MICROLENSING, STRUCTURE OF THE GALACTIC HALO AND DETERMINATION OF THEMASS FUNCTION OF DARK OBJECTS

We study the accuracy and systematic error of inference of the mass fu nction of massive halo objects (MHOs or 'MACHOs') from microlensing ev ents observed in the direction of the Large Magellanic Cloud. Assuming that the spatial distribution and kinematics of the objects are known , the slope and the range of the MHO mass function (modelled here by a simple power law) can be determined from 100-1000 detected events if the slope is in the range -2.5 less than or similar to alpha less than or similar to - 0.5, with the statistical errors reaching their minim a at alpha = -1.5. Outside this range the errors grow rapidly, making the inference difficult even at very large numbers of events (N approx imate to 10 000). On the other hand, the average mass of the MHOs will be determined to better than about 30 per cent accuracy from N approx imate to 100 events for any slope. Overall, we find that the accuracy of inference at fixed N will not be strongly affected by the presently available event-duration-dependent detection efficiencies if the typi cal MHO masses are in the range (order of magnitude 0.1 M.) indicated by the events detected so far. We also estimate the effects of the unc ertainty of the spatial distribution and kinematics of the massive obj ects on the determination of their mass function. The halo models of t he massive objects considered are all spherical, but we allow for vari ous density profiles and a radius-dependent, anisotropic velocity disp ersion. We find that while the mass function slope and range (i.e. the 'shape') are weakly affected for -2 less than or similar to alpha les s than or similar to 0, the error in the average mass due to the halo structure uncertainties could be reduced to less than about 50 per cen t only through the detection of about 1000 or more events. Reliable in ference of the halo structure itself [density profile and (anisotropic ) velocity dispersion profile] can start only at very large numbers of detections (N greater than or similar to 10 000).