In a cataclysmic variable the white dwarf accretor has radius and orbits a donor of…

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Celestial mechanics and planetary systems · Stellar death and compact objects

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

Problem

In a cataclysmic variable the white dwarf accretor has radius

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

and orbits a donor of mass ratio

q = M_2/M_1 = 0.2

(donor over accretor) at separation

a = 4\times10^{8}\,\mathrm{m}

. The distance from the accretor to the inner Lagrangian point

L_1

fits

b_1/a \approx 0.500 - 0.227\log_{10}q

, and the circularisation radius of the stream is

R_{\rm circ} = (b_1^4/a^3)(1+q)

. ((a)) Compute

R_{\rm circ}

. ((b)) State how many times the white dwarf's radius this is, and what it implies about whether the transferred gas can reach the white dwarf directly.

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