2005MNRAS.361..128S

Perhaps as many as 30 parallax microlensing events are known, thanks to the efforts of the Massive Compact Halo Object (MACHO), Optical Gravitational Lensing Experiment (OGLE), Experience pour la Recherche d'Objets Sombres (EROS) and Microlensing Observations in Astrophysics (MOA) experiments monitoring the bulge. Using Galactic models, we construct mock catalogues of microlensing light curves towards the bulge, allowing for the uneven sampling and observational error bars of the OGLE-II experiment. As a working definition of a parallax event, we require the improvement Δχ² on incorporating parallax effects in the microlensing light curve to exceed 50. This enables us to carry out a fair comparison between our theoretical predictions and the observations. The fraction of parallax events in the OGLE-II data base is ∼1 per cent, though higher fractions are reported by some other surveys. This is in accord with expectations from standard Galactic models. The fraction of parallax events depends strongly on the Einstein crossing time t_E, being less than 5 per cent at t_E~ 50 d but rising to 50 per cent at t_E≳ 1 yr. We find that the existence of parallax signatures is essentially controlled by the acceleration of the observer normalized to the projected Einstein radius on the observer plane divided by t²_E. The properties of the parallax events - time-scales, projected velocities, source and lens locations - in our mock catalogues are analysed. Typically, ∼38 per cent of parallax events are caused by a disc star microlensing a bulge source, while ∼33 per cent are caused by a disc star microlensing a disc source (of these disc sources, one sixth are at a distance of 5 kpc or less). There is a significant shift in mean time-scale from 32 d for all events to ∼130 d for our parallax events. There are corresponding shifts for other parameters, such as the lens-source velocity projected on to the observer plane ( ∼1110 km/s for all events versus ∼80 km/s for parallax events) and the lens distance (6.7 kpc versus 3.7 kpc). We also assess the performance of parallax mass estimators and investigate whether our mock catalogue can reproduce events with features similar to a number of conjectured `black hole' lens candidates.