Envelopes of embedded super-Earths – II. Three-dimensional isothermal simulations

Abstract

Massive planetary cores embedded in protoplanetary discs are believed to accrete extended atmospheres, providing a pathway to forming gas giants and gas-rich super-Earths. The properties of these atmospheres strongly depend on the nature of the coupling between the atmosphere and the surrounding disc. We examine the formation of gaseous envelopes around massive planetary cores via three-dimensional inviscid and isothermal hydrodynamic simulations. We focus the changes in the envelope properties as the core mass varies from low (sub-thermal) to high (super-thermal) values, a regime relevant to close-in super-Earths. We show that global envelope properties such as the amount of rotational support or turbulent mixing are mostly sensitive to the ratio of the Bondi radius of the core to its physical size. High-mass cores are fed by supersonic inflows arriving along the polar axis and shocking on the densest parts of the envelope, driving turbulence and mass accretion. Gas flows out of the core's Hill sphere in the equatorial plane, describing a global mass circulation through the envelope. The shell of shocked gas atop the core surface delimits regions of slow (inside) and fast (outside) material recycling by gas from the surrounding disc. While recycling hinders the runaway growth towards gas giants, the inner regions of protoplanetary atmospheres, more immune to mixing, may remain bound to the planet.

Radial Gradients in Dust-to-gas Ratio Lead to Preferred Region for Giant Planet Formation

“…Previous studies have proposed three potential solutions: 1) accretion of metal rich gas, which increases the envelope opacity and slows the gas accretion rate during the cooling growth phase (e.g. Lee et al 2014;Chen et al 2020), 2) late-time core assembly, so that there is a very short period for the planet to accrete prior to the dispersal of the gas disk (Lee & Chiang 2016), and 3) a flow of high entropy gas into the Hill sphere of the growing planet that prevents it from cooling (Ormel et al 2015;Béthune & Rafikov 2019, but see Kurokawa & Tanigawa 2018). Scenario 1 in and of itself applies for either dusty or dust-free accretion but it is more effective for dusty accretion as its overall higher opacity delays accretion even more.…”

Circumplanetary Disk Dynamics in the Isothermal and Adiabatic Limits

“…Gas tends to flow vertically toward the planet from the poles, and is expelled radially near the midplane. Qualitatively, this pattern persists email: fung@ias.edu whether the gas is isothermal (Machida et al 2008;Tanigawa et al 2012;Fung et al 2015;Ormel et al 2015;Béthune & Rafikov 2019), isentropic (Fung et al 2017), or is modeled with more sophisticated thermodynamics (D'Angelo & Bodenheimer 2013;Szulágyi et al 2016;Szulágyi 2017;Cimerman et al 2017;Lambrechts & Lega 2017;Schulik et al 2019). In simulations where the planet is modeled as a sink cell, the equatorial outflow is reduced or even stopped, but the inflow is still primarily vertical (Bate et al 2003;D'Angelo et al 2003;Paardekooper & Mellema 2008).…”

“…A related unresolved issue is the CPD mass. Some suggest that mass is zero, as the entire CPD is unbound (Ormel et al 2015;Cimerman et al 2017;Béthune & Rafikov 2019), a situation referred to as "atmospheric recycling." Others disagree (D'Angelo & Bodenheimer 2013;Lambrechts & Lega 2017;Lambrechts et al 2019).…”

Accreting protoplanets: Spectral signatures and magnitude of gas and dust extinction at Hα

“…From angular momentum conservation, and by analogy with objects across a large range of mass scales, a part of the matter likely goes through a CPD (which in its outer regions may be a decretion disc, i.e. exhibit an outflow; Tanigawa et al 2012; the general theory of decretion discs is presented in Lynden- Bell & Pringle 1974;Pringle 1991;Nixon & Pringle 2021) while the rest could fall directly onto the proto-gas-giant with a polar shock (see Béthune & Rafikov 2019;Béthune 2019). However, the fraction of the gas processed through a CPD is unknown, as is how the gas leaves the CPD to be incorporated into the planet.…”