8.2. Microlensing Optical Depth
One of the most important reasons for seeking to understand the
vertical structure of the LMC is to understand the results from
microlensing surveys. The observed microlensing optical depth towards
the LMC is obs =
12+4-3 × 10-8 with an
additional 20-30% of systematic error
(Alcock et al. 2000a).
It has generally been found that equilibrium models for the LMC do not predict enough LMC self-lensing events to account for the observed
optical depth
(Gyuk, Dalal & Griest
2000;
Jetzer, Mancini &
Scarpetta 2002).
For the most favored set of LMC model parameters in
the Gyuk et al. study the predicted self-lensing optical depth is
self = 2.2 ×
10-8, a factor of 5.5 less than
the observed value. To account for the lenses it is therefore
necessary to assume that some ~ 20% of the Milky Way dark halo
is made up of lenses of mass 0.15-0.9
M
(Alcock et al. 2000a).
However, it is a mystery what the composition of this lensing
component could be. A large population of old white dwarfs has been
suggested, but this interpretation is not without problems (e.g.,
Fields, Freese, & Graff
2000;
Flynn, Holopainen, &
Holmberg 2003).
It is therefore worthwhile to investigate whether the models
that have been used to estimate the LMC self-lensing might have been
oversimplified. This is particularly important since there is evidence
from the observed microlensing events themselves that many of the
lenses may reside in the LMC
(Sahu 2003).
To lowest order, the self-lensing optical depth in simple disk models
of the LMC depends exclusively on the observed velocity
dispersion and not separately on either the galaxy mass or scale height
(Gould 1995).
One way to increase the self-lensing predicted by LMC models is
therefore to assume that a much larger fraction of the LMC mass
resides in high velocity dispersion populations than has previously
been believed.
Salati et al. (1999)
showed that the observed optical
depth can be reproduced if one assumes that 70% of the mass in the
LMC disk consists of objects with
ranging from
25 km s-1 to 60 km s-1. However, this would seem
difficult to explain on the basis
of present data. Although RR Lyrae stars have now been observed to
have a high velocity dispersion, these old stars make up only 2% of
the visible mass. So their influence on self-lensing predictions is
negligible. A better way to account for the observed optical depth
might be to assume that the vertical structure of the LMC is more
complicated than for normal disk galaxies. The self-lensing optical
depth might then have been considerably underestimated.