The physical parameters of Markarian 501 during flaring activity

We analyse an N -body simulation of the Small Magellanic Cloud (SMC), that of Gardiner & Noguchi, to determine its microlensing statistics. We find that the optical depth owing to self-lensing in the simulation is low, 0.4×10⁻⁷, but still consistent (at the 90 per cent level) with that observed by the EROS and MACHO collaborations. This low optical depth is due to the relatively small line-of-sight thickness of the SMC produced in the simulation. The proper motions and time-scales of the simulation are consistent with those observed assuming a standard mass function for stars in the SMC. The time-scale distribution from the standard mass function generates a significant fraction of short time-scale events: future self-lensing events towards the SMC may have the same time-scales as events observed towards the Large Magellanic Cloud (LMC). Although some debris was stripped from the SMC during its collision with the LMC about 2×10⁸ yr ago, the optical depth of the LMC owing to this debris is low, a few ×10⁻⁹, and thus cannot explain the measured optical depth towards the LMC.