Probing the mass function of halo dark matter via microlensing

The simplest interpretation of the microlensing events observed towards the Large Magellanic Clouds is that approximately half of the mass of the Milky Way halo is in the form of MAssive Compact Halo Objects with $M \sim 0.5 M_{\odot}$. It is not possible, due to limits from star counts and chemical abundance arguments, for faint stars or white dwarves to comprise such a large fraction of the halo mass. This leads to the consideration of more exotic lens candidates, such as primordial black holes, or alternative lens locations. If the lenses are located in the halo of the Milky Way, then constraining their mass function will shed light on their nature. Using the current microlensing data we find, for four halo models, the best fit parameters for delta-function, primordial black hole and various power law mass functions. The best fit primordial black hole mass functions, despite having significant finite width, have likelihoods which are similar to, and for one particular halo model greater than, those of the best fit delta functions . We then use Monte Carlo simulations to investigate the number of microlensing events necessary to determine whether the MACHO mass function has significant finite width. If the correct halo model is known, then $\sim$ 500 microlensing events will be sufficient, and will also allow determination of the mass function parameters to $\sim 5%$.