= Cannibal-sector temperature ratio
{title2=$T_\gamma/T_\phi$}
For a massive real scalar with one internal degree of freedom with $x=m/T_\phi\gg1$, fixed <separately conserved visible and dark entropy> ratio $\xi$, and relativistic visible bath with entropy degrees of freedom $g_{*s}^{\rm SM}$,
$$
\frac{T_\gamma}{T_\phi}\sim\left[\frac{45}{2\pi^2(2\pi)^{3/2}}\right]^{1/3}\left(\frac\xi{g_{*s}^{\rm SM}}\right)^{1/3}x^{5/6}e^{-x/3}.
$$
Indeed, equate $s_{\rm SM}=(2\pi^2/45)g_{*s}^{\rm SM}T_\gamma^3$ to $\xi s_\phi$ and use <nonrelativistic entropy at zero chemical potential>. For $g$ internal states the right side gains $g^{1/3}$. The nonrelativistic species cannot be assigned a constant relativistic entropy count.
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