Planets Form Quickly Around Low-Mass Stars (Planetary Science)

According to Brianna Zawadzki and colleagues planets form quickly around low mass stars (of 0.2 M), long before the gas disc dissipates.

NASA’s TESS mission is expected to discover hundreds of M dwarf planets. However, few studies focus on how planets form around low-mass stars. Now, Zawadzki and colleagues aim to better characterize the formation process of M dwarf planets to fill this gap and aid in the interpretation of TESS results.

Protoplanetary discs consist of gas and dust that provide the initial conditions for planet formation. Disc properties vary with the spectral type of the central star, implying that planet formation is probably not uniform across all spectral types. This motivates studies of planet formation around M dwarfs.

Regardless of stellar spectral type, the first stage of planet formation is the coagulation of dust grains into larger particles. As dust grains grow larger, the collision speeds increase. Close to the star, particle growth is likely
to be fragmentation-limited, so that the particle size is set by the fragmentation speed of the grain material.

Because these parameters vary by location in the disc, the maximum grain size is dependent on where in the disc grains form. The inner disc is largely dominated by fragmentation, leading to a dust surface density that goes as ๐‘Ÿยฏ1.5, while the outer disc is dominated by radial drift which cannot sustain high enough relative velocities for fragmentation over the disc lifetime. Zawadzki and colleagues simulations focus on planet formation in the inner disc of an M dwarf, so this study includes models in which the embryos are initially distributed according to an ๐‘Ÿยฏ1.5 surface density profile. However, the distribution of solids may be rearranged as dust grains are converted into planetesimals. In addition to the fragmentation-limited case, they also considered the case where the solid distribution of embryos mirrors that of the turbulent gas disc and are initially distributed according to an ๐‘Ÿยฏ0.6 surface density profile. They investigated whether the resulting planetary systems can be used to distinguish between these two initial surface density profiles. One distinguishing feature of their study is that their simulations take the early stellar evolution of the M dwarf into account, including calculations for the changing stellar mass accretion rate and disc parameters. This is particularly important for M dwarfs due to the rate and length of their contraction onto the main sequence, but is not commonly accounted for in studies of M dwarf planet formation.

Figure 1. The number of collisions for each Mix model with respect to time. The number of collisions for Frag.base is also provided for comparison, but Frag results do not differ significantly from Mix results. In general, planets form quickly, with embryo collisions peaking at approximately 10ยณ yr for models Mix.base, Mix.edge, and Mix.nogas, as well as the corresponding Frag models. Models Mix.wide and Mix.icy initialize the embryos across a wider range of semi-major axes, so the embryos require more time to collide. Collisions peak around 10โด yr for Mix.wide runs and between 105-106 yr for Mix.icy runs, suggesting that even more widely dispersed embryos quickly form planets. Note that in most models, an insignificant number of collisions occur after the gas disc dissipates, indicating that late M dwarf planets largely form while the gas disc is still present. However, some collisions occur inside the disc cavity ยฉ Zawadzki et al.

Aerodynamic drag causes the dust to drift radially inward in the turbulent disc. As the solids continue to orbit, this radial drift combined with the turbulent motions in the disc cause particles to collide and either stick or fragment, depending on the collision speed and grain size. Particle growth stalls at around cm-size pebbles, meaning some other process is likely needed for continued growth. Currently, the most promising mechanism to concentrate particles is a radial convergence of particle drift known as the streaming instability. The streaming instability causes particles to concentrate into long, dense azimuthal filaments which can gravitationally collapse into planetesimals. Another aerodynamic process that may play an important role is the concentration of particles inside turbulent eddies.

As planetesimals collide to form embryos, they experience runaway growth followed by oligarchic growth. During runaway growth, the mass growth of planetesimals is given by ๐‘€ยค /๐‘€ โˆ ๐‘€^1/3. When a small number of embryos become large enough to dominate the neighboring planetesimals, the system enters a stage of oligarchic growth. During this stage, growth is slower (๐‘€ยค /๐‘€ โˆ ๐‘€^โ€“1/3) and proceeds until the oligarchs reach their isolation mass.

The gas in the disc exerts torques on the embryos which can cause planets to migrate. There are two principal modes of planet migration:

Type I: Small planets embedded in the disc experience Type I migration. In it, the planet forms spiral density waves associated with its Lindblad resonances, and causes nearly co-orbital gas to follow horseshoe orbits. The associated overdensities lead to negative Lindblad torques and positive co-rotation torques, respectively.

Type II: When a planet is massive enough to open a gap in the disc, the co-rotation torque is all but eliminated and the Lindblad torque is reduced. The planet becomes coupled to the viscous evolution of the disc and orbital migration greatly slows down.

For current work, Zawadzki and colleagues have shown their interest in Type I migration.

“We showed that planets form quickly around 0.2๐‘€ stars, long before the gas disc dissipates. When planets become locked into resonant chains, they can be pushed far into the disc cavity via Type I migration of the outermost planet in the chain.”

โ€” told Zawadzki, lead author of the study

They used ten sets of N-body planet formation simulations which vary in whether a gas disc is present, initial range of embryo semi-major axes, and initial solid surface density profile. Each simulation begins with 147 equal-mass embryos around a 0.2 solar mass star and runs for 100 Myr. Their simulations lead them to 4 main conclusions:

1) The planets form quickly around 0.2๐‘€ stars with most collisions occurring within the first 1 million year (Myr), long before the gas disc dissipates. When planets become locked into resonant chains, they can be pushed far into the disc cavity via Type I migration of the outermost planet in the chain.

2) Planet formation reshapes the solid distribution and destroys memory of initial conditions. The solid surface density of the final planets does not appear to be related to the initial distribution of embryos. Thus, it may not be possible to infer the initial distribution of solids from present-day observations of planetary systems.

3) The presence of a gas disc reduces the final number of planets relative to a gas-free environment and causes planets to migrate inward.

4) Roughly a quarter of planetary systems experience their final giant impact inside the gas disc. Because these planets largely form inside the gas disc, they may retain an atmosphere even after migrating into the disc cavity.

They also found that systems that form in the presence of gas tend to be more stable than those that did not.

They concluded that future models that span a larger range of stellar masses combined with new TESS observations will further develop our understanding of planet formation around M dwarfs.

Reference: Brianna Zawadzki, Daniel Carrera, Eric Ford, “Rapid Formation of Super-Earths Around Low-Mass Stars”, ArXiv, pp. 1-17, 2021.

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