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 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 1 ð Þd 1 / À1 1 d 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 1 k 5 ; 10 33 G cm 3 and P orb > 3 hr will evolve into polars, while those with 1 P 5 ; 10 33 G cm 3 and P orb > 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.

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. 216

ESUMENPreseiitainos los rosnltados d(' sirnulacionos quo exploran la variedad de flujos de acrecion posibles en variables cal-aclisiiiicas iiiay,iieliras (mCVs). Niiestras simulaciories evoliicionan hasta alcanzar periodos de equilibrio qne abarcaii 0.01 < /3;pir,/Porb < 0.6, y los flujos resultantes varian desde sistemas alimentados por disco en Pspin/Porb ~ 0.01 -0.1 a sistciiias alinuaitados por corrientes en Pspin/Porb ~ 0.1 -0.5 y sistemas alimentados d('sd(' un anillo ('ii el borde <'xl,ei ioi-del lobnlo de Roche de la enana blanca, en Pspin/Porb ~ 0.6. ABSTRACT '•V(' present l lu' results of simulations that explore the variety of accretion flows possible in magnetic cataclysmic variabk's (mCVs). Our simulations evolv(' to equilibrium periods spanning 0.01 < Pspin/Porb < 0.6 and the resulting flows vary from disc-fed systems at, Pspin/Porb ~ 0.01 -0.1, to stream fed systems at Pgpin/Porb 0 .1 -0.5 and systenns led from a ring at tlu' outer edge of the white dwarf's Roche lobe at Pspin/Porb ~ 0.6.

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