Gap-opening Planets Research Articles

Shoulder of Dust Rings Formed by Planet–Disk Interactions

Recent analyses of millimeter-wavelength protoplanetary disk observations have revealed several emission excesses on the previously identified dust rings, referred to as dust shoulders. The prevalence of dust shoulders suggests that they trace a common but unclear mechanism. In this work, we combine 3D, multifluid hydrodynamic simulations with radiative transfer calculations to explain the formation of dust shoulders. We find that the ring-shoulder pairs can result from the 3D planet–disk interactions with massive, gap-opening planets. The key driver is the dust filtration effect at the local pressure maximum due to planet-driven outward gas flows. Our work provides a possible explanation for the outer dust shoulders in recent super-resolution analyses of Atacama Large Millimeter/submillimeter Array observations. It also provides insights into the formation of the inner dust shoulder in the PDS 70 disk and highlights the role of 3D effects in planet–disk interaction studies.

Mid-infrared evidence for iron-rich dust in the multi-ringed inner disk of HD 144432

Context. Rocky planets form by the concentration of solid particles in the inner few au regions of planet-forming disks. Their chemical composition reflects the materials in the disk available in the solid phase at the time the planets were forming. Studying the dust before it gets incorporated in planets provides a valuable diagnostic for the material composition. Aims. We aim to constrain the structure and dust composition of the inner disk of the young Herbig Ae star HD 144432, using an extensive set of infrared interferometric data taken by the Very Large Telescope Interferometer (VLTI), combining PIONIER, GRAVITY, and MATISSE observations. Methods. We introduced a new physical disk model, TGMdust, to image the interferometric data, and to fit the disk structure and dust composition. We also performed equilibrium condensation calculations with GGchem to assess the hidden diversity of minerals occurring in a planet-forming disk such as HD 144432. Results. Our best-fit model has three disk zones with ring-like structures at 0.15, 1.3, and 4.1 au. Assuming that the dark regions in the disk at ~0.9 au and at ~3 au are gaps opened by planets, we estimate the masses of the putative gap-opening planets to be around a Jupiter mass. We find evidence for an optically thin emission (τ < 0.4) from the inner two disk zones (r < 4 au) at λ > 3 µm. Our silicate compositional fits confirm radial mineralogy gradients, as for the mass fraction of crystalline silicates we get around 61% in the innermost zone (r < 1.3 au), mostly from enstatite, while only ~20% in the outer two zones. To identify the dust component responsible for the infrared continuum emission, we explore two cases for the dust composition, one with a silicate+iron mixture and the other with a silicate+carbon one. We find that the iron-rich model provides a better fit to the spectral energy distribution. Our GGchem calculations also support an iron-rich and carbon-poor dust composition in the warm disk regions (r < 5 au, T > 300 K). Conclusions. We propose that in the warm inner regions (r < 5 au) of typical planet-forming disks, most if not all carbon is in the gas phase, while iron and iron sulfide grains are major constituents of the solid mixture along with forsterite and enstatite. Our analysis demonstrates the need for detailed studies of the dust in inner disks with new mid-infrared instruments such as MATISSE and JWST/MIRI.

The Dependence of the Structure of Planet-opened Gaps in Protoplanetary Disks on Radiative Cooling

Planets can excite density waves and open annular gas gaps in protoplanetary disks. The depth of gaps is influenced by the evolving angular momentum carried by density waves. While the impact of radiative cooling on the evolution of density waves has been studied, a quantitative correlation to connect gap depth with the cooling timescale is lacking. To address this knowledge gap, we employ the grid-based code Athena++ to simulate disk-planet interactions, treating cooling as a thermal relaxation process. We establish quantitative dependencies of steady-state gap depth (Equation 36) and width (Equation 41) on planetary mass, Shakura–Sunyaev viscosity, disk scale height, and thermal relaxation timescale (β). We confirm previous results that gap opening is the weakest when the thermal relaxation timescale is comparable to the local dynamical timescale. Significant variations in gap depth, up to an order of magnitude, are found with different β. In terms of width, a gap is at its narrowest around β = 1, approximately 10%–20% narrower compared to the isothermal case. When β ∼ 100, it can be ∼20% wider, and higher viscosity enhances this effect. We derive possible masses of the gas gap-opening planets in AS 209, HD 163296, MWC 480, and HL Tau, accounting for the uncertainties in the local thermal relaxation timescale.

3D global simulations of accretion onto gap-opening planets: implications for circumplanetary disc structures and accretion rates

ABSTRACT We perform a series of 3D simulations to study the accretion of giant planet embedded in protoplanetary discs (PPDs) over gap-opening time-scales. We find that the accretion mass flux mainly comes from the intermediate latitude above the disc mid-plane. The circumplanetary disc (CPD) for a super-thermal planet is rotation-supported up to ∼20–30 per cent of the planet Hill radius. While both mass inflow and outflow exists in the CPD mid-plane, the overall trend is an outflow that forms a meridional circulation with high-latitude inflows. We confirm the absence of accretion outburst from disc eccentricity excited by massive planets in our 3D simulations, contrary to the consensus of previous 2D simulations. This suggests the necessity of 3D simulations of accretion even for super-Jupiters. The accretion rates of planets measured in a steady state can be decomposed into the ‘geometric’ and ‘density depletion’ factors. Through an extensive parameter survey, we identify a power-law scaling for the geometric factor $\propto q_{\rm th}^{2/3}$ for super-thermal planets (qth being the thermal mass ratio), which transform to $\propto q_{\rm th}^{2}$ for less massive cases. The density depletion factor is limited by the disc accretion rate for mildly super-thermal planets and by gap-opening for highly super-thermal ones. Moderate planetary eccentricities can enhance the accretion rates by a factor of 2–3 by making the gap shallower, but it does not impact the flow geometry. We have applied our simulations results to accreting protoplanet system PDS 70 and can satisfactorily explain the accretion rate and CPD size in observations.

Distinguishing magnetized disc winds from turbulent viscosity through substructure morphology in planet-forming discs

ABSTRACT The traditional paradigm of viscosity-dominated evolution of protoplanetary discs has been recently challenged by existence of magnetized disc winds. However, distinguishing wind-driven and turbulence-driven accretion through observations has been difficult. In this study, we present a novel approach to identifying their separate contribution to angular momentum transport by studying the gap and ring morphology of planet-forming discs in the ALMA continuum. We model the gap-opening process of planets in discs with both viscous evolution and wind-driven accretion by 2D multifluid hydrodynamical simulations. Our results show that gap-opening planets in wind-driven accreting discs generate characteristic dust substructures that differ from those in purely viscous discs. Specifically, we demonstrate that discs where wind-driven accretion dominates the production of substructures exhibit significant asymmetries. Based on the diverse outputs of mock images in the ALMA continuum, we roughly divide the planet-induced features into four regimes (moderate-viscosity dominated, moderate-wind dominated, strong-wind dominated, and inviscid). The classification of these regimes sets up a potential method to constrain the strength of magnetized disc wind and viscosity based on the observed gap and ring morphology. We discuss the asymmetry feature in our mock images and its potential manifestation in ALMA observations.

The ALMA view of MP Mus (PDS 66): A protoplanetary disk with no visible gaps down to 4 au scales

Aims. We aim to characterize the protoplanetary disk around the nearby (d ~ 100 pc), young solar analog MP Mus (PDS 66) and to reveal any signs of planets or ongoing planet formation in the system. Methods. We present new ALMA observations of MP Mus at 0.89 mm, 1.3 mm, and 2.2 mm with angular resolutions of ~1″, 0.05″, and 0.25″, respectively. These data probe the dust and gas in the disk with unprecedented detail and sensitivity. Results. The disk appears smooth down to the 4 au resolution of the 1.3 mm observations, in contrast with most disks observed at comparable spatial scales. The dust disk has a radius of 60±5 au, a dust mass of 0.14-0.06+0.11 MJup, and a millimeter spectral index <2 in the inner 30 au, suggesting optically thick emission from grains with a high albedo in this region. Several molecular gas lines are also detected extending up to 130±15 au, similar to small grains traced by scattered light observations. Comparing the fluxes of different CO isotopologues with previous models yields a gas mass of 0.1–1 MJup, implying a gas-to-dust ratio of 1–10. We also measured a dynamical stellar mass of Mdyn = 1.30±0.08 M⊙ and derived an age of 7–10 Myr. Conclusions. The survival of large grains in an evolved disk without gaps or rings is surprising, and it is possible that existing substructures remain undetected due to optically thick emission at 1.3 mm. Alternatively, small structures may still remain unresolved with the current observations. Based on simple scaling relations for gap-opening planets and gap widths, this lack of substructures places upper limits to the masses of planets in the disk as low as 2 M⊕−0.06 MJup at r > 40 au. The lack of millimeter emission at radii r > 60 au also suggests that the gap in scattered light between 30 and 80 au is likely not a gap in the disk density, but a shadow cast by a puffed-up inner disk.

A recipe for orbital eccentricity damping in the type-I regime for low-viscosity 2D discs

Context. It is well known that partial and deep gap opening depends on a disc’s viscosity; however, damping formulas for orbital eccentricities have only been derived at high viscosities, ignoring partial gap opening. Aims. In this work, we aim to obtain a simple formula to model eccentricity damping of the type-I regime in low-viscosity discs, where even small planets of a few to a few tens of Earth masses may start opening partial gaps in the gas surface density around their orbit. Methods. We performed high-resolution, 2D, locally isothermal hydrodynamical simulations of planets with varying masses on fixed orbits in discs with varying aspect ratios and viscosities. We determined the torque and power felt by the planet to ultimately derive migration and eccentricity damping timescales. Results. We first find a lower limit to the gap depths below which vortices appear; this happens roughly at the transition between type-I and classical type-II migration regimes. For the simulations that remain stable, we obtain a fit to the observed gap depth in the limit of vanishing eccentricities that is similar to the one currently used in the literature but accurate down to α = 3.16 × 10−5. We then record the eccentricity damping efficiency as a function of the observed gap depth and the initial eccentricity. When the planet has opened a deep enough gap such that the surface density is less than ~80% of the unperturbed disc surface density, a clear linear trend is observed independently of the planet’s eccentricity; at shallower gaps, this linear trend is preserved at low eccentricities, while it deviates to more efficient damping when e is comparable to the disc’s scale height. Both trends can be understood on theoretical grounds and are reproduced by a simple fitting formula. Conclusions. Our combined fits for the gap depth and eccentricity damping efficiency yield a simple recipe to implement type-I eccentricity damping in N-body codes in the case of partial gap opening planets that is consistent with high-resolution 2D hydrodynamical simulations. The typical error of the final fit is of the order of a few percent, and at most ~20%, which is the error of type-I torque formulas widely used in the literature. This will allow a more self-consistent treatment of planet-disc interactions of the type-I regime for population synthesis models at low viscosities.

Gap-opening Planets Make Dust Rings Wider

As one of the most commonly observed disk substructures, dust rings from high-resolution disk surveys appear to have different radial widths. Recent observations on PDS 70 and AB Aur reveal not only planets in the disk, but also the accompanying wide dust rings. We use three-dimensional dust-and-gas disk simulations to study whether gap-opening planets are responsible for the large ring width in disk observations. We find that gap-opening planets can widen rings of dust trapped at the pressure bump via planetary perturbations, even with the midplane dust-to-gas ratio approaching order unity and with the dust back-reaction accounted for. We show that the planet-related widening effect of dust rings can be quantified using diffusion-advection theory, and we provide a generalized criterion for an equilibrated dust ring width in three-dimensional disk models. We also suggest that the ring width can be estimated using the gas turbulent viscosity α turb, but with cautions about the Schmidt number being greater than order unity.

Trapping (sub-)Neptunes similar to TOI-216b at the inner disk rim

Context. The occurrence rate of observed sub-Neptunes has a break at 0.1 au, which is often attributed to a migration trap at the inner rim of protoplanetary disks where a positive co-rotation torque prevents inward migration. Aims. We argue that conditions in inner disk regions are such that sub-Neptunes are likely to open gaps, lose the support of the co-rotation torque as their co-rotation regions become depleted, and the trapping efficiency then becomes uncertain. We study what it takes to trap such gap-opening planets at the inner disk rim. Methods. We performed 2D locally isothermal and non-isothermal hydrodynamic simulations of planet migration. A viscosity transition was introduced in the disk to (i) create a density drop and (ii) mimic the viscosity increase as the planet migrated from a dead zone towards a region with active magneto-rotational instability (MRI). We chose TOI-216b as a Neptune-like upper-limit test case, but we also explored different planetary masses, both on fixed and evolving orbits. Results. For planet-to-star mass ratios q ≃ (4–8) × 10−5, the density drop at the disk rim becomes reshaped due to a gap opening and is often replaced with a small density bump centred on the planet's co-rotation. Trapping is possible only if the bump retains enough gas mass and if the co-rotation region becomes azimuthally asymmetric, with an island of librating streamlines that accumulate a gas overdensity ahead of the planet. The overdensity exerts a positive torque that can counteract the negative torque of spiral arms. Under suitable conditions, the overdensity turns into a Rossby vortex. In our model, efficient trapping depends on the a viscosity and its contrast across the viscosity transition. In order to trap TOI-216b, αDZ = 10−3 in the dead zone requires αMRI ≳ 5 × 10−2 in the MRI-active zone. If αDZ = 5 × 10−4, αMRI ≳ 7.5 × 10−2 is needed. Conclusions. We describe a new regime of a migration trap relevant for massive (sub-)Neptunes that puts valuable constraints on the levels of turbulent stress in the inner part of their natal disks.

Single fluid versus multifluid: comparison between single-fluid and multifluid dust models for disc–planet interactions

ABSTRACT Recent observations of substructures such as dust gaps and dust rings in protoplanetary discs have highlighted the importance of including dust into purely gaseous disc models. At the same time, computational difficulties arise with the standard models of simulating the dust and gas separately. These include the cost of accurately simulating the interactions between well-coupled dust and gas and issues of dust concentration in areas below resolution of the gas phase. We test a single-fluid approach that incorporates the terminal velocity approximation valid for small particles, which can overcome these difficulties, through modification of FARGO3D. We compare this single-fluid model with a multifluid model for a variety of planet masses. We find differences in the dust density distribution in all cases. For high-mass, gap-opening planets, we find differences in the amplitude of the resulting dust rings, which we attribute to the failure of the terminal velocity approximation around shocks. For low-mass planets, both models agree everywhere except in the corotation region, where the terminal velocity approximation shows overdense dust lobes. We tentatively interpret these as dusty equivalents of thermal lobes seen in non-isothermal simulations with thermal diffusion, but more work is necessary to confirm this. At the same resolution, the computational time for the terminal velocity approximation model is significantly less than a two-fluid model. We conclude that the terminal velocity approximation is a valuable tool for modelling a protoplanetary disc, but care should be taken when shocks are involved.

Calibrated gas accretion and orbital migration of protoplanets in 1D disc models

Context. Orbital migration and gas accretion are two interdependent key processes that govern the evolution of planets in protoplanetary discs. The final planetary properties such as masses and orbital periods strongly depend on the treatment of those two processes. Aims. Our aim is to develop a simple prescription for migration and accretion in 1D disc models, calibrated with results of 3D hydro-dynamic simulations. Our focus lies on non-self-gravitating discs, but we also discuss to what degree our prescription could be applied when the discs are self-gravitating. Methods. We studied migration using torque densities. Our model for the torque density is based on existing fitting formulas, which we subsequently modify to prevent premature gap-opening. At higher planetary masses, we also apply torque densities from hydrody-namic simulations directly to our 1D model. These torque densities allow us to model the orbital evolution of an initially low-mass planet that undergoes runaway-accretion to become a massive planet. The two-way exchange of angular momentum between disc and planet is included. This leads to a self-consistent treatment of gap formation that only relies on directly accessible disc parameters. We present a formula for Bondi and Hill gas accretion in the disc-limited regime. This formula is self-consistent in the sense that mass is removed from the disc in the location from where it is accreted. The prescription is appropriate when the planet is smaller than, comparable to, or larger than the disc scale height. Results. We find that the resulting evolution in mass and semi-major axis in the 1D framework is in good agreement with those from 3D hydrodynamical simulations for a range of parameters. Conclusions. Our prescription is valuable for simultaneously modelling migration and accretion in 1D models, which allows a planet’s evolution to be followed over the entire lifetime of a disc. It is applicable also in situations where the surface density is significantly disturbed by multiple gap-opening planets or processes like infall. We conclude that it is appropriate and beneficial to apply torque densities from hydrodynamic simulations in 1D models, at least in the parameter space we study here. More work is needed in order to determine whether our approach is also applicable in an even wider parameter space and in situations with more complex disc thermodynamics, or when the disc is self-gravitating.

Emerging population of gap-opening planets around type-A stars

Context. The presence of forming planets embedded in their protoplanetary disks has been inferred from the detection of multiring structures in such disks. Most of these suspected planets are undetectable by direct imaging observations at current measurement sensitivities. Inward migration and accretion might make these putative planets accessible to the Doppler method, but the actual extent of growth and orbital evolution remains unconstrained. Aims. Under the premise that the gaps in the disk around HD 163296 originate from new-born planets, we investigate if and under which circumstances the gap-opening planets could represent progenitors of the exoplanet population detected around A-type stars. In particular, we study the dependence of final planetary masses and orbital parameters on the viscosity of the disk. Methods. The evolution of the embedded planets was simulated throughout the disk lifetime and up to 100 Myr after the dispersal of the disk, taking the evolving disk structure and a likely range of disk lifetimes into account. We modeled the temperature and density structure of the disk based on observational results following the widely used α disk prescription and we varied planetary and disk parameters within the available observational constraints. Results. We find that the final configuration of the planets is largely determined by the α viscosity parameter of the disk and less dependent on the choice for the disk lifetime and the initial planetary parameters. If we assume that planets such as those in HD 163296 evolve to form the observed exoplanet population of A-type stars, a α parameter on the order of 3.16 × 10−4 ≲ α ≲ 10−3 is required for the disks to induce sufficiently high migration rates. Depending on whether or not future direct imaging surveys will uncover a larger number of planets with mpl ≲ 3 MJup and apl ≳ 10 AU, we expect the α parameter to be at the lower or upper end of this range, always under the assumption that such disks indeed harbor wide orbit planets.

Testing planet formation from the ultraviolet to the millimetre

ABSTRACT Gaps imaged in protoplanetary discs are suspected to be opened by planets. We compute the present-day mass accretion rates $\dot{M}_{\rm p}$ of seven hypothesized gap-embedded planets, plus the two confirmed planets in the PDS 70 disc. The accretion rates are based on disc gas surface densities Σgas from C18O observations, and planet masses Mp from simulations fitted to observed gaps. Assuming accretion is Bondi-like, we find in eight out of nine cases that $\dot{M}_{\rm p}$ is consistent with the time-averaged value given by the current planet mass and system age, Mp/tage. As system ages are comparable to circumstellar disc lifetimes, these gap-opening planets may be undergoing their last mass doublings, reaching final masses of $M_{\rm p} \sim 10\rm{\!-\!}10^2 \, M_\oplus$ for the non-PDS 70 planets, and $M_{\rm p} \sim 1\!-\!10 \, M_{\rm J}$ for the PDS 70 planets. For another 15 gaps without C18O data, we predict Σgas by assuming their planets are accreting at their time-averaged $\dot{M}_{\rm p}$. Bondi accretion rates for PDS 70b and c are orders of magnitude higher than accretion rates implied by measured U-band and H α fluxes, suggesting most of the accretion shock luminosity emerges in as yet unobserved wavebands, or that the planets are surrounded by dusty, highly extincting, quasi-spherical circumplanetary envelopes. Thermal emission from such envelopes or from circumplanetary discs, on Hill sphere scales, peaks at wavelengths in the mid-to-far-infrared and can reproduce observed mm-wave excesses.

Survival of planet-induced vortices in 2D disks

Context. Several observations of protoplanetary disks reveal non-axisymmetric features, which are often interpreted as vortices. Numerical modeling has repeatedly shown that gap-opening planets are capable of producing large and long-lasting vortices at their outer gap edge, making massive planets popular candidates as the source of such features. Aims. We explore the lifetime of vortices generated by Jupiter-sized planets as a function of the thermal relaxation timescale, the level of turbulence, and the effect of disk self-gravity. Methods. We conduct 2D numerical simulations using the hydrodynamics codes PLUTO and FARGO, scanning through several physical and numerical parameters. Vortex properties are automatically extracted from thousands of simulation snapshots. Results. We find that vortices that spawn at the outer gap edge can survive for about 100–3000 planetary orbits, with the shortest lifetimes occurring for moderately efficient dissipation and cooling. However, we also observe a different regime of long-lasting vortices with lifetimes of at least 15 000 orbits for very low viscosity and very short thermal relaxation timescales. Disk self-gravity significantly shortens the lifetime of regular vortices but still allows long-lived ones to survive. Conclusions. Our results suggest that the cooling timescale plays an important role in vortex formation and lifetime and that planet-generated vortices should be observable at large distances from the star for typical thermal relaxation timescales and low turbulence levels.

The fate of planetesimals formed at planetary gap edges

The presence of rings and gaps in protoplanetary disks are often ascribed to planet–disk interactions, where dust and pebbles are trapped at the edges of planetary-induced gas gaps. Recent works have shown that these are likely sites for planetesimal formation via the streaming instability. Given the large amount of planetesimals that potentially form at gap edges, we address the question of their fate and their ability to radially transport solids in protoplanetary disks. We performed a series ofN-body simulations of planetesimal orbits, taking into account the effect of gas drag and mass loss via ablation. We considered two planetary systems: one that is akin to the young Solar System and another inspired by the structures observed in the protoplanetary disk around HL Tau. In both systems, the proximity to the gap-opening planets results in large orbital excitations, causing the planetesimals to leave their birth locations and spread out across the disk soon after formation. We find that collisions between pairs of planetesimals are rare and should not affect the outcome of our simulations. Collisions with planets occur for ~1% of the planetesimals in the Solar System and for ~20% of the planetesimals in the HL Tau system. Planetesimals that end up on eccentric orbits interior of ~10 au experience efficient ablation and lose all mass before they reach the innermost disk region. In our nominal Solar System simulation, with a stellar gas accretion rate ofṀ0= 10−7M⊙yr−1andα= 10−2, we find that 70% of the initial planetesimal mass has been ablated after 500 kyr. Since the protoplanets are located further away from the star in the HL Tau system, the ablation rate is lower and only 11% of the initial planetesimal mass has been ablated after 1 Myr using the same disk parameters. The ablated material consist of a mixture of solid grains and vaporized ices, where a large fraction of the vaporized ices re-condense to form solid ice. Assuming that the solid grains and ices grow to pebbles in the disk midplane, this results in a pebble flux of ~10−100M⊕Myr−1through the inner disk. This occurred in the Solar System at a time so early in its evolution that there is not likely to be any record of it. Our results demonstrate that scattered planetesimals can carry a significant flux of solids past planetary-induced gaps in young and massive protoplanetary disks.

Migration of gap-opening planets in 3D stellar-irradiated accretion disks

Context. The origin of giant planets at moderate separations ≃1–10 au is still not fully understood because numerical studies of Type II migration in protoplanetary disks often predict a decay of the semi-major axis that is too fast. According to recent 2D simulations, inward migration of a gap-opening planet can be slowed down or even reversed if the outer gap edge becomes heated by irradiation from the central star, and puffed up. Aims. Here, we study how stellar irradiation reduces the disk-driven torque and affects migration in more realistic 3D disks. Methods. Using 3D hydrodynamic simulations with radiation transfer, we investigated the static torque acting on a single gap-opening planet embedded in a passively heated accretion disk. Results. Our simulations confirm that a temperature inversion is established at the irradiated outer gap edge and the local increase of the scale height reduces the magnitude of the negative outer Lindblad torque. However, the temperature excess is smaller than assumed in 2D simulations and the torque reduction only becomes prominent for specific parameters. For the viscosity α = 10−3, the total torque is reduced for planetary masses ranging from 0.1 to 0.7 Jupiter mass, with the strongest reduction being by a factor of − 0.17 (implying outward migration) for a Saturn-mass planet. For a Jupiter-mass planet, the torque reduction becomes stronger with increasing α (the torque is halved when α = 5 × 10−3). Conclusions. We conclude that planets that open moderately wide and deep gaps are subject to the largest torque modifications and their Type II migration can be stalled due to gap edge illumination. We then argue that the torque reduction can help to stabilize the orbits of giant planets forming at ≳ 1 au.

Radial Migration of Gap-opening Planets in Protoplanetary Disks. II. The Case of a Planet Pair

Abstract When two planets are born in a protoplanetary disk, they may enter into mean-motion resonance as a consequence of convergent planetary migration. The formation of mean-motion resonances is important for understanding how planetary systems are shaped in disk environments. Motivated by recent progress in the comprehension of the migration of partial gap-opening planets, we have investigated the orbital evolution of planet pairs in a wide range of masses and disk properties with the aim to find out when resonance capture is likely to happen. Using the formula for the migration timescale of a gap-opening planet developed in our previous work, we have derived a simple criterion that allows us to predict when the migration will be convergent (divergent). Further, we have verified the criterion using two-dimensional hydrodynamic simulations. We have found that the resonant pair of planets formed at the early phase of evolution can depart from resonance at later times because the migration speed of the outer planet slows down due to gap formation. Moreover, adopting our formula for the migration timescale, we have also carried out three-body simulations, which confirm the results of hydrodynamic simulations. Finally, we have compared our predictions with observations, selecting a sample of known two-planet systems.

Probing the Protosolar Disk Using Dust Filtering at Gaps in the Early Solar System

Abstract Jupiter and Saturn formed early, before the gas disk dispersed. The presence of gap-opening planets affects the dynamics of the gas and embedded solids and halts the inward drift of grains above a certain size. A drift barrier can explain the absence of calcium–aluminum-rich inclusions (CAIs) in chondrites originating from parent bodies that accreted in the inner solar system. Employing an interdisciplinary approach, we use a μ-X-ray-fluorescence scanner to search for large CAIs and a scanning electron microscope to search for small CAIs in the ordinary chondrite NWA 5697. We carry out long-term, two-dimensional simulations including gas, dust, and planets to characterize the transport of grains within the viscous α-disk framework exploring the scenarios of a stand-alone Jupiter, Jupiter and Saturn in situ, or Jupiter and Saturn in a 3:2 resonance. In each case, we find a critical grain size above which drift is halted as a function of the physical conditions in the disk. From the laboratory search we find four CAIs with a largest size of ≈200 μm. Combining models and data, we provide an estimate for the upper limit of the α-viscosity and the surface density at the location of Jupiter, using reasonable assumptions about the stellar accretion rate during inward transport of CAIs, and assuming angular momentum transport to happen exclusively through viscous effects. Moreover, we find that the compound gap structure in the presence of Saturn in a 3:2 resonance favors inward transport of grains larger than CAIs currently detected in ordinary chondrites.

Circumbinary discs with radiative cooling and embedded planets

Context. As of today, ten circumbinary planets orbiting solar type main sequence stars have been discovered. Nearly all orbit around the central binary very closely to the region of instability where it is difficult to form them in situ. Hence, it is assumed that they formed further out and then migrated to their observed position, which is determined by binary, disc and planet properties. Aims. We extend previous studies to a more realistic thermal disc structure and determine what parameter influence the final parking location of a planet around a binary star. Methods. We performed two-dimensional numerical simulations of viscous accretion discs around a central binary. These simulations include viscous heating and radiative cooling from the disc surfaces. We vary the binary eccentricity as well as disc viscosity and mass. Results. Concerning the disc evolution, we find that it can take well over 100 000 binary orbits until an equilibrium state is reached. As seen previously, we find that the central cavity opened by the binary becomes eccentric and precesses slowly in a prograde sense. Embedded planets migrate to the inner edge of the disc. In cases of lower disc viscosity they migrate further in maintaining a circular orbit, while for high viscosity they are parked further out on an eccentric orbit. Conclusions. Discs around binary stars are eccentric, and precess very slowly around the binary. The final location of an embedded planet is linked to its ability to open a gap in the disc. Gap-opening planets separate inner from outer disc, preventing eccentricity excitation in the latter and making it more circular. This allows embedded planets to migrate closer to the binary, in agreement with the observations. The necessary conditions for gap opening and the final planet position depend on the planet mass and disc viscosity.

Migrating super-Earths in low-viscosity discs: unveiling the roles of feedback, vortices, and laminar accretion flows

We present the highest resolution study to date of super-Earths migrating in inviscid and low-viscosity discs, motivated by the connection to laminar, wind-driven models of protoplanetary discs. Our models unveil the critical role of vortices in determining the migration behaviour for partial gap-opening planets. Vortices form in pressure maxima at gap edges, and prevent the disc-feedback stopping of migration for intermediate planets in low-viscosity and inviscid discs, contrary to the concept of the `inertial limit' or `disc feedback' halting predicted from analytical models. Vortices may also form in the corotation region, and can dramatically modify migration behaviour through direct gravitational interaction with the planet. These features become apparent at high resolution, and for all but the highest viscosities there exist significant difficulties in obtaining numerically converged results. The migration of partial gap-opening planets, however, clearly becomes chaotic for sufficiently low viscosities. At moderate viscosity, a smooth disc-feedback regime is found in which migration can slow substantially, and the migration time-scale observed corresponds to migration being driven by diffusive relaxation of the gap edges. At high viscosity classical Type I migration is recovered. For Jupiter-analogue planets in inviscid discs, a wide, deep gap is formed. Transient Type II migration occurs over radial length-scales corresponding to the gap width, beyond which migration can stall. Finally, we examine the particle trapping driven by structures left in inviscid discs by a migrating planet, and find that particle traps in the form of multiple rings and vortices can persist long after the planet has passed. In this case, the observation of particle traps by submillimetre interferometers such as ALMA cannot be used to infer the current presence of an adjacent planet.