To cool is to accrete: Analytic scalings for nebular accretion of planetary atmospheres

Journal Article · Sun Sep 20 04:00:00 EDT 2015 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/811/1/41· OSTI ID:22882628

Lee, Eve J.; Chiang, Eugene ^[1]

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1. Department of Astronomy, University of California Berkeley, Berkeley, CA 94720-3411 (United States)

Planets acquire atmospheres from their parent circumstellar disks. We derive a general analytic expression for how the atmospheric mass grows with time t as a function of the underlying core mass M{sub core} and nebular conditions, including the gas metallicity Z. Planets accrete as much gas as can cool: an atmosphere's doubling time is given by its Kelvin–Helmholtz time. Dusty atmospheres behave differently from atmospheres made dust-free by grain growth and sedimentation. The gas-to-core mass ratio (GCR) of a dusty atmosphere scales as GCR ∝ t{sup 0.4}M{sub core}{sup 1.7}Z{sup −0.4}μ{sub rcb}{sup 3.4}, where μ{sub rcb}∝1/(1−Z) (for Z not too close to 1) is the mean molecular weight at the innermost radiative–convective boundary. This scaling applies across all orbital distances and nebular conditions for dusty atmospheres; their radiative–convective boundaries, which regulate cooling, are not set by the external environment, but rather by the internal microphysics of dust sublimation, H{sub 2} dissociation, and the formation of H{sup −}. By contrast, dust-free atmospheres have their radiative boundaries at temperatures T{sub rcb} close to nebular temperatures T{sub out}, and grow faster at larger orbital distances where cooler temperatures, and by extension lower opacities, prevail. At 0.1 AU in a gas-poor nebula, GCR ∝ t{sup 0.4}T{sub rcb}{sup −1.9}M{sub core}{sup 1.6}Z{sup −0.4}μ{sub rcb}{sup 3.3}, while beyond 1 AU in a gas-rich nebula, GCR ∝ t{sup 0.4}T{sub rcb}{sup −1.5}M{sub core}{sup 1}Z{sup −0.4}μ{sub rcb}{sup 2.2}. We confirm our analytic scalings against detailed numerical models for objects ranging in mass from Mars (0.1M{sub ⊕}) to the most extreme super-Earths (10–20M{sub ⊕}), and explain why heating from planetesimal accretion cannot prevent the latter from undergoing runaway gas accretion.

• OSTI ID: 22882628
• Journal Information: Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 1 Vol. 811; ISSN ASJOAB; ISSN 0004-637X
• Country of Publication: United Kingdom
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
COSMIC DUST
DISSOCIATION
DISTANCE
HYDROGEN
HYDROGEN IONS 1 MINUS
MASS
METALLICITY
MOLECULAR WEIGHT
NEBULAE
PLANETARY ATMOSPHERES
SATELLITE ATMOSPHERES
SATELLITES
SCALING
SUBLIMATION