Runaway Migration Research Articles

Using planet migration and dust drift to weigh protoplanetary discs

ABSTRACT ALMA has spatially resolved over 200 annular structures in protoplanetary discs, many of which are suggestive of the presence of planets. Constraining the mass of these putative planets is quite degenerate for it depends on the disc physical properties, and for simplicity a steady-state is often assumed whereby the planet position is kept fixed and there is a constant source of dust at the outer edge of the disc. Here, we argue against this approach by demonstrating how the planet and dust dynamics can lift degeneracies of such steady-state models. We take main disc parameters from the well-known protoplanetary disc HD 163296 with a suspected planet at R ≈ 86 au as an example. By running gas and dust hydrodynamical simulations post-processed with dust radiative transfer calculations, we first find steady-state disc and planet parameters that reproduce ALMA continuum observations fairly well. For the same disc mass, but now allowing the planet to migrate in the simulation, we find that the planet undergoes runaway migration and reaches the inner disc in ∼0.2 Myr. Further, decreasing the disc mass slows down planet migration, but it then also increases the dust’s radial drift, thereby depleting the disc dust faster. We find that the opposing constraints of planet migration and dust drift require the disc mass to be at most $0.025~{\rm {\rm M}_{\odot }}$, must less massive than previously estimated, and for the dust to be porous rather than compact. We propose that similar analysis should be extended to other sources with suspected planetary companions.

Intermittent planet migration and the formation of multiple dust rings and gaps in protoplanetary discs

ABSTRACT A key challenge for protoplanetary discs and planet formation models is to be able to make a reliable connection between observed structures in the discs emission, like bright and dark rings or asymmetries, and the supposed existence of planets triggering these structures. The observation of N dark rings of emission is often interpreted as evidence for the presence of N planets which clear dust gaps around their orbit and form dust-trapping pressure maxima in the disc. The vast majority of the models that studied the impact of planets on the dynamics of dust and gas in a protoplanetary disc assumed planets on fixed orbits. Here, we go a different route and examine how the large-scale inward migration of a single planet structures the dust content of a massive disc. In many circumstances, the migration of a partial gap-opening planet with a mass comparable to Saturn is found to run away intermittently. By means of 2D gas and dust hydrodynamical simulations, we show that intermittent runaway migration can form multiple dust rings and gaps across the disc. Each time migration slows down, a pressure maximum forms beyond the planet gap that traps the large dust. Post-processing of our simulations results with 3D dust radiative transfer calculations confirms that intermittent runaway migration can lead to the formation of multiple sets of bright and dark rings of continuum emission in the (sub)millimeter beyond the planet location.

Low-mass planet migration in magnetically torqued dead zones – II. Flow-locked and runaway migration, and a torque prescription

We examine the migration of low mass planets in laminar protoplanetary discs, threaded by large scale magnetic fields in the dead zone that drive radial gas flows. As shown in Paper I, a dynamical corotation torque arises due to the flow-induced asymmetric distortion of the corotation region and the evolving vortensity contrast between the librating horseshoe material and background disc flow. Using simulations of laminar torqued discs containing migrating planets, we demonstrate the existence of the four distinct migration regimes predicted in Paper I. In two regimes, the migration is approximately locked to the inward or outward radial gas flow, and in the other regimes the planet undergoes outward runaway migration that eventually settles to fast steady migration. In addition, we demonstrate torque and migration reversals induced by midplane magnetic stresses, with a bifurcation dependent on the disc surface density. We develop a model for fast migration, and show why the outward runaway saturates to a steady speed, and examine phenomenologically its termination due to changing local disc conditions. We also develop an analytical model for the corotation torque at late times that includes viscosity, for application to discs that sustain modest turbulence. Finally, we use the simulation results to develop torque prescriptions for inclusion in population synthesis models of planet formation.

ON THE ORBITAL EVOLUTION OF A GIANT PLANET PAIR EMBEDDED IN A GASEOUS DISK. I. JUPITER-SATURN CONFIGURATION

We carry out a series of high-resolution (1024 × 1024) hydrodynamical simulations to investigate the orbital evolution of Jupiter and Saturn embedded in a gaseous protostellar disk. Our work extends the results in the classical papers of Masset & Snellgrove and Morbidelli & Crida by exploring various surface density profiles (σ), where σ ∝ r−α. The stability of the mean motion resonances (MMRs) caused by the convergent migration of the two planets is studied as well. Our results show that (1) the gap formation process of Saturn is greatly delayed by the tidal perturbation of Jupiter. These perturbations cause inward or outward runaway migration of Saturn, depending on the density profiles on the disk. (2) The convergent migration rate increases as α increases and the type of MMRs depends on α as well. When 0 < α < 1, the convergent migration speed of Jupiter and Saturn is relatively slow, thus they are trapped into 2:1 MMR. When α>4/3, Saturn passes through the 2:1 MMR with Jupiter and is captured into the 3:2 MMR. (3) The 3:2 MMR turns out to be unstable when the eccentricity of Saturn (es) increases too high. The critical value above which instability will set in is es ∼ 0.15. We also observe that the two planets are trapped into 2:1 MMR after the break of 3:2 MMR. This process may provide useful information for the formation of orbital configuration between Jupiter and Saturn in the solar system.

Iapetus: Unique Surface Properties and a Global Color Dichotomy from Cassini Imaging

Since 2004, Saturn's moon Iapetus has been observed repeatedly with the Imaging Science Subsystem of the Cassini spacecraft. The images show numerous impact craters down to the resolution limit of approximately 10 meters per pixel. Small, bright craters within the dark hemisphere indicate a dark blanket thickness on the order of meters or less. Dark, equator-facing and bright, poleward-facing crater walls suggest temperature-driven water-ice sublimation as the process responsible for local albedo patterns. Imaging data also reveal a global color dichotomy, wherein both dark and bright materials on the leading side have a substantially redder color than the respective trailing-side materials. This global pattern indicates an exogenic origin for the redder leading-side parts and suggests that the global color dichotomy initiated the thermal formation of the global albedo dichotomy.

Formation of Iapetus’ Extreme Albedo Dichotomy by Exogenically Triggered Thermal Ice Migration

The extreme albedo asymmetry of Saturn's moon Iapetus, which is about 10 times as bright on its trailing hemisphere as on its leading hemisphere, has been an enigma for three centuries. Deposition of exogenic dark material on the leading side has been proposed as a cause, but this alone cannot explain the global shape, sharpness, and complexity of the transition between Iapetus' bright and dark terrain. We demonstrate that all these characteristics, and the asymmetry's large amplitude, can be plausibly explained by runaway global thermal migration of water ice, triggered by the deposition of dark material on the leading hemisphere. This mechanism is unique to Iapetus among the saturnian satellites because its slow rotation produces unusually high daytime temperatures and water ice sublimation rates for a given albedo.

The dynamical role of the circumplanetary disc in planetary migration

<i>Context. <i/>Numerical simulations of planets embedded in protoplanetary gaseous discs are a precious tool for studying the planetary migration; however, some approximations have to be made. Most often, the selfgravity of the gas is neglected. In that case, it is not clear in the literature how the material inside the Roche lobe of the planet should be taken into account.<i>Aims. <i/>Here, we want to address this issue by studying the influence of various methods so far used by different authors on the migration rate.<i>Methods. <i/>We performed high-resolution numerical simulations of giant planets embedded in discs. We compared the migration rates with and without gas selfgravity, testing various ways of taking the circum-planetary disc (CPD) into account.<i>Results. <i/>Different methods lead to significantly different migration rates. Adding the mass of the CPD to the perturbing mass of the planet accelerates the migration. Excluding a part of the Hill sphere is a very touchy parameter that may lead to an artificial suppression of the type III, runaway migration. In fact, the CPD is smaller than the Hill sphere. We recommend excluding no more than a 0.6 Hill radius and using a smooth filter. Alternatively, the CPD can be given the acceleration felt by the planet from the rest of the protoplanetary disc.<i>Conclusions. <i/>The gas inside the Roche lobe of the planet should be very carefully taken into account in numerical simulations without any selfgravity of the gas. The entire Hill sphere should not be excluded. The method used should be explicitly given. However, no method is equivalent to computing the full selfgravity of the gas.

On the Orbital Evolution of a Jovian Planet Embedded in a Self‐Gravitating Disk

We performed a series of hydrodynamic simulations to investigate the orbital evolution of a Jovian planet embedded in a protostellar disk. In order to take into account of the effect of the disk's self-gravity, we developed and adopted an ANTARES code which is based on a 2D Godunov scheme to obtain the exact Reimann solution for isothermal or polytropic gas, with nonreflecting boundary conditions. Our simulations indicate that in the study of runaway (type III) migration it is important to carry out a fully self-consistent treatment of the gravitational interaction between the disk and the embedded planet. Through a series of convergence tests, we show that adequate numerical resolution, especially within the planet's Roche lobe, critically determines the outcome of the simulations. We consider a variety of initial conditions and show that isolated, noneccentric protoplanets do not undergo type III migration. We attribute the difference between our and previous simulations to the contribution of a self-consistent representation of the disk's self-gravity. Nevertheless, type III migration cannot be completely suppressed, and its onset requires finite-amplitude perturbations such as that induced by planet-planet interaction. We determine the radial extent of type III migration as a function of the disk's self-gravity.

Runaway migration in a multiple-protoplanet system

AbstractWe investigate the migration of two giant planets embedded in a proto-stellar disk. The inner planet(initially located at R10=1) is of 1 Jupiter mass and the outer one(R20=1.5) is of 1 Saturn mass. We find that due to the existence of the inner massive planet, the outer planet can not open a clear gap. Instead of an inward migration and being captured by the mean motion resonance of the inner planet, the outer planet undergoes an outward runaway migration. We conclude that this runaway migration is caused by the co-rotation torque in the co-orbital region of the outer planet and sustained by the wave(flow) driven by the inner massive planet.

The effect of planetary migration on the corotation resonance

The migration of a planet through a gaseous disc causes the locations of their resonant interactions to drift and can alter the torques exerted between the planet and the disc. We analyse the time-dependent dynamics of a non-coorbital corotation resonance under these circumstances. The ratio of the resonant torque in a steady state to the value given by Goldreich & Tremaine depends essentially on two dimensionless quantities: a dimensionless turbulent diffusion time-scale and a dimensionless radial drift speed. The dimensionless diffusion time-scale is a characteristic ratio of the time-scale of turbulent viscous diffusion across the librating region of the resonance to the time-scale of libration; in the absence of migration, this parameter alone determines the degree of saturation of the resonance. The dimensionless radial drift speed is the characteristic ratio of the drift speed of the resonance to the radial velocity in the librating region; this parameter determines the shape of the streamlines. When the drift speed is comparable to the libration speed and the viscosity is small, the torque can become much larger than the unsaturated value in the absence of migration, but is still proportional to the large-scale vortensity gradient in the disc. Fluid that is trapped in the resonance and drifts with it acquires a vortensity anomaly relative to its surroundings. If the anomaly is limited by viscous diffusion in a steady state, the resulting torque is inversely proportional to the viscosity, although a long time may be required to achieve this state. A further, viscosity-independent, contribution to the torque comes from fluid that streams through the resonant region. In other cases, torque oscillations occur before the steady value is achieved. We discuss the significance of these results for the evolution of eccentricity in protoplanetary systems. We also describe the possible application of these findings to the coorbital region and the concept of runaway (or type III) migration.

Starbursts near supermassive black holes: young stars in the Galactic Centre, and gravitational waves in LISA band

We propose a scenario in which massive stars form in a self-gravitating gaseous disc around a supermassive black hole (SMBH). We analyse the dynamics of a disc forming around an SMBH, in which the angular momentum is transported by turbulence induced by the disc's self-gravity. We find that once the surface density of the disc exceeds a critical value, the disc fragments into dense clumps. We argue that the clumps accrete material from the remaining disc and merge into larger clumps; the upper mass of a merged clump is a few tens to a few hundreds of solar mass. This picture fits well with the observed young stellar discs near the SgrA* black hole in the Galactic Centre. In particular, we show how the masses and spatial distribution of the young stars, and the total mass in the Galactic Centre discs can be explained. However, explaining the origin of the several young stars closest to the black hole (the S-stars) is more problematic: their orbits are compact, eccentric, and have random orientation. We propose that the S-stars were born in a previous starburst(s), and then migrated through their parent disc via type-I or runaway migration. Their orbits were then randomized by the Rauch–Tremaine resonant relaxation. We then explore the consequences of the star formation scenario for AGN discs, which are continuously resupplied with gas. We argue that some compact remnants generated by the starburst will get embedded in the disc. The disc-born stellar mass black holes will interact gravitationally with the massive accretion disc and be dragged towards the central black hole. Merger of a disc-born black hole with the central black hole will produce a burst of gravitational waves. If the central black hole is accreting at a rate comparable to the Eddington limit, the gas drag from the accretion disc will not alter significantly the dynamics of the final year of merger, and the gravitational waves should be observable by Laser Interferometer Space Antenna (LISA). For a reasonable range of parameters such mergers will be detected monthly, and that the gravitational-wave signal from these mergers is distinct from that of other merger scenarios. Also, for some plausible black hole masses and accretion rates, the burst of gravitational waves should be accompanied by a detectable change in the optical luminosity of the central engine.

Planetary migration in a planetesimal disk: why did Neptune stop at 30 AU?

We study planetary migration in a gas-free disk of planetesimals. In the case of our Solar System we show that Neptune could have had either a damped migration, limited to a few AUs, or a forced migration up to the disk's edge, depending on the disk's mass density. We also study the possibility of runaway migration of isolated planets in very massive disk, which might be relevant for extra-solar systems. We investigate the problem of the mass depletion of the Kuiper belt in the light of planetary migration and conclude that the belt lost its pristine mass well before that Neptune reached its current position. Therefore, Neptune effectively hit the outer edge of the proto-planetary disk. We also investigate the dynamics of massive planetary embryos embedded in the planetesimal disk. We conclude that the elimination of Earth-mass or Mars-mass embryos originally placed outside the initial location of Neptune also requires the existence of a disk edge near 30 AU.

Statistical properties of exoplanets

Interesting emerging observational properties of the period-mass distribution of extra-solar planets are discussed. New recent detections confirm the already emphasized lack of massive planets () on short-period orbits ( days). Furthermore, we point out i) a shortage of planets in the 10–100 day period range as well as ii) a lack of light planets () on orbits with periods larger than ~100 days. The latter feature is shown not to be due to small-number statistics with Monte-Carlo simulations. These observational period-related characteristics are discussed in the context of the migration process of exoplanets. They are found to be in agreement with recent simulations of planet interactions with viscous disks. The observed valley at a few tens of days in the period distribution is interpreted as a transition region between two categories of planets that suffered different migration scenarios. The lack of light planets on longer-period orbits and the corresponding intriguing sharp limit in mass is tentatively explained by the runaway migration process recently studied by Masset & Papaloizou (2003). The observed properties also have implications for the observation strategies of the on-going surveys and of future higher-precision searches.

Runaway Migration and the Formation of Hot Jupiters

We evaluate the coorbital corotation torque on a migrating protoplanet. The coorbital torque is assumed to come from orbit crossing fluid elements that exchange angular momentum with the planet when they execute a U-turn at the end of horseshoe streamlines. When the planet migrates inward, the fluid elements of the inner disk undergo one such exchange as they pass to the outer disk. The angular momentum they gain is removed from the planet, and this corresponds to a negative contribution to the corotation torque, which scales with the drift rate. In addition, the material trapped in the coorbital region drifts radially with the planet, giving a positive contribution to the corotation torque, which also scales with the drift rate. These two contributions do not cancel out if the coorbital region is depleted, in which case there is a net corotation torque that scales with the drift rate and the mass deficit in the coorbital region and has the same sign as the drift rate. This leads to a positive feedback on the migrating planet. In particular, if the coorbital mass deficit is larger than the planet mass, the migration rate undergoes a runaway that can vary the protoplanet semimajor axis by 50% over a few tens of orbits. This can happen only if the planet mass is sufficient to create a dip or gap in its surrounding region and if the surrounding disk mass is larger than the planet mass. This typically corresponds to planet masses in the sub-Saturnian to Jovian mass range embedded in massive protoplanetary disks. Runaway migration is a good candidate to account for the orbital characteristics of close orbiting giant planets, most of which have sub-Jovian masses. These are known to cluster at short periods, whereas planets of greater than two Jovian masses are rare at short periods, indicating a different type of migration process operated for the two classes of object. Further, we show that in the runaway regime, migration can be directed outward, which makes this regime potentially rich in a variety of important effects in shaping a planetary system during the last stages of its formation.