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Register a new userOutward migration of Jupiter and Saturn in 3:2 or 2:1 resonance in radiative disks: implications for the Grand Tack and Nice models
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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 parameter $alpha$ between $10^{-3}$ and $10^{-2} $. In disks with relatively low-mass ($M_{disk} lesssim M_{MMSN}$) , Jupiter and Saturn get captured in 2:1 resonance and can even migrate outward in low-viscosity disks ($alpha le 10^{-4}$). Such disks have a very small aspect ratio ($hsim 0.02-0.03$) that favors outward migration after capture in 2:1 resonance, as confirmed by isothermal runs which resulted in a similar outcome for $h sim 0.02$ and $alpha le 10^{-4}$. We also performed N-body runs of the outer Solar System starting from the results of our hydrodynamical simulations and including 2-3 ice giants. After dispersal of the gaseous disk, a Nice model instability starting with Jupiter and Saturn in 2:1 resonance results in good Solar Systems analogs. We conclude that in a cold Solar Nebula, the 2:1 resonance between Jupiter and Saturn can lead to outward migration of the system, and this may represent an alternative scenario for the evolution of the Solar System.
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If the Solar system had a history of planet migration, the signature of that migration may be imprinted on the populations of asteroids and comets that were scattered in the planets wake. Here, we consider the dynamical and collisional evolution of inner Solar system asteroids which join the Oort cloud. We compare the Oort cloud asteroid populations produced by migration scenarios based on the `Nice and `Grand Tack scenarios, as well as a null hypothesis where the planets have not migrated, to the detection of one such object, C/2014 S3 (PANSTARRS). Our simulations find that the discovery of C/2014 S3 (PANSTARRS) only has a greater than one percent chance of occurring if the Oort cloud asteroids evolved on to Oort cloud orbits when the Solar system was not more than about one million years old, as this early transfer to the Oort cloud is necessary to keep the amount of collisional evolution low. We argue this only occurs when a giant (greater than thirty Earth masses) planet orbits at 1 ~ 2 au, and thus our results strongly favour a `Grand Tack-like migration having occurred early in the Solar systems history.
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 planets orbital dynamics at different epochs of Saturns growth. We find that the evolution of initially compact orbital configurations is dependent on the value of Delta a_SJ . This implies that an evolution as that proposed in the Grand Tack model depends on the precise initial orbits of Jupiter and Saturn and on the timescales for their formation. Capture in the 1:2 MMR and inward or (nearly) stalled migration are highly favoured. Within its limits, our work suggests that the reversed migration, associated with the resonance capture of Jupiter and Saturn, may be a low probability evolutionary scenario, so that other planetary systems with giant planets are not expected to have experienced a Grand Tack-like evolutionary path.
We present an analytical and numerical study of the orbital migration and resonance capture of fictitious two-planet systems with masses in the super-Earth range undergoing Type-I migration. We find that, depending on the flare index and proximity to the central star, the average value of the period ratio, $P_2/P_1$, between both planets may show a significant deviation with respect to the nominal value. For planets trapped in the 2:1 commensurability, offsets may reach values on the order of $0.1$ for orbital periods on the order of $1$ day, while systems in the 3:2 mean-motion resonance (MMR) show much smaller offsets for all values of the semimajor axis. These properties are in good agreement with the observed distribution of near-resonant exoplanets, independent of their detection method. We show that 2:1-resonant systems far from the star, such as HD82943 and HR8799, are characterized by very small resonant offsets, while higher values are typical of systems discovered by Kepler with orbital periods approximately a few days. Conversely, planetary systems in the vicinity of the 3:2 MMR show little offset with no significant dependence on the orbital distance. In conclusion, our results indicate that the distribution of Kepler planetary systems around the 2:1 and 3:2 MMR are consistent with resonant configurations obtained as a consequence of a smooth migration in a laminar flared disk, and no external forces are required to induce the observed offset or its dependence with the commensurability or orbital distance from the star.
Resonant dynamics plays a significant role in the past evolution and current state of our outer Solar System. The population ratios and spatial distribution of Neptunes resonant populations are direct clues to understanding the history of our planetary system. The orbital structure of the objects in Neptunes 2:1 mean-motion resonance (emph{twotinos}) has the potential to be a tracer of planetary migration processes. Different migration processes produce distinct architectures, recognizable by well-characterized surveys. However, previous characterized surveys only discovered a few twotinos, making it impossible to model the intrinsic twotino population. With a well-designed cadence and nearly 100% tracking success, the Outer Solar System Origins Survey (OSSOS) discovered 838 trans-Neptunian objects, of which 34 are securely twotinos with well-constrained libration angles and amplitudes. We use the OSSOS twotinos and the survey characterization parameters via the OSSOS Survey Simulator to inspect the intrinsic population and orbital distributions of twotino. The estimated twotino population, 4400$^{+1500}_{-1100}$ with $H_r<8.66$ (diameter$sim$100km) at 95% confidence, is consistent with the previous low-precision estimate. We also constrain the width of the inclination distribution to a relatively narrow value of $sigma_i$=6$^circ$$^{+1}_{-1}$, and find the eccentricity distribution is consistent with a Gaussian centered on $e_mathrm{c}=0.275$ with a width $e_mathrm{w}=0.06$. We find a single-slope exponential luminosity function with $alpha=0.6$ for the twotinos. Finally, we for the first time meaningfully constrain the fraction of symmetric twotinos, and the ratio of the leading asymmetric islands; both fractions are in a range of 0.2--0.6. These measurements rule out certain theoretical models of Neptunes migration history.
We examine how the late divergent migration of Jupiter and Saturn may have perturbed the terrestrial planets. We identify six secular resonances between the nu_5 apsidal eigenfrequency of Jupiter and Saturn and the four eigenfrequencies of the terrestrial planets (g_{1-4}). We derive analytic upper limits on the eccentricity and orbital migration timescale of Jupiter and Saturn when these resonances were encountered to avoid perturbing the eccentricities of the terrestrial planets to values larger than the observed ones. If Jupiter and Saturn migrated with eccentricities comparable to their present day values, smooth migration with exponential timescales characteristic of planetesimal-driven migration (tau~5-10 Myr) would have perturbed the eccentricities of the terrestrial planets to values greatly exceeding the observed ones. This excitation may be mitigated if the eccentricity of Jupiter was small during the migration epoch, migration was very rapid (e.g. tau<~ 0.5 Myr perhaps via planet-planet scattering or instability-driven migration) or the observed small eccentricity amplitudes of the j=2,3 terrestrial modes result from low probability cancellation of several large amplitude contributions. Further, results of orbital integrations show that very short migration timescales (tau<0.5 Myr), characteristic of instability-driven migration, may also perturb the terrestrial planets eccentricities by amounts comparable to their observed values. We discuss the implications of these constraints for the relative timing of terrestrial planet formation, giant planet migration, and the origin of the so-called Late Heavy Bombardment of the Moon 3.9+/-0.1 Ga ago. We suggest that the simplest way to satisfy these dynamical constraints may be for the bulk of any giant planet migration to be complete in the first 30-100 Myr of solar system history.
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