Detection efficiencies of microlensing data sets to stellar and planetary companions

Microlensing light curves are now being monitored with the temporal samplin g and photometric precision required to detect small perturbations due to p lanetary companions of the primary lens. Microlensing is complementary to o ther planetary search techniques, both in the mass and orbital separation o f 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 g iven mass ratio and angular separation can be detected in observed microlen sing data sets; such an analysis is required in order to draw statistical i nferences about lensing companions. Our method incorporates the actual samp ling, photometric precision, and monitored duration of individual light cur ves. We apply the method to simulated (but realistic) data to explore the d ependence of detection efficiencies on observational parameters, the impact parameter of the event, the finite size of the background source, the amou nt of unlensed (blended) light, and the criterion used to define a detectio n. We find that: (1) the detection efficiency depends strongly on the impac t 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 t o 10(-2)), (3) finite sources can dramatically alter the detection efficien cy 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 ac curate determination of the detection efficiency of individual events. Sugg estions are given for addressing complications associated with computing ac curate detection efficiencies of observed data sets.