A Caustic View of Halo Microlensing

Abstract

The only microlensing events towards the Magellanic Clouds for which the location of the lens is strongly constrained are the two binary caustic crossing events. In at least one and possibly both cases, the lens lies at, or close to, the clouds themselves. On the face of it, this seems an improbable occurrence if the Galactic dark halo provides the bulk of the lensing population, as suggested by standard analyses of the MACHO dataset towards the Large Magellanic Cloud (LMC). We use a binomial statistic to assess the prior probability of observing $M$ non-halo binary caustic events given a total sample of $N$ caustic binaries. We generalize for the case of multi-component Galactic and Magellanic Cloud models the Bayesian likelihood method for determining the lens mass and halo fraction from the observed timescales. We introduce a new statistic, the ``outcome discriminator'', which measures the consistency between the binary caustic data, prior expectation, and the MACHO LMC dataset as a whole. If the clouds are not embedded in their own dark halos of MACHOs, then the discovery of two non-halo caustic binary events out of two ($M = N = 2$) is inconsistent with expectation given the MACHO dataset. Galactic models in which $M = 1$ is the likeliest outcome are also inconsistent with the data, though models in which $M = 1$ has a reasonable prior probability are not. We consider the possibilities that the Magellanic Clouds are embedded in dark haloes of their own, or that the Galactic halo is intrinsically deficient in the binary systems which produce caustic crossing events. Either of these possibilities provide greater compatibility between observation and prior expectation, though the idea of Magellanic haloes is perhaps the more natural of the two and has support from kinematical studies.