Timing analysis in microlensing

Timing analysis is a powerful tool used to determine periodic features of physical phenomena. Here we review two applications of timing analysis to gravitational microlensing events. The first one, in particular cases, allows the estimation of the orbital period of binary lenses, which in turn enables the breaking of degeneracies. The second one is a method to measure the rotation period of the lensed star by observing signatures due to stellar spots on its surface.Comment: 11 pages, 4 figures. To be published in International Journal of Modern Physics D (IJMPD

Absence of a metallicity effect for ultra-short-period planets

Ultra-short-period (USP) planets are a newly recognized class of planets with periods shorter than one day and radii smaller than about 2 Earth radii. It has been proposed that USP planets are the solid cores of hot Jupiters that lost their gaseous envelopes due to photo-evaporation or Roche lobe overflow. We test this hypothesis by asking whether USP planets are associated with metal-rich stars, as has long been observed for hot Jupiters. We find the metallicity distributions of USP-planet and hot-Jupiter hosts to be significantly different ($p = 3\times 10^{-4}$), based on Keck spectroscopy of Kepler stars. Evidently, the sample of USP planets is not dominated by the evaporated cores of hot Jupiters. The metallicity distribution of stars with USP planets is indistinguishable from that of stars with short-period planets with sizes between 2--4~$R_\oplus$. Thus it remains possible that the USP planets are the solid cores of formerly gaseous planets smaller than Neptune.Comment: AJ, in pres

Classifying Exoplanets with Gaussian Mixture Model

Recently, Odrzywolek and Rafelski (arXiv:1612.03556) have found three distinct categories of exoplanets, when they are classified based on density. We first carry out a similar classification of exoplanets according to their density using the Gaussian Mixture Model, followed by information theoretic criterion (AIC and BIC) to determine the optimum number of components. Such a one-dimensional classification favors two components using AIC and three using BIC, but the statistical significance from both the tests is not significant enough to decisively pick the best model between two and three components. We then extend this GMM-based classification to two dimensions by using both the density and the Earth similarity index (arXiv:1702.03678), which is a measure of how similar each planet is compared to the Earth. For this two-dimensional classification, both AIC and BIC provide decisive evidence in favor of three components.Comment: 8 pages, 7 figure