Formation of Multiple-planet Systems in Resonant Chains around M Dwarfs

Abstract

Recent observations have revealed the existence of multiple-planet systems composed of Earth-mass planets around late M dwarfs. Most of their orbits are close to commensurabilities, which suggests that planets were commonly trapped in resonant chains in their formation around low-mass stars. We investigate the formation of multiple-planet systems in resonant chains around low-mass stars. A time-evolution model of the multiple-planet formation via pebble accretion in the early phase of the disk evolution is constructed based on the formation model for the TRAPPIST-1 system by Ormel et al. Our simulations show that knowing the protoplanet appearance timescale is important for determining the number of planets and their trapped resonances: as the protoplanet appearance timescale increases, fewer planets are formed, which are trapped in more widely separated resonances. We find that there is a range of the protoplanet appearance timescale for forming stable multiple-planet systems in resonant chains. This range depends on the stellar mass and disk size. We suggest that the protoplanet appearance timescale is a key parameter for studying the formation of multiple-planet systems with planets in resonant chains around low-mass stars. The composition of the planets in our model is also discussed.

Rapid-then-slow migration reproduces mass distribution of TRAPPIST-1 system

“…As a different formation model, Ormel et al (2017) proposed that planets grow near the water snowline (r < 1 au), mainly by pebble accretion. In this model, the average planetary mass (Schoonenberg et al 2019) and resonant relation (Lin et al 2021;Huang & Ormel 2021) could be reproduced. In contrast, the mass was determined by the pebble isolation mass; therefore, the planetary mass was almost uniform in the system.…”

“…The TRAPPIST-1 system is characterized by resonant relations. Previous studies (e.g., Coleman et al 2019;Lin et al 2021;Huang & Ormel 2021) investigated how the resonant relations are reproduced. Although this study does not focus on reproducing the resonance relations, we also investigated whether the period ratio agrees with that of the TRAPPIST-1 system.…”

The dynamics of the TRAPPIST-1 system in the context of its formation

“…We assume the gas disc is truncated at a radius 𝑟 c by the magnetic field from the star, where the gas ram pressure is comparable to the magnetic stress (Pringle & Rees 1972). We assume the inner disc is viscously relaxed (Shakura & Sunyaev 1973;Lynden-Bell & Pringle 1974) within the snowline 𝑟 ice ∼ 0.1 au (Schoonenberg et al 2019;Lin et al 2021b), implying constant 𝑀 = 3𝜋𝜈Σ where 𝜈 is the viscosity. The aspect ratio is fixed at ℎ = 0.03 following Ormel et al (2017), whose value is motivated by viscous heating and lamppost heating (Rafikov & De Colle 2006) and the spectral energy distribution fitting (Mulders & Dominik 2012).…”

“…We insert planets sequentially at the beginning of the simulation with fixed masses following Table 1. Ormel et al (2017), Schoonenberg et al (2019) and Lin et al (2021b) hypothesize that the TRAPPIST-1 planets are formed at the snowline (≈0.1 au) and quickly accreted material. However, in the context of this work planets could also have formed further out; we simply fix the mass of every planets during the simulation.…”

“…Conceivably, the innermost two planet pairs were near 3:2 MMR just after planet formation because it is the first order MMR closest to the current period ratio, whereafter the inner three planets separated from each other. Lin et al (2021b) presented an analytical model in which Earth-mass planets in discs around low mass stars end up in first order MMRs chain. However, they did not investigate the deviation from first order MMRs for the inner three planets.…”