Toward a Galactic Distribution of Planets . I . Methodology and Planet Sensitivities of the 2015 High-cadence Spitzer Microlens Sample

We analyze an ensemble of microlensing events from the 2015 Spitzer microlensing campaign, all of which were densely monitored by ground-based high-cadence survey teams. The simultaneous observations from Spitzer and the ground yield measurements of the microlensing parallaxvector π_E, from which compact constraints on the microlensproperties are derived, including ≾25% uncertainties on the lens mass and distance. With the current sample, we demonstrate that the majority of microlenses are indeed in the mass range of M dwarfs. The planetsensitivities of all 41 events in the sample are calculated, from which we provide constraints on the planetdistribution function. In particular, assuming a planetdistribution function that is uniform in log q, where q is the planet-to-star mass ratio, we find a 95% upper limit on the fraction of stars that host typical microlensing planetsof 49%, which is consistent with previous studies. Based on this planet-free sample, we develop the methodology to statistically study the Galactic distribution of planetsusing microlensing parallaxmeasurements. Under the assumption that the planetdistributions are the same in the bulgeas in the disk, we predict that ~1/3 of all planetdetections from the microlensing campaigns with Spitzer should be in the bulge. This prediction will be tested with a much larger sample, and deviations from it can be used to constrain the abundance of planetsin the bulgerelative to the disk.