Spatially varying mass function of MACHOs in the galactic halo and interpretation of microlensing results

The gravitational microlensing experiments in the direction of Large Magellanic Cloud (LMC) predict a large amount of white dwarfs ($\sim 20%$) filling the galactic halo. However, the predicted white dwarfs have not been observed at the galactic halo. To interpret the microlensing results and resolving the mentioned problems, we use the hypothesis of spatially varying mass function of MACHOs, proposed by \cite{ker98} (hereafter KE). However the KE model is not compatible with the duration distribution of events \cite{rah04a}. Here we use more realistic power-law model of MF, $dn/dm\propto m^{\alpha}$ for the MACHOs of halo. The index of MF in this model changes from -2.7 for stars with $m>1 M_{\bigodot}$ at the central part of galactic halo to the substellar regime with an upper limit of -1 at the edge of halo. We show that in contrast to the abundant brown dwarfs of galactic halo, heavy MACHOs can be responsible for the microlensing events in the direction of LMC.