The characteristic inner temperature of a steady thin accretion disc (thin-disc…

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Radiation, radiative transfer and stellar atmospheres · Stellar death and compact objects

Stars from the Inside, Ch Accretion power: mass transfer, discs and the weighing of black holes

Problem

The characteristic inner temperature of a steady thin accretion disc (thin-disc model) is approximated by

T_* \approx \left[\dfrac{3GM\dot M}{8\pi\sigma R_*^3}\right]^{1/4},

where

\sigma

is the Stefan-Boltzmann constant. ((a)) A cataclysmic variable has a white dwarf accretor of mass

M = 1.0\,M_\odot

and radius

R_* = 5\times10^{6}\,\mathrm{m}

, fed at

\dot M = 5\times10^{-10}\,M_\odot\,\mathrm{yr^{-1}}

. Compute

T_*

, and using Wien's law

\lambda_{\max}T = 2.898\times10^{-3}\,\mathrm{m\,K}

say in which waveband the inner disc radiates. ((b)) The same mass-transfer rate instead feeds a neutron star of mass

M = 1.6\,M_\odot

and radius

R_* = 1.2\times10^{4}\,\mathrm{m}

. Compute

T_*

and

k_BT_*

in keV, and say in which waveband it radiates.

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