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

Abstract

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 parallax vector p E , from which compact constraints on the microlens properties 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 planet sensitivities of all 41 events in the sample are calculated, from which we provide constraints on the planet distribution function. In particular, assuming a planet distribution function that is uniform in q log , where q is the planet-to-star mass ratio, we find a 95% upper limit on the fraction of stars that host typical microlensing planets of 49%, which is consistent with previous studies. Based on this planet-free sample, we develop the methodology to statistically study the Galactic distribution of planets using microlensing parallax measurements. Under the assumption that the planet distributions are the same in the bulge as in the disk, we predict that ∼1/3 of all planet detections 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 planets in the bulge relative to the disk.

OGLE-2016-BLG-1190Lb: The First Spitzer Bulge Planet Lies Near the Planet/Brown-dwarf Boundary

“…A key issue in the analysis of these events has been to break this fourfold degeneracy, in particular the twofold degeneracy that impacts the mass and distance estimates. Although in some cases Zhu et al 2015) this degeneracy has been broken by various fairly weak effects, in the great majority of cases, the degeneracy was broken only statistically (Calchi Novati et al 2015a;Zhu et al 2017b). …”

“…The corresponding (+, −) diagram looks essentially identical, but inverted with respect to the x-axis. Yee et al (2015a) do not specify what precision is required for an "adequate" parallax, but this was discussed in Zhu et al (2017b). They established a condition…”

“…In addition, they specifically did not investigate how their criteria applied to the two Spitzer microlens planets that were previously discovered Street et al 2016) until after these criteria were decided. The Zhu et al (2017b) criteria, as they apply to nonplanetary events, are quite easy to state once the appropriate definitions are in place (Section 5.2). A crucial point, however, is that for planetary events, these same criteria must be applied to the point-lens event that would have been observed in the absence of planets.…”

“…Yee et al (2015a) did not specify what was "adequate" because this requires the study of real data. Zhu et al (2017b) carried out such a study based on a sample of 41 Spitzer microlensing events without planets, which meant that these authors could not be biased-even unconsciously-by a "desire" to get more planets into the sample. In addition, they specifically did not investigate how their criteria applied to the two Spitzer microlens planets that were previously discovered Street et al 2016) until after these criteria were decided.…”

OGLE-2017-BLG-1130: The First Binary Gravitational Microlens Detected from Spitzer Only

“…We begin our Bayesian analysis by extracting from the MCMC the best fit a 0,i and covariance c ij of the three measured quantities a v v t , , We consider bulge sources and disk or bulge lenses drawn randomly from the Galactic model in Zhu et al (2017a), and for each trial we draw a mass of the primary star randomly from a Kroupa (2001) …”