Gravitational lensing in eclipsing binary stars

Abstract

I consider the effect of the gravitational deflection of light upon the light curves of eclipsing binary stars, focussing mainly upon systems containing at least one white dwarf component. In absolute terms the effects are small, however they are strongest at the time of secondary eclipse when the white dwarf transits its companion, and act to reduce the depth of this feature. If not accounted for, this may lead to under-estimation of the radius of the white dwarf compared to that of its companion. I show that the effect is significant for plausible binary parameters, and that it leads to ~25% reduction in the transit depth in the system KPD 1930+2752. The reduction of eclipse depth is degenerate with the stellar radius ratio, and therefore cannot be used to establish the existence of lensing. A second order effect of the light bending is to steepen the ingress and egress features of the secondary eclipse relative to the primary eclipse, although it will be difficult to see this in practice. I consider also binaries containing neutron stars and black-holes. I conclude that, although relatively large effects are possible in such systems, a combination of rarity, faintness and intrinsic variability make it unlikely that lensing will be detectable in them.