectral distortions.

Potential applications in analyzing radio lines in extragalactic sources.

Abstract

We discuss a new solution of the Kompaneets-equation for physical situations in which low frequency photons, forming relatively narrow spectral details, are Compton scattered in an isotropic, infinite medium with an intense ambient blackbody field that is very close to full thermodynamic equilibrium with the free electrons. In this situation the background-induced stimulated Compton scattering slows down the motion of photons toward higher frequencies by a factor of 3 in comparison with the solution that only takes into account Doppler-broadening and boosting. This new solution is important for detailed computations of cosmic microwave background spectral distortions arising due to uncompensated atomic transitions of hydrogen and helium in the early Universe. In addition we derive another analytic solution that only includes the background-induced stimulated Compton scattering and is valid for power-law ambient radiation fields. This solution might have interesting applications for radio lines arising inside of bright extra-galactic radio source, where according to our estimates line shifts because of background-induced stimulated scattering could be amplified and even exceed the line broadening due to the Doppler-effect.