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 _ { 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 _ { p } - a distribution .
Our results reproduce the observed lack of planets with intermediate mass M _ { p } = 10 –100 M _ { \oplus } and a \lesssim 3 AU and with large mass M _ { p } \gtrsim 10 ^ { 3 } M _ { \oplus } and a \lesssim 0.2 AU .
Based on the simulated M _ { 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 .