Red Clump Stars as a Tracer of Microlensing Optical Depth

Zaritsky and Lin have recently suggested that the color magnitude diagram ofthe Large Magellanic Cloud (LMC) contains evidence of foreground red clumpstars. They interpret this as evidence of tidal debris or a dwarf galaxy at adistance of $\sim 35$ kpc which may be responsible for the large gravitationalmicrolensing optical depth observed by the MACHO Collaboration. I derive arelationship between the microlensing optical depth of such a foregroundpopulation and the observed density of foreground red clump stars. Recentobservational determinations for Pop I and Pop II stellar mass functions areused to show that the surface density of foreground red clump stars claimed byZaritsky and Lin implies a microlensing optical depth in the range $\tau_{fg} =0.8-3.6\times 10^{-8}$ which is only 3-13% of $\tau_{LMC}$ as determined by theMACHO Collaboration. If the foreground population has a similar star formationhistory to the LMC, then the implied $\tau_{fg}$ is only 3-4% of $\tau_{LMC}$.Comment: 7 pages, 1 figur