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The standard thin-disk dissipation flux, summed over both faces, follows by substituting the Keplerian accretion disk profile into the viscous heating rate:The Stefan–Boltzmann law gives $\mathcal{C}=2\sigma T^4$ because there are two emitting faces. Local radiative equilibrium consequently gives the effective-temperature profile of a zero-torque diskHere $\sigma$ is the Stefan-Boltzmann constant. The scale $T_{\mathrm{in}}$ is not the temperature exactly at the inner boundary: the zero-torque inner boundary condition makes that formal temperature zero. Maximizing $T^4$ shows that the maximum effective temperature of a zero-torque disk occurs at $r=49r_{\ast }/36$, with $T_{\max }\simeq 0.488T_{\mathrm{in}}$.

At equal central mass and accretion rate, characteristic effective temperatures scale as $r_{\ast }^{-3/4}$. Thus, comparing corresponding values of $r/r_{\ast }$,The neutron-star disk is about 180 times hotter. The Planck law and Wien displacement law move its characteristic emission to about 180 times higher frequency, or 180 times shorter wavelength. A white dwarf disk commonly emits in optical and ultraviolet bands, while the hotter neutron star disk can emit in X-rays. Absolute bands require an actual accretion rate; the relative shift follows directly from the stated scaling.

The four equations describe, respectively, vertical hydrostatic equilibrium in the central object's gravity, the vertical divergence of radiative flux balancing viscous dissipation, optically thick radiative diffusion, and the equation of state combining ideal gas gas pressure with radiation pressure. Here $\mu$ is dynamic viscosity, not the mean molecular weight ${\mu }_m$; $\kappa$ is the opacity, $\sigma$ the Stefan-Boltzmann constant, and $\Omega$ the local orbital frequency.

In the radiation-pressure limit, $p=4\sigma T^4/(3c)$, so radiative diffusion givesCompare this with vertical hydrostatic equilibrium. Wherever $\rho \ne 0$,At fixed radius, constant opacity makes $dF/dz=c{\Omega }^2/\kappa$. The viscous dissipation equation therefore yieldsindependent of height within the optically thick radiation-supported layer. The result assumes the supplied gravity, heating and diffusion equations; optically thin surface corrections are outside that approximation.

The Stefan-Boltzmann constant $\sigma$ is the proportionality constant in the blackbody flux $F=\sigma T^4$. The blackbody radiation pressure is $p_{\mathrm{rad}}=4\sigma T^4/(3c)$.