Formation of planetary systems by pebble accretion and migration: growth of gas giants

Abstract

Giant planets migrate though the protoplanetary disc as they grow their solid core and attract their gaseous envelope. Previously, we have studied the growth and migration of an isolated planet in an evolving disc. Here, we generalise such models to include the mutual gravitational interaction between a high number of growing planetary bodies. We have investigated how the formation of planetary systems depends on the radial flux of pebbles through the protoplanetary disc and on the planet migration rate. Our N-body simulations confirm previous findings that Jupiter-like planets in orbits outside the water ice line originate from embryos starting out at 20-40 AU when using nominal type-I and type-II migration rates and a pebble flux of approximately 100-200 Earth masses per million years, enough to grow Jupiter within the lifetime of the solar nebula. The planetary embryos placed up to 30 AU migrate into the inner system (r P < 1AU). There they form super-Earths or hot and warm gas giants, producing systems that are inconsistent with the configuration of the solar system, but consistent with some exoplanetary systems. We also explored slower migration rates which allow the formation of gas giants from embryos originating from the 5-10 AU region, which are stranded exterior to 1 AU at the end of the gas-disc phase. These giant planets can also form in discs with lower pebbles fluxes (50-100 Earth masses per Myr). We identify a pebble flux threshold below which migration dominates and moves the planetary core to the inner disc, where the pebble isolation mass is too low for the planet to accrete gas efficiently. In our model, giant planet growth requires a sufficiently-high pebble flux to enable growth to out-compete migration. An even higher pebble flux produces systems with multiple gas giants. We show that planetary embryos starting interior to 5 AU do not grow into gas giants, even if migration is slow and the pebble flux is large. These embryos instead grow to just a few Earth masses, the mass regime of super-Earths. This stunted growth is caused by the low pebble isolation mass in the inner disc and is therefore independent of the pebble flux. Additionally we show that the long term evolution of our formed planetary systems can naturally produce systems with inner super-Earths and outer gas giants as well as systems of giant planets on very eccentric orbits.

Influence of sub- and super-solar metallicities on the composition of solid planetary building blocks

“…However, planetary systems most likely contain more than one planet, which then results in a different dynamical history of the system. The N-body simulations of Izidoro et al (2019) and Bitsch et al (2019a) use the same disc model and show that planetary embryos can migrate inwards in a convoy. This is caused by the mutual interactions between the bodies, which increase their eccentricity.…”

Jupiter formed as a pebble pile around the N2 ice line

“…Pebble accretion seems especially promising as building a core from pebbles would leave the N 2 on the pebbles until it is captured within the gravitational influence. Models by Bitsch et al (2019) show that, as long as the pebble flux is high enough in the outer disk, it is possible to form a cold Jupiter starting core growth as far out as 50 AU. Taking an optimistic estimate for both the pebble accretion efficiency (10% Ormel & Liu 2018) and the total mass of pebble accreted onto the proto-Jupiter (7.5 lates in to disks with radii between 30 and 100 AU, assuming a surface density power law slope between -1 and -0.5 (Tazzari et al 2016).…”

Are the observed gaps in protoplanetary discs caused by growing planets?

“…Reduction of accretion rates translate into reduced gas surface densities, which in turn reduce viscous heating and thus the discs temperature. The same disc model was used in the pebble-based planet formation simulations (Bitsch et al 2015b;Bitsch & Johansen 2016;Ndugu et al 2018) and in N-body simulations (Izidoro et al 2017Bitsch et al 2019a). The disc model used in our work has a lifetime which can span all the way up to 10 My as expected by observation (Hartmann et al 1998;Mamajek 2009).…”

“…This has been discussed in detail in Bitsch et al (2018a). We thus here just scale the pebble flux by S peb to allow faster planetary growth, similar to the approach used by Izidoro et al (2019) and Bitsch et al (2019b). When the planet reaches pebble isolation mass, it accelerates the gas outside its orbit to super-Keplerian velocities, which generate pressure bumps halting pebble accretion, trapping inward moving pebbles and allows the planet to transition into a stage of gas accretion .…”

“…We note that these gas accretion rates might be too generous and allow the formation of too many gas giants (e.g. Brügger et al 2018;Bitsch et al 2019b), however, until the planets reach pebble isolation mass gas accretion can be neglected. We will investigate different gas accretion rates in an upcoming publication and first tests imply that different gas accretion rates do not influence our results significantly.…”