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 (rP < 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.
Highlights
The discovery of the first planet around another star yielded a surprise, because the detected planet was nothing like the planets in our own solar system (Mayor & Queloz 1995)
The eccentricity distribution of these giant planets increases with host star metallicity, meaning that giant planets are more likely on eccentric orbits if the metallicity is large (Buchhave et al 2018), an attribute associated with the formation of multiple giant planets
In the simulations with nominal migration rates, we confirm the result of Bitsch et al (2015a) that planetary embryos growing to form gas giants exterior to 1 AU have to originate from 20–40 AU using nominal planet migration rates
Summary
The discovery of the first planet around another star yielded a surprise, because the detected planet was nothing like the planets in our own solar system (Mayor & Queloz 1995). The planet is in the mass regime of Jupiter and orbits its host star on a three-day orbit, which gave the name of this planetary class: hot Jupiters. Today we know that ∼1% of solar like stars host hot Jupiter planets, while their cold analogues (rP > 1 AU) are found around 10% of stars (Johnson et al 2010). The occurrence rate of Jupiter planets in general seems to increase with their host star metallicity (Fischer & Valenti 2005). The eccentricity distribution of these giant planets increases with host star metallicity, meaning that giant planets are more likely on eccentric orbits if the metallicity is large (Buchhave et al 2018), an attribute associated with the formation of multiple giant planets. The exact growth mechanism of giant planet systems still remains a mystery
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