The impact of spheroid stars for Macho microlensing surveys of the Andromeda galaxy

The Andromeda galaxy (M31) is an important test case for a number of microlensing surveys looking for massive compact halo objects (Machos). A long‐standing theoretical prediction is that the high inclination of the M31 disc should induce an asymmetry in the spatial distribution of M31 Macho events, whereas the distribution of variable stars and microlensing events in the M31 disc should be symmetric. We examine the role of stars in the M31 visible spheroid as both lenses and sources to microlensing events. We compute microlensing event number density maps and estimate pixel‐lensing rates and event durations for three‐component models of M31 which are consistent with the observed rotation curve, surface brightness profile and dynamical mass estimates. Three extreme models are considered: a massive spheroid model; a massive disc model; and a massive Macho halo model. An important consequence of the spheroid is that, even if Machos are absent in M31, an asymmetric spatial signature is still generally expected from stellar lensing alone. The lensing of disc sources by spheroid stars produces an asymmetry of the same sign as that of Machos, whereas lensing by disc stars against spheroid sources produces an asymmetry of the opposite sign. The relative mass‐to‐light ratio of the spheroid and disc populations controls which of these signatures dominates the overall stellar spatial distribution. We find that the inclusion of the spheroid weakens the M31 Macho spatial asymmetry by about 20–30 per cent over a disc‐only asymmetry for the models considered. We also find for our models that Machos dominate over most of the far disc, provided that they contribute at least ∼ 25 per cent of the halo dark matter density. This is a conservative limit because many stellar events are too short to be detected by present surveys. The presence of the spheroid also has beneficial consequences for M31 lensing surveys. The stellar spatial asymmetry is likely to be important in distinguishing a spheroidal Macho halo from a highly flattened halo or from a dark‐matter‐dominated disc, because spatial asymmetries of opposing signs are expected in these cases.