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 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 magnetic CVs 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) d mu_1 proportional to 1/mu_1 d mu_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 > 5 x 10^33 G cm^3 and P_orb > 3h will evolve into polars, whilst those with mu_1 < 5 x 10^33 G cm^3 and P_orb > 3h will either evolve into low field strength polars which 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 re-surface when the mass accretion rate reduces. We speculate that EX Hya-like systems may have low magnetic field strength secondaries and so avoid synchronisation. Finally we note that the equilibria we have investigated correspond to a variety of different types of accretion flow, including disc-like accretion at small P_spin / P_orb values, stream-like 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.