Context. Modeling how cold giant planets form around M dwarfs remains a challenge, both because their protoplanetary disks can lack sufficient mass and because such planets are expected to migrate inward while interacting with the disk. Moreover, it remains unknown whether inner rocky planets can survive in systems that host a cold giant around very low-mass stars, which could have important implications for the habitability of rocky worlds. Aims. We investigated the conditions required for the formation of giant planets at large orbital distances (1- 3 au) around a 0.1 M_· star, and explored the circumstances under which a close-in rocky planet can survive. Methods. We performed N-body simulations in which planetary embryos grow through pebble accretion, followed by gas accretion during the disk lifetime. Assuming a local disk turbulent viscosity (α_t) of 10^{- 4}, we included planet-disk interactions throughout the disk evolution, using a new prescription that accounts for the onset of outward migration when the planet-to-star mass ratio (q) exceeds 0.002. Results. We find that a cold giant planet can form around a late M dwarf, even with an initial pebble mass of only 6 M_·, provided the disk gas mass is 10% of the stellar mass. This outcome requires a compact 20 au disk in which the inner, viscosity-dominated region has a high gas surface density set by a low accretion viscosity (α_g=10^{- 4}), that planet- planet collisions assemble a a∼ 5 M_· core within 1 Myr, and that the gas disk survives for 10 Myr. In addition, an inner rocky planet can survive in a close-in orbit if it migrates into the inner disk cavity before the outer body grows into a giant. Conclusions. The initial dust mass required for giant planet formation around very low-mass stars does not need to be as extreme as previously thought. A combination of planet- planet collisions, efficient pebble accretion, and a long disk lifetime plays a key role in enabling the formation of cold giant planets with masses between those of Saturn and Jupiter.

Context. Dust grains embedded in a gas flow give rise to a class of hydrodynamic instabilities that can occur whenever there exists a relative velocity between gas and dust. These instabilities have predominantly been studied for single grain sizes, for which a strong interaction can be found between drifting dust and a travelling gas wave leading to fast-growing perturbations (growth rates ∝√μ) even at small dust-to-gas ratios μ. They are called resonant drag instabilities. We focus on the acoustic resonant drag instability, which is potentially important in AGB star outflows, around supernova remnants, and star clusters in starburst galaxies. Aims. We study the acoustic resonant drag instability, taking into account a continuous spectrum of grain sizes, to determine whether it survives in the polydisperse regime and how the resulting growth rates compare to the monodisperse case. Methods. We solved the linear equations for a polydisperse fluid for the acoustic drag instability, focusing on small dust-to-gas ratios. Results. Size distributions that have a realistic width turn the fast-growing perturbations ∝√μ of the monodisperse limit into slower growing perturbations ∝ μ due to the fact that the backreaction on the gas involves an integration over the resonance. Furthermore, the large wave numbers that grow fastest in the monodisperse regime are stabilised by a size distribution, severely limiting the growth rates in the polydisperse regime. Conclusions. The acoustic resonant drag instability turns from a singularly perturbed problem in μ in the monodisperse limit into a regular perturbation for a sufficiently wide size distribution. It can still grow exponentially in the polydisperse regime, but at a slower pace compared to the single size case.

Context. Dust grains embedded in gas flow give rise to a class of hydrodynamic instabilities called resonant drag instabilities, some of which are thought to be important during the process of planet formation. These instabilities have predominantly been studied for single grain sizes, in which case they are found to grow fast. Non-linear simulations indicate that strong dust overdensities can form, aiding the formation of planetesimals. In reality, however, there is going to be a distribution of dust sizes, which may have significant consequences. Aims. We aim to study two different resonant drag instabilities - the streaming instability and the settling instability - taking into account a continuous spectrum of grain sizes, to determine whether these instabilities survive in the polydisperse regime and how the resulting growth rates compare to the monodisperse case. Methods. We solved the linear equations for a polydisperse fluid in an unstratified shearing box to recover the streaming instability and, for approximate stratification, the settling instability, in all cases focusing on low dust-to-gas ratios. Results. Size distributions of realistic widths turn the singular perturbation of the monodisperse limit into a regular perturbation due to the fact that the back-reaction on the gas involves an integration over the resonance. The contribution of the resonance to the integral can be negative, as in the case of the streaming instability, which as a result does not survive in the polydisperse regime; or positive, which is the case in the settling instability. The latter therefore has a polydisperse counterpart, with growth rates that can be comparable to the monodisperse case. Conclusions. Wide size distributions in almost all cases remove the resonant nature of drag instabilities. This can lead to reduced growth, as is the case in large parts of parameter space for the settling instability, or complete stabilisation, as is the case for the streaming instability.

This study investigates the orbital migration of a planet located near the truncated edge of protoplanetary disks, induced by X-ray photo-evaporation originating from the central star. The combined effects of turbulent viscous accretion and stellar X-ray photo-evaporation give rise to the formation of a cavity in the central few astronomical units in disks. Once the cavity is formed, the outer disk experiences rapid mass loss and the cavity expands from the inside out. We conducted 2D hydrodynamical simulations of planet-disk interaction for various planet masses and disk properties. Our simulations demonstrate that planets up to about Neptune masses experience a strong positive corotation torque along the cavity edge that leads to sustained outward migration – a phenomenon previously termed rebound migration. Rebound migration is more favorable in disks with moderate stellar photo-evaporation rates of ~10⁻⁸ M_⊙ yr⁻¹. Saturn-mass planets only experience inward migration, due to significant gas depletion in their co-orbital regions. In contrast, Jupiter-mass planets are found to undergo modest outward migration as they cause the residual disk to become eccentric. This work presents the first 2D hydrodynamical simulations that confirm the existence and viability of rebound outward migration during the inside-out clearing in protoplanetary disks.

While planet migration has been extensively studied for classical viscous discs, planet-disc interaction in nearly inviscid discs has mostly been explored with greatly simplified thermodynamics. In such environments, motivated by models of wind-driven accretion discs, even Earth-mass planets located interior to 1 au can significantly perturb the disc, carving gaps and exciting vortices on their edges. Both processes are influenced by radiative transfer, which can both drive baroclinic forcing and influence gap opening. We perform a set of high-resolution radiation hydrodynamics simulations of planet-disc interaction in the feedback and gap-opening regimes, aiming to understand the role of radiation transport in the migration of super-Earth-mass planets representative of the observed exoplanet population. We find that radiative cooling drives baroclinic forcing during multiple stages of the planet's migration in the feedback regime (), significantly delaying the onset of vortex formation at the gap edge but ultimately resulting in type-III runaway migration episodes. For super-thermal-mass planets (), radiative cooling is fundamentally linked to the gap-opening process, with the planet stalling instead of undergoing vortex-assisted migration as expected from isothermal or adiabatic models. This stalling of migration can only be captured when treating radiative effects, and since it affects super-thermal-mass planets its implications for both the final configuration of planetary systems and population synthesis modelling are potentially huge. Combining our findings with previous related studies, we present a map of migration regimes for radiative, nearly-inviscid discs, with the cooling-mediated gap-opening regime playing a central role in determining the planet's orbital properties.

Dust rings in protoplanetary discs are often observed in thermal dust emission and could be fa v ourable environments for planet formation. While dust rings readily form in gas pressure maxima, their long-term stability is key to both their observability and potential to assist in planet formation. We investigate the stability of the dust ring generated by interactions of a protoplanetary disc with a Neptune-sized planet and consider its possible long-term evolution using the FARGO3D Multifluid code. We look at the onset of the Rossby Wave Instability (RWI) and compare how the addition of dust in a disc can alter the stability of the gas phase. We find that with the addition of dust, the rings generated by planet-disc interactions are more prone to RWI and can cause the gas phase to become unstable. The instability is shown to occur more easily for higher Stokes number dust, as it accumulates into a more narrow ring which triggers the RWI, while the initial dust fraction plays a more minor role in the stability properties. We show that the dusty RWI generates vortices that collect dust in their cores, which could be sites for further planetesimal formation. We conclude that the addition of dust can cause a ring in a protoplanetary disc to become more prone to instability leading to a different long-term evolution compared to gas-only simulations of the RWI.

Low-mass planets migrate in the type-I regime. In the inviscid limit, the contrast between the vortensity trapped inside the planet's corotating region and the background disc vortensity leads to a dynamical corotation torque, which is thought to slow down inward migration. We investigate the effect of radiative cooling on low-mass planet migration using inviscid 2D hydrodynamical simulations. We find that cooling induces a baroclinic forcing on material U-turning near the planet, resulting in vortensity growth in the corotating region, which in turn weakens the dynamical corotation torque and leads to 2-3 × faster inw ard migration. This mechanism is most efficient when cooling acts on a time-scale similar to the U-turn time of material inside the corotating region, but is none the less rele v ant for a substantial radial range in a typical disc ( R ~5-50 au). As the planet migrates inwards, the contrast between the vortensity inside and outside the corotating region increases and partially regulates the effect of baroclinic forcing. As a secondary ef fect, we sho w that radiati ve damping can further weaken the vortensity barrier created by the planet's spiral shocks, supporting inward migration. Finally, we highlight that a self-consistent treatment of radiative diffusion as opposed to local cooling is critical in order to avoid overestimating the vortensity growth and the resulting migration rate.

In radiatively inefficient, laminar protoplanetary discs, embedded planets can excite a buoyancy response as gas gets deflected vertically near the planet. This results in vertical oscillations that drive a vortensity growth in the planet's corotating region, speeding up inward migration in the type-I regime. We present a comparison between pluto/idefix and fargo3D using 3D, inviscid, adiabatic numerical simulations of planet-disc interaction that feature the buoyancy response of the disc, and show that pluto/idefix struggle to resolve higher-order modes of the buoyancy-related oscillations, weakening vortensity growth, and the associated torque. We interpret this as a drawback of total-energy-conserving finite-volume schemes. Our results indicate that a very high resolution or high-order scheme is required in shock-capturing codes in order to adequately capture this effect.