Planet Formation by Gas-assisted Accretion of Small Solids

Abstract

We compute the accretion efficiency of small solids, with radii 1 cm ≤ R _s ≤ 10 m, on planets embedded in gaseous disks. Planets have masses 3 ≤ M _p ≤ 20 Earth masses ( M _⊕ ) and orbit within 10 au of a solar mass star. Disk thermodynamics is modeled via 3D radiation-hydrodynamics calculations that typically resolve the planetary envelopes. Both icy and rocky solids are considered, explicitly modeling their thermodynamic evolution. The maximum efficiencies of 1 ≤ R _s ≤ 100 cm particles are generally ≲10%, whereas 10 m solids tend to accrete efficiently or be segregated beyond the planet’s orbit. A simplified approach is applied to compute the accretion efficiency of small cores, with masses M _p ≤ 1 M _⊕ and without envelopes, for which efficiencies are approximately proportional to ${M}_{p}^{2/3}$ . The mass flux of solids, estimated from unperturbed drag-induced drift velocities, provides typical accretion rates dM _p / dt ≲ 10 ^−5 M _⊕ yr ^−1 . In representative disk models with an initial gas-to-dust mass ratio of 70–100 and total mass of 0.05–0.06 M _⊙ , the solids’ accretion falls below 10 ^−6 M _⊕ yr ^−1 after 1–1.5 Myr. The derived accretion rates, as functions of time and planet mass, are applied to formation calculations that compute dust opacity self-consistently with the delivery of solids to the envelope. Assuming dust-to-solid coagulation times of ≈0.3 Myr and disk lifetimes of ≈3.5 Myr, heavy-element inventories in the range 3–7 M _⊕ require that ≈90–150 M _⊕ of solids cross the planet’s orbit. The formation calculations encompass a variety of outcomes, from planets a few times M _⊕ , predominantly composed of heavy elements, to giant planets. The peak luminosities during the epoch of the solids’ accretion range from ≈10 ^−7 to ≈10 ^−6 L _⊙ .

Keywords

• Stellar accretion disks
• Radiative magnetohydrodynamics
• Astrophysical fluid dynamics
• Computational methods
• Planet formation
• Planetary-disk interactions