The formation and retention of gas giant planets around stars with a range of metallicities

The apparent dependence of detection frequency of extrasolar planets on the metallicity of their host stars is investigated with Monte Carlo simulations using a deterministic core-accretion planet formation model. According to this model, gas giants formed and acquired their mass $M_{\rm p}$ through planetesimal coagulation followed by the emergence of cores onto which gas is accreted. These protoplanets migrate and attain their asymptotic semi-major axis $a$ through their tidal interaction with their nascent disk. Based on the observed properties of protostellar disks, we generate $M_{\rm p}$-$a$ distribution. Our results reproduce the observed lack of planets with intermediate mass $M_{\rm p} = 10$--100$M_{\oplus}$ and $a \la 3$AU and with large mass $M_{\rm p} \ga 10^3 M_{\oplus}$ and $a \la 0.2$AU. Based on the simulated $M_{\rm p}$-$a$ distributions, we also evaluate the metallicity dependence of fraction of stars harboring planets that are detectable with current radial velocity survey. If protostellar disks attain the same fraction of heavy elements which are contained in their host stars, the detection probability around metal-rich stars would be greatly enhanced because protoplanetary cores formed in them can grow to several Earth masses prior to their depletion. These large masses are required for the cores to initiate rapid gas accretion and to transform into giant planets. The theoretically extrapolated metallicity dependence is consistent with the observation. This correlation does not arise naturally in the gravitational-instability scenario. We also suggest other metallicity dependence of the planet distributions that can be tested by on-going observations.