Statistical Determination of the MACHO Mass Spectrum

The mass function of 51 Massive Compact Objects (MACHOs) detected toward the Galactic bulge is statistically estimated from Einstein ring crossing times $t_{\mathrm{e}}$. For a Gaussian mass function, the best fitting parameters are $⟨\log (m\mathrm{/}{M}_{\odot })⟩=-1.12$ and $\sigma_{\log (m/M_{\odot})} = 0.57$. If the mass function follows a power-law distribution, the best fitting mass cut-off and power are $m_{\mathrm{c}\mathrm{u}\mathrm{t}}=0.04M_{\odot }$ and $p=-2.1$. Both mass spectra indicate that a significant fraction of events are caused by MACHOs in substellar mass range. Both best determined mass functions are compared with that obtained from Hubble Space Telescope (HST) observations. The power law is marginally favored ($2.3\sigma$) over the Gaussian mass function, and significantly over HST mass function ($5.5\sigma$), indicating that MACHOs have a different mass function from stars in the solar neighborhood. In addition, the fact that all the models have very poor fits to the longest four events with $t_e\ge 70\mathrm{d}\mathrm{a}\mathrm{y}\mathrm{s}$ remains a puzzle.