Probability of Detecting a Planetary Companion during a Microlensing Event

Abstract

The averaged probability of detecting a planetary companion of a lensing star during a microlensing event toward the Galactic center when the planet to star mass ratio q = 0.001 is shown to have a maximum exceeding 10% at an orbit semimajor axis near 1.5 AU for a uniform distribution of impact parameters. This peak value is somewhat lower than the maximum of 17% obtained by Gould & Loeb in 1992, but it is raised to more than 20% for a distribution of source-lens impact parameters that is determined by the efficiency of event detection. Although these probabilities, based on a signal-to-noise ratio (S/N) detection criterion, are model and assumption dependent, the fact that they change in predictable ways as functions of the orbit semimajor axes but remain robust for plausible variations of all the relevant Galactic parameters implies that they are representative of real values. In addition, the averaging procedures are carefully defined, and they determine the dependence of the detection probabilities on several properties of the Galaxy. The probabilities for other planet to star mass ratios can be estimated from an approximate scaling of q1/2. A planet is assumed detectable if the perturbation of the single-lens light curve exceeds 2/(S/N) sometime during the event, where it is understood that at least 20 consecutive photometric points during the perturbation are necessary to confirm the detection. S/N is the instantaneous value for the amplified source. In addition, 2 m telescopes with 60 s integrations in I band with high time resolution photometry throughout the duration of an ongoing event are assumed. The probabilities are derived as a function of semimajor axis a of the planetary orbit, where the peak probability occurs where a is approximately the mean Einstein ring radius of the distribution of lenses along the line of sight. The probabilities remain significant for 0.6 a 10 AU. Dependence of the detection probabilities on the lens mass function, luminosity function of the source stars as modified by extinction, distribution of source-lens impact parameters, and the line of sight to the source are also determined, and the probabilities are averaged over the distribution of the projected position of the planet onto the lens plane, over the lens mass function, over the distribution of impact parameters, over the distribution of lens and sources along the line of sight, and over the I-band luminosity function of the sources adjusted for the source distance and extinction. The probability for a particular impact parameter and particular source I magnitude but averaged over remaining degenerate parameters also follows from the analysis. In the latter case, the extraction of the probability as a function of a for a particular q from the empirical data from a particular event is indicated.