The dwarf nova VW Hydri has a white dwarf of mass (Sion et al

PHYSICS · Multi-part · 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

The dwarf nova VW Hydri has a white dwarf of mass M=0.71 M⊙M = 0.71\,M_\odot (Sion et al. 1995) and an orbital period of 106.9 min106.9\,\mathrm{min}. During a normal outburst its accretion disc extends to about R=5.0×107 mR = 5.0\times10^7\,\mathrm{m}, with aspect ratio H/R=0.02H/R = 0.02 typical of an ionised outburst disc, and its light curve declines with an e-folding time tdecline≈2.0 dt_{\rm decline}\approx2.0\,\mathrm{d} (Warner, Cataclysmic Variable Stars, Cambridge University Press, 1995). ((a)) Compute the Keplerian angular frequency ΩK\Omega_K at RR. ((b)) Identifying the observed decline time with the disc's viscous time tν=α−1(R/H)2ΩK−1t_\nu = \alpha^{-1}(R/H)^2\Omega_K^{-1}, estimate the value of the disc viscosity parameter α\alpha for this outburst.

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