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

We have used a model of magnetic accretion to investigate the rotationalequilibria of magnetic cataclysmic variables (mCVs). The results of ournumerical simulations demonstrate that there is a range of parameter space inthe P_spin / P_orb versus mu_1 plane at which rotational equilibrium occurs.This has allowed us to calculate the theoretical histogram describing thedistribution of magnetic CVs as a function of P_spin / P_orb. We show that thisagrees with the observed distribution assuming that the number of systems as afunction of white dwarf magnetic moment is distributed approximately accordingto N(mu_1) d mu_1 proportional to 1/mu_1 d mu_1. The rotational equilibria alsoallow us to infer approximate values for the magnetic moments of all knownintermediate polars. We predict that intermediate polars with mu_1 > 5 x 10^33G cm^3 and P_orb > 3h will evolve into polars, whilst those with mu_1 < 5 x10^33 G cm^3 and P_orb > 3h will either evolve into low field strength polarswhich are (presumably) unobservable, and possibly EUV emitters, or, if theirfields are buried by high accretion rates, evolve into conventional polars oncetheir magnetic fields re-surface when the mass accretion rate reduces. Wespeculate that EX Hya-like systems may have low magnetic field strengthsecondaries and so avoid synchronisation. Finally we note that the equilibriawe have investigated correspond to a variety of different types of accretionflow, including disc-like accretion at small P_spin / P_orb values, stream-likeaccretion at intermediate P_spin / P_orb values, and accretion fed from a ringat the outer edge of the white dwarf Roche lobe at higher P_spin / P_orbvalues.Comment: Accepted for publication in ApJ. Figre 3 included here as a low resolution gif onl