*Astron. Astrophys. 330, 963-974 (1998)*
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## Estimating physical quantities
for an observed galactic microlensing event
**
M. Dominik
**
Institut für Physik, Universität Dortmund,
D-44221 Dortmund, Germany
*Received 12 December 1996 / Accepted 17 October 1997*
**Abstract**
For a given spatial distribution of the lenses and distribution of
the transverse velocity of the lens relative to the line-of-sight, a
probability distribution for the lens mass for a single observed event
is derived. In addition, similar probability distributions are derived
for the Einstein radius and the separation of the lens objects and
their rotation period for a binary lens. These probability
distributions are distinct from the distributions for the lens
population, as investigated e.g. by the mass moment method of De
Rújula et al. (1991). It is shown that the expectation value
for the mass of a certain event as derived in this paper coincides
with the estimated average mass of the underlying mass spectrum as
found with the mass moment method when only one event is considered.
The special cases of a Maxwellian velocity distribution and of a
constant velocity are discussed in detail. For a rudimentary model of
the Galactic halo, the probability distributions are shown and the
relations between the expectation values of the physical quantities
and the event timescale are given. For this model it is shown that
within a 95.4 %-interval around the expectation value the mass
varies by a factor of 800. For the observed events towards the LMC -
including the binary lens models for MACHO LMC#1 (Dominik &
Hirshfeld 1996) and MACHO LMC#9 (Bennett et al. 1996) - the results
are shown explicitly. I discuss what information can be extracted and
how additional information from the ongoing microlensing observations
influences the results.
**Key words:** gravitational
lensing
dark matter
stars: low-mass, brown
dwarfs
Galaxy: halo
planetary systems
© European Southern Observatory (ESO) 1998
Online publication: January 27, 1998
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