M Dwarf Exoplanet Surface Density Distribution: A Log-Normal Fit from 0.07-400 AU

We fit a log-normal function to the M dwarf orbital surface density distribution of gas giant planets, over the mass range 1-10 times that of Jupiter, from 0.07-400 AU. We use a Markov Chain Monte Carlo approach to explore the likelihoods of various parameter values consistent with point estimates of the data given our assumed functional form. This fit is consistent with radial velocity, microlensing, and direct imaging observations, is well-motivated from theoretical and phenomenological viewpoints, and makes predictions of future surveys. We present probability distributions for each parameter as well as a Maximum Likelihood Estimate solution. We suggest this function makes more physical sense than other widely used functions, and explore the implications of our results on the design of future exoplanet surveys.