The spin periods and magnetic moments of white dwarfs in magnetic cataclysmic variables

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 P-spin/P-orb versus mu(1) plane at which rotational equilibrium occurs. This has allowed us to calculate the theoretical histogram describing the distribution of mCVs as a function of P-spin/P-orb. 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(mu(1)) dmu(1) proportional to mu(1)(-1) dmu(1). 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 mu(1) greater than or similar to 5 x 10(33) G cm(3) and P-orb > 3 hr will evolve into polars, while those with mu(1) less than or similar to 5 x 10(33) G cm(3) and Porb > 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 P-spin/P-orb values, streamlike accretion at intermediate P-spin/P-orb values, and accretion fed from a ring at the outer edge of the white dwarf Roche lobe at higher P-spin/P-orb values.