A neutron star of mass and radius accretes steadily at through a 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

A neutron star of mass M=1.6 M⊙M = 1.6\,M_\odot and radius R∗=11 kmR_* = 11\,\mathrm{km} accretes steadily at M˙=2.0×10−9 M⊙ yr−1\dot M = 2.0\times10^{-9}\,M_\odot\,\mathrm{yr^{-1}} through a thin disc. Take the characteristic inner-disc temperature to be T∗=[3GMM˙8πσR∗3]1/4.T_* = \left[\frac{3GM\dot M}{8\pi\sigma R_*^3}\right]^{1/4}. ((a)) Find T∗T_* and kBT∗k_BT_* in keV, and state the waveband in which the disc shines. ((b)) Find the accretion efficiency η=GM/R∗c2\eta = GM/R_*c^2, the Eddington luminosity LEddL_{\rm Edd} (assume fully ionised hydrogen, so the electron scattering opacity is κes=σT/mp\kappa_{\rm es}=\sigma_T/m_p), and the corresponding Eddington accretion rate M˙Edd=LEdd/ηc2\dot M_{\rm Edd} = L_{\rm Edd}/\eta c^2, and say what fraction of M˙Edd\dot M_{\rm Edd} the star is actually accreting.

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