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Abstract:
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Statistical estimation of the joint distribution of exoplanet masses and radii plays a fundamental role in understanding the physical and chemical composition of exoplanets. The majority of recent works in this active area of astronomy are based on an assumed parametric power-law regression model for masses as a function of radii. However, there are some arbitrary choices made in the parametric model, including how to choose a proper distribution to describe the intrinsic scatter of masses; how to choose the functional radius dependence of that distribution's variance; and even whether to assume a power-law function or not. In this paper, we present a nonparametric model to estimate the underlying joint distribution of masses and radii for exoplanets. The model is flexible enough to allow us to drop the assumptions made in the parametric model. We applied our model to the dataset used in Wolfgang, Rogers and Ford (2016), derived the conditional distribution of masses given radii from the joint mass, radius distribution, and found that a power-law is a valid assumption for the planets with radius less than 4 R_Earth. We also found the variance of the conditional distribution is not a constant. Furthermore, we applied our model to a larger dataset which consists of all the Kepler observations in the NASA Exoplanet Archive. Finally, we created a tool for astronomers to predict planet mass given its radius.
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