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

Abstract

V407 Vul and RX J0806.3 + 1527 are X-ray emitting stars with X-ray light curves that are 100 per cent modulated on periods of 569 and 321 s, respectively. These periods and no others are also seen at optical and infrared wavelengths. These properties have led to the suggestion that the periods are the orbital periods of ultracompact 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 colatitude) 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 J0806.3 + 1527 if the sparser set of observations of this star have been unluckily timed.