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Planet Traps and Planetary Cores: Origins of the Planet-Metallicity Correlation

Massive exoplanets are observed preferentially around high metallicity ([Fe/H]) stars while low-mass exoplanets do not show such an effect. This so-called planet-metallicity correlation generally favors the idea that most observed gas giants at $r<10$ AU are formed via a core accretion process. We investigate the origin of this phenomenon using a semi-analystical model, wherein the standard core accretion takes place at planet traps in protostellar disks where rapid type I migrators are halted. We focus on the three major exoplanetary populations - hot-Jupiters, exo-Jupiters located at $r \simeq 1$ AU, and the low-mass planets. We show using a statistical approach that the planet-metallicity correlations are well reproduced in these models. We find that there are specific transition metallicities with values [Fe/H]$=-0.2$ to $-0.4$, below which the low-mass population dominates, and above which the Jovian populations take over. The exo-Jupiters significantly exceed the hot-Jupiter population at all observed metallicities. The low-mass planets formed via the core accretion are insensitive to metallicity, which may account for a large fraction of the observed super-Earths and hot-Neptunes. Finally, a controlling factor in building massive planets is the critical mass of planetary cores ($M_{c,crit}$) that regulates the onset of runaway gas accretion. Assuming the current data is roughly complete at [Fe/H]$>-0.6$, our models predict that the most likely value of the "mean" critical core mass of Jovian planets is $\braket{M_{c,crit}} \simeq 5 M_{\oplus}$ rather than $10 M_{\oplus}$. This implies that grain opacities in accreting envelopes should play an important role in lowering $M_{c,crit}$.