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We identify observational signatures suggesting a history of dynamical instability in 26 out of 34 M-dwarf multi-planet systems containing no large planets. These systems may have primarily formed in a gas-rich environment, potentially hosted more planets, and were more compact. We extend previous simulations of the formation of the TRAPPIST-1 system to 100 Myr to test the stability of these systems without gas. We find that the absence of a strong mean motion resonance in the innermost planet pair and the absence of three-body resonances throughout the system are likely to result in the merging and ejection of planets after the gas disk disperses. The runs that experience such an instability tend to produce final systems with lower multiplicities, period ratios larger than two, increased orbital spacings, higher planetary angular momentum deficits, and slightly smaller mass ratios between adjacent planets. Remarkably, we find these same trends in the observations of M-dwarf multi-planet systems containing no large planets. Our work allows us to identify specific systems that may have experienced an instability, and it suggests that only  ∼25% of these systems formed in their current observed state, while most systems were likely more compact and multiplicitous earlier in time. Previous research indicates that planets that have experienced a late-stage giant impact may potentially be more habitable than those that did not. With this in mind, we suggest systems around M-dwarfs that contain period ratios larger than two be given priority in the search for habitable worlds. 

Abstract The streaming instability (SI) is a leading mechanism for concentrating solid particles into regions dense enough to form planetesimals. Its efficiency in clumping particles depends primarily on the dimensionless stopping time (τ_s, a proxy for particle size) and dust-to-gas surface density ratio (Z). Previous simulations identified a criticalZ(Z_crit) above which strong clumping occurs, where particle densities exceed the Hill density (thus satisfying a condition for gravitational collapse), over a wide range ofτ_s. These works found that, forτ_s≤ 0.01,Z_critwas above the interstellar medium value (∼0.01). In this work, we reexamine the clumping threshold using 2D axisymmetric, stratified simulations at high resolution and with relatively large (compared to many previous simulations) domain sizes. Our main results are as follows: First, whenτ_s = 0.01, strong clumping occurs even atZ ≲ 0.01, lower thanZ_critfound in all previous studies. Consequently, we revise a previously published fit to theZ_critcurve to account for this updatedZ_crit. Second, higher resolution results in a thicker dust layer, which may result from other instabilities manifesting, such as the vertically shearing SI. Third, despite this thicker layer, higher resolution can lead to strong clumping even with a lower midplane dust-to-gas density ratios (which results from the thicker particle layer) so long asZ ≳ Z_crit. Our results demonstrate the efficiency of the SI in clumping small particles atZ ∼ 0.01, which is a significant refinement of the conditions for planetesimal formation by the SI. 

Abstract The streaming instability (SI) is a leading candidate for planetesimal formation, which can concentrate solids through two-way aerodynamic interactions with the gas. The resulting concentrations can become sufficiently dense to collapse under particle self-gravity, forming planetesimals. Previous studies have carried out large parameter surveys to establish the critical particle to gas surface density ratio (Z), above which SI-induced concentration triggers planetesimal formation. The thresholdZdepends on the dimensionless stopping time (τ_s, a proxy for dust size). However, these studies neglected both particle self-gravity and external turbulence. Here, we perform 3D stratified shearing box simulations with both particle self-gravity and turbulent forcing, which we characterize via a turbulent diffusion parameter,α_D. We find that forced turbulence, at amplitudes plausibly present in some protoplanetary disks, can increase the thresholdZby up to an order of magnitude. For example, forτ_s= 0.01, planetesimal formation occurs whenZ≳ 0.06, ≳0.1, and ≳0.2 atα_D= 10⁻⁴, 10^−3.5, and 10⁻³, respectively. We provide a single fit to the criticalZrequired for the SI to work as a function ofα_Dandτ_s(although limited to the rangeτ_s= 0.01–0.1). Our simulations also show that planetesimal formation requires a mid-plane particle-to-gas density ratio that exceeds unity, with the critical value being largely insensitive toα_D. Finally, we provide an estimation of particle scale height that accounts for both particle feedback and external turbulence.