ULTRACAM photometry of the ultracompact binaries V407 Vul and HM Cnc

V407 Vul (RXJ1914.4+2456) and HM Cnc (RXJ0806.3+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 are thought possibly to represent the orbital periods of close pairs of white dwarfs. In this paper we present optical light curves taken with the high-speed CCD camera ULTRACAM on the 4.2-m William Hershel Telescope in 2003 May and 2005 August and with the VLT in 2005 November. The optical and X-ray light curves of HM Cnc have been reported as being in antiphase, but we find that in fact the X-rays peak around 0.2 cycles after the maximum of the optical light, as seen also in V407 Vul. The X-ray/optical phase shifts are well explained under the accreting models of the systems if most of the optical modulation comes from the heated faces of the mass donors and if the X-ray emitting spots are positioned in advance of the mass donors, as is expected given the angular momentum of the accreting material. Some optical emission may also come from the vicinity of the X-ray spot, and we further show that this can explain the non-sinusoidal light curves of HM Cnc. On the basis of this model we constrain the temperature of the heated face of the companion star finding a bolometric luminosity >1033 erg s−1 and a distance, d > 1.1 kpc. We can identify no explanation for the X-ray/optical phase shifts under the intermediate polar and unipolar inductor models of the systems. The only significant difference between the two stars is that V407 Vul is observed to have the spectrum of a G star. The variation in position on the sky of a blend of a variable and a constant star can be used as a measure of their separation, and is sensitive to values well below the limit set by seeing. We apply this ‘pulsation astrometry’ to deduce that the G star is separated from the variable by about 0.027 arcsec and hence plays no role in the variability of V407 Vul. We show that light traveltime variations could influence the period change in V407 Vul if it forms a triple system with the G star.