Buoyancy torques prevent low-mass planets from stalling in low-turbulence radiative discs

Low-mass planets migrating inwards in laminar protoplanetary discs (PPDs) experience a dynamical corotation torque (DCT), which is expected to slow down migration to a stall. However, baroclinic effects can reduce or even reverse this effect, leading to rapid inward migration. In the radiatively inefficient inner disc, one such mechanism is the buoyancy response of the disc to an embedded planet. Recent work has suggested that radiative cooling can quench this response, but for parameters that are not necessarily representative of the inner regions of PPDs. We perform global 3D inviscid radiation hydrodynamics simulations of planet-disc interaction to investigate the effect of radiative cooling on the buoyancy-driven torque in a more realistic disc model. We find that the buoyancy response exerts a negative DCT - albeit partially damped due to radiative cooling - resulting in sustained, rapid inward migration. Models that adopt a local cooling prescription significantly overestimate the impact of the buoyancy response, highlighting the importance of a realistic treatment of radiation transport that includes radiative diffusion. Our results suggest that low-mass planets should migrate inwards faster than has been previously expected in radiative discs, with implications for the formation and orbital distribution of super-Earths and sub-Neptunes at intermediate distances from their host stars, unless additional physical processes that can slow down migration are considered

Hydrodynamic turbulence in disks with embedded planets

The vertical shear instability (VSI) is a source of hydrodynamic turbulence that can drive vigorous vertical mixing and moderate levels of accretion in protoplanetary disks, and it could be observable in the near future. With high-resolution three-dimensional numerical hydrodynamics simulations, we modeled the behavior of the VSI in protoplanetary disks with and without embedded planets. We then measured its accretion and mixing capabilities by comparing the full Reynolds stress, which includes the contribution of nonaxisymmetric features, such as spiral arms and vortices, to the Reynolds stress due to the azimuthally averaged velocity field, which can be attributed to good approximation to the VSI. We verified that the VSI can contribute to the accretion stress and showed that, depending on disk conditions, an embedded planet can coexist with or suppress VSI turbulent stress. Specifically, the presence of spiral shocks launched by a planet or planet-generated vortices can interfere with the VSI near the planet’s vicinity, with the instability recovering at large enough distances from the planet or vortex. Our results suggest that observations of VSI signatures are unlikely in disks that contain massive, nonaxisymmetric features

Migration of low-mass planets in inviscid discs: the effect of radiation transport on the dynamical corotation torque

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 inward 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 relevant 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 effect, we show that radiative 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

Buoyancy response of a disc to an embedded planet: a cross-code comparison at high resolution

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

Razor-thin dust layers in protoplanetary disks:Limits on the vertical shear instability

Context. Recent observations with the Atacama Large Millimeter Array (ALMA) have shown that the large dust aggregates observed at millimeter wavelengths settle to the midplane into a remarkably thin layer. This sets strong limits on the strength of the turbulence and other gas motions in these disks. Aims. We intend to find out if the geometric thinness of these layers is evidence against the vertical shear instability (VSI) operating in these disks. We aim to verify if a dust layer consisting of large enough dust aggregates could remain geometrically thin enough to be consistent with the latest observations of these dust layers, even if the disk is unstable to the VSI. If this is falsified, then the observed flatness of these dust layers proves that these disks are stable against the VSI, even out to the large radii at which these dust layers are observed. Methods. We performed hydrodynamic simulations of a protoplanetary disk with a locally isothermal equation of state, and let the VSI fully develop. We sprinkled dust particles with a given grain size at random positions near the midplane and followed their motion as they got stirred up by the VSI, assuming no feedback onto the gas. We repeated the experiment for different grain sizes and determined for which grain size the layer becomes thin enough to be consistent with ALMA observations. We then verified if, with these grain sizes, it is still possible (given the constraints of dust opacity and gravitational stability) to generate a moderately optically thick layer at millimeter wavelengths, as observations appear to indicate. Results. We found that even very large dust aggregates with Stokes numbers close to unity get stirred up to relatively large heights above the midplane by the VSI, which is in conflict with the observed geometric thinness. For grains so large that the Stokes number exceeds unity, the layer can be made to remain thin, but we show that it is hard to make dust layers optically thick at ALMA wavelengths (e.g., τ1.3mm ≳ 1) with such large dust aggregates. Conclusions. We conclude that protoplanetary disks with geometrically thin midplane dust layers cannot be VSI unstable, at least not down to the disk midplane. Explanations for the inhibition of the VSI out to several hundreds of au include a high dust-to-gas ratio of the midplane layer, a modest background turbulence, and/or a reduced dust-to-gas ratio of the small dust grains that are responsible for the radiative cooling of the disk. A reduction of small grains by a factor of between 10 and 100 is sufficient to quench the VSI. Such a reduction is plausible in dust growth models, and still consistent with observations at optical and infrared wavelengths

Measuring the Numerical Viscosity in Simulations of Protoplanetary Disks in Cartesian Grids -- The Viscously Spreading Ring Revisited

Hydrodynamical simulations solve the governing equations on a discrete grid of space and time. This discretization causes numerical diffusion similar to a physical viscous diffusion, whose magnitude is often unknown or poorly constrained. With the current trend of simulating accretion disks with no or very low prescribed physical viscosity, it becomes essential to understand and quantify this inherent numerical diffusion, in the form of a numerical viscosity. We study the behavior of the viscous spreading ring and the spiral instability that develops in it. We then use this setup to quantify the numerical viscosity in Cartesian grids and study its properties. We simulate the viscous spreading ring and the related instability on a two-dimensional polar grid using PLUTO as well as FARGO, and ensure convergence of our results with a resolution study. We then repeat our models on a Cartesian grid and measure the numerical viscosity by comparing results to the known analytical solution, using PLUTO and Athena++. We find that the numerical viscosity in a Cartesian grid scales with resolution as approximately $\nu_{num}\propto\Delta x^2$ and is equivalent to an effective $\alpha\sim10^{-4}$ for a common numerical setup. We also show that the spiral instability manifests as a single leading spiral throughout the whole domain on polar grids. This is contrary to previous results and indicates that sufficient resolution is necessary in order to correctly resolve the instability. Our results are relevant in the context of models where the origin should be included in the computational domain, or when polar grids cannot be used. Examples of such cases include models of disk accretion onto a central binary and inherently Cartesian codes

Measuring the numerical viscosity in simulations of protoplanetary disks in Cartesian grids. The viscously spreading ring revisited

Context. Hydrodynamical simulations solve the governing equations on a discrete grid of space and time. This discretization causes numerical diffusion similar to a physical viscous diffusion, whose magnitude is often unknown or poorly constrained. With the current trend of simulating accretion disks with no or very low prescribed physical viscosity, it becomes essential to understand and quantify this inherent numerical diffusion, in the form of a numerical viscosity. Aims. We study the behavior of the viscous spreading ring and the spiral instability that develops in it. We then use this setup to quantify the numerical viscosity in Cartesian grids and study its properties. Methods. We simulate the viscous spreading ring and the related instability on a two-dimensional polar grid using PLUTO as well as FARGO, and ensure the convergence of our results with a resolution study. We then repeat our models on a Cartesian grid and measure the numerical viscosity by comparing results to the known analytical solution, using PLUTO and Athena++. Results. We find that the numerical viscosity in a Cartesian grid scales with resolution as approximately νnum ∝ ∆x 2 and is equivalent to an effective α ∼ 10−4 for a common numerical setup. We also show that the spiral instability manifests as a single leading spiral throughout the whole domain on polar grids. This is contrary to previous results and indicates that sufficient resolution is necessary in order to correctly resolve the instability. Conclusions. Our results are relevant in the context of models where the origin should be included in the computational domain, or when polar grids cannot be used. Examples of such cases include models of disk accretion onto a central binary and inherently Cartesian codes

How cooling influences circumbinary discs

Circumbinary disc observations and simulations show large, eccentric inner cavities. Recent work has shown that the shape and size of these cavities depend on the aspect ratio and viscosity of the disc, as well as the binary eccentricity and mass ratio. It has been further shown that, for gaps created by planets, the cooling timescale significantly affects the shape and size of the gap. In this study, we consider the effect of different cooling models on the cavity shape in a circumbinary disc. We compare locally isothermal and radiatively cooled disc models to ones with a parametrised cooling timescale (β-cooling), implemented in 2D numerical simulations for varying binary eccentricities. While the shape of the cavity for radiative and locally isothermal models remains comparable, the inner disc structure changes slightly, leading to a change in the precession rate of the disc. With β-cooled models, the shape and size of the cavity changes dramatically towards values of β = 1. Based on our findings, we introduce a parametrised β model that accounts for the shorter cooling timescale inside the cavity while adequately reproducing the results of the radiative model, and we highlight that accurate treatment of the thermodynamics inside the cavity has a significant impact in modelling circumbinary systems

The impact of planet wakes on the location and shape of the water ice line in a protoplanetary disk

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Migration of Jupiter-mass planets in low-viscosity discs

International audienceContext. Type-II migration of giant planets has a speed proportional to the disc’s viscosity for values of the α viscosity parameter larger than 10−4. Previous studies based on two-dimensional simulations, have shown that, at even lower viscosities, migration can be very chaotic and is often characterised by phases of fast migration. The reason is that vortices appear in low-viscosity discs due to the Rossby-wave instability at the edges of the gap opened by the planet. Migration is then determined by vortex-planet interactions.Aims. Our goal is to study giant planet migration in low-viscosity discs with 3D simulations. In 3D, vortices are more complex than the simple vertical extension of their 2D counterparts; their impact on planet migration is therefore not obvious.Methods. We performed numerical simulations using two grid-based codes: FARGOCA for three-dimensional simulations and FARGO-ADSG for the two dimensional case. Two-dimensional simulations were used mainly for preliminary tests to check the impact of self-gravity on vortex formation and on vortex-disc dynamics. After selecting disc masses for which self-gravity is not important at the planet location, three-dimensional simulations without self-gravity can be safely used. We have considered an adiabatic equation of state with exponential damping of temperature perturbations in order to avoid the development of the vertical shear instability. In our nominal simulation, we set α = 0 so that only numerical viscosity is present. We then performed simulations with non-zero α values to assess the threshold of prescribed viscosity below which the new migration processes appear.Results. We show that for α ≲ 10−5 two migration modes are possible, which differ from classical Type-II migration in the sense that they are not proportional to the disc’s viscosity. The first occurs when the gap opened by the planet is not very deep. This occurs in 3D simulations and/or when a big vortex forms at the outer edge of the planetary gap, diffusing material into the gap. The de-saturation of co-orbital and co-rotation resonances keeps the planet’s eccentricity low. Inward planet migration then occurs as long as the disc can refill the gap left behind by the migrating planet, either due to diffusion caused by the presence of the vortex or to the inward migration of the vortex itself due to its interaction with the disc. We call this type of migration ‘vortex-driven migration’, which differs from ‘vortex-induced’ migration described in Lin & Papaloizou (2010, MNRAS, 405, 1473, and 2011a, MNRAS, 415, 1445). This migration is very slow and cannot continue indefinitely because eventually the vortex dissolves. The second migration mode occurs when the gap is deep so that the planet’s eccentricity grows to a value e ~ 0.2 due to inefficient eccentricity damping by co-rotation resonances. Once the planet is on an eccentric orbit, gas can pass through the gap and planet migration unlocks from the disc’s viscous evolution. This second, faster migration mode appears to be typical of two-dimensional models in discs with slower damping of temperature perturbations.Conclusions. Vortex-driven migration in low-viscosity discs can be very slow and eventually reverses and stops, offering an interesting mechanism to explain the existence of the cold-Jupiter population, even if these planets originally started growing at the disc’s snowline