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Astron. Astrophys. 330, 963-974 (1998)

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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 [FORMULA] when the event occurs and the characteristic timescale [FORMULA] related to its duration. While the point of time [FORMULA] does not yield any relevant information, all physical quantities related to the observed event which involve a dimension depend on [FORMULA]. 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 [FORMULA] of the lens of mass M at a distance [FORMULA] from the observer, where the source is at a distance [FORMULA] from the observer and at a distance [FORMULA] from the lens. The Einstein radius [FORMULA] is then given by

[EQUATION]

With [FORMULA] and [FORMULA], [FORMULA] can be written as

[EQUATION]

where

[EQUATION]

The characteristic time scale [FORMULA] is given by

[EQUATION]

where [FORMULA] 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.

For a given [FORMULA], the mass [FORMULA] therefore follows as

[EQUATION]

where [FORMULA] is a characteristic velocity and [FORMULA]. One sees that [FORMULA] depends on the timescale [FORMULA] as well as on x and [FORMULA]. By assuming distributions of x and [FORMULA] (where the distribution of [FORMULA] may depend on x), it should in principle be possible to derive a probability distribution for [FORMULA]. For doing this, I have a look at the event rate in the next section.

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© European Southern Observatory (ESO) 1998

Online publication: January 27, 1998
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