Geometrical constraints upon the unipolar model of V407 Vul and RXJ0806.3+1527

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Abstract
V407 Vul and RX J0806.3+1527 are X-ray emitting stars with X-ray light curves that are 100% modulated on periods of 569 and 321 seconds respectively. These periods and no others are also seen at optical and infra-red wavelengths. These properties have led to the suggestion that the periods are the orbital period of ultra-compact pairs of white dwarfs. There are two main double white dwarf models: the unipolar inductor model analogous to the Jupiter-Io system and the direct impact model analogous to Algol. In this paper we consider geometrical constraints on the unipolar inductor model, in particular what parameter values (component masses, orbital inclination and magnetic co-latitude) can describe the X-ray and optical light curves. We find that for a dipole field on the primary star, the unipolar inductor model fails to match the data on V407 Vul for any combination of parameters, and can only match RX 0806.3+1527 if the sparser set of observations of this star have been unluckily timed.

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