共查询到20条相似文献，搜索用时 31 毫秒
1.
J. C. B. Papaloizou 《Celestial Mechanics and Dynamical Astronomy》2016,126(1-3):157-187
We study orbital evolution of multi-planet systems with masses in the terrestrial planet regime induced through tidal interaction with a protoplanetary disk assuming that this is the dominant mechanism for producing orbital migration and circularization. We develop a simple analytic model for a system that maintains consecutive pairs in resonance while undergoing orbital circularization and migration. This model enables migration times for each planet to be estimated once planet masses, circularization times and the migration time for the innermost planet are specified. We applied it to a system with the current architecture of Kepler 444 adopting a simple protoplanetary disk model and planet masses that yield migration times inversely proportional to the planet mass, as expected if they result from torques due to tidal interaction with the protoplanetary disk. Furthermore the evolution time for the system as a whole is comparable to current protoplanetary disk lifetimes. In addition we have performed a number of numerical simulations with input data obtained from this model. These indicate that although the analytic model is inexact, relatively small corrections to the estimated migration rates yield systems for which period ratios vary by a minimal extent. Because of relatively large deviations from exact resonance in the observed system of up to 2 %, the migration times obtained in this way indicate only weak convergent migration such that a system for which the planets did not interact would contract by only \({\sim }1\,\%\) although undergoing significant inward migration as a whole. We have also performed additional simulations to investigate conditions under which the system could undergo significant convergent migration before reaching its final state. These indicate that migration times have to be significantly shorter and resonances between planet pairs significantly closer during such an evolutionary phase. Relative migration rates would then have to decrease allowing period ratios to increase to become more distant from resonances as the system approached its final state in the inner regions of the protoplanetary disk. 相似文献
2.
Alice C. Quillen † 《Monthly notices of the Royal Astronomical Society》2006,365(4):1367-1382
A migrating planet can capture planetesimals into mean motion resonances. However, resonant trapping can be prevented when the drift or migration rate is sufficiently high. Using a simple Hamiltonian system for first- and second-order resonances, we explore how the capture probability depends on the order of the resonance, drift rate and initial particle eccentricity. We present scaling factors as a function of the planet mass and resonance strength to estimate the planetary migration rate above which the capture probability drops to less than half. Applying our framework to multiple extrasolar planetary systems that have two planets locked in resonance, we estimate lower limits for the outer planet's migration rate, allowing resonance capture of the inner planet.
Mean motion resonances are comprised of multiple resonant subterms. We find that the corotation subterm can reduce the probability of capture when the planet eccentricity is above a critical value. We present factors that can be used to estimate this critical planet eccentricity. Applying our framework to the migration of Neptune, we find that Neptune's eccentricity is near the critical value that would make its 2 : 1 resonance fail to capture twotinos. The capture probability is affected by the separation between resonant subterms and so is also a function of the precession rates of the longitudes of periapse of both planet and particle near resonance. 相似文献
Mean motion resonances are comprised of multiple resonant subterms. We find that the corotation subterm can reduce the probability of capture when the planet eccentricity is above a critical value. We present factors that can be used to estimate this critical planet eccentricity. Applying our framework to the migration of Neptune, we find that Neptune's eccentricity is near the critical value that would make its 2 : 1 resonance fail to capture twotinos. The capture probability is affected by the separation between resonant subterms and so is also a function of the precession rates of the longitudes of periapse of both planet and particle near resonance. 相似文献
3.
V. V. Emel’yanenko 《Solar System Research》2012,46(5):321-328
According to current observational data, planets of many exoplanetary systems have resonant motion. The formation of resonance configurations is studied within a unified model of planetary migration. Planets in the observed systems 24 Sex, HD 37124, HD 73526, HD 82943, HD 128311, HD 160691, Kepler 9, NN Ser, which are moving in the 2: 1 resonance, could have been captured into this resonance due to both the Type I and II migration with a wide range of parameters. The migration conditions are defined for the formation of HD 45364 and HD 200964 that are in the 3: 2 and 4: 3 first-order resonances, correspondingly. The results obtained for HD 200964 show that planets can be captured in the first-order resonances, when the outer-to-inner orbital period ratios for the planets are less than 3: 2, only if Type I migration rates are large, and the mass of at least one planet is substantially less than the modern masses of the observed giant planets. The formation of the HD 102272, HD 108874, HD 181433 and HD 202206 systems with planets in high-order resonances is considered. The capture into these resonances can be realized with very slow Type II migration. Possible bounds for migration parameters are considered. In particular, it has been found that the capture of HD 108874 into the 4: 1 resonance is possible only if the angle between the plane of planetary orbits and the plane of sky is appreciably less than 90°, i.e., the planetary masses are a few times larger than the minimum values. The capture of HD 202206 into the 5: 1 resonance is possible at low migration rates; however, another mechanism is required to explain the high observed eccentricity of the inner planet (for example, strong gravitational interaction between the planets). Resonant configurations can be disrupted due to the interaction between planets and remaining fragments of the planetesimal disk as, for example, may occur in the three-planet system 47 UMa. The specific orbital features observed for this system are explained. 相似文献
4.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1982,27(3):305-322
The factors which affect the linear stability of a periodic planetary orbit in the plane are studied. It is proved that planetary systems with two planets describing nearly circular orbits in the same direction are linearly stable and no perturbation exists which destroys the stability, unless a resonance of the form 1/3, 3/5, 5/7, ... among the orbits of the planets occurs. This latter resonant case is always unstable. Retrograde motion is always linearly stable. Planetary systems with three or more planets in nearly circular orbits in the same direction are proved to be unstable, in the sense that a Hamiltonian perturbation always exists which destroys the stability. The generation of instability in the case of three or more planets is not only due to the existence of resonances, as in the case of two planets, but also to the nonexistence of integrals of motion, apart from the energy and angular momentum integrals. It is also proved that planetary systems with nearly elliptic orbits of the planets are unstable. 相似文献
5.
John D. Hadjidemetriou Dionyssia Psychoyos George Voyatzis 《Celestial Mechanics and Dynamical Astronomy》2009,104(1-2):23-38
We study orbits of planetary systems with two planets, for planar motion, at the 1/1 resonance. This means that the semimajor axes of the two planets are almost equal, but the eccentricities and the position of each planet on its orbit, at a certain epoch, take different values. We consider the general case of different planetary masses and, as a special case, we consider equal planetary masses. We start with the exact resonance, which we define as the 1/1 resonant periodic motion, in a rotating frame, and study the topology of the phase space and the long term evolution of the system in the vicinity of the exact resonance, by rotating the orbit of the outer planet, which implies that the resonance and the eccentricities are not affected, but the symmetry is destroyed. There exist, for each mass ratio of the planets, two families of symmetric periodic orbits, which differ in phase only. One is stable and the other is unstable. In the stable family the planetary orbits are in antialignment and in the unstable family the planetary orbits are in alignment. Along the stable resonant family there is a smooth transition from planetary orbits of the two planets, revolving around the Sun in eccentric orbits, to a close binary of the two planets, whose center of mass revolves around the Sun. Along the unstable family we start with a collinear Euler–Moulton central configuration solution and end to a planetary system where one planet has a circular orbit and the other a Keplerian rectilinear orbit, with unit eccentricity. It is conjectured that due to a migration process it could be possible to start with a 1/1 resonant periodic orbit of the planetary type and end up to a satellite-type orbit, or vice versa, moving along the stable family of periodic orbits. 相似文献
6.
7.
We use numerical integrations to investigate the dynamical evolution of resonant Trojan and quasi-satellite companions during the late stages of migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. Our migration simulations begin with Jupiter and Saturn on orbits already well separated from their mutual 2:1 mean-motion resonance. Neptune and Uranus are decoupled from each other and have orbital eccentricities damped to near their current values. From this point we adopt a planet migration model in which the migration speed decreases exponentially with a characteristic timescale τ (the e-folding time). We perform a series of numerical simulations, each involving the migrating giant planets plus test particle Trojans and quasi-satellites. We find that the libration frequencies of Trojans are similar to those of quasi-satellites. This similarity enables a dynamical exchange of objects back and forth between the Trojan and quasi-satellite resonances during planetary migration. This exchange is facilitated by secondary resonances that arise whenever there is more than one migrating planet. For example, secondary resonances may occur when the circulation frequencies, f, of critical arguments for the Uranus-Neptune 2:1 mean-motion near-resonance are commensurate with harmonics of the libration frequency of the critical argument for the Trojan and quasi-satellite 1:1 mean-motion resonance . Furthermore, under the influence of these secondary resonances quasi-satellites can have their libration amplitudes enlarged until they undergo a close-encounter with their host planet and escape from the resonance. High-resolution simulations of this escape process reveal that ≈80% of jovian quasi-satellites experience one or more close-encounters within Jupiter’s Hill radius (RH) as they are forced out of the quasi-satellite resonance. As many as ≈20% come within RH/4 and ≈2.5% come within RH/10. Close-encounters of escaping quasi-satellites occur near or even below the 2-body escape velocity from the host planet. Finally, the exchange and escape of Trojans and quasi-satellites continues to as late as 6-9τ in some simulations. By this time the dynamical evolution of the planets is strongly dominated by distant gravitational perturbations between the planets rather than the migration force. This suggests that exchange and escape of Trojans and quasi-satellites may be a contemporary process associated with the present-day near-resonant configuration of some of the giant planets in our Solar System. 相似文献
8.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):141-154
Families of nearly circular periodic orbits of the planetary type are studied, close to the 3/1 mean motion resonance of the two planets, considered both with finite masses. Large regions of instability appear, depending on the total mass of the planets and on the ratio of their masses.Also, families of resonant periodic orbits at the 2/1 resonance have been studied, for a planetary system where the total mass of the planets is the 4% of the mass of the sun. In particular, the effect of the ratio of the masses on the stability is studied. It is found that a planetary system at this resonance is unstable if the mass of the outer planet is smaller than the mass of the inner planet.Finally, an application has been made for the stability of the observed extrasolar planetary systems HD82943 and Gliese 876, trapped at the 2/1 resonance. 相似文献
9.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》2008,102(1-3):69-82
We study the evolution of an extrasolar planetary system with two planets, for planar motion, starting from an exact resonant periodic motion and increasing the deviation from the equilibrium solution. We keep the semimajor axes and the eccentricities of the two planets fixed and we change the initial conditions by rotating the orbit of the outer planet by Δω. In this way the resonance is preserved, but we deviate from the exact periodicity and there is a transition from order to chaos as the deviation increases. There are three different routes to chaos, as far as the evolution of (ω 2 ? ω 1) is concerned: (a) Libration → rotation → chaos, with intermittent transition from libration to rotation in between, (b) libration → chaos and (c) libration → intermittent interchange between libration and rotation → chaos. This indicates that resonant planetary systems where the angle (ω 2 ? ω 1) librates or rotates are not different, but are closely connected to the exact periodic motion. 相似文献
10.
We compute the growth of isolated gaseous giant planets for several values of the density of the protoplanetary disk, several distances from the central star and two values for the (fixed) radii of accreted planetesimals. Calculations were performed in the frame of the core instability mechanism and the solids accretion rate adopted is that corresponding to the oligarchic growth regime. We find that for massive disks and/or for protoplanets far from the star and/or for large planetesimals, the planetary growth occurs smoothly. However, notably, there are some cases for which we find an envelope instability in which the planet exchanges gas with the surrounding protoplanetary nebula. The timescale of this instability shows that it is associated with the process of planetesimals accretion. The presence of this instability makes it more difficult the formation of gaseous giant planets. 相似文献
11.
We present the results of an extensive study of the final stage of terrestrial planet formation in disks with different surface density profiles and for different orbital configurations of Jupiter and Saturn. We carried out simulations in the context of the classical model with disk surface densities proportional to \({r^{-0.5}}, {r^{-1}}\) and \({r^{-1.5}}\), and also using partially depleted, non-uniform disks as in the recent model of Mars formation by Izidoro et al. (Astrophys J 782:31, 2014). The purpose of our study is to determine how the final assembly of planets and their physical properties are affected by the total mass of the disk and its radial profile. Because as a result of the interactions of giant planets with the protoplanetary disk, secular resonances will also play important roles in the orbital assembly and properties of the final terrestrial planets, we will study the effect of these resonances as well. In that respect, we divide this study into two parts. When using a partially depleted disk (Part 1), we are particularly interested in examining the effect of secular resonances on the formation of Mars and orbital stability of terrestrial planets. When using the disk in the classical model (Part 2), our goal is to determine trends that may exist between the disk surface density profile and the final properties of terrestrial planets. In the context of the depleted disk model, results of our study show that in general, the \(\nu _5\) resonance does not have a significant effect on the dynamics of planetesimals and planetary embryos, and the final orbits of terrestrial planets. However, \(\nu _6\) and \(\nu _{16}\) resonances play important roles in clearing their affecting areas. While these resonances do not alter the orbits of Mars and other terrestrial planets, they strongly deplete the region of the asteroid belt ensuring that no additional mass will be scattered into the accretion zone of Mars so that it can maintain its mass and orbital stability. In the context of the classical model, the effects of these resonances are stronger in disks with less steep surface density profiles. Our results indicate that when considering the classical model (Part 2), the final planetary systems do not seem to show a trend between the disk surface density profile and the mean number of the final planets, their masses, time of formation, and distances to the central star. Some small correlations were observed where, for instance, in disks with steeper surface density profiles, the final planets were drier, or their water contents decreased when Saturn was added to the simulations. However, in general, the final orbital and physical properties of terrestrial planets seem to vary from one system to another and depend on the mass of the disk, the spatial distribution of protoplanetary bodies (i.e., disk surface density profile), and the initial orbital configuration of giant planets. We present results of our simulations and discuss their implications for the formation of Mars and other terrestrial planets, as well as the physical properties of these objects such as their masses and water contents. 相似文献
12.
V. V. Emel’yanenko 《Solar System Research》2011,45(5):402-409
The discovered exoplanetary systems have highly diverse dynamic properties, which differ from those of the Solar System. A
single model including planet migration effects and their gravitational interaction is used to investigate the features of
dynamic processes that lead to the formation of giant-planet systems with different orbital characteristics. It is shown for
a system of four giant planets similar to the Solar System how Type I migration could lead to all the planets being captured
into resonant configurations. The resonant motion can continue for a long period of time after the transition to Type II migration
and after the dissipation of the gas-and-dust disk. The three-planet system of GJ 876 is used to investigate the migration
of the planets inward the orbit of the most massive planet and their capture into low-order resonant configurations under
the conditions of Type II migration. A system similar to the exoplanetary system of HD 102272 is used to study the capture
into high-order resonances followed by an increase in the orbit’s eccentricity. 相似文献
13.
Sean N. Raymond †‡ Rory Barnes Avi M. Mandell †‡ 《Monthly notices of the Royal Astronomical Society》2008,384(2):663-674
To date, two planetary systems have been discovered with close-in, terrestrial-mass planets . Many more such discoveries are anticipated in the coming years with radial velocity and transit searches. Here we investigate the different mechanisms that could form 'hot Earths' and their observable predictions. Models include: (1) in situ accretion; (2) formation at larger orbital distance followed by inward 'type 1' migration; (3) formation from material being 'shepherded' inward by a migrating gas giant planet; (4) formation from material being shepherded by moving secular resonances during dispersal of the protoplanetary disc; (5) tidal circularization of eccentric terrestrial planets with close-in perihelion distances and (6) photoevaporative mass-loss of a close-in giant planet. Models 1–4 have been validated in previous work. We show that tidal circularization can form hot Earths, but only for relatively massive planets with very close-in perihelion distances (≲0.025 au), and even then the net inward movement in orbital distance is at most only 0.1–0.15 au. For planets of less than , photoevaporation can remove the planet's envelope and leave behind the solid core on a Gyr time-scale, but only for planets inside 0.025–0.05 au. Using two quantities that are observable by current and upcoming missions, we show that these models each produce unique signatures, and can be observationally distinguished. These observables are the planetary system architecture (detectable with radial velocities, transits and transit timing) and the bulk composition of transiting close-in terrestrial planets (measured by transits via the planet's radius). 相似文献
14.
Althea V. Moorhead 《Icarus》2005,178(2):517-539
This paper presents a parametric study of giant planet migration through the combined action of disk torques and planet-planet scattering. The torques exerted on planets during Type II migration in circumstellar disks readily decrease the semi-major axes a, whereas scattering between planets increases the orbital eccentricities ?. This paper presents a parametric exploration of the possible parameter space for this migration scenario using two (initial) planetary mass distributions and a range of values for the time scale of eccentricity damping (due to the disk). For each class of systems, many realizations of the simulations are performed in order to determine the distributions of the resulting orbital elements of the surviving planets; this paper presents the results of ∼8500 numerical experiments. Our goal is to study the physics of this particular migration mechanism and to test it against observations of extrasolar planets. The action of disk torques and planet-planet scattering results in a distribution of final orbital elements that fills the a-? plane, in rough agreement with the orbital elements of observed extrasolar planets. In addition to specifying the orbital elements, we characterize this migration mechanism by finding the percentages of ejected and accreted planets, the number of collisions, the dependence of outcomes on planetary masses, the time spent in 2:1 and 3:1 resonances, and the effects of the planetary IMF. We also determine the distribution of inclination angles of surviving planets and the distribution of ejection speeds for exiled planets. 相似文献
15.
In this paper we present a new semianalytical model of oligarchic growth of planets considering a distribution of planetesimal sizes, fragmentation of planetesimals in mutual collisions, sublimation of ices through the snow line, random velocities out of equilibrium and merging of planetary embryos. We show that the presence of several planetary embryos growing simultaneously at different locations in the protoplanetary disk affects the whole accretion history, specially for the innermost planets. The results presented here clearly indicate the relevance of considering a distribution of planetesimal sizes. Fragmentation occurring during planetesimal-planetesimal collisions represent only a marginal effect in shaping the surface density of solid material in the protoplanetary disc. 相似文献
16.
In a previous paper, we have found that the resonance structure of the present Jupiter Trojan swarms could be split up into four different families of resonances. Here, in a first step, we generalize these families in order to describe the resonances occurring in Trojan swarms embedded in a generic planetary system. The location of these families changes under a modification of the fundamental frequencies of the planets and we show how the resonant structure would evolve during a planetary migration. We present a general method, based on the knowledge of the fundamental frequencies of the planets and on those that can be reached by the Trojans, which makes it possible to predict and localize the main events arising in the swarms during migration. In particular, we show how the size and stability of the Trojan swarms are affected by the modification of the frequencies of the planets. Finally, we use this method to study the global dynamics of the Jovian Trojan swarms when Saturn migrates outwards. Besides the two resonances found by Morbidelli et al. which could have led to the capture of the current population just after the crossing of the 2:1 orbital resonance, we also point out several sequences of chaotic events that can influence the Trojan population. 相似文献
17.
Orbital resonances may have played an important role in determining the locations where the planetesimal swarm eventually accreted into full-size planets. Several pairs of planets do indeed have commensurable orbital periods at present, but the case for control of planet formation by resonances is weakened by the fact that many pairs are not commensurable and that those which are do not necessarily exist at the strongest resonances. However, the mass loss and redistribution that occurred in the early solar system evolution can substantially alter the positions of planets and planetary embryos within the swarm. A cascaded resonance structure is hypothesized where planetesimal growth was accelerated at 2:1 interior and 1:2 exterior resonances with an early-formed Jupiter producing runaway growth of planetary embryos. These embryos produce their own resonances which, in turn, lead to additional embryos in a process that successively propagates inward and outward to generate a resonant configuration of embryos. In this manner, the early presence of Jupiter imposed a harmonic structure on the accumulating planetesimal swarm. For an accretion disk with surface density obeying a power law of index ?1.2 the positions of the planetary embryos can be moved into a reasonably good agreement with most of the present planetary positions that is as good as that given by the Titius-Bode law. 相似文献
18.
S. Camera D. Bertacca A. Diaferio N. Bartolo S. Matarrese 《Monthly notices of the Royal Astronomical Society》2009,399(4):1995-2003
This paper is an extension of the work done by Pierens & Nelson in which they investigated the behaviour of a two-planet system embedded in a protoplanetary disc. They put a Jupiter mass gas giant on the internal orbit and a lower mass planet on the external one. We consider here a similar problem taking into account a gas giant with mass in the range 0.5 to 1 M J and a Super-Earth (i.e. a planet with mass ≤10 M ⊕ ) as the outermost planet. By changing disc parameters and planet masses, we have succeeded in getting the convergent migration of the planets which allows for the possibility of their resonant locking. However, in the case in which the gas giant has the mass of Jupiter, before any mean-motion first-order commensurability could be achieved, the Super-Earth is caught in a trap when it is very close to the edge of the gap opened by the giant planet. This confirms the result obtained by Pierens & Nelson in their simulations. Additionally, we have found that, in a very thin disc, an apsidal resonance is observed in the system if the Super-Earth is captured in the trap. Moreover, the eccentricity of the small planet remains low, while the eccentricity of the gas giant increases slightly due to the imbalance between Lindblad and corotational resonances. We have also extended the work of Pierens & Nelson by studying analogous systems in which the gas giant is allowed to take sub-Jupiter masses. In this case, after conducting an extensive survey over all possible parameters, we have succeeded in getting the 1:2 mean-motion resonant configuration only in a disc with low aspect ratio and low surface density. However, the resonance is maintained just for a few thousand orbits. Thus, we conclude that for typical protoplanetary discs the mean-motion commensurabilities are rare if the Super-Earth is located on the external orbit relative to the gas giant. 相似文献
19.
W. Kley 《Celestial Mechanics and Dynamical Astronomy》2003,87(1-2):85-97
We study the evolution of a system consisting of two protoplanets still embedded in a protoplanetary disk. Results of two different numerical approaches are presented. In the first kind of model the motion of the disk material is followed by fully viscous hydrodynamical simulations, and the planetary motion is determined by N-body calculations including exactly the gravitational potential from the disk material. In the second kind we only solve the N-body part and add additional analytically given forces which model the effect of the torques of the disk. This type of modeling is of course orders of magnitudes faster than the full hydro-model. Another advantage of this two-fold approach is the possibility of adjusting the otherwise unknown parameters of the simplified model.The results give very good agreement between the methods. Using two different initial setups for the planets and disk, we obtain in the first case a resonant trapping into the 3:1 resonance, and in the second case a trapping into the 2:1 resonance. Resonant capture leads to a rise in the eccentricity and to an alignment of the spatial orientation of orbits. The characteristics of the numerical results agree very favorably with those of three observed planetary systems (GJ 876, HD 82943, and 55 Cnc) known to be in mean motion resonances. 相似文献
20.
The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on inclined orbits through both analytical techniques and extensive numerical scattering experiments. We derive a criterion for two equal mass planets on circular inclined orbits to achieve Hill stability, and conclude that significant radial migration and eccentricity pumping of both planets occurs predominantly by 2:1 and 5:3 mean motion resonant interactions. Using Laplace-Lagrange secular theory, we obtain analytical secular solutions for the orbital inclinations and longitudes of ascending nodes, and use those solutions to distinguish between the secular and resonant dynamics which arise in numerical simulations. We also illustrate how encounter maps, typically used to trace the motion of massless particles, may be modified to reproduce the gross instability seen by the numerical integrations. Such a correlation suggests promising future use of such maps to model the dynamics of more coplanar massive planet systems. 相似文献