Formation of Red Dwarf Exoplanets

Title: Rapid Formation of Super-Earths Around Low-Mass Stars

Authors: Brianna Zawadzki, Daniel Carrera, Eric Ford

First Author’s Institution: Department of Astronomy and Astrophysics and Center for Exoplanets & Habitable Worlds, The Pennsylvania State University, PA, USA

Status: Accepted for publication in MNRAS (open access on arXiv)

In recent years, the discovery of thousands of exoplanets – planets that reside outside our Solar System – has revolutionised our understanding of the formation and evolution of planetary systems. The bulk of these discovered exoplanets orbit Sun-like stars, yet fewer studies have focused on how planets form around low-mass stars such as red dwarfs (also called M dwarfs). TRAPPIST-1, a compact star system that made waves in 2017, is notable for containing several Earth-like planets orbiting in the star’s habitable zone. Around 80% of all stars in our galaxy are red dwarfs, making them extremely important in the search for habitable planets, yet their low luminosities make exoplanets hard to detect (for more, see this article and this Astrobite on detection methods). This is where NASA’s Transiting Exoplanet Survey Satellite (TESS) comes in; its highly sensitive instruments are expected to detect hundreds of exoplanets in orbit around red dwarfs (hereafter M dwarf planets). The authors of today’s paper use a suite of N-body simulations to study how such M dwarf planets form.

Let There Be Planets

Planets initially form from the accumulation and coagulation of dust grains within a protoplanetary disc, forming planetesimals that themselves collide with each other to form embryos. Crucially, it is known that the properties of this disc vary according to the spectral type of the parent star; the rules for the Sun do not necessarily apply to red dwarfs. These embryos are subject to many physical processes: tidal forces, torques, aerodynamic drag and accretion. The authors thus use a standard N-body simulation, with the addition of custom forces to represent some of these physical processes. The authors use 10 different models, each with 147 embryos, with different initial configurations of the protoplanetary disc, and whether gas is present in the disc. This latter point is important as the presence of gas leads to resonant torques. Figure 1 shows how each embryo’s semi-major axis evolves over time in a typical simulation. In this example, three planets are formed. All of these M dwarf planets are Super-Earths, with masses between 2.5 and 5.1 Earth masses. The initial 147 embryos are quick to collide; averaged over all simulations, 96% of collisions occur in the first 1 Myr of the simulation. In models that include gas, 99% of collisions occur before the gas disc dissipates. Thus most planets are fully formed over the lifetime of the disc.

Figure 1: Plot of the semi-major axis (maximum radius from the parent star) of all embryos (in astronomical units) as a function of simulation time (in years). Both axes are logarithmic. The shaded region represents the protoplanetary disc. Embryos are coloured according to their initial semi-major axis. (Figure 3 in the paper)

Universe Sandbox

Among the more spectacular events that occur in the formation of a planetary system are giant impacts, such as the collision that is believed to have formed the Moon. The authors define these as impacts between two sufficiently sized embryos (with a combined mass equal to 0.5 Earth masses), with one embryo no more than 5 times more massive than the other. Figure 2 shows these giant impacts across four different simulation models. Most of these collisions occur before the disk dissipates, while late giant impacts are comparatively rarer. Although many late-stage impacts occurred outside the disk (or after it dissipated), about a quarter of simulations with gas had the final impact occur within the disc. These planets are hence likelier to retain atmospheres as they are able to re-accrete gas from the disc.

Figure 2: Scatter-plot of all giant impacts across all simulations (same axes as Figure 1) coloured according to four different models, and with the final giant impacts shown in black. (Figure 5 in the paper)

Keplerian Revolutions

It’s one thing to simulate the formation of planets, but in order to compare the simulated models with observational data the authors considered the period ratios of pairs of planets for each stellar system. They then compared histograms of these period ratios with the period ratios of sample planetary systems observed by the Kepler space telescope. Fig 3 shows a weighted histogram of period ratios, peaking at around 2 (one planet in the pair takes twice as long to orbit that star compared to the other planet). The Kepler sample peaks more around a period ratio of 3/2 (corresponding to a 2:3 orbital resonance); the authors attribute this to the fact that most Kepler planets orbit higher mass stars.

Figure 3: Histograms of the period ratios (weighted according to the probability of both planets in the pair transiting) for the base simulation (purple, filled), the simulation with no gas (blue, dashed) and the sample of planetary pairs found by Kepler. (Bottom panel of Figure 8 in the paper)

Many-Worlds Investigation

There are several key results that can be drawn from these simulations. The first is that M dwarf planets rapidly form, well before the disc dissipates, and that these planets tend to migrate inwards. A more subtle conclusion here is that this inward migration, and subsequent collisions, destroys any “memory” of the initial conditions. In other words, the final density distribution of the planets is unrelated to the initial distribution of embryos, making it impossible to reconstruct the initial conditions of a planetary system based on current observations (the authors note that further investigation is needed to definitively rule this out). Despite this, the second key result is that the location and number of planets in the system is linked to whether a gas disc was present during their formation. Systems formed in models with gas tended to have fewer, close-in planets, while models without gas produced more planets albeit more separated. Planets whose final collisions occur in gas discs are also slightly more likely to retain atmospheres. TESS is expected to detect many hundreds of M dwarf planets, ultimately sampling a greater range of parameter values (such as masses, radii, etc.). This will help to provide tighter constraints on the outputs of future simulations, unlocking the secrets of how red dwarf exoplanets form.

Edited by: Jamie Sullivan
Featured image credit: ESO

The author acknowledges the Whadjuk peoples of the Noongar nation, the traditional custodians of the land on which this post was written, and pays respects to Elders past and present.

About Mitchell Cavanagh

Mitchell is a PhD student in astrophysics at the University of Western Australia. His research is focused on the applications of machine learning to the study of galaxy formation and evolution. Outside of research, he is an avid bookworm and enjoys gaming, languages and code jams.

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