Probing the Mass Function of Halo Dark Matter via Microlensing

The simplest interpretation of the microlensing events observed towards theLarge Magellanic Clouds is that approximately half of the mass of the Milky Wayhalo is in the form of MAssive Compact Halo Objects with $M \sim 0.5M_{\odot}$. It is not possible, due to limits from star counts and chemicalabundance arguments, for faint stars or white dwarves to comprise such a largefraction of the halo mass. This leads to the consideration of more exotic lenscandidates, such as primordial black holes, or alternative lens locations. Ifthe lenses are located in the halo of the Milky Way, then constraining theirmass function will shed light on their nature. Using the current microlensingdata we find, for four halo models, the best fit parameters for delta-function,primordial black hole and various power law mass functions. The best fitprimordial black hole mass functions, despite having significant finite width,have likelihoods which are similar to, and for one particular halo modelgreater than, those of the best fit delta functions . We then use Monte Carlosimulations to investigate the number of microlensing events necessary todetermine whether the MACHO mass function has significant finite width. If thecorrect halo model is known, then $\sim$ 500 microlensing events will besufficient, and will also allow determination of the mass function parametersto $\sim 5%$.Comment: 28 pages including 14 figures, version to appear in ApJ, minor changes to discussio