Compton y parameter ($y=\frac{{\sigma }_T}{m_e{c}^2}\int n_e{k}_B{T}_{e}d\ell$)

The Compton y parameter is the Thomson scattering optical depth weighted by the dimensionless Electron temperature. It measures the integrated electron pressure along a line of sight. When hot, nonrelativistic electrons scatter much colder photons, the first-order radiation energy gain is $4y$ times the incident energy. The spectrum is redistributed while the total photon number density is conserved locally by scattering.