The Bimodal Distribution in Exoplanet Radii: Considering Varying Core Compositions and $\rm H_{2}$ Envelope's Sizes

Several models have been introduced in order to explain the radius distribution in exoplanet radii observed by Fulton et al. (2017) with one peak at $\rm \sim 1.3 R_{\oplus}$ the other at $\rm \sim 2.4 R_{\oplus}$ and the minimum at $\rm \sim 1.75R_{\oplus}$. In this paper we focus on the hypothesis that the exoplanet size distribution is caused by stellar XUV-induced atmospheric loss. We evolve $10^{6}$ synthetic exoplanets by exposing them to XUV irradiation from synthetic ZAMS stars. For each planet we set a different interior composition which ranged from $\rm 100 \: wt\%$ Fe (very dense) through $\rm 100 \: wt\%$ $\rm MgSiO_{3}$ (average density) and to $\rm 100 \: wt\%$ $\rm H_{2}O$ ice (low density) with varying hydrogen envelop sizes which varied from $\rm 0 \: wt\%$ (a negligible envelop) to $\rm 100 \: wt\%$ (a negligible core). Our simulations were able to replicate the bimodal distribution in exoplanet radii. We argue that in order to reproduce the distribution by Fulton et al. (2017) it is mandatory for there to be a paucity of exoplanets with masses above $\rm \sim 8M_{\oplus}$. Furthermore, our best-fit result predicts an initial flat distribution in exoplanet occurrence for $\rm M_{P} \lesssim 8M_{\oplus}$ with a strong deficiency for planets with $\rm \lesssim 3M_{\oplus}$. Our results are consistent with the $\rm \sim 1.3R_{\oplus}$ radius peak mostly encompassing denuded exoplanets whilst the $\rm \sim 2.4R_{\oplus}$ radius peak mainly comprising exoplanets with large hydrogen envelops