Detection efficiencies of microlensing data sets to stellar and planetary companions

Microlensing light curves are now being monitored with the temporal sampling and photometric precision required to detect small perturbations due to planetary companions of the primary lens. Microlensing is complementary to other planetary search techniques, both in the mass and orbital separation of the planets to which it is sensitive and its potential for measuring the abundance of planets beyond the solar neighborhood. We present an algorithm to analyze the efficiency with which the presence of lensing binaries of given mass ratio and angular separation can be detected in observed microlensing data sets; such an analysis is required in order to draw statistical inferences about lensing companions. Our method incorporates the actual sampling, photometric precision, and monitored duration of individual light curves. We apply the method to simulated (but realistic) data to explore the dependence of detection efficiencies on observational parameters, the impact parameter of the event, the finite size of the background source, the amount of unlensed (blended) light, and the criterion used to define a detection. We find that: (1) the detection efficiency depends strongly on the impact parameter of the monitored event, (2) the detection efficiency is robust to changes in detection criterion for strict criteria (Delta chi(2) greater than or similar to 100) and large mass ratios (q greater than or similar to 10(-2)), (3) finite sources can dramatically alter the detection efficiency to companions with mass ratios q less than or similar to 10(-3), and (4) accurate determination of the blended light fraction is crucial for the accurate determination of the detection efficiency of individual events. Suggestions are given for addressing complications associated with computing accurate detection efficiencies of observed data sets.