Models of the in Situ Formation of Detected Extrasolar Giant Planets

By P. Bodenheimer, O. Hubickyj, Jack J. Lissauer. 2021

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Abstract We present numerical simulations of the formation of the planetary companions to 47 UMa, ρ CrB, and 51 Peg. They are assumed to have formed in situ according to the basic model that a core formed first by accretion of solid particles, then later it captured substantial amounts of gas from the protoplanetary disk. In most of the calculations we prescribe a constant accretion rate for the solid core. The evolution of the gaseous envelope is calculated according to the following assumptions: (1) it is in quasi-hydrostatic equilibrium, (2) the gas accretion rate is determined by the requirement that the outer radius of the planet is the place at which the thermal velocity of the gas allows it to reach the boundary of the planet's Hill sphere, (3) the gas accretion rate is limited, moreover, by the prescribed maximum rate at which the nebula can supply the gas, and (4) the growth of the planet stops once it obtains approximately the minimum mass determined from radial velocity measurements (in one case the planet is allowed to grow to twice this limit). Calculations are carried out through an initial phase during which solid accretion dominates, past the point of crossover when the masses of solid and gaseous material are equal, through the phase of rapid gas accretion, and into the final phase of contraction and cooling at constant mass. Alternative calculations are presented for the case of 47 UMa in which the solid accretion rate is calculated, not assumed, and the dissolution of planetesimals within the gaseous envelope is considered. In all cases there is a short phase of high luminosity (10 −3 –10 −2 L ⊙ ) associated with rapid gas accretion. The height and duration of this peak depend on uncertain model parameters. The conclusion is reached that in situ formation of all of these companions is possible under some conditions. However, it is more likely that orbital migration was an important component of the evolution, at least for the planets around ρ CrB and 51 Peg.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/46d8c9cd54ee62a2260e7d35323867cd1f369de7

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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).”
Statistical properties of exoplanets. III. Planet properties and stellar multiplicity (2004, background): “Formation at larger distances followed by inward migration seems to be a better explanation to the existence of these planets (e.g. Lin et al. 1996; Bodenheimer et al. 2000).”
The GAPS Programme with HARPS-N at TNG - XIV. Investigating giant planet migration history via improved eccentricity and mass determination for 231 transiting planets (2017, unknown): “These planets are thought to be formed beyond the water-ice line ( a (cid:38) 1 − 3 au) in the protoplanetary disc, where solid material is abundant because of ice condensation, and then migrate towards their host stars (Bodenheimer et al. 2000; Raﬁkov 2006).”
An Estimate of the Age Distribution of Terrestrial Planets in the Universe: Quantifying Metallicity as a Selection Effect (2000, background): “A im s O bservations ofprotoplanetary disks around young stars in star-form ing regions support the widely accepted idea thatplanetform ation isa com m on by-productofstarform ation (e.g. Beckwith etal.”
Evolution of "51 Pegasus b-like" planets (2002, unknown): “In this context, Bodenheimer et al. (2000, 2001) assume that the temperature at optical depth 2 = 3 (corresponding in their model to a pressure of the order (cid:24) 1 mbar) is equal to the e(cid:11)ective temperature T e(cid:11) , an approximation that leads to an underestimation of the actual…”
THE IMPRINT OF EXOPLANET FORMATION HISTORY ON OBSERVABLE PRESENT-DAY SPECTRA OF HOT JUPITERS (2016, background): “The boundary conditions that are necessary to solve the internal structure equations differ depending on whether the planet is in the attached phase at low core masses or in the detached phase during runaway gas accretion (Bodenheimer et al. 2000; Mordasini et al. 2012c).”
Toward a Deterministic Model of Planetary Formation. III. Mass Distribution of Short-Period Planets around Stars of Various Masses (2005, background): “Under the general concept of sequential accretion scenario, dynamically-isolated close-in plan- ets may also form in situ (Bodenheimer et al. 2000).”
On the Luminosity of Young Jupiters (2006, methodology): “In this section, we briefly review the particular implementation of this model by Pollack et al. (1996) and collaborators (Bodenheimer et al. 2000; Hubickyj et al. 2005) and inform the reader of important model assumptions.”
FORMATION AND STRUCTURE OF LOW-DENSITY EXO-NEPTUNES (2011, background): “At the surface, gaseous mass of solar composition is added at a sufficient rate to maintain an outer radius Rp = Reff , which is given by (Bodenheimer et al. 2000) as Reff = GMp c2s + GMp KRH , (9) where RH is the Hill sphere radius, cs is the sound speed in the disk outside the planet, Mp is the…”
UNVEILING THE STRUCTURE OF PRE-TRANSITIONAL DISKS (2010, background): “These cores can become terrestrial planets or, if the cores are massive enough, gas giant cores which can accrete the surrounding gas in the disk (Pollack et al. 1996; Bodenheimer et al. 2000).”
Models of Jupiter's growth incorporating thermal and hydrodynamic constraints (2008, methodology): “…factors that limit the ability of a planet to retain gas (Bodenheimer and Pollack 1986, hereafter BP86; Pollack et al. 1996, hereafter PHBLPG96; Bodenheimer et al. 2000, hereafter BHL00; Ikoma et al. 2000; Hubickyj et al. 2005, hereafter HBL05; Alibert et al. 2005a,b; Marley et al. 2007) or…”