= Radiative-zero white-dwarf envelope
{title2=$P\propto T^{17/4},\quad\rho\propto T^{13/4}$}
In a negligible-mass <white dwarf> envelope, take enclosed mass and <luminosity> constant, neglect <radiation pressure>, and use an <ideal gas> with the <Kramers' opacity law>. Dividing <hydrostatic pressure support equation> by <radiative diffusion in a star> gives $P\,dP\propto(M/L)T^{15/2}dT$. Neglecting the surface integration constant produces the displayed <pressure> and <mass density> laws. It is a deep-envelope approximation, not a finite-temperature photospheric boundary condition.
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