Perhaps as many as 30 parallax microlensing events are known , thanks to the efforts of the MACHO , OGLE , EROS and 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 \Delta \chi ^ { 2 } 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 observations .
The fraction of parallax events in the OGLE-II database is around \sim 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 } \approx 50 days but rising to 50 per cent at t _ { E } \ga 1 yr. We find that the existence of parallax signatures is essentially controlled by the acceleration of the observer normalised to the projected Einstein radius on the observer plane divided by t _ { E } ^ { 2 } .
The properties of the parallax events – time-scales , projected velocities , source and lens locations – in our mock catalogues are analysed .
Typically , \sim 38 per cent of parallax events are caused by a disk star microlensing a bulge source , while \sim 33 per cent are caused by a disk star microlensing a disk source ( of these disk 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 \sim 130 d for our parallax events .
There are corresponding shifts for other parameters , such as the lens-source velocity projected onto the observer plane ( \sim 1110 km s ^ { -1 } for all events versus \sim 80 km s ^ { -1 } 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 .