2. Information from a fit of a galactic microlensing event
From a fit of the light curve to the observed data of a galactic microlensing event, the only dimensional parameters are the point of time when the event occurs and the characteristic timescale related to its duration. While the point of time does not yield any relevant information, all physical quantities related to the observed event which involve a dimension depend on . This is true not only for the `standard model' of Galactic microlensing - a point-mass lens and a point source -, but also for `anomalous' events (binary sources and lenses, parallax effects, blending, finite size of the source and the lens). 1 The geometry of the microlensing events depends on a length scale which can be chosen as the Einstein radius of the lens of mass M at a distance from the observer, where the source is at a distance from the observer and at a distance from the lens. The Einstein radius is then given by
With and , can be written as
The characteristic time scale is given by
where is the transverse velocity of the lens relative to the line-of-sight source-observer. Note that motions of the source and the observer are also absorbed into this quantity.
where is a characteristic velocity and . One sees that depends on the timescale as well as on x and . By assuming distributions of x and (where the distribution of may depend on x), it should in principle be possible to derive a probability distribution for . For doing this, I have a look at the event rate in the next section.
© European Southern Observatory (ESO) 1998
Online publication: January 27, 1998