Our motivation for this work is manifold. First, we have incorporated the gas-accretion models of Papaloizou  Nelson (2005) into the combined N-body and protoplanetary disc evolution code presented in Coleman  Nelson (2014, 2016a), in order to increase the realism of the planetary system formation simulations that can be computed with this numerical tool. The purpose of this paper is to provide a simplified examination of gas accretion on to isolated, non-interacting planetary cores at a variety of orbital locations using the evolving disc models from Coleman  Nelson (2016a), as a precursor to presenting simulations that consider the contemporaneous accretion of solids and gas on to protoplanets under the influence of migration within the evolving disc models. A second motivation is to examine how accreting planets with different initial core masses at different locations in the disc evolve within disc lifetimes. Observations indicate the presence of exoplanets (super-Earths, Neptunes and Jupiters) that are likely to be gas bearing with a broad range of orbital radii, covering the interval 0.04au  ap  100au (e.g. Marois etal. 2008; Borucki etal. 2011). Analysis of the occurrence rates as a function of planet radius in the Kepler data suggests that planets with radii in the range 0.85  Rp  4R are present around 50percent of Sun-like stars (e.g. Fressin etal. 2013), which is consonant with the results from earlier radial velocity surveys that focused on low-mass planets (Mayor etal. 2011). Transit timing variations (Wu  Lithwick 2013; Hadden  Lithwick 2016) and radial velocity measurements (Marcy etal. 2014; Weiss etal. 2016) indicate that the super-Earths and Neptunes in the Kepler data with radii Rp4R have masses in the range 2  Mp  15M, and show a tendency for the bulk density to increase for Rp1.5R and decrease for 1.5Rp4R, indicating that the smaller planets are composed almost entirely of solids, whereas the larger planets have larger radii due to the presence of significant gaseous envelopes that have been accreted during formation. Comparing theoretical models with the data suggests that the gaseous envelopes contribute little to the total masses of the super-Earths and Neptunes (Lopez  Fortney 2014), with recent estimates indicating that planets with Rp  1.2R contain 1percent gas by mass, rising to 5percent for planets with Rp3R (Wolfgang  Lopez 2015). Considering the gas giant exoplanets, numerous attempts have been made to constrain the core masses and total heavy element abundances of those transiting planets that have mass estimates from radial velocity measurements using evolutionary models of the internal structure (Guillot etal. 2006; Burrows etal. 2007; Miller  Fortney 2011; Thorngren etal. 2016). These studies provide a strong indication that the majority of gas giant exoplanets are substantially enriched with heavy elements relative to their host stars, with heavy element masses typically being 20M or larger. These results are consistent with the idea that giant planets form when a sufficiently massive (i.e. in the range 1015M) core forms that is able to accrete gas and undergo runaway gas accretion sufficiently early in the disc lifetime, in basic agreement with the theoretical core accretion models. In the absence of a sufficiently massive core that forms early enough, a more common outcome is the formation of super-Earths or Neptunes that fail to become gas giants because of the relatively slow rate of gas accretion until the envelope mass becomes comparable to the core mass. It is clearly of interest to address the above observational results through theoretical modelling of in situ planet formation, and to compare the outcomes of our calculations with recent work that has considered gas accretion on to planets with short (Lee, Chiang  Ormel 2014; Batygin, Bodenheimer  Laughlin 2016) and long orbital periods (Piso  Youdin 2014; Piso, Youdin  Murray-Clay 2015). Our third motivation is to consider the longer term cooling and contraction of the gaseous envelopes for those planets that remain in a state of quasi-static equilibrium throughout the period of gas accretion when the disc is present. Since the observations are typically relevant to exoplanets that have existed around their stars for Gyrs, they will have evolved for time periods of this duration after the epoch of formation. This is the first time that our models have been used to examine this longer term evolution, and our approach is similar to that used in recent population synthesis studies (see the recent review by Mordasini etal. 2015).
Citation: Wu  Lithwick 2013
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Citation: Marcy etal. 2014
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