Accretion Geometries

Matter overflowing the Roche lobe of the secondary tends to form an accretion disk around the white dwarf. Depending on the magnetic field strength of the white dwarf, the disk extends to its surface (r = R) or is disrupted by the field at ri > R. Accretion can effectively take place only when ri < rco, with rco = (GM/ the corotation radius and Q* the angular velocity of the white dwarf. A disk can form only when ri < rcirc, where rcirc is the circularization radius at which the Ke-plerian specific angular momentum equals that of matter passing through the inner Lagrangian point L1. For ri > rcirc, a ring-like structure forms or the stream couples directly to the magnetosphere [62].

Disruption of the disk occurs when the tangential magnetic stresses overcome the viscous stresses. The resulting inner disk radius may be expressed in terms of the magnetospheric radius rM for spherical accretion by ri = nr^ = n (2GM)-1/1 M-2/1 b0/7r12/7 , where M is the white dwarf mass, M the accretion rate, and B0 the surface field strength of the white dwarf in the orbital plane. From discussions of the disk-field interaction [10,52], one finds n — 0 5 - 1. 5 for ri / rco = 1.0 - 0.3 somewhat larger than the originally suggested and frequently quoted value n — 0 52 [20]. Approximate field strengths separating nonmagnetic CVs and IPs on the one hand or IPs and polars on the other hand are obtained by equating ri to R or to the binary separation a, respectively. Hence, the disk remains unaffected by the field for

while the CV may synchronize as a polars for

where M9 is the accretion rate in units of 10-9 MQ yr-1, P4 is the orbital period in units of 4h, q = Msec/M is the mass ratio, and we have used M = 0.6MQ with

R = 9 x 108 cm. The latter limit appears reasonable since the smallest field strength in a short-period polar is around 7 MG [98]. The former limit suggests that many CVs considered as nonmagnetic may, in fact, harbor white dwarfs with magnetic field strengths too small to be directly detected and to effectively channel the flow far out of the orbital plane. The estimate suggests also that "nonmagnetic" CVs may switch from an IP-like accretion geometry in quiescence to equatorial accretion in the high-M outbursts.

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