K Band Microlensing of the Inner Galaxy

Abstract

Microlensing searches toward the inner galaxy $(|l|,|b|\leq 22.\hskip-2pt'5)$ have several major advantages. First, the event rate is strongly dominated by bulge-bulge lensing events where both the source and lens lie in the bulge. Second, these bulge-bulge events have very short time scales $t_e\sim 2\,$days and are therefore easily distinguished from the less frequent and much longer bulge-disk and disk-disk events. Third, since the optical depth is similar to that at higher impact parameters, while the events are shorter, the event rate is high $\Gamma\sim 3\times 10^{-7}\rm day^{-1}$. Fourth, because the Einstein rings are small, $r_e\sim 5\times 10^{12}\,$cm, and the source stars are large $r_s\gsim 10^{12}\,$cm, the lens will transit the face of the source for a significant fraction $(\sim 20\%)$ of events. For these transit events it will often be possible to measure a second lens parameter, the angular Einstein radius (or proper motion). In addition to the bulge-bulge events, the optical depth of the disk is $\sim 7$ times larger toward the inner Galaxy than toward Baade's Window. A microlensing search toward the inner Galaxy can be carried out by making frequent $(\sim4\,\rm day^{-1})$ K band images of a large area $\sim 0.5\,\rm deg^2$ to a depth of $K\sim 16$, and hence requires either a $1024^2$ infrared array on a dedicated 2m telescope or four such arrays on a 1m telescope.