Monte Carlo analysis of MEGA microlensing events towards M 31

We perform an analytical study and a Monte Carlo (MC) analysis of the main features for microlensing events in pixel lensing observations towards M 31. 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 M 31 and the standard model for our galaxy, we estimate the MACHO-to-self lensing probability and the event time duration towards M 31. 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_max. For a MACHO mass of 0.5~M_⊙ we find typical values of t_1/2 ≃ 20 day and R_max ≃ 22, for both MACHO-lensing and self-lensing events occurring beyond about 10 arcmin from the M 31 center. A comparison of the observed features (t_1/2 and R_max) with our MC results shows that for a MACHO mass > 0.1~M_⊙ the four innermost MEGA events are most likely self-lensing events, whereas the six outermost events must be genuine MACHO-lensing events.