IntroductionEnvelope Size and Maximum Gas Accretion RatesOuter Boundary of Planet's EnvelopeGas Accretion RatesEffects of Circumsolar Disk Hydrodynamics on Jupiter's Accretion of GasParameters of our SimulationsResultsImplications for Capture of Irregular SatellitesSummary and ConclusionsJanuary 4, 2009Preprint typeset using LATEX style emulateapj v. 03/07/07MODELS OF JUPITER’S GROWTH INCORPORATING THERMAL AND HYDRODYNAMIC CONSTRAINTS†Jack J. Lissauer, Olenka Hubickyj1, Gennaro D’Angelo2NASA Ames Research Center, Space Science and Astrobiology Division, MS 245-3, Moffett Field, CA 94035, USAandPeter BodenheimerUCO/Lick Observatory, Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USAJanuary 4, 2009ABSTRACTWe model the growth of Jupiter via core nucleated accretion, applying constraints from hydrody-namical processes that result from the disk–planet interaction. We compute the planet’s internalstructure using a well tested planetary formation code that is based upon a Henyey-type stellarevolution code. The planet’s interactions with the protoplanetary disk are calculated using 3-D hy-drodynamic simulations. Previous models of Jupiter’s growth have taken the radius of the planet tobe approximately one Hill sphere radius, RH. However, 3-D hydrodynamic simulations show that onlygas within ∼ 0.25 RHremains bound to the planet, with the more distant gas eventually participatingin the shear flow of the protoplanetary disk. Therefore in our new simulations, the planet’s outerboundary is placed at the location where gas has the thermal energy to reach the portion of the flownot bound to the planet. We find that the smaller radius increases the time required for planetarygrowth by ∼ 5%. Thermal pressure limits the rate at which a planet less than a few dozen times asmassive as Earth can accumulate gas from the protoplanetary disk, whereas hydrodynamics regulatesthe growth rate for more massive planets. Within a moderately viscous disk, the accretion rate peakswhen the planet’s mass is about equal to the mass of Saturn. In a less viscous disk hydrodynamicallimits to accretion are smaller, and the accretion rate peaks at lower mass. Observations suggestthat the typical lifetime of massive disks around young stellar objects is ∼ 3 Myr. To account forthe dissipation of such disks, we perform some of our simulations of Jupiter’s growth within a diskwhose surface gas density decreases on this timescale. In all of the cases that we simulate, the planet’seffective radiating temperature rises to well above 1000 K soon after hydrodynamic limits begin tocontrol the rate of gas accretion and the planet’s distended envelope begins to contract. According toour simulations, proto-Jupiter’s distended and thermally-supported envelope was too small to capturethe planet’s current retinue of irregular satellites as advocated by Pollack et al. [Pollack, J.B., Burns,J.A., Tauber, M.E., 1979. Icarus 37, 587–611].Subject headings: Jovian planets; Jupiter, interior; Accretion; Planetary formation; Planet-disk inter-action1. INTRODUCTIONAccording to the core nucleated accretion model, gi-ant planets begin their growth via the same processof agglomeration of solid bodies as do terrestrial plan-ets; however, unlike terrestrials, the solid cores of giantplanets reach masses large enough to capture substantialamounts of gas from their star’s protoplanetary disk be-fore said disk dissipates (Lissauer and Stevenson 2007).Previous models of this process have simulated either thethermal factors that limit the ability of a planet to re-tain gas (Bodenheimer and Pollack 1986, hereafter BP86;Pollack et al. 1996, hereafter PHBLPG96; Bodenheimeret al. 2000, hereafter BHL00; Ikoma et al. 2000; Hubickyjet al. 2005, hereafter HBL05; Alibert et al. 2005a,b; Mar-ley et al. 2007) or the disk interaction physics that gov-erns the flow of gas to a planet (Nelson et al. 2000;Electronic address: [email protected] address: [email protected] address: [email protected] address: [email protected] at UCO/Lick Observatory, University of California, SantaCruz.2NASA Postdoctoral Fellow.†To appear in the journal Icarus.D’Angelo et al. 2003, hereafter DKH03; Bate et al. 2003).Here we consider both thermal and gas flow limits to gi-ant planet growth, and present the first models of thegrowth of Jupiter that are constrained by detailed simu-lations of both of these factors.A planet of order one to several Earth masses (M⊕)at a distance of about 5 AU from the central star is ableto capture an atmosphere from the protoplanetary diskbecause the escape speed from its surface is large com-pared to the thermal velocity of gas in the disk. How-ever, such an atmosphere is very tenuous and distended,with thermal pressure pushing gas outwards and therebylimiting further accretion of gas. The key factor gov-erning the ability of planet to accumulate additional gaswhen the mass of the atmosphere is less than the massof the core is the planet’s ability to radiate the energythat is provided to it by the accretion of planetesimalsand gravitationally-induced compression of gas. The es-cape of this energy cools the gaseous envelope, allowingit to shrink and thereby enabling more gas to enter theplanet’s gravitational domain. Evolution occurs slowly,and hydrostatic structure is generally a very good ap-proximation. Once a planet has enough mass for its self-gravity to compress the envelope substantially, its abilityarXiv:0810.5186v1 [astro-ph] 29 Oct 20082 Lissauer, Hubickyj, D’Angelo, & Bodenheimerto accrete additional gas is limited only by the amount ofgas available. Hydrodynamic limits allow quite rapid gasflow to a planet in an unperturbed disk. But a planet al-ters the disk by accreting material from it and by exertinggravitational torques upon it (Lin and Papaloizou 1979;Goldreich and Tremaine 1980). Both of these processescan lead to gap formation and isolation of the planetfrom the surrounding gas.Our approach is to follow the physical structureand thermal evolution of the growing giant planetin the spherically symmetric (one-dimensional) quasi-hydrostatic approximation, and to incorporate the three-dimensional hydrodynamic interactions between theplanet and the circumstellar disk via boundary con-ditions at the planet’s outer ‘surface’. Mass and en-ergy transport within the planet are followed using
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