= Thermal Sunyaev-Zeldovich effect
{title2=$\Delta T/T=y[x\coth(x/2)-4]$}
For a <Planck photon distribution>, the hot-electron <Kompaneets equation> gives $\Delta n=yx e^x(e^x-1)^{-2}[x\coth(x/2)-4]$, where $x=h\nu/(k_BT_\gamma)$. The equivalent thermodynamic <temperature> perturbation has the displayed form, while the <Rayleigh-Jeans law> gives $\Delta T/T=-2y$. The distortion changes sign at $x\simeq3.830$. This first-order expression assumes a small <Compton y parameter> and nonrelativistic thermal <Electrons>.
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