Formation of Planetary Populations I: Metallicity & Envelope Opacity Effects

Abstract

We present a comprehensive body of simulations of the formation of exoplanetary populations that incorporate the role of planet traps in slowing planetary migration. The traps we include in our model are the water ice line, the disk heat transition, and the dead zone outer edge. We reduce our model parameter set to two physical parameters: the opacity of the accreting planetary atmospheres ($\kappa_{\rm{env}}$) and a measure of the efficiency of planetary accretion after gap opening ($f_{\rm{max}}$). We perform planet population synthesis calculations based on the initial observed distributions of host star and disk properties - their disk masses, lifetimes, and stellar metallicities. We find the frequency of giant planet formation scales with disk metallicity, in agreement with the observed Jovian planet frequency-metallicity relation. We consider both X-ray and cosmic ray disk ionization models, whose differing ionization rates lead to different dead zone trap locations. In both cases, Jovian planets form in our model out to 2-3 AU, with a distribution at smaller radii dependent on the disk ionization source and the setting of envelope opacity. We find that low values of $\kappa_{\rm{env}}$ (0.001-0.002 cm$^2$ g$^{-1}$) and X-ray disk ionization are necessary to obtain a separation between hot Jupiters near 0.1 AU, and warm Jupiters outside 0.6 AU, a feature present in the data. Our model also produces a large number of super Earths, but the majority are outside of 2 AU. As our model assumes a constant dust to gas ratio, we suggest that radial dust evolution must be taken into account to reproduce the observed super Earth population.