Atmospheres of Protoplanetary Cores: Critical Mass for Nucleated Instability

By R. Rafikov. 2004

265 citations recorded by the source corpus.

We systematically study quasi-static atmospheres of accreting protoplanetary cores for different opacity behaviors and realistic planetesimal accretion rates in various parts of the protoplanetary nebula. We demonstrate that there are two important classes of atmospheres: (1) those having an outer convective zone that smoothly merges with the surrounding nebular gas, and (2) those possessing an almost isothermal outer radiative region that effectively decouples the atmospheric interior from the nebula. The type of atmosphere accumulating around a given core depends on the core mass, nebular parameters, and accretion luminosity of the core. Cores in the inner parts of the protoplanetary disk (within roughly 0.3 AU from the Sun) have large luminosities resulting in atmospheres of the first type, while cores in the giant planet region (beyond several AU) have small accretion luminosities and always accumulate massive atmospheres of the second type. The critical core mass needed for the nucleated instability to commence is found to vary considerably as a function of distance from the Sun. This mass is 5-20 M⊕ at 0.1-1 AU, which is too large to permit the formation of "hot Jupiters" by nucleated instability around the cores that have grown in situ. In the region of giant planets the critical core mass depends on the gas opacity and planetesimal accretion rate but is insensitive to the nebular temperature or density provided that the opacity in the outer radiative region does not depend on the gas density (e.g., dust opacity). The critical mass in the region of giant planets can be as high as 20-60 M⊕ (for an opacity of 0.1 cm2 g-1) if planetesimal accretion is fast enough for protoplanetary cores to form prior to the nebular gas dissipation.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/4584a3f9c31ae0c4138dfdf425256c51884b5685

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Citations in the corpus

Tidal obliquity evolution of potentially habitable planets (2011, background): “6 in Rafikov 2006), typically much less massive.”
MIGRATION THEN ASSEMBLY: FORMATION OF NEPTUNE-MASS PLANETS INSIDE 1 AU (2011, background): “Part of this consensus was the finding, from detailed calculations of the core accretion process, that in situ formation was unlikely (Bodenheimer et al. 2000; Ikoma et al. 2001; Rafikov 2006).”
A FRAMEWORK FOR QUANTIFYING THE DEGENERACIES OF EXOPLANET INTERIOR COMPOSITIONS (2009, background): “We show the full quaternary diagram because planets in the intermediate-mass range 6− 10 M⊕ (such as GJ 581d) may still accrete a significant mass of H- rich gas (Alibert et al. 2006; Rafikov 2006) and retain it under the right conditions.”
Rapid growth of gas-giant cores by pebble accretion (2012, background): “…we can assign it an uncompressed radius of Rc = 890 ( ρ 2 g/cm3 )−1/3 ( Mc 10−3 M⊕ )1/3 km. (14) The critical core mass for runaway accretion of a gaseous envelope is approximately 10 M⊕ (Mizuno 1980), only weakly dependent on the orbital radius outside the terrestrial planet region (Rafikov 2006).”
Outgassing History and Escape of the Martian Atmosphere and Water Inventory (2015, background): “He which form gaseous envelopes around the rocky core (e.g., Hayashi et al. 1979; Rafikov 2006).”
IN SITU FORMATION AND DYNAMICAL EVOLUTION OF HOT JUPITER SYSTEMS (2015, background): “Traditionally, in situ conglomeration has been discounted because of a lack of sufficiently massive cores at small orbital radii (Rafikov 2006).”
Separating gas-giant and ice-giant planets by halting pebble accretion (2014, methodology): “B.3 corresponds to the opacity used in this study, where we assume the dust opacity is reduced by a factor of 10 with respect to the disc (Rafikov 2006).”
Planet Formation around Stars of Various Masses: The Snow Line and the Frequency of Giant Planets (2007, background): “25 (where Ṁcore is the rate at which planetesimals are accreted onto the core in units of 10−7 M⊕ yr −1, and κ is the grain opacity in units of cm2 g−1, Ikoma et al. 2000, see also Rafikov (2006)).”
MAKE SUPER-EARTHS, NOT JUPITERS: ACCRETING NEBULAR GAS ONTO SOLID CORES AT 0.1 AU AND BEYOND (2014, methodology): “For the strictly adiabatic envelopes assumed by Rafikov (2006) at ∼0.1 AU, replacing his RB with the smaller RH implies that 7-”
The minimum-mass extrasolar nebula: in situ formation of close-in super-Earths (2012, background): “Planetary accretion luminosities are so high (see §3.1), and dust-laden gas in the dense inner disk so optically thick, that the energy is likely transported by convection — i.e., the atmospheres are adiabatic, not isothermal (e.g., Rafikov 2006; Ikoma & Hori 2012).”
ATMOSPHERIC ESCAPE FROM HOT JUPITERS (2008, background): “Since stellar heating inhibits the formation of gas giants around Sun-like stars at such distances (e.g., Rafikov 2006), these “hot Jupiters” likely migrated inward by disk torques from where they were born (e.g., Papaloizou et al. 2007, and references therein).”
SUPER-EARTH ATMOSPHERES: SELF-CONSISTENT GAS ACCRETION AND RETENTION (2015, methodology): “Hydrostatic equilibrium sets the following adiabatic temperature profile (see also Rafikov 2006; Piso & Youdin 2014; Inamdar & Schlichting 2015) T (r) Teq = 1 + R′B r − R ′ B rout ≈ 1 r = rout R′B/rout r . rout R′B/r r rout , (1) where Teq ∼ 103 K is the temperature of the surrounding nebula, and…”
GIANT PLANETS ORBITING METAL-RICH STARS SHOW SIGNATURES OF PLANET–PLANET INTERACTIONS (2013, background): “Valley gas giants are unlikely to have formed in situ (Rafikov 2006) and exhibit a range of eccentricities (e) (Figure 1).”
Habitable planets around the star Gliese 581 (2007, background): “Rafikov (2006) found that planets more massive than 6 M⊕ could have accreted a significant fraction of their mass as H2-He.”
HAT-P-11b: A SUPER-NEPTUNE PLANET TRANSITING A BRIGHT K STAR IN THE KEPLER FIELD (2009, background): “As the expected limit for gravitational capture of H/He is ∼ 10M⊕ (Rafikov 2006), it is hardly surprising that HAT-P-11b has some H/He, even if evaporation played an important role during its evolution.”