ABSTRACT
We investigate the gravitational interaction between low- to intermediate-mass planets ($M_p \in 0.06-210\, \mathrm{ M}_{\oplus }$) and two previously formed pressure bumps in a gas-dust ...protoplanetary disc. We explore how the disc structure changes due to planet-induced perturbations and also how the appearance of vortices affects planet migration. We use multifluid 2D hydrodynamical simulations and the dust is treated in the pressureless-fluid approximation, assuming a single grain size of $5\, \mu {\mathrm{m}}$. The initial surface density profiles containing two bumps are motivated by recent observations of the protoplanetary disc HD163296. When planets are allowed to migrate, either a single planet from the outer pressure maximum or two planets from each pressure maximum, the initial pressure bumps quickly spread and merge into a single bump which is radially wide and has a very low amplitude. The redistribution of the disc material is accompanied by the Rossby Wave Instability and an appearance of mini-vortices that merge in a short period of time to form a large vortex. The large vortex induces perturbations with a spiral wave pattern that propagate away from the vortex as density waves. We found that these vortex-induced spiral waves strongly interact with the spiral waves generated by the planet and we called this mechanism the ‘Faraway Interaction’. It facilitates much slower and/or stagnant migration of the planets and it excites their orbital eccentricities in some cases. Our study provides a new explanation for how rocky planets can come to have a slow migration in protoplanetary discs where vortex formation occurs.
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.
Context. Planetary embryos can continue to grow by pebble accretion until they become giant planet cores. Simultaneously, these embryos mutually interact and also migrate due to torques arising from ...the protoplanetary disk. Aims. Our aim is to study how pebble accretion alters the orbital evolution of embryos undergoing Type-I migration. In particular, we try to determine whether or not the embryos establish resonant chains, and if so, whether or not these chains are prone to instabilities. Further, we investigate the possibility that giant planet cores form through embryo merging which can be more rapid than pebble accretion alone. Methods. For the first time, we perform self-consistent global-scale radiative hydrodynamic simulations of a two-fluid protoplanetary disk consisting of gas and pebbles, the latter being accreted by embedded embryos. Accretion heating, along with other radiative processes, is accounted for to correctly model the Type-I migration. Results. We track the evolution of four super-Earth-like embryos, initially located in a region where the disk structure allows for a convergent migration. Generally, embryo merging is facilitated by rapidly increasing embryo masses and breaks the otherwise oligarchic growth. Moreover, we find that the orbital eccentricity of each embryo is considerably excited (≃0.03) due to the presence of an asymmetric under-dense lobe of gas – a so-called “hot trail” – produced by accretion heating of the embryo’s vicinity. Eccentric orbits lead the embryos to frequent close encounters and make resonant locking more difficult. Conclusions. Embryo merging typically produces one massive core (≳10 ME) in our simulations, orbiting near 10 AU. Pebble accretion is naturally accompanied by the occurrence of eccentric orbits which should be considered in future efforts to explain the structure of exoplanetary systems.
ABSTRACT
Planets can carve gaps in the surface density of protoplanetary discs. The formation of these gaps can reduce the corotation torques acting on the planets. In addition, gaps can halt the ...accretion of solids on to the planets as dust and pebbles can be trapped at the edge of the gap. This accumulation of dust could explain the origin of the ring-like dust structures observed using high-resolution interferometry. In this work, we provide an empirical scaling relation for the depth of the gap cleared by a planet on an eccentric orbit as a function of the planet-to-star mass ratio q, the disc aspect ratio h, Shakura–Sunyaev viscosity parameter α, and planetary eccentricity e. We construct the scaling relation using a heuristic approach: we calibrate a toy model based on the impulse approximation with 2D hydrodynamical simulations. The scaling reproduces the gap depth for moderate eccentricities (e ≤ 4h) and when the surface density contrast outside and inside the gap is ≤102. Our framework can be used as the basis of more sophisticated models aiming to predict the radial gap profile for eccentric planets.
Protoplanets of super-Earth size may get trapped in convergence zones for planetary migration and form gas giants there. These growing planets undergo accretion heating, which triggers a hot-trail ...effect that can reverse migration directions, increase planetary eccentricities, and prevent resonant captures of migrating planets. In this work, we study populations of embryos that are accreting pebbles under different conditions, by changing the surface density, viscosity, pebble flux, mass, and the number of protoplanets. For modelling, we used the FARGO-THORIN two-dimensional (2D) hydrocode, which incorporates a pebble disc as a second pressure-less fluid, the coupling between the gas and pebbles, and the flux-limited diffusion approximation for radiative transfer. We find that massive embryos embedded in a disc with high surface density (Σ = 990 g cm−2 at 5.2 au) undergo numerous “unsuccessful” two-body encounters that do not lead to a merger. Only when a third protoplanet arrives in the convergence zone do three-body encounters lead to mergers. For a low-viscosity disc (ν = 5 × 1013 cm2 s−1), a massive co-orbital is a possible outcome, for which a pebble isolation develops and the co-orbital is further stabilised. For more massive protoplanets (5 M⊕), the convergence radius is located further out, in the ice-giant zone. After a series of encounters, there is an evolution driven by a dynamical torque of a tadpole region, which is systematically repeated several times until the co-orbital configuration is disrupted and planets merge. This may be a way to solve the problem that co-orbitals often form in simulations but they are not observed in nature. In contrast, the joint evolution of 120 low-mass protoplanets (0.1 M⊕) reveals completely different dynamics. The evolution is no longer smooth, but rather a random walk. This is because the spiral arms, developed in the gas disc due to Lindblad resonances, overlap with each other and affect not only a single protoplanet but several in the surrounding area. Our hydrodynamical simulations may have important implications for N-body simulations of planetary migration that use simplified torque prescriptions and are thus unable to capture protoplanet dynamics in its full glory.
Aims.
Asteroid (31) Euphrosyne is one of the biggest objects in the asteroid main belt and it is also the largest member of its namesake family. The Euphrosyne family occupies a highly inclined ...region in the outer main belt and contains a remarkably large number of members, which is interpreted as an outcome of a disruptive cratering event.
Methods.
The goals of this adaptive-optics imaging study are threefold: to characterize the shape of Euphrosyne, to constrain its density, and to search for the large craters that may be associated with the family formation event.
Results.
We obtained disk-resolved images of Euphrosyne using SPHERE/ZIMPOL at the ESO 8.2 m VLT as part of our large program (ID: 199.C-0074, PI: Vernazza). We reconstructed its 3D shape via the
ADAM
shape modeling algorithm based on the SPHERE images and the available light curves of this asteroid. We analyzed the dynamics of the satellite with the
Genoid
meta-heuristic algorithm. Finally, we studied the shape of Euphrosyne using hydrostatic equilibrium models.
Conclusions.
Our SPHERE observations show that Euphrosyne has a nearly spherical shape with the sphericity index of 0.9888 and its surface lacks large impact craters. Euphrosyne’s diameter is 268 ± 6 km, making it one of the top ten largest main belt asteroids. We detected a satellite of Euphrosyne – S/2019 (31) 1 – that is about 4 km across, on a circular orbit. The mass determined from the orbit of the satellite together with the volume computed from the shape model imply a density of 1665 ± 242 kg m
−3
, suggesting that Euphrosyne probably contains a large fraction of water ice in its interior. We find that the spherical shape of Euphrosyne is a result of the reaccumulation process following the impact, as in the case of (10) Hygiea. However, our shape analysis reveals that, contrary to Hygiea, the axis ratios of Euphrosyne significantly differ from those suggested by fluid hydrostatic equilibrium following reaccumulation.
Aims.
The Euphrosyne asteroid family occupies a unique zone in orbital element space around 3.15 au and may be an important source of the low-albedo near-Earth objects. The parent body of this family ...may have been one of the planetesimals that delivered water and organic materials onto the growing terrestrial planets. We aim to characterize the compositional properties as well as the dynamical properties of the family.
Methods.
We performed a systematic study to characterize the physical properties of the Euphrosyne family members via low-resolution spectroscopy using the NASA Infrared Telescope Facility. In addition, we performed smoothed-particle hydrodynamics (SPH) simulations and
N
-body simulations to investigate the collisional origin, determine a realistic velocity field, study the orbital evolution, and constrain the age of the Euphrosyne family.
Results.
Our spectroscopy survey shows that the family members exhibit a tight taxonomic distribution, suggesting a homogeneous composition of the parent body. Our SPH simulations are consistent with the Euphrosyne family having formed via a reaccumulation process instead of a cratering event. Finally, our
N
-body simulations indicate that the age of the family is 280
−80
+180
Myr, which is younger than previous estimates.
The 2:1 mean-motion resonance with Jupiter harbours two distinct groups of asteroids. The short-lived population is known to be a transient group sustained in steady state by the Yarkovsky semimajor ...axis drift. The long-lived asteroids, however, can exhibit dynamical lifetimes comparable to 4 Gyr. They reside near two isolated islands of the phase space denoted A and B, with an uneven population ratio B/A ≃ 10. The orbits of A-island asteroids are predominantly highly inclined, compared to island B. The size–frequency distribution is steep but the orbital distribution lacks any evidence of a collisional cluster. These observational constraints are somewhat puzzling and therefore the origin of the long-lived asteroids has not been explained so far. With the aim to provide a viable explanation, we first update the resonant population and revisit its physical properties. Using an N-body model with seven planets and the Yarkovsky effect included, we demonstrate that the dynamical depletion of island A is faster, in comparison with island B. Then we investigate (i) the survivability of primordial resonant asteroids and (ii) capture of the population during planetary migration, following a recently described scenario with an escaping fifth giant planet and a jumping-Jupiter instability. We also model the collisional evolution of the resonant population over past 4 Gyr. Our conclusion is that the long-lived group was created by resonant capture from a narrow part of hypothetical outer main-belt family during planetary migration. Primordial asteroids surviving the migration were probably not numerous enough to substantially contribute to the observed population.
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,
α
DZ
= 10
−3
in the dead zone requires
α
MRI
≳ 5 × 10
−2
in the MRI-active zone. If
α
DZ
= 5 × 10
−4
,
α
MRI
≳ 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.
PDF
