Formation of Jupiter's Core and Early Stages of Envelope Accretion

We are performing calculations of the formation of Jupiter via core nucleated accretion and gas capture. The core starts as a seed body of a few hundred kilometers in radius and orbits within a swarm of planetesimals whose initial size distribution ranges from ~10 m to ~100 km. The planetesimals are immersed in a gaseous disk, representative of an early solar nebula. The evolution of the swarm of planetesimals accounts for collisions and gravitational stirring due to mutual interactions among bodies, and for migration and velocity damping due to interactions with the nebula gas. Collisions among planetesimals lead to growth and/or fragmentation, altering the size distribution of the swarm over time. Collisions of planetesimals with the seed body lead to its growth, resulting in the formation of a planetary core. Gas capture by the core leads to the accumulation of a tenuous atmosphere, which later becomes a massive envelope, increasing the size-dependent effective cross-section of the planet for planetesimals' accretion. Planetesimals that travel through the core's envelope release energy, affecting the thermal budget of the envelope, and deliver mass, affecting the opacity of the envelope. The calculation of dust opacity, which is especially important for envelope contraction, is performed self-consistently, accounting for coagulation and sedimentation of dust and small particles that are released in the envelope as passing planetesimals are ablated. We find that, in a disk of planetesimals with a surface density of about 10 g/cm2 at 5.2 AU, a one Earth mass core accumulates in less than 1e5 years, and that it takes over 1.5e6 years to accumulate a core of 3 Earth masses, when the core's geometrical cross-section is used for the accretion of planetesimals. Gas drag in the core's envelope increases the ability of the planet to accrete planetesimals. Smaller planetesimals are affected to a greater extent than are larger planetesimals. We find that the effective, envelope-enhanced cross-section leads to the growth of a core of 3 Earth masses in less than 1e5 years and of a core of 5 Earth masses in less than 2e5 years. By the time the total planet mass reaches about 6 Earth masses, the accretion rate of solids has dropped below ~1e-6 Earth masses per year. Support for this research from NASA Outer Planets Research Program is gratefully acknowledged.