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Register a new userThe spin periods and magnetic moments of white dwarfs in magnetic cataclysmic variables
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A.J. Norton The Openn University
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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.
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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(mu_1) d mu_1 ~ mu_1^{-2} d mu_1.
The origin of magnetic fields in isolated and binary white dwarfs has been investigated in a series of recent papers. One proposal is that magnetic fields are generated through an alpha-omega dynamo during common envelope evolution. Here we present population synthesis calculations showing that this hypothesis is supported by observations of magnetic binaries.
Some magnetic CVs like BY Cam are characterized by unusual CNO line ratios compared to other polars and non-solar abundances have been suggested to explain this anomaly. We present here a first attempt to constrain the elemental abundances in these systems by applying a specific ionisation model combined with a geometrical description of the accretion column where these lines are thought to be formed. The line luminosities have been computed using the CLOUDY plasma code for different ionisation spectra and column extension. We show here selected results and compare to the values observed in peculiar magnetic CVs. The model applied to BY Cam confirms that ionization models with solar abundances fail to reproduce the observed line intensity ratios. Assuming the model to be valid, the induced best abundances imply an overabundance of N (x25), underabundance of C (:8) and nearly solar O (:2), in line with CNO reprocessing.
In a series of recent papers, it has been proposed that high field magnetic white dwarfs are the result of close binary interaction and merging. Population synthesis calculations have shown that the origin of isolated highly magnetic white dwarfs is consistent with the stellar merging hypothesis. In this picture, the observed fields are caused by an alpha-Omega dynamo driven by differential rotation. The strongest fields arise when the differential rotation equals the critical break-up velocity and result from the merging of two stars (one of which has a degenerate core) during common envelope evolution or from the merging of two white dwarfs. We now synthesise a population of binary systems to investigate the hypothesis that the magnetic fields in the magnetic cataclysmic variables also originate during stellar interaction in the common envelope phase. Those systems that emerge from common envelope more tightly bound form the cataclysmic variables with the strongest magnetic fields. We vary the common envelope efficiency parameter and compare the results of our population syntheses with observations of magnetic cataclysmic variables. We find that common envelope interaction can explain the observed characteristics of these magnetic systems if the envelope ejection efficiency is low.
We use the complete, X-ray flux-limited ROSAT Bright Survey (RBS) to measure the space density of magnetic cataclysmic variables (mCVs). The survey provides complete optical identification of all sources with count rate >0.2/s over half the sky ($|b|>30^circ$), and detected 6 intermediate polars (IPs) and 24 polars. If we assume that the 30 mCVs included in the RBS are representative of the intrinsic population, the space density of mCVs is $8^{+4}_{-2} times 10^{-7},{rmpc^{-3}}$. Considering polars and IPs separately, we find $rho_{polar}=5^{+3}_{-2} times 10^{-7},{rm pc^{-3}}$ and $rho_{IP}=3^{+2}_{-1} times 10^{-7},{rm pc^{-3}}$. Allowing for a 50% high-state duty cycle for polars (and assuming that these systems are below the RBS detection limit during their low states) doubles our estimate of $rho_{polar}$ and brings the total space density of mCVs to $1.3^{+0.6}_{-0.4} times 10^{-6},{rm pc^{-3}}$. We also place upper limits on the sizes of faint (but persistent) mCV populations that might have escaped detection in the RBS. Although the large uncertainties in the $rho$ estimates prevent us from drawing strong conclusions, we discuss the implications of our results for the evolutionary relationship between IPs and polars, the fraction of CVs with strongly magnetic white dwarfs (WDs), and for the contribution of mCVs to Galactic populations of hard X-ray sources at $L_X ga 10^{31} {rm erg/s}$. Our space density estimates are consistent with the very simple model where long-period IPs evolve into polars and account for the whole short-period polar population. We find that the fraction of WDs that are strongly magnetic is not significantly higher for CV primaries than for isolated WDs. Finally, the space density of IPs is sufficiently high to explain the bright, hard X-ray source population in the Galactic Centre.
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