From Planetesimal to Planet in Turbulent Disks. II. Formation of Gas Giant Planets

In the core accretion scenario, gas giant planets are formed form solid cores with several Earth masses via gas accretion. We investigate the formation of such cores via collisional growth from kilometer-sized planetesimals in turbulent disks. The stirring by forming cores induces collisional fragmentation and surrounding planetesimals are ground down until radial drift. The core growth is therefore stalled by the depletion of surrounding planetesiamls due to collisional fragmentation and radial drift. The collisional strength of planetesimals determines the planetesimal-depletion timescale, which is prolonged for large planetesiamls. The size of planetesiamls around growing cores is determined by the planetesimal size distribution at the onset of runaway growth. Strong turbulence delays the onset of runaway growth, resulting in large planetesimals. Therefore, the core mass evolution depends on turbulent parameter $\alpha$; the formation of cores massive enough without significant depletion of surrounding planetesimals needs strong turbulence of $\alpha \gtrsim 10^{-3}$. However, the strong turbulence with $\alpha \gtrsim 10^{-3}$ leads to a significant delay of the onset of runaway growth and prevents the formation of massive cores within the disk lifetime. The formation of cores massive enough within several millions years therefore requires the several times enhancement of the solid surface densities, which is achieved in the inner disk $\lesssim 10$AU due to pile-up of drifting dust aggregates. In addition, the collisional strength $Q_{\rm D}^*$ even for kilometer-sized or smaller bodies affects the growth of cores; $Q_{\rm D}^* \gtrsim 10^7 \,{\rm erg/g}$ for bodies $\lesssim 1$ km is likely for this gas giant formation.