On the Super-Earths locked in the 3:2 mean-motion resonance (original) (raw)
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On the migration of two planets in a disc and the formation of mean motion resonances
Monthly Notices of the Royal Astronomical Society, 2015
We study the dynamics of a system of two super-Earths embedded in a protoplanetary disc. We build a simple model of an irradiated viscous disc and use analytical prescriptions for the planet-disc interactions which lead to migration. We show that depending on the disc parameters, planets' masses and their positions in the disc, the migration of each planet can be inward or outward and the migration of a two-planet system can be convergent (which may lead to formation of a first order mean motion resonance, MMR) or divergent (a system moves away from MMR). We performed 3500 simulations of the migration of two-planet systems with various masses and initial orbits. Almost all of them end up as resonant configurations, although the period ratios may be very distant from the nominal values of a given MMR. We found that almost all the systems resulting from the migration are periodic configurations.
Planetary migration and extrasolar planets in the 2/1 mean-motion resonance
Monthly Notices of the Royal Astronomical Society, 2005
We analyze the possible relationship between the current orbital elements fits of known exoplanets in the 2/1 mean-motion resonance and the expected orbital configuration due to migration. We find that, as long as the orbital decay was sufficiently slow to be approximated by an adiabatic process, all captured planets should be in apsidal corotations. In other words, they should show a simultaneous libration of both the resonant angle and the difference in longitudes of pericenter.
Conditions for the occurrence of mean-motion resonances in a low mass planetary system
The dynamical interactions that occur in newly formed planetary systems may reflect the conditions occurring in the protoplanetary disk out of which they formed. With this in mind, we explore the attainment and maintenance of orbital resonances by migrating planets in the terrestrial mass range. Migration time scales varying between ∼ 10 6 yr and ∼ 10 3 yr are considered. In the former case, for which the migration time is comparable to the lifetime of the protoplanetary gas disk, a 2:1 resonance may be formed. In the latter, relatively rapid migration regime commensurabilities of high degree such as 8:7 or 11:10 may be formed. However, in any one large-scale migration several different commensurabilities may be formed sequentially, each being associated with significant orbital evolution. We also use a simple analytic theory to develop conditions for first order commensurabilities to be formed. These depend on the degree of the commensurability, the imposed migration and circularization rates, and the planet mass ratios. These conditions are found to be consistent with the results of our simulations.
The Astrophysical Journal, 2008
We present a numerical study of several two-planet systems based on the motions of Jupiter and Saturn, in which the two giant planets move in low eccentric orbits close to a mean motion resonance. It is more likely to find two planets with similar characteristics in a system than a clone of the Jupiter-Saturn pair of our solar system. Therefore, we vary the distance between the two planets and their mass ratio by changing Saturn's semimajor axis from 8 to 11 AU and increasing its mass by factors of 2-40. The different two-planets were analyzed for the interacting perturbations due to the mean motion resonances of the giant planets. We select several mass ratios for the gas giants, for which we study their influence on test bodies (with negligible mass) moving in the habitable zone (HZ ) of a Sun-like star. The orbits are calculated for 2 ; 10 7 yr. In all cases the HZ is dominated by a significant curved band, indicating higher eccentricity, which corresponds to a secular resonance with Jupiter. Interesting results of this study are finding (1) an increase of Venus's eccentricity for the real Jupiter and Saturn masses and the actual semimajor axis of Saturn; (2) an increase of the eccentricity of a test planet at Earth's position when Saturn's mass was increased by a factor of 3 or more; and (3) if the two giant planets are in 2 : 1 resonance, we observe a strong influence on the outer region of the HZ. Subject headingg s: methods: n-body simulations -planetary systemsplanets and satellites: individual (Jupiter, Saturn)
Monthly Notices of the Royal Astronomical Society, 2016
We study the migration of three-planet systems in an irradiated 1+1D α-disc with photoevaporation. We performed 2700 simulations with various planets' masses and initial orbits. We found that most of the systems which ended up as compact configurations form chains of mean motion resonances (MMRs) of the first and higher orders. Most of the systems involved in chains of MMRs are periodic configurations. The period ratios of such system, though, are not necessarily close to exact commensurability. If a given system resides in a divergent migration zone in the disc, the period ratios increase and evolve along resonant divergent migration paths at (P 2 /P 1 , P 3 /P 2) diagram, where P 1 , P 2 , P 3 are the orbital periods of the first, second and third planet, respectively. The observed systems, though, do not lie on those paths. We show that agreement between the synthetic and the observed system distributions could be achieved if the orbital circularization was slower than it results from models of the planet-disc interactions. Therefore, we conclude that most of those systems unlikely formed as a result of divergent migration out of nominal chains of MMRs.
The orbital stability of planets trapped in the first-order mean-motion resonances
Icarus, 2012
Many extrasolar planetary systems containing multiple super-Earths have been discovered. N-body simulations taking into account standard type-I planetary migration suggest that protoplanets are captured into mean-motion resonant orbits near the inner disk edge at which the migration is halted. Previous N-body simulations suggested that orbital stability of the resonant systems depends on number of the captured planets. In the unstable case, through close scattering and merging between planets, non-resonant multiple systems are finally formed. In this paper, we investigate the critical number of the resonantly trapped planets beyond which orbital instability occurs after disk gas depletion. We find that when the total number of planets (N) is larger than the critical number (N crit), crossing time that is a timescale of initiation of the orbital instability is similar to non-resonant cases, while the orbital instability never occurs within the orbital calculation time (10 8 Kepler time) for N ≤ N crit. Thus, the transition of crossing time across the critical number is drastic. When all the planets are trapped in 7:6 resonance of adjacent pairs, N crit = 4. We examine the dependence of the critical number of 4:3, 6:5 and 8:7 resonance by changing the orbital separation in mutual Hill radii and planetary mass. The critical number increases with increasing the orbital separation in mutual Hill radii with fixed planetary mass and increases with increasing planetary mass with fixed the orbital separation in mutual Hill radii. We also calculate the case of a system which is not composed of
Astronomy & Astrophysics, 2017
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 HD 82943 and HR 8799, 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.
Observational consequences of a different mass planet migration
EAS Publications Series, 2010
We have investigated the evolution of a pair of interacting planets embedded in a gaseous disc considering a possibility of the resonant capture of a Super-Earth by an inward-migrating Jupiter mass gas giant. It has been found that the terrestrial planet is scattered from the disc or the gas giant captures the Super-Earth into an interior 3:2 or 4:3 mean motion resonance and the stability of such configuration depends on the initial planet positions and eccentricity evolution. The behaviour of the resulting resonant system has been studied numerically by means of the full 2D hydrodynamical simulations. The results are particularly interesting in light of the recent exoplanet discoveries and provide predictions of what will become observationally testable in the near future.
Influence of an inner disc on the orbital evolution of massive planets migrating in resonance
Astronomy and Astrophysics, 2008
Context. The formation of resonant pairs of planets in exoplanetary systems involves planetary migration in the protoplanetary disc. After a resonant capture, the subsequent migration in this configuration leads to a large increase of planetary eccentricities if no damping mechanism is applied. This has led to the conclusion that the migration of resonant planetary systems cannot occur over large radial distances and has to be terminated sufficiently rapidly through disc dissipation. Aims. In this study, we investigate whether the presence of an inner disc might supply an eccentricity damping of the inner planet, and if this effect could explain the observed eccentricities in some systems. Methods. To investigate the influence of an inner disc, we first compute hydrodynamic simulations of giant planets orbiting with a given eccentricity around an inner gas disc, and measure the effect of the latter on the planetary orbital parameters. We then perform detailed long term calculations of the GJ 876 system. We also run N-body simulations with artificial forces on the planets mimicking the effects of the inner and outer discs. Results. We find that the influence of the inner disc can not be neglected, and that it might be responsible for the observed eccentricities. In particular, we reproduce quite well the orbital parameters of a few systems engaged in 2:1 mean motion resonances : GJ 876, HD 73 526, HD 82 943 and HD 128 311. Finally, we derive analytically the effect that the inner disc should have on the inner planet to reach a specific orbital configuration with a given damping effect of the outer disc on the outer planet. Conclusions. We conclude that an inner disc, even though difficult to model properly in hydro-dynamical simulations, should be taken into account because of its damping effect on the eccentricity of the inner planet. By including this effect, we can explain quite naturally the observed orbital elements of the pairs of known resonant exoplanets.