Abstract. We have used a model of magnetic accretion to investigate the rotational equilibria of magnetic cataclysmic variables (MCVs). This has enabled us to derive a set of equilibrium spin periods as a function of orbital period and magnetic moment which we use to estimate the magnetic moments of all known intermediate polars. We further show how these equilibrium spin periods relate to the polar synchronisation condition and use these results to calculate the theoretical histogram describing the distribution of magnetic CVs as a function of P spin /P orb . We demonstrate that this is in remarkable agreement with the observed distribution assuming that the number of systems as a function of white dwarf magnetic moment is distributed according to N (µ 1 )dµ 1 ∝ µ −2 1 dµ 1 .
The sample of MCVsAs shown in Figure 1, the MCVs occupy a wide range of parameter space in the spin period (P spin ) versus orbital period (P orb ) plane. This indicates that accretion occurs by a variety of different types of magnetically controlled flow. However, certain regions of the diagram are sparsely populated. In order to understand this distribution we use a model of magnetic accretion to investigate the rotational equilibria of these systems. First we discuss the systems included in Figure 1 and their characteristics.
Synchronous polarsWe include 67 synchronous polars ranging from CV Hyi with a period of 77.8 min to V1309 Ori with a period of 7.98 h. Magnetic field strength estimates exist for 52 of these, spanning the range µ 1 ∼ 3 × 10 33 − 10 35 G cm 3 . It is apparent that a true period gap no longer exists for polars, however we note that there are 22 synchronous systems with P spin = P orb > 2.5 h and a further 45 systems with P spin = P orb < 2.5 h.
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