Microlensing, structure of the galactic halo and determination of dark objects' mass function

Abstract

We study the accuracy of inference of the massive halo objects' (MHO or `Macho') mass function from microlensing events observed toward LMC. Assuming the spatial distribution and kinematics of the objects are known, the slope and the range of the MHO mass function (modeled here by a simple power law) will be possible to determine from 100-1000 detected events if the slope αis in the range [-2.5, -0.5], with the statistical errors reaching their minima at α=-1.5. Outside this range the errors grow rapidly making the inference difficult even at very large numbers of events (N\approx 10000). On the other hand, the average mass of the MHOs will be determined to better than about 30% accuracy from N\approx 100 events for any slope. We find that the accuracy of inference at fixed N will not be strongly affected by the presently available detection efficiencies if the typical MHO masses are in the range indicated by the events detected so far. We also estimate the effects of uncertainty of the MHOs' spatial distribution and kinematics on the determination of their mass function. The halo models considered are all spherical but we allow for various density profiles and a radius-dependent, anisotropic velocity dispersion. We find that, while the mass function slope and range are weakly affected for -2 < α< 0, the error in the average mass due to the halo uncertainties could be reduced to less than 50% only through the detection of about 1000 or more events. Reliable estimates of the halo structure itself [density profile and velocity dispersion profile] can start only at very large numbers of detections (N ~ 10000).