Hydrodynamics of Embedded Planets' First Atmospheres. I. A Centrifugal Growth Barrier for 2D Flows

Abstract

In the core accretion paradigm of planet formation, gas giants only form a massive atmosphere after their progenitors exceeded a threshold mass: the critical core mass. Most (exo)planets, being smaller and rock/ice-dominated, never crossed this line. Nevertheless, they were massive enough to attract substantial amounts of gas from the disc, while their atmospheres remained in pressure-equilibrium with the disc. Our goal is to characterise the hydrodynamical properties of the atmospheres of such embedded planets and their implication for their (long-term) evolution. In this paper -- the first in series -- we start to investigate the properties of an isothermal and inviscid flow past a small, embedded planet by conducting local, 2D hydrodynamical simulations. Using the PLUTO code we confirm that the flow is steady and bound. This steady outcome is most apparent for the log-polar grid (with the grid spacing proportional to the distance from the planet). For low-mass planets, Cartesian grids are somewhat less efficient as they have difficulty to follow the circular, large speeds in the deep atmosphere. Relating the amount of rotation to the gas fraction of the atmosphere, we find that more massive atmospheres rotate faster -- a finding consistent with Kelvin's circulation theorem. Rotation therefore limits the amount of gas that planets can acquire from the nebula. Dependent on the Toomre-Q parameter of the circumstellar disc, the planet's atmosphere will reach Keplerian rotation before self-gravity starts to become important.

16 pages, 12 figures, accepted for publication in MNRAS

References in corpus (10)

• PLUTO: a Numerical Code for Computational Astrophysics
• Models of the in situ formation of detected extrasolar giant planets
• Constraints on the mass of a habitable planet with water of nebular origin
• Formation of Jupiter using opacities based on detailed grain physics
• Treating gravity in thin disk simulations
• An Atmospheric Structure Equation for Grain Growth
• Gas accretion onto planetary cores: three-dimensional self-gravitating radiation hydrodynamical calculations
• On the width and shape of the corotation region for low-mass planets
• On the Viability of the Magnetorotational Instability in Circumplanetary Disks
• Formation of Isothermal Disks around Protoplanets. I. Introductory Three-Dimensional Global Simulations for Sub-Neptune-Mass Protoplanets

Cited by in corpus (32)

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• Hydrodynamics of embedded planets' first atmospheres - III. The role of radiation transport for super-Earth planets
• Coorbital thermal torques on low-mass protoplanets
• Convergence of the critical cooling rate for protoplanetary disk fragmentation achieved; the key role of numerical dissipation of angular momentum
• Effects of the Planetary Temperature on the Circumplanetary Disk and on the Gap
• Tidal Inflation Reconciles Low-Density Sub-Saturns with Core Accretion
• Detectability of embedded protoplanets from hydrodynamical simulations
• Envelopes of embedded super-Earths II. Three-dimensional isothermal simulations
• Super-Earths and Earth-like Exoplanets
• Gas flow around a planet embedded in a protoplanetary disc: the dependence on the planetary mass
• The Preservation of Super Earths and the Emergence of Gas Giants after Their Progenitor Cores have Entered the Pebble Isolation Phase
• Recycling of the first atmospheres of embedded planets: Dependence on core mass and optical depth
• Atmospheric Recyling of Volatiles by Pebble-Accreting Planets
• Influences of three-dimensional gas flow induced by protoplanets on pebble accretion --$\mathrm{I}$. shear regime
• Physics of Planet Trapping with Applications to HL Tau
• Prograde and Retrograde Gas Flow around Disk-embedded Companions: Dependence on Eccentricity, Mass and Disk Properties
• TW Hya: an old protoplanetary disc revived by its planet
• The Growth of Protoplanets via the Accretion of Small Bodies in Disks Perturbed by the Planetary Gravity
• Pebble-driven migration of low-mass planets in the 2D regime of pebble accretion
• Gap opening by planets in discs with magnetised winds
• Episodic accretion and mergers during growth of massive protostars
• Envelopes of embedded super-Earths I. Two-dimensional simulations
• Spin of protoplanets generated by pebble accretion: Influences of protoplanet-induced gas flow
• The Dynamic Proto-atmospheres around Low-Mass Planets with Eccentric Orbits
• Self-gravitating planetary envelopes and the core-nucleated instability
• Meridional Circulation driven by Planetary Spiral Wakes in Radiative and Magnetized Protoplanetary Discs
• Dust ring and gap formation by gas flow induced by low-mass planets embedded in protoplanetary disks $\mathrm{I}$. Steady-state model
• The influence of a static planetary atmosphere on spin transfer during pebble accretion
• Accretion rates of stellar-mass compact objects embedded in AGN discs
• Ohmic dissipation during the formation of super-Earth
• Interior dynamics of envelopes around disk-embedded planets