Binary Source Parallactic Effect in Gravitational Micro-lensing

Abstract

The first micro-lensing event discovered towards the Small Magellanic Cloud by the MACHO collaboration (Alcock et al. 1997b) had a very long time scale, t_0 = 123 days. The EROS collaboration (Palanque-Delabrouille et al. 1997) discovered a 2.5% brightness variation with a period P = 5.1 days. The OGLE collaboration (Udalski et al. 1997) established that the variation persists while the micro-lensing event is over, and the variable star is the one which has been micro-lensed, not its blend. The simplest explanation of the periodic variability is in terms of a binary star with the orbital period P(orb) = 10.2 days, with its component(s) tidally distorted. Such objects are known as ellipsoidal variables. The binary nature should be verified spectroscopically. Binary motion of the source introduces a parallactic effect into micro-lensing light curve, and a few examples are shown. The effect is relatively strong if the light center and the mass center of a binary are well separated, i.e. if the binary has a large photometric dipole moment. The diversity of binary parameters is large, and the corresponding diversity of photometric effects is also large. The presence or absence of the effect may constrain the lens mass and its distance from the source.