An Analytic Model Approach to the Frequency of Exoplanets

Abstract

The underlying population of exoplanets around stars in the Kepler sample can be inferred by a simulation that includes binning the Kepler planets in radius and period, invoking an empirical noise model, assuming a model exoplanet distribution function, randomly assigning planets to each of the Kepler target stars, asking whether each planet's transit signal could be detected by Kepler, binning the resulting simulated detections, comparing the simulations with the observed data sample, and iterating on the model parameters until a satisfactory fit is obtained. The process is designed to simulate the Kepler observing procedure. The key assumption is that the distribution function is the product of separable functions of period and radius. Any additional suspected biases in the sample can be handled by adjusting the noise model or selective editing of the range of input planets. An advantage of this overall procedure is that it is a forward calculation designed to simulate the observed data, subject to a presumed underlying population distribution, minimizing the effect of bin-to-bin fluctuations. Another advantage is that the resulting distribution function can be extended to values of period and radius that go beyond the sample space, including, for example, application to estimating eta-sub-Earth, and also estimating the expected science yields of future direct-imaging exoplanet missions such as WFIRST-AFTA.