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S.J. Peale (Dept. of Physics, UCSB)
It is by now well known that a planetary companion of a star that is amplifying a source toward the center of the Galaxy through gravitational lensing (microlensing) can make its presence known by perturbing the otherwise smooth bell shaped light curve of the event. The probability of detecting such a planet, based on a photometric signal to noise criterion (a perturbation of 2/(S/N) is assumed detectable), is determined as a function of the semimajor axis a of the planetary orbit. The probability is averaged over the distribution of lenses along the line of sight, over the mass function of the lenses, over the I band luminosity function of the sources and over the distribution of visible sources along the line of sight for a fixed planet-star mass ratio m/M>10-4. The distribution of stars in the galaxy is assumed to be a combination of the Bahcall-Soneira (1980) disk model and Zhao (1996) triaxial bulge model. The averaged probability is a function of the line of sight for the particular galactic model, the extinction along the line of sight, and the lens mass function. For m/M=0.001 and a line of sight toward Baade's window (AI=0.76), [(\ell,b)=(1\circ,4\circ)], and a Holtzman et al. (1998) mass function, the maximum averaged probability of detection is near 11.5% for a near 2 AU and falls to about 6% and 2% for a=0.6 AU and 10 AU respectively. If more M stars are added to the Holtzman et al. mass function by increasing the index above 1, the peak probability is moved to smaller semimajor axes. The probability varies as \sqrt{m/M}. The motivation for a dedicated, well funded microlensing search for planets is the possibly rapid accumulation of statistics of planetary occurrence. However, observational constraints reduce the detection probabilities, and such statistics for, say, Jupiter mass planets near 5 AU from their stars may have already been largely obtained through radial velocity measurements by the time such a dedicated search becomes operational. This work is partially supported by the NASA OSS Program under grant NAG5 7177.