## 3. Event rate and mass spectrum
Consider a coordinate system where the lens is at rest and let the
source move on a straight line projected onto the lens plane with
velocity . Following Mao &
Paczynski (1991), the
characteristic width For variable lens position, the area number density of the lenses
has to be replaced by an integral of the volume number density
as area number density of the lenses. If the mass spectrum does not
depend on where the function follows the volume mass density as , so that at the reference distance where . The total volume number density of lenses at the reference distance is so that the probability for a mass which gives the mass spectrum. With being the probability of finding the perpendicular velocity in the interval , one obtains for the event rate or with the average mass . Let be a characteristic velocity and . The probability density for is then given by Note that may depend on With these definitions and , one gets © European Southern Observatory (ESO) 1998 Online publication: January 27, 1998 |