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.