(a) A dwarf-nova disc around a white dwarf of mass has, at radius ,…

PHYSICS · Subjective · Fermi University Physics · Astrophysics & Cosmology · Stellar death and compact objects · Astrophysical fluid dynamics and plasmas

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

Problem

(a) A dwarf-nova disc around a white dwarf of mass

M = 1.0\,M_\odot

has, at radius

R = 5\times10^{7}\,\mathrm{m}

, thickness-to-radius ratio

H/R = 0.02

and viscosity parameter

\alpha = 0.2

(both calibrated). Using

t_\nu = \alpha^{-1}(R/H)^2\Omega_K^{-1}

with

\Omega_K = \sqrt{GM/R^3}

, estimate the viscous time in days. (b) A neutron star of mass

M = 1.4\,M_\odot

and radius

R_* = 1.0\times10^{4}\,\mathrm{m}

, with surface dipole field

B = 2\times10^{8}\,\mathrm{T}

, accretes at

\dot M = 1\times10^{15}\,\mathrm{kg\,s^{-1}}

. Using pressure balance between the dipole field and the free-falling gas,

r_m = \left[\frac{2\pi B^2R_*^6}{\mu_0\dot M\sqrt{2GM}}\right]^{2/7},

compute the magnetospheric radius, and the spin period

P_{\rm eq} = 2\pi\sqrt{r_m^3/GM}

at which the star would corotate with the flow there.

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