The Spin Periods and Magnetic Moments of White Dwarfs in Magnetic Cataclysmic Variables

Abstract

We have used a model of magnetic accretion to investigate the rotational equilibria of magnetic cataclysmic variables (mCVs). The results of our numerical simulations demonstrate that there is a range of parameter space in the Pspin/Porb versus μ1 plane at which rotational equilibrium occurs. This has allowed us to calculate the theoretical histogram describing the distribution of mCVs as a function of Pspin/Porb. We show that this agrees with the observed distribution, assuming that the number of systems as a function of white dwarf magnetic moment is distributed approximately according to N(μ1)dμ1~μ-11dμ1. The rotational equilibria also allow us to infer approximate values for the magnetic moments of all known intermediate polars. We predict that intermediate polars with μ1>~5×1033 G cm3 and Porb>3 hr will evolve into polars, while those with μ1 3 hr will either evolve into low field strength polars that are (presumably) unobservable, and possibly EUV emitters, or, if their fields are buried by high accretion rates, evolve into conventional polars, once their magnetic fields resurface when the mass accretion rate reduces. We speculate that EX Hya-like systems may have low magnetic field strength secondaries and so avoid synchronization. Finally, we note that the equilibria we have investigated correspond to a variety of different types of accretion flow, including disklike accretion at small Pspin/Porb values, streamlike accretion at intermediate Pspin/Porb values, and accretion fed from a ring at the outer edge of the white dwarf Roche lobe at higher Pspin/Porb values.