The microlensing optical depth towards the Large Magellanic Cloud: is there a puzzle?

Using neural networks, Belokurov, Evans & Le Du (2003, 2004) showed that 7 out of the 29 microlensing candidates towards the Large Magellanic Cloud (LMC) of the MACHO collaboration are consistent with blended microlensing and added Gaussian noise. We then estimated the microlensing optical depth to the LMC to be 0.3×10 −7 ∼ < τ ∼ < 0.5 × 10 −7, lower than the value τ = 1.2 +0.4 −0.3 × 10−7 claimed by the MACHO collaboration (Alcock et al. 2000). There have been independent claims of a low optical depth to the LMC by the EROS collaboration, who have most recently reported τ < 0.36 × 10 −6 (Tisserand et al. 2006). Griest & Thomas (2005) have contested our calculations. Unfortunately, their paper contains a number of scientific misrepresentations of our work, which we clarify here. We stand by our application of the neural networks to microlensing searches, and believe it to be a technique of great promise. Rather, the main cause of the disparity between Griest & Thomas (2005) and Belokurov et al. (2004) lies in the very different datasets through which these investigators look for microlensing events. Whilst not everything is understood about the microlensing datasets towards the LMC, the latest downward revisions of the optical depth to (1.0 ±0.3) ×10−7 (Bennett 2005) is within < 2σ of the theoretical prediction from stellar populations alone. Efficiency calculations can correct for the effects of false negatives, but they cannot correct for the effects of false positives (variable stars that are mistaken for microlensing). In our opinion, the best strategy in a microlensing experiment is to eschew a decision boundary altogether and so sidestep the vagaries of candidate selection and efficiency calculations. Rather, each lightcurve should be assigned a probability that it is a bona fide microlensing event and the microlensing rate calculated by summing over the probabilities of all such lightcurves.