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S. J. Peale (UCSB)
The averaged probability of detecting a planetary companion of a lensing star during a gravitational microlensing event toward the Galactic center when the planet-lens mass ratio is 0.001 is shown to have a maximum exceeding 20% for a distribution of source-lens impact parameters that is determined by the efficiency of event detection, and a maximum exceeding 10% for a uniform distribution of impact parameters. The probability varies as the square root of the planet-lens mass ratio. A planet is assumed detectable if the perturbation of the light curve exceeds 2/(S/N) for a significant number of data points, where S/N is the signal-to noise ratio for the photometry of the source. The probability peaks at a planetary semimajor axis a that is close to the mean Einstein ring radius of the lenses of about 2 AU along the line of sight, and remains significant for 0.6\leq a\leq 10 AU. The low value of the mean Einstein ring radius results from the dominance of M stars in the mass function of the lenses. The probability is 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 along the line of sight to the source star, over the I band luminosity function of the sources adjusted for the source distance, and over the source distribution along the line of sight. If two or more parameters of the lensing event are known, such as the I magnitude of the source and the impact parameter, the averages over these parameters can be omitted and the probability of detection determined for a particular event. The calculated probabilities behave as expected with variations in the line of sight, the mass function of the lenses, the extinction and distance to and magnitude of the source, and with a more demanding detection criterion. The relatively high values of the probabilities are robust to plausible variations in the assumptions. The high probabilities offer the promise of gaining statistics rapidly on the frequency of planets in long period orbits, and thereby encourage the expansion of ground based microlensing searches for planets with enhanced capabilities. A ground based microlensing search for planets complements the highly successful radial velocity searches and expanding transit searches by being most sensitive to distant, long period planets, whereas both radial velocity and transit searches are most sensitive to close, massive planets. Existing and proposed astrometric searches are also most sensitive to distant planets, but only with a data time span that is a significant fraction of the orbit period.
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