Theory of pixel lensing towards M31 - I. The density contribution and mass of MACHOs

POINT-AGAPE is an Angle-French collaboration which is employing the Isaac Newton Telescope (INT) to conduct a pixel-lensing survey towards M31. Pixel lensing is a technique which permits the detection of microlensing against unresolved stellar fields. The survey aims to constrain the stellar population in M31, and also the distribution and nature of massive compact halo objects (MACHOs) in both M31 and the Galaxy. In this paper we investigate what we can learn from pixel-lensing observables about the MACHO mass and fractional contribution in M31 and the Galaxy for the case of spherically symmetric, near-isothermal haloes. We employ detailed pixel-lensing simulations which include many of the factors that affect the observables, such as non-uniform sampling and signal-to-noise ratio degradation owing to changing observing conditions. For a maximum MACHO halo we predict an event rate in V of up to 100 per observing season for M31 and 40 per season for the Galaxy. However, the Einstein radius crossing time is measurable for less than 10 per cent of the events, and the observed full-width at half-maximum duration provides only a weak tracer of lens mass. None the less, we find that the near-far asymmetry in the spatial distribution of M31 MACHOs provides significant information on their mass and density contribution. We present a Likelihood estimator for measuring the fractional contribution and mass of both M31 and Galaxy MACHOs, which permits an unbiased determination to be made of MACHO parameters, even from data sets strongly contaminated by variable stars. If M31 does not have a significant population of MACHOs in the mass range 0.001-1 M., strong limits will result from the first season of INT observations. Simulations based on currently favoured density and mass values indicate that, after three seasons, the M31 MACHO parameters should be constrained to within a factor of 4 uncertainty in halo fraction and an order of magnitude uncertainty in mass (90 per cent confidence). Interesting constraints on Galaxy MACHOs may also be possible. For a campaign lasting 10 years, comparable to the lifetime of current LMC surveys, reliable estimates of MACHO parameters in both galaxies should be possible.