Formation of giant planets: Dependences on core accretion rate and grain opacity

We have investigated the formation of gaseous envelopes of giant planets wi th wide ranges of parameters through quasi-static evolutionary simulations. In the nucleated instability model, rapid gas accretion is triggered when the solid core mass exceeds a critical mass. The gas accretion should be re gulated essentially by core accretion rate and grain opacity in the outermo st envelope. The conventional critical core mass similar to 5-20 M+ (M+: Ea rth's mass), however, is based on some nominal values of these quantities. The discovery of extrasolar giant planets requires investigation of the gas accretion processes under various circumstances. Furthermore, the current planetary accretion theory points out that the cores of Jupiter and Saturn would have been isolated from planetesimals and the core accretion would ha ve almost stopped in their later stage of formation before their masses rea ched the conventional critical core mass. Through numerical simulations of quasi-static evolution of the gaseous envelope, we have investigated the ch aracteristic growth times of the envelope mass for wide ranges of core accr etion rate and grain opacity. We also studied the case where core accretion stops before onset of rapid gas accretion. Our main results are (1) the gr owth time of the envelope mass tau(g) depends strongly on the core mass, mo derately on the grain opacity, and weakly on the past core accretion proces s, and (2) tau(g) is expressed approximately as tau(g) similar to 10(8)(M-c ore/M+)(-2.5) (kappa(gr)/1 cm(2) g(-1)) yr, where M-core is the core mass a nd kappa(gr) is the grain opacity. Our results combined with the recent pla netary accretion theory suggest surface density of solid materials twice as massive as that of the minimum-mass solar nebula model and the longer life time of the nebula than the 10(8) yr needed to form Jupiter and Saturn; oth erwise migration of protoplanets may have to be considered. Our extensive p arametric study not only cofirms the difficulty in the formation of the gia nt planets quantitatively and rigorously, it also gives essential informati on in considering the problem of the formation, which is quite useful in ap plications.