Microlensing optical depth toward the galactic bulge using clump giants from the MACHO survey

Using 7 yr of MACHO survey data, we present a new determination of the optical depth to microlensing toward the Galactic bulge. We select the sample of 62 microlensing events ( 60 unique) on clump giant sources and perform a detailed efficiency analysis. We use only the clump giant sources because these are bright bulge stars and are not as strongly affected by blending as other events. Using a subsample of 42 clump events concentrated in an area of 4.5 deg(2) with 739,000 clump giant stars, we find tau 2.17(-0.38)(+0.47) x 10(-6) at (l, b) (1.degrees 50; -2.degrees 68), somewhat smaller than found in most previous MACHO studies but in excellent agreement with recent theoretical predictions. We also present the optical depth in each of the 19 fields in which we detected events and find limits on optical depth for fields with no events. The errors in optical depth in individual fields are dominated by Poisson noise. We measure optical depth gradients of (1.06 +/- 0.71)x 10(-6) deg(-1) and (0.29 +/- 0.43)x 10(-6) deg(-1) in the Galactic latitude b and longitude l directions, respectively. Finally, we discuss the possibility of anomalous duration distribution of events in the field 104 centered on (l; b) (3 degrees.11, -3 degrees.01), as well as investigate spatial clustering of events in all fields.