= Optical-depth rescaling at fixed temperature
{title2=$\widetilde B(\widetilde\tau)=B(\widetilde\tau/a)$}
Multiplying an absorber abundance by $a$ with fixed cross sections and physical <temperature> profile multiplies <optical depth> by $a$. The <Planck function> as a function of the new coordinate must therefore be composed with division by $a$. A term proportional to $\tau^n$ acquires coefficient $a^{-n}$. Holding its old optical-depth coefficient fixed would instead change the physical temperature profile. This is the immediate radiative comparison before thermal adjustment.
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