Critical Core Masses for Gas Giant Formation with Grain-Free Envelopes

We investigate the critical core mass and the envelope growth timescale, assuming grain-free envelopes, to examine how small cores are allowed to form gas giants in the framework of the core accretion model. This is motivated by a theoretical dilemma concerning Jupiter formation: Modelings of Jupiter's interior suggest that it contains a small core of < 10 Earth mass, while many core accretion models of Jupiter formation require a large core of > 10 Earth mass to finish its formation by the time of disk dissipation. Reduction of opacity in the accreting envelope is known to hasten gas giant formation. Almost all the previous studies assumed grain-dominated opacity in the envelope. Instead, we examine cases of grain-free envelopes in this study. Our numerical simulations show that an isolated core of as small as 1.7 Earth mass is able to capture disk gas to form a gas giant on a timescale of million years, if the accreting envelope is grain-free; that value decreases to 0.75 Earth mass, if the envelope is metal-free, namely, composed purely of hydrogen and helium. It is also shown that alkali atoms, which are known to be one of the dominant opacity sources near 1500 K in the atmospheres of hot Jupiters, have little contribution to determine the critical core mass. Our results confirm that sedimentation and coagulation of grains in the accreting envelope is a key to resolve the dilemma about Jupiter formation.