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

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