Capture of solids by growing proto-gas giants: effects of gap formation and supply limited growth

Abstract

Studies of internal structure of gas giant planets suggest that their envelopes are enriched with heavier elements than hydrogen and helium relative to their central stars. Such enrichment likely occurred by solid accretion during late formation stages of gas giant planets in which gas accretion dominates protoplanetary growth. Some previous studies performed orbital integration of planetesimals around a growing protoplanet with the assumption of an uniform circumstellar disc to investigate how efficiently the protoplanet captures planetesimals. However, not only planetesimals but also disc gas are gravitationally perturbed by the protoplanet in its late formation stages, resulting in gap opening in the circumstellar disc. In this study, we investigate the effects of such gap formation on the capture of planetesimals by performing dynamical simulations of planetesimals around a growing proto-gas giant planet. Gap formation reduces the surface density of disc gas, makes a steep pressure gradient and limits the growth rate of the protoplanet. We find that the first effect enhances the capture of planetesimals, while the others reduce it. Consequently the amount of planetesimals captured during the gas accretion is estimated to be at most ∼ 3 M ⊕ . We conclude that the in-situ capture of planetesimals needs the initial solid surface density more than five times higher than that of the minimum mass solar nebula for explaining the inferred large amount of heavy element in Jupiter. For highly dense warm Jupiters, we would need additional processes enhancing the capture and/or supply of planetesimals.

The origin of the high metallicity of close-in giant exoplanets

“…Planetesimals are represented by test particles and, therefore, they are affected only by the gravitational forces from the central star and planet, and the drag force by the disc gas. The dynamical integration for these bodies is performed using the numerical simulation developed in Shibata & Ikoma (2019), where the detailed scheme and benchmark results are described.…”

“…The gap's structure is modelled in the same way as in Shibata & Ikoma (2019); namely, we use the empirical formula for the radial density profile in the gap derived from the twodimensional hydrodynamical simulations of Kanagawa et al (2017). Combining the surface density profiles of the circumstellar disc and the gap, we express the gas surface density Σ gas as…”

“…After the onset of the runaway gas accretion, the rapidly expanding feeding zone permits the further accretion of planetesimals that are distributed around the planet. During that phase, up to 30% of the planetesimals inside the planet's feeding zone can be accreted by the planet (Shibata & Ikoma 2019). As we show here, a higher mass of heavy elements can be captured when planetary migration is considered.…”

“…Further enrichment of the planet during runaway gas accretion is difficult; indeed, theoretical studies show that only several Earth masses of heavy elements can be captured in situ during the gas accretion phase when a minimummass solar nebula is assumed (Zhou & Lin 2007;Shiraishi & Ida 2008;Shibata & Ikoma 2019). If the solid mass is several times higher than the heavy-element mass of the minimum-mass solar nebula, the enrichments of Jupiter and Saturn could be explained by such an in situ accretion during the gas accretion stages (Shibata & Ikoma 2019). However, the accreted masses are found to be significantly smaller than the inferred several tens (or more) of Earth masses of the detected warm-Jupiters (Thorngren et al 2016).…”

The Bimodal Distribution in Exoplanet Radii: Considering Varying Core Compositions and H2 Envelope’s Sizes

“…Ida & Lin 2004, 2005Mordasini et al 2009). However, as systems undergo runaway growth planetesimals are also accreted which could increase the mass of the core (Shiraishi & Ida 2008;Shibata & Ikoma 2019). This extra growth of the core needs to be balanced with the core erosion induced from deposited energy but the latter effect is believed to be inefficient (Moll et al 2017).…”