Spin of protoplanets generated by pebble accretion: Influences of protoplanet-induced gas flow

Abstract

We investigate the spin state of a protoplanet during the pebble accretion influenced by the gas flow in the gravitational potential of the protoplanet and how it depends on the planetary mass, the headwind speed, the distance from the host star, and the pebble size. We perform nonisothermal three-dimensional hydrodynamical simulations in a local frame to obtain the gas flow around the planet. We then numerically integrate three-dimensional orbits of pebbles under the obtained gas flow. Finally, assuming uniform spatial distribution of incoming pebbles, we calculate net spin by summing up specific angular momentum that individual pebbles transfer to the protoplanet at impacts. We find that a protoplanet with the envelope acquires prograde net spin rotation regardless of the planetary mass, the pebble size, and the headwind speed of the gas. This is because accreting pebbles are dragged by the envelope that commonly has prograde rotation. As the planetary mass or orbital radius increases, the envelope is thicker and the prograde rotation is faster, resulting in faster net prograde spin. When the dimensionless thermal mass of the planet, $m=R_{\mathrm{Bondi}}/H$, where $R_{\mathrm{Bondi}}$ and $H$ are the Bondi radius and the disk gas scale height, is larger than a certain critical mass ($m\gtrsim 0.3$ at $0.1\mathrm{au}$ or $m\gtrsim 0.1$ at $1\mathrm{au}$), the spin rotation exceeds the breakup one. The predicted spin frequency reaches the breakup one at the planetary mass $m_{\mathrm{iso},\mathrm{rot}}\sim 0.1(a/1\mathrm{au}{)}^{-1/2}$ (where $a$ is the orbital radius), suggesting that the protoplanet cannot grow beyond $m_{\mathrm{iso},\mathrm{rot}}$. It is consistent with the Earth's current mass and could help the formation of the Moon by a giant impact on fast-spinning proto-Earth.

arXiv comment14 pages, 10 figures, Accepted for publication in Astronomy and Astrophysics (A&A)

References in corpus (32)

• Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks
• Rapid growth of gas-giant cores by pebble accretion
• Particle Stirring in Turbulent Gas Disks: Including Orbital Oscillations
• The effect of gas drag on the growth of protoplanets -- Analytical expressions for the accretion of small bodies in laminar disks
• The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers
• Separating gas-giant and ice-giant planets by halting pebble accretion
• Pebble isolation mass --- scaling law and implications for the formation of super-Earths and gas giants
• An Extension of the Athena++ Code Framework for GRMHD Based on Advanced Riemann Solvers and Staggered-Mesh Constrained Transport
• Hydrodynamics of Embedded Planets' First Atmospheres. II. A Rapid Recycling of Atmospheric Gas
• Asynchronous rotation of Earth-mass planets in the habitable zone of lower-mass stars
• On the water delivery to terrestrial embryos by ice pebble accretion
• The radial dependence of pebble accretion rates: A source of diversity in planetary systems I. Analytical formulation
• Reduced gas accretion on super-Earths and ice giants
• Global Models of Planet Formation and Evolution
• How much does turbulence change the pebble isolation mass for planet formation?
• Hydrodynamics of embedded planets' first atmospheres - III. The role of radiation transport for super-Earth planets
• The 3D Flow Field Around an Embedded Planet
• Angular Momentum Accretion onto a Gas Giant Planet
• Hydrodynamics of Embedded Planets' First Atmospheres. I. A Centrifugal Growth Barrier for 2D Flows
• Understanding how planets become massive. I. Description and validation of a new toy model
• Suppression of atmospheric recycling of planets embedded in a protoplanetary disc by buoyancy barrier
• Circumplanetary Disk Dynamics in the Isothermal and Adiabatic Limits
• The maximum mass of planetary embryos formed in core-accretion models
• Steady State by Recycling prevents Premature Collapse of Protoplanetary Atmospheres
• Envelopes of embedded super-Earths II. Three-dimensional isothermal simulations
• Gas flow around a planet embedded in a protoplanetary disc: the dependence on the planetary mass
• Uranian Satellite Formation by Evolution of a Water Vapor Disk Generated by a Giant Impact
• Recycling of the first atmospheres of embedded planets: Dependence on core mass and optical depth
• Spinning up planetary bodies by pebble accretion
• Influences of three-dimensional gas flow induced by protoplanets on pebble accretion --$\mathrm{I}$. shear regime
• Influences of protoplanet-induced three-dimensional gas flow on pebble accretion $\mathrm{I}\mathrm{I}$. Headwind regime
• Dust ring and gap formation by gas flow induced by low-mass planets embedded in protoplanetary disks $\mathrm{I}$. Steady-state model

Cited by in corpus (7)

• Pebble-driven migration of low-mass planets in the 2D regime of pebble accretion
• Sublimation of refractory minerals in the gas envelopes of accreting rocky planets
• An extremely low-density exoplanet spins slow
• The influence of a static planetary atmosphere on spin transfer during pebble accretion
• Forming Earth-like and Low-Mass Rocky Exoplanets Through Pebble and Planetesimal Accretion
• Impact of rotation on synthetic mass-radius relationships of two-layer rocky planets and water worlds
• Synchronisation of a tidal binary by inward orbital migration. The case of Pluto and Charon