Theory of Pixel Lensing toward M31. II. The Velocity Anisotropy and Flattening of the MACHO Distribution

The POINT-AGAPE collaboration is currently searching for massive compact haloobjects (MACHOs) towards the Andromeda galaxy (M31). The survey aims to exploitthe high inclination of the M31 disk, which causes an asymmetry in the spatialdistribution of M31 MACHOs. Here, we investigate the effects of halo velocityanisotropy and flattening on the asymmetry signal using simple halo models. Fora spherically symmetric and isotropic halo, we find that the underlyingpixel-lensing rate in far-disk M31 MACHOs is more than 5 times the rate ofnear-disk events. We find that the asymmetry is increased further by about 30%if the MACHOs occupy radial orbits rather than tangential orbits, but issubstantially reduced if the MACHOs lie in a flattened halo. However, even forhaloes with a minor-to-major axis ratio q = 0.3, the numbers of M31 MACHOs inthe far-side outnumber those in the near-side by a factor of ~2. We show that,if positional information is exploited in addition to number counts, then thenumber of candidate events required to confirm asymmetry for a range offlattened and anisotropic halo models is achievable, even with significantcontamination by variable stars and foreground microlensing events. Forpixel-lensing surveys which probe a representative portion of the M31 disk, asample of around 50 candidates is likely to be sufficient to detect asymmetrywithin spherical haloes, even if half the sample is contaminated, or to detectasymmetry in haloes as flat as q = 0.3 provided less than a third of the samplecomprises contaminants. We also argue that, provided its mass-to-light ratio isless than 100, the recently observed stellar stream around M31 is notproblematic for the detection of asymmetry. (Abstract slightly abridged.)Comment: latex, including 6 figures. Accepted for publication in Ap