It has recently been shown that the terrestrial planets and asteroid belt can be reproduced if the giant planets underwent an inward-then-outward migration (the "Grand Tack"; Walsh et al 2011). Inward migration occurs when Jupiter opens a gap and type II migrates inward. The planets "tack" and migrate outward when Saturn reaches the gap-opening mass and is caught in the 3:2 resonance with Jupiter. The aim is to test the viability of the Grand Tack model and to study the dynamical evolution of Jupiter and Saturn during their growth from 10 Earth masses cores. We have performed numerical simulations using a grid-based hydrodynamical code. Most of our simulations assume an isothermal equation of state for the disk but a subset use a fully-radiative version of the code. For an isothermal disk the two phase migration of Jupiter and Saturn is very robust and independent of the mass-growth history of these planets provided the disk is cool enough. For a radiative disk the we find some outcomes with two phase migrations and others with more complicated behavior. We construct a simple, 1-D model of an evolving viscous disk to calculate the evolution of the disk's radiative properties: the disk transitions from radiative to isothermal from its outermost regions inward in time. We show that a two-phase migration is a natural outcome at late times even under the limiting assumption that isothermal conditions are required. Thus, our simulations provide strong support for the Grand Tack scenario.
Embedded in the gaseous protoplanetary disk, Jupiter and Saturn naturally become trapped in 3:2 resonance and migrate outward. This serves as the basis of the Grand Tack model. However, previous hydrodynamical simulations were restricted to isothermal disks, with moderate aspect ratio and viscosity. Here we simulate the orbital evolution of the gas giants in disks with viscous heating and radiative cooling. We find that Jupiter and Saturn migrate outward in 3:2 resonance in modest-mass ($M_{disk} \approx M_{MMSN}$, where MMSN is the "minimum-mass solar nebula") disks with viscous stress parame…
Reproducing Uranus and Neptune remains a challenge for simulations of solar system formation. The ice giants' peculiar obliquities suggest that they both suffered giant collisions during their formation. Thus, there must have been an epoch of accretion dominated by collisions among large planetary embryos in the primordial outer solar system. We test this idea using N-body numerical simulations including the effects of a gaseous protoplanetary disk. One strong constraint is that the masses of the ice giants are very similar -- the Neptune/Uranus mass ratio is $\sim1.18$. We show that similar-s…
The outward migration of a pair of resonant-orbit planets, driven by tidal interactions with a gas-dominated disk, is studied in the context of evolved solar nebula models. The planets' masses, M1 and M2, correspond to those of Jupiter and Saturn. Hydrodynamical calculations in two and three dimensions are used to quantify the migration rates and analyze the conditions under which the outward migration mechanism may operate. The planets are taken to be fully formed after 1e6 and before 3e6 years. The orbital evolution of the planets in an evolving disk is then calculated until the disk's gas i…
We study the dynamical evolution of Jupiter and Saturn embedded in a gaseous, solar-nebula-type disc by means of hydrodynamics simulations with the FARGO2D1D code. We study the evolution for different initial separations of the planets' orbits, Delta a_SJ , to investigate whether they become captured in mean motion resonance (MMR) and the direction of the subsequent migration of the planet (inward or outward). We also provide an assessment of the planet's orbital dynamics at different epochs of Saturn's growth. We find that the evolution of initially compact orbital configurations is dependent…
Recent simulations show that giant planets of about one Jupiter mass migrate inward at a rate that differs from the Type II prediction. Here we show that at higher masses, planets migrate outward. Our result differs from previous ones because of our longer simulation times, lower viscosity, and our boundary conditions that allow the disk to reach viscous steady state. We show that, for planets on circular orbits, the transition from inward to outward migration coincides with the known transition from circular to eccentric disks that occurs for planets more massive than a few Jupiters. In an ec…
Using N-body simulations with planet-disk interactions, we present a mechanism capable of forming compact systems of hot super Earths such as Kepler 11. Recent studies show that outward migration is common in the inner parts of radiative disks. However we show that two processes naturally tip the balance in favor of inward migration. First the corotation torque is too weak to generate outward migration for planetary embryos less massive than $4\mearth$. Second, system of multiple embryos generate sustained non-zero eccentricities that damp the corotation torque and again favor inward migration…
We have investigated Saturn's core formation at a radial pressure maximum in a protoplanetary disk, which is created by gap opening by Jupiter. A core formed via planetesimal accretion induces the fragmentation of surrounding planetesimals, which generally inhibits further growth of the core by removal of the resulting fragments due to radial drift caused by gas drag. However, the emergence of the pressure maximum halts the drift of the fragments, while their orbital eccentricities and inclinations are efficiently damped by gas drag. As a result, the core of Saturn rapidly grows via accretion …
We carry out a series of high-resolution (1024 X 1024) hydrodynamic simulations to investigate the orbital evolution of a Saturn-Jupiter pair embedded in a gaseous disk. This work extends the results of our previous work by exploring a different orbital configuration---Jupiter lies outside Saturn (q<1, where q= M_i/M_o is the mass ratio of the inner planet and the outer one). We focus on the effects of different initial separations (d) between the two planets and the various surface density profiles of the disk, where σ\propto r^{-α}. We also compare the results of different orbital configurat…
Concurrent Accretion and Migration of Giant Planets in their Natal Disks with Consistent Accretion Torque (II): Parameter Survey and Condition for Outward Migration
The inner moons of Jupiter and Saturn migrate outwards due to tidal energy dissipation within the planets, the details of which remain poorly understood. We demonstrate that resonance locking between moons and internal oscillation modes of the planet can produce rapid tidal migration. Resonance locking arises due to the internal structural evolution of the planet and typically produces an outward migration rate comparable to the age of the solar system. Resonance locking predicts a similar migration timescale but a different effective tidal quality factor $Q$ governing the migration of each mo…
Recent studies on the planet-dominated regime of Type II migration showed that, contrary to the conventional wisdom, massive planets can migrate outwards. Using `fixed-planet' simulations these studies found a correlation between the sign of the torques acting on the planet and the parameter $K'$ (which describes the depth of the gap carved by the planet in the disc). We perform `live-planet' simulations exploring a range of $K'$ and disc mass values to test and extend these results. The excitation of planet eccentricity in live-planet simulations breaks the direct dependence of migration rate…
In this paper we consider a new mechanism for stopping the inward migration of a low-mass planet embedded in a gaseous protoplanetary disc. It operates when a low-mass planet (for example a super-Earth), encounters outgoing density waves excited by another source in the disc. This source could be a gas giant in an orbit interior to that of the low-mass planet. As the super-Earth passes through the wave field, angular momentum is transferred to the disc material and then communicated to the planet through coorbital dynamics, with the consequence that its inward migration can be halted or even r…
Vega has been shown to host multiple dust populations, including both hot exo-zodiacal dust at sub-AU radii and a cold debris disk extending beyond 100 AU. We use dynamical simulations to show how Vega's hot dust can be created by long-range gravitational scattering of planetesimals from its cold outer regions. Planetesimals are scattered progressively inward by a system of 5-7 planets from 30-60 AU to very close-in. In successful simulations the outermost planets are typically Neptune-mass. The back-reaction of planetesimal scattering causes these planets to migrate outward and continually in…
Planetary embryos embedded in gaseous protoplanetary disks undergo Type I orbital migration. Migration can be inward or outward depending on the local disk properties but, in general, only planets more massive than several $M_\oplus$ can migrate outward. Here we propose that an embryo's migration history determines whether it becomes a hot super-Earth or the core of a giant planet. Systems of hot super-Earths (or mini-Neptunes) form when embryos migrate inward and pile up at the inner edge of the disk. Giant planet cores form when inward-migrating embryos become massive enough to switch direct…
There is a long-standing debate regarding the origin of the terrestrial planets' water as well as the hydrated C-type asteroids. Here we show that the inner Solar System's water is a simple byproduct of the giant planets' formation. Giant planet cores accrete gas slowly until the conditions are met for a rapid phase of runaway growth. As a gas giant's mass rapidly increases, the orbits of nearby planetesimals are destabilized and gravitationally scattered in all directions. Under the action of aerodynamic gas drag, a fraction of scattered planetesimals are deposited onto stable orbits interior…
Tidal dissipation inside giant planets is important for the orbital evolution of their natural satellites. It is conventionally treated by parameterized equilibrium tidal theory, in which the tidal torque declines rapidly with distance, and orbital expansion was faster in the past. However, Lainey et al. (2017) find that some Saturnian satellites are currently migrating outward faster than predicted by equilibrium tidal theory. Resonance locking between satellites and internal oscillations of Saturn, proposed by Fuller et al. (2016), naturally matches the observed migration rates. Here, we sho…
For the very first time we present 3D simulations of planets embedded in stellar irradiated discs. It is well known that thermal effects could reverse the direction of planetary migration from inwards to outwards, potentially saving planets in the inner, optically thick parts of the protoplanetary disc. When considering stellar irradiation in addition to viscous friction as a source of heating, the outer disc changes from a shadowed to a flared structure. Using a suited analytical formula it has been shown that in the flared part of the disc the migration is inwards; planets can migrate outwar…
Recent observations have found a valley in the size distribution of close-in super-Earths that is interpreted as a signpost that close-in super-Earths are mostly rocky in composition. However, new models predict that planetesimals should first form at the water ice line such that close-in planets are expected to have a significant water ice component. Here we investigate the water contents of super-Earths by studying the interplay between pebble accretion, planet migration and disc evolution. Planets' compositions are determined by their position relative to different condensation fronts (ice …
The migration of planets plays an important role in the early planet-formation process. An important problem has been that standard migration theories predict very rapid inward migration, which poses problems for population synthesis models. However, it has been shown recently that low-mass planets (20-30 Earth Masses) that are still embedded in the protoplanetary disc can migrate outwards under certain conditions. Simulations have been performed mostly for planets at given radii for a particular disc model. Here, we plan to extend previous work and consider different masses of the disc to qua…
We carry out a series of high resolution ($1024\times 1024$) 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 (2001) and Morbidelli & Crida (2007) by exploring various surface density profiles ($σ$), where $σ\propto r^{-α}$. 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 per…
Planets of 1-4 times Earth's size on orbits shorter than 100 days exist around 30-50% of all Sun-like stars. In fact, the Solar System is particularly outstanding in its lack of "hot super-Earths" (or "mini-Neptunes"). These planets -- or their building blocks -- may have formed on wider orbits and migrated inward due to interactions with the gaseous protoplanetary disk. Here, we use a suite of dynamical simulations to show that gas giant planets act as barriers to the inward migration of super-Earths initially placed on more distant orbits. Jupiter's early formation may have prevented Uranus …
Protoplanets formed in a marginally gravitationally unstable (MGU) disk by either core accretion or disk instability will be subject to dynamical interactions with massive spiral arms, possibly resulting in inward or outward orbital migration, mergers with each other, or even outright ejection from the protoplanetary system. The latter process has been hypothesized as a possible formation scenario for the unexpectedly high frequency of unbound gas giant exoplanets (free floating planets, FFP). Previous calculations with the EDTONS fixed grid three dimensional (3D) hydrodynamics code found that…
Inward migration of giant planets is predicted by hydrodynamical simulations during the gas phase of the protoplanetary disc. The phenomenon is also invoked to explain resonant and near-resonant exoplanetary system structures. The early inward migration may also have affected our Solar System and sculpted its different minor planet reservoirs. In this study we explore how the early inward migration of the giant planets shapes the Kuiper Belt. We test different scenarios with only Neptune and Uranus and with all the four giant planets, including also some models with the subsequent outward plan…
The four massive Galilean satellites are believed to have formed within a circumplanetary disk during the last stages of Jupiter's formation. While the existence of a circum-jovian disk is supported by hydrodynamic simulations, no consensus exists regarding the origin and delivery mechanisms of the building blocks of the forming satellites. The opening of a gap in the circumsolar disk would have efficiently isolated Jupiter from the main sources of solid material. However, a reservoir of planetesimals should have existed at the outer edge of Jupiter's gap, where solids were trapped and accumul…
Earth-mass planets embedded in gaseous protoplanetary disks undergo Type I orbital migration. In radiative disks an additional component of the corotation torque scaling with the entropy gradient across the horseshoe region can counteract the general inward migration, Type I migration can then be directed either inward or outward depending on the local disk properties. Thus, special locations exist in the disk toward which planets migrate in a convergent way. Here we present N-body simulations of the convergent migration of systems of low-mass (M=1-10 m_earth) planets. We show that planets do …
The strength and direction of migration of low mass embedded planets depends on the disk's thermodynamic state, where the internal dissipation is balanced by radiative transport, and the migration can be directed outwards, a process which extends the lifetime of growing embryos. Very important parameters determining the structure of disks, and hence the direction of migration, are the viscosity and the adiabatic index. In this paper we investigate the influence of different viscosity prescriptions (alpha-type and constant) and adiabatic indices on disk structures and how this affects the migra…
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 aluminium 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…
Context: As a result of Titan's migration and Saturn's probable capture in secular spin-orbit resonance, recent works show that Saturn's obliquity could be steadily increasing today and may reach large values in the next billions of years. Satellites around high-obliquity planets are known to be unstable near their Laplace radius, but the approximations used so far are invalidated in this regime. Aims: We aim to investigate the behaviour of a planet and its satellite when the satellite crosses its Laplace radius while the planet is locked in secular spin-orbit resonance. Methods: We expand on …
The planet migration due to the disk--planet interaction is one of the most important processes to determine the architecture of planetary systems. A sufficiently massive planet forms a density gap and migrates together with the gap. By carrying out two-dimensional and two-fluid (gas and dust grains) hydrodynamic simulations, we investigated the effects of the dust feedback on the migration of the gap-opening planet, which was not considered in previous studies. We found that the gas surface density at the outer edge of the gap becomes smaller due to the dust feedback, and thus the torque exer…
We examine the dynamics of small bodies in orbits similar to that of comet 29P/Schwassmann-Wachmann 1, i.e. near-circular orbits between Jupiter and Saturn. As of late 2019, there are 14 other known bodies in this region that lie in similar orbits. Previous research has shown that this region of the solar system, which in this work we call the "near Centaur region" (NCR), is not stable, suggesting that any bodies found in it would have very short lifetimes. We performed 20 Myr high-precision numerical simulations of the evolution of massless particles, initially located in the Kuiper belt but …
Due to the angular momentum exchange with planetesimals, Neptune might have migrated outward to the current position, and captured many Kuiper belt objects (KBOs) into resonances. We set up a semi-analytic model to simulate the outward migration of Neptune, and the processes of resonant captures. Our model can naturally explain Neptune's currently observed semi-major axis and eccentricity. The results show that the current population ratio between 3:2 and 2:1 is mainly due to the original density distribution of KBOs, which might be related to drag-induced inward migrations of proto-KBOs.
Tidal effects in planetary systems are the main driver in the orbital migration of natural satellites. They result from physical processes occurring deep inside celestial bodies, whose effects are rarely observable from surface imaging. For giant planet systems, the tidal migration rate is determined by poorly understood dissipative processes in the planet, and standard theories suggest an orbital expansion rate inversely proportional to the power 11/2 in distance, implying little migration for outer moons such as Saturn's largest moon, Titan. Here, we use two independent measurements obtained…
The torques exerted by a locally isothermal disk on an embedded planet lead to rapid inward migration. Recent work has shown that modeling the thermodynamics without the assumption of local isothermality reveals regions where the net torque on an embedded planet is positive, leading to outward migration of the planet. When a region with negative torque lies directly exterior to this, planets in the inner region migrate outwards and planets in the outer region migrate inwards, converging where the torque is zero. We incorporate the torques from an evolving non-isothermal disk into an N-body sim…
While planets in the solar system only have a low inclination with respect to the ecliptic there is mounting evidence that in extrasolar systems the inclination can be very high, at least for close-in planets. One process to alter the inclination of a planet is through planet-disc interactions. Recent simulations considering radiative transport have shown that the evolution of migration and eccentricity can strongly depend on the thermodynamic state of the disc. We extend previous studies to investigate the planet-disc interactions of fixed and moving planets on inclined and eccentric orbits. …
Jupiter and Saturn play host to an impressive array of satellites, making it reasonable to suspect that similar systems of moons might exist around giant extrasolar planets. Furthermore, a significant population of such planets is known to reside at distances of several Astronomical Units (AU), leading to speculation that some moons thereof might support liquid water on their surfaces. However, giant planets are thought to undergo inward migration within their natal protoplanetary disks, suggesting that gas giants currently occupying their host star's habitable zone formed further out. Here we…
The global evolution of protoplanetary disks (PPDs) has recently been shown to be largely controlled by the amount of poloidal magnetic flux threading the disk, which is further controlled by the poorly understood process of magnetic flux transport. In weakly ionized gas as in PPDs, magnetic flux is largely frozen in the electron fluid, except when resistivity is large. When the disk is largely laminar, we show that the relative drift between the electrons and ions (the Hall-drift), and the ions and neutral fluids (ambipolar-drift) can play a dominant role on the transport of magnetic flux. Us…
Calcium-aluminum-rich inclusions (CAIs) are the oldest solar system solids known in primitive meteorites (chondrites). They predate the other components by 1-2 Myr, and likely condensed within a short time interval, close to the Sun in the gaseous protoplanetary disk. Their preservation must counterbalance both the sunward drift caused by gas drag and the general inward motion of the entraining gas. We propose that an efficient outward transport of CAIs can be achieved by advection as a result of the viscous expansion of the disk, provided it is initially less than 10 AU in size, which we argu…
We report here on an extension of a previous study by Kirsh et al. (2009) of planetesimal-driven migration using our N-body code SyMBA (Duncan et al., 1998). The previous work focused on the case of a single planet of mass Mem, immersed in a planetesimal disk with a power-law surface density distribution and Rayleigh distributed eccentricities and inclinations. Typically 10^4-10^5 equal-mass planetesimals were used, where the gravitational force (and the back-reaction) on each planetesimal by the Sun and planetwere included, while planetesimal-planetesimal interactions were neglected. The runs…
We use the current orbital structure of large (>50km) asteroids in the main asteroid belt to constrain the evolution of the giant planets when they migrated from their primordial orbits to their current ones. Minton & Malhotra (2009) showed that the orbital distribution of large asteroids in the main belt can be reproduced by an exponentially-decaying migration of the giant planets on a time scale of tau ~ 0.5My. However, self-consistent numerical simulations show that the planetesimal-driven migration of the giant planets is inconsistent with an exponential change in their semi major axes on …
In a previous paper (Hedman and Nicholson 2013), we developed tools that allowed us to confirm that several of the waves in Saturn's rings were likely generated by resonances with fundamental sectoral normal modes inside Saturn itself. Here we use these same tools to examine eight additional waves that are probably generated by structures inside the planet. One of these waves appears to be generated by a resonance with a fundamental sectoral normal mode with azimuthal harmonic number m=10. If this attribution is correct, then the m=10 mode must have a larger amplitude than the modes with m=5-9…
Fast inward migration of planetary cores is a common problem in the current planet formation paradigm. Even though dust is ubiquitous in protoplanetary disks, its dynamical role in the migration history of planetary embryos has not been assessed. In this Letter, we show that the scattered pebble-flow induced by a low-mass planetary embryo leads to an asymmetric dust-density distribution that is able to exert a net torque. By analyzing a large suite of multifluid hydrodynamical simulations addressing the interaction between the disk and a low-mass planet on a fixed circular orbit, and neglectin…
Turbulence, a ubiquitous phenomenon in interplanetary space, is crucial for the energy conversion of space plasma at multiple scales. This work focuses on the propagation, polarization and wave composition properties of the solar wind turbulence within 0.3AU, and its variation with heliocentric distances at MHD scales (from 10s to 1000s in the spacecraft frame). We present the probability density function of propagation wavevectors (${\rm{PDF}}(k_\parallel,k_\perp)$) for solar wind turbulence winthin 0.3 AU for the first time: (1) wavevectors cluster quasi-(anti-)parallel to the local backgrou…
Planets close to their stars are thought to form farther out and migrate inward due to angular momentum exchange with gaseous protoplanetary disks. This process can produce systems of planets in co-orbital (Trojan or 1:1) resonance, in which two planets share the same orbit, usually separated by 60 degrees. Co-orbital systems are detectable among the planetary systems found by the Kepler mission either directly or by transit timing variations. However, no co-orbital systems have been found within the thousands of Kepler planets and candidates. Here we study the orbital evolution of co-orbital …
The statistics of extrasolar planetary systems indicate that the default mode of planet formation generates planets with orbital periods shorter than 100 days, and masses substantially exceeding that of the Earth. When viewed in this context, the Solar System is unusual. Here, we present simulations which show that a popular formation scenario for Jupiter and Saturn, in which Jupiter migrates inward from a > 5 AU to a ~ 1.5 AU before reversing direction, can explain the low overall mass of the Solar System's terrestrial planets, as well as the absence of planets with a < 0.4 AU. Jupiter's inwa…
We investigate via numerical modeling the effects of two planets locked in resonance, and migrating outward, on the dust distribution of the natal circumstellar disk. We aim to test whether the dust distribution exhibits peculiar features arising from the interplay among the gravitational perturbations of the planets in resonance, the evolution of the gas, and its influence on the dust grains' dynamics. We focus on the 3:2 and 2:1 resonance, where the trapping may be caused by the convergent migration of a Jupiter- and Saturn-mass planet, preceding the common gap formation and ensuing outward …
We study torques on migrating low-mass planets in locally isothermal discs. Previous work on low-mass planets generally kept the planet on a fixed orbit, after which the torque on the planet was measured. In addition to these static torques, when the planet is allowed to migrate it experiences dynamical torques, which are proportional to the migration rate and whose sign depends on the background vortensity gradient. We show that in discs a few times more massive than the Minimum Mass Solar Nebula, these dynamical torques can have a profound impact on planet migration. Inward migration can be …
The migration of growing protoplanets depends on the thermodynamics of the ambient disc. Standard modelling, using locally isothermal discs, indicate in the low planet mass regime an inward (type-I) migration. Taking into account non-isothermal effects, recent studies have shown that the direction of the type-I migration can change from inward to outward. In this paper we extend previous two-dimensional studies, and investigate the planet-disc interaction in viscous, radiative discs using fully three-dimensional radiation hydrodynamical simulations of protoplanetary accretion discs with embedd…
The `Grand Tack' model proposes that the inner Solar System was sculpted by the giant planets' orbital migration in the gaseous protoplanetary disk. Jupiter first migrated inward then Jupiter and Saturn migrated back outward together. If Jupiter's turnaround or "tack" point was at ~1.5 AU the inner disk of terrestrial building blocks would have been truncated at ~1 AU, naturally producing the terrestrial planets' masses and spacing. During the gas giants' migration the asteroid belt is severely depleted but repopulated by distinct planetesimal reservoirs that can be associated with the present…
