Monte Carlo analysis of the MEGA microlensing events towards M31

We perform an analytical study and a Monte Carlo (MC) analysis of the main features for microlensing events in pixel lensing observations towards M31. Our main aim is to investigate the lens nature and location of the 14 candidate events found by the MEGA collaboration. Assuming a reference model for the mass distribution in M31 and the standard model for our galaxy, we estimate the MACHO-to-self lensing probability and the event time duration towards M31. Reproducing the MEGA observing conditions, as a result we get the MC event number density distribution as a function of the event full-width half-maximum duration $t_{1/2}$ and the magnitude at maximum $R_{\mathrm {max}}$. For a MACHO mass of $0.5 M_{\odot}$ we find typical values of $t_{1/2} \simeq 20$ day and $R_{\mathrm {max}} \simeq 22$, for both MACHO-lensing and self-lensing events occurring beyond about 10 arcminutes from the M31 center. A comparison of the observed features ($t_{1/2}$ and $R_{\mathrm {max}}$) with our MC results shows that for a MACHO mass $>0.1 M_{\odot}$ the four innermost MEGA events are most likely self-lensing events, whereas the six outermost events must be genuine MACHO-lensing events.