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1.
An automatic Bayesian Kepler periodogram has been developed for identifying and characterizing multiple planetary orbits in precision radial velocity data. The periodogram is powered by a parallel tempering Markov chain Monte Carlo (MCMC) algorithm which is capable of efficiently exploring a multiplanet model parameter space. The periodogram employs an alternative method for converting the time of an observation to true anomaly that enables it to handle much larger data sets without a significant increase in computation time. Improvements in the periodogram and further tests using data from HD 208487 have resulted in the detection of a second planet with a period of 90982−92 d, an eccentricity of 0.370.26−0.20, a semimajor axis of 1.870.13−0.14 au and an M sin  i = 0.45+0.11−0.13 M J. The revised parameters of the first planet are period = 129.8 ± 0.4 d, eccentricity = 0.20 ± 0.09, semimajor axis = 0.51 ± 0.02 au and M sin  i = 0.41 ± 0.05  M J. Particular attention is paid to several methods for calculating the model marginal likelihood which is used to compare the probabilities of models with different numbers of planets.  相似文献   

2.
Planets orbiting a planetesimal circumstellar disc can migrate inward from their initial positions because of dynamical friction between planets and planetesimals. The migration rate depends on the disc mass and on its time evolution. Planets that are embedded in long-lived planetesimal discs, having total mass of 10−4– 0.01 M⊙ , can migrate inward a large distance and can survive only if the inner disc is truncated or as a result of tidal interaction with the star. In this case the semimajor axis, a , of the planetary orbit is less than 0.1 au. Orbits with larger a are obtained for smaller values of the disc mass or for a rapid evolution (depletion) of the disc. This model may explain not only several of the orbital features of the giant planets that have been discovered in recent years orbiting nearby stars, but also the metallicity enhancement found in several stars associated with short-period planets.  相似文献   

3.
We use numerical simulations to model the migration of massive planets at small radii and compare the results with the known properties of 'hot Jupiters' (extrasolar planets with semimajor axes   a < 0.1  au). For planet masses   M pl sin  i > 0.5 M J  , the evidence for any 'pile-up' at small radii is weak (statistically insignificant), and although the mass function of hot Jupiters is deficient in high-mass planets as compared to a reference sample located further out, the small sample size precludes definitive conclusions. We suggest that these properties are consistent with disc migration followed by entry into a magnetospheric cavity close to the star. Entry into the cavity results in a slowing of migration, accompanied by a growth in orbital eccentricity. For planet masses in excess of 1 Jupiter mass we find eccentricity growth time-scales of a few ×105 yr, suggesting that these planets may often be rapidly destroyed. Eccentricity growth appears to be faster for more massive planets which may explain changes in the planetary mass function at small radii and may also predict a pile-up of lower mass planets, the sample of which is still incomplete.  相似文献   

4.
A Bayesian multiplanet Kepler periodogram has been developed for the analysis of precision radial velocity data. The periodogram employs a parallel tempering Markov chain Monte Carlo algorithm. The HD 11964 data have been re-analysed using 1, 2, 3 and 4 planet models. Assuming that all the models are equally probable a priori, the three planet model is found to be ≥600 times more probable than the next most probable model which is a two planet model. The most probable model exhibits three periods of  38.02+0.06−0.05, 360+4−4 and 1924+44−43 d  , and eccentricities of  0.22+0.11−0.22, 0.63+0.34−0.17 and 0.05+0.03−0.05  , respectively. Assuming the three signals (each one consistent with a Keplerian orbit) are caused by planets, the corresponding limits on planetary mass ( M sin  i ) and semimajor axis are     respectively. The small difference (1.3σ) between the 360-d period and one year suggests that it might be worth investigating the barycentric correction for the HD 11964 data.  相似文献   

5.
On the migration of a system of protoplanets   总被引：1，自引：0，他引：1  
The evolution of a system consisting of a protoplanetary disc with two embedded Jupiter-sized planets is studied numerically. The disc is assumed to be flat and non-self-gravitating; this is modelled by the planar (two-dimensional) Navier–Stokes equations. The mutual gravitational interaction of the planets and the star, and the gravitational torques of the disc acting on the planets and the central star are included. The planets have an initial mass of one Jupiter mass M Jup each, and the radial distances from the star are one and two semimajor axes of Jupiter, respectively.
During the evolution a joint wide annular gap is created by the planets. Both planets increase their mass owing to accretion of gas from the disc: after about 2500 orbital periods of the inner planet it has reached a mass of 2.3  M Jup, while the outer planet has reached a mass of 3.2  M Jup. The net gravitational torques exerted by the disc on the planets result in an inward migration of the outer planet on time-scales comparable to the viscous evolution time of the disc. The semimajor axis of the inner planet remains constant as there is very little gas left in its vicinity to induce any migration. When the distance of close approach eventually becomes smaller than the mutual Hill radius, the eccentricities increase strongly and the system may become unstable.
If disc depletion occurs rapidly enough before the planets come too close to each other, a stable system similar to our own Solar system may remain. Otherwise the orbits may become unstable and produce systems like υ And.  相似文献   

6.
Recent observations point to the presence of structured dust grains in the discs surrounding young brown dwarfs, thus implying that the first stages of planet formation take place also in the substellar regime. Here, we investigate the potential for planet formation around brown dwarfs and very low-mass stars according to the sequential core accretion model of planet formation. We find that, for a brown dwarf mass 0.05 M⊙, our models predict a maximum planetary mass of  ∼5   M⊕  , orbiting with semimajor axis ∼ 1 au. However, we note that the predictions for the mass–semimajor axis distribution are strongly dependent upon the models chosen for the disc surface density profiles and the assumed distribution of disc masses. In particular, if brown dwarf disc masses are of the order of a few Jupiter masses, Earth-mass planets might be relatively frequent, while if typical disc masses are only a fraction of Jupiter mass, we predict that planet formation would be extremely rare in the substellar regime. As the observational constraints on disc profiles, mass dependencies and their distributions are poor in the brown dwarf regime, we advise caution in validating theoretical models only on stars similar to the Sun and emphasize the need for observational data on planetary systems around a wide range of stellar masses. We also find that, unlike the situation around solar-like stars, Type II migration is totally absent from the planet formation process around brown dwarfs, suggesting that any future observations of planets around brown dwarfs would provide a direct measure of the role of other types of migration.  相似文献   

7.
We have performed N -body numerical simulations of the exchange of angular momentum between a massive planet and a 3D Keplerian disc of planetesimals. Our interest is directed at the study of the classical analytical expressions of the lineal theory of density waves, as representative of the dynamical friction in discs 'dominated by the planet' and the orbital migration of the planets with regard to this effect. By means of a numerical integration of the equations of motion, we have carried out a set of numerical experiments with a large number of particles  ( N ≥10 000)  , and planets with the mass of Jupiter, Saturn and one core mass of the giant planets in the Solar system  ( M c=10 M⊕)  . The torque, measured in a phase in which a 'steady forcing' is clearly measurable, yields inward migration in a minimum-mass solar disc  (Σ∼10 g cm-2  ), with a characteristic drift time of ∼ a few 106 yr. The planets predate the disc, but the orbital decay rate is not sufficient to allow accretion in a time-scale relevant to the formation of giant planets. We found reductions of the measured torque on the planet, with respect to the linear theory, by a factor of 0.38 for M c, 0.04 for Saturn and 0.01 for Jupiter, due to the increase in the perturbation on the disc. The behaviour of planets whose mass is larger than M c is similar to the one of type II migrators in gaseous discs. Our results suggest that, in a minimum mass, solar planetesimals disc, type I migrations occur for masses smaller than M c, whereas for this mass value it could be a transition zone between the two types of migration.  相似文献   

8.
In this paper we develop further the model for the migration of planets introduced in Del Popolo et al. We first model the protoplanetary nebula as a time-dependent accretion disc, and find self-similar solutions to the equations of the accretion disc that give us explicit formulae for the spatial structure and the temporal evolution of the nebula. These equations are then used to obtain the migration rate of the planet in the planetesimal disc, and to study how the migration rate depends on the disc mass, on its time evolution and on some values of the dimensionless viscosity parameter α . We find that planets that are embedded in planetesimal discs, having total mass of  10-4-0.1 M⊙  , can migrate inward a large distance for low values of α (e.g.,   α ≃10-3-10-2)  and/or large disc mass, and can survive only if the inner disc is truncated or because of tidal interaction with the star. Orbits with larger a are obtained for smaller values of the disc mass and/or for larger values of α . This model may explain several orbital features of the recently discovered giant planets orbiting nearby stars.  相似文献   

9.
We analyse the non-linear, three-dimensional response of a gaseous, viscous protoplanetary disc to the presence of a planet of mass ranging from 1 Earth mass (1 M⊕) to 1 Jupiter mass (1 MJ) by using the zeus hydrodynamics code. We determine the gas flow pattern, and the accretion and migration rates of the planet. The planet is assumed to be in a fixed circular orbit about the central star. It is also assumed to be able to accrete gas without expansion on the scale of its Roche radius. Only planets with masses   M p≳ 0.1 MJ  produce significant perturbations in the surface density of the disc. The flow within the Roche lobe of the planet is fully three-dimensional. Gas streams generally enter the Roche lobe close to the disc mid-plane, but produce much weaker shocks than the streams in two-dimensional models. The streams supply material to a circumplanetary disc that rotates in the same sense as the orbit of the planet. Much of the mass supply to the circumplanetary disc comes from non-coplanar flow. The accretion rate peaks with a planet mass of approximately 0.1 MJ and is highly efficient, occurring at the local viscous rate. The migration time-scales for planets of mass less than 0.1 MJ, based on torques from disc material outside the Roche lobes of the planets, are in excellent agreement with the linear theory of type I (non-gap) migration for three-dimensional discs. The transition from type I to type II (gap) migration is smooth, with changes in migration times of about a factor of 2. Starting with a core which can undergo runaway growth, a planet can gain up to a few MJ with little migration. Planets with final masses of the order of 10 MJ would undergo large migration, which makes formation and survival difficult.  相似文献   

10.
We argue that all transient searches for planets in globular clusters have a very low detection probability. Planets of low-metallicity stars typically do not reside at small orbital separations. The dependence of planetary system properties on metallicity is clearly seen when the quantity   I e ≡ M p[ a (1 − e )]2  is considered;   M p, a   and e are the planet mass, semimajor axis and eccentricity, respectively. In high-metallicity systems, there is a concentration of systems at high and low values of I e , with a low-populated gap near   I e ∼ 0.3 M J au2  , where M J is Jupiter's mass. In low-metallicity systems, the concentration is only at the higher range of I e , with a tail to low values of I e . Therefore, it is still possible that planets exist around main-sequence stars in globular clusters, although at small numbers because of the low metallicity, and at orbital periods of ≳10 d. We discuss the implications of our conclusions on the role that companions can play in the evolution of their parent stars in globular clusters, for example, influencing the distribution of horizontal branch stars on the Hertzsprung–Russell diagram of some globular clusters, and in forming low-mass white dwarfs.  相似文献   

11.
We investigate the gravitational interaction between a planet and an optically thin protoplanetary disc, performing local three-dimensional hydrodynamical simulations. In the present study, we take account of radiative energy transfer in optically thin discs. Before the stage of planetary accretion, dust opacity is expected to decrease significantly because of grain growth and planetesimal formation. Thus, it would be reasonable to consider optically thin discs in the disc–planet interaction. Furthermore, we focus on small planets that can neither capture disc gas nor open a disc gap. The one-sided torque exerted on a planet by an optically thin disc is examined for various values of the disc optical thickness (<1). In optically thin discs, the temperature behind the density waves is lower than the unperturbed value because of radiative cooling. Heating due to shock dissipation is less effective than radiative cooling. Because of radiative cooling, the density distribution around the planet is not axisymmetric, which exerts an additional torque on the planet. The torque enhancement becomes maximum when the cooling time is comparable with the Keplerian period. The enhancement is significant for low-mass planets. For planets with  3 M⊕  , the additional one-sided torque can be 40 per cent of the torque in the isothermal case. The radiative cooling is expected to change the differential torque and the migration speed of planets, too.  相似文献   

12.
Self-gravitating protostellar discs are unstable to fragmentation if the gas can cool on a time-scale that is short compared with the orbital period. We use a combination of hydrodynamic simulations and N -body orbit integrations to study the long-term evolution of a fragmenting disc with an initial mass ratio to the star of   M disc/ M *= 0.1  . For a disc that is initially unstable across a range of radii, a combination of collapse and subsequent accretion yields substellar objects with a spectrum of masses extending (for a Solar-mass star) up to  ≈0.01 M⊙  . Subsequent gravitational evolution ejects most of the lower mass objects within a few million years, leaving a small number of very massive planets or brown dwarfs in eccentric orbits at moderately small radii. Based on these results, systems such as HD 168443 – in which the companions are close to or beyond the deuterium burning limit – appear to be the best candidates to have formed via gravitational instability. If massive substellar companions originate from disc fragmentation, while lower-mass planetary companions originate from core accretion, the metallicity distribution of stars which host massive substellar companions at radii of ∼1 au should differ from that of stars with lower mass planetary companions.  相似文献   

13.
We study the coorbital flow for embedded, low-mass planets. We provide a simple semi-analytic model for the corotation region, which is subsequently compared to high-resolution numerical simulations. The model is used to derive an expression for the half-width of the horseshoe region, x s, which in the limit of zero softening is given by   x s/ r p= 1.68( q / h )1/2  , where q is the planet to central star mass ratio, h is the disc aspect ratio and   r p  is the orbital radius. This is in very good agreement with the same quantity measured from simulations. This result is used to show that horseshoe drag is about an order of magnitude larger than the linear corotation torque in the zero-softening limit. Thus, the horseshoe drag, the sign of which depends on the gradient of specific vorticity, is important for estimates of the total torque acting on the planet. We further show that phenomena, such as the Lindblad wakes, with a radial separation from corotation of approximately a pressure scaleheight H can affect x s, even though for low-mass planets   x s≪ H   . The effect is to distort streamlines and reduce x s through the action of a back pressure. This effect is reduced for smaller gravitational softening parameters and planets of higher mass, for which x s becomes comparable to H .  相似文献   

14.
In this work, we study the stability of hypothetical satellites of extrasolar planets. Through numerical simulations of the restricted elliptic three-body problem we found the borders of the stable regions around the secondary body. From the empirical results, we derived analytical expressions of the critical semimajor axis beyond which the satellites would not remain stable. The expressions are given as a function of the eccentricities of the planet, e P, and of the satellite, e sat. In the case of prograde satellites, the critical semimajor axis, in the units of Hill's radius, is given by a E≈ 0.4895   (1.0000 − 1.0305 e P− 0.2738 e sat). In the case of retrograde satellites, it is given by a E≈ 0.9309  (1.0000 − 1.0764 e P− 0.9812 e sat). We also computed the satellite stability region ( a E) for a set of extrasolar planets. The results indicate that extrasolar planets in the habitable zone could harbour the Earth-like satellites.  相似文献   

15.
We investigate the dynamics of putative Earth-mass planets in the habitable zone (HZ) of the extrasolar planetary system OGLE-2006-BLG-109L, a close analogue of the Solar system. Our work is inspired by the work of Malhotra & Minton. Using the linear Laplace–Lagrange theory, they identified a strong secular resonance that may excite large eccentricity of orbits in the HZ. However, due to uncertain or unconstrained orbital parameters, the subsystem of Jupiters may be found in a dynamically active region of the phase space spanned by low-order mean-motion resonances. To generalize this secular model, we construct a semi-analytical averaging method in terms of the restricted problem. The secular orbits of large planets are approximated by numerically averaged osculating elements. They are used to calculate the mean orbits of terrestrial planets by means of a high-order analytic secular theory developed in our previous works. We found regions in the parameter space of the problem in which stable, quasi-circular orbits in the HZ are permitted. The excitation of eccentricity in the HZ strongly depends on the apsidal angle of jovian orbits. For some combinations of that angle, eccentricities and semimajor axes consistent with the observations, a terrestrial planet may survive in low eccentric orbits. We also study the effect of post-Newtonian gravity correction on the innermost secular resonance.  相似文献   

16.
Discs in the 6 Myr old cluster η Chamaeleontis were searched for emission from hot H2. Around the M3 star ECHA J0843.3−7905, we detect circumstellar gas orbiting at ∼2 au. If the gas is ultraviolet excited, the ro-vibrational line traces a hot gas layer supported by a disc of mass  ∼0.03 M⊙  , similar to the minimum mass solar nebula. Such a gas reservoir at 6 Myr would promote the formation and the inwards migration of gas giant planets.  相似文献   

17.
We report Doppler measurements of the stars HD 187085 and HD 20782 which indicate two high eccentricity low-mass companions to the stars. We find HD 187085 has a Jupiter-mass companion with a ∼1000-d orbit. Our formal 'best-fitting' solution suggests an eccentricity of 0.47, however, it does not sample the periastron passage of the companion and we find that orbital solutions with eccentricities between 0.1 and 0.8 give only slightly poorer fits (based on rms and  χ2ν  ) and are thus plausible. Observations made during periastron passage in 2007 June should allow for the reliable determination of the orbital eccentricity for the companion to HD 187085. Our data set for HD 20782 does sample periastron and so the orbit for its companion can be more reliably determined. We find the companion to HD 20782 has   M sin   i = 1.77 ± 0.22  M Jup  , an orbital period of 595.86 ± 0.03 d and an orbit with an eccentricity of 0.92 ± 0.03. The detection of such high-eccentricity (and relatively low-velocity amplitude) exoplanets appears to be facilitated by the long-term precision of the Anglo-Australian Planet Search. Looking at exoplanet detections as a whole, we find that those with higher eccentricity seem to have relatively higher velocity amplitudes indicating higher mass planets and/or an observational bias against the detection of high-eccentricity systems.  相似文献   

18.
Transiting exoplanetary systems are surpassingly important among the planetary systems since they provide the widest spectrum of information for both the planet and the host star. If a transiting planet is on an eccentric orbit, the duration of transits T D is sensitive to the orientation of the orbital ellipse relative to the line of sight. The precession of the orbit results in a systematic variation in both the duration of individual transit events and the observed period between successive transits,   P obs  . The periastron of the ellipse slowly precesses due to general relativity and possibly the presence of other planets in the system. This secular precession can be detected through the long-term change in   P obs  (transit timing variations, TTV) or in T D (transit duration variations, TDV). We estimate the corresponding precession measurement precision for repeated future observations of the known eccentric transiting exoplanetary systems (XO-3b, HD 147506b, GJ 436b and HD 17156b) using existing or planned space-borne instruments. The TDV measurement improves the precession detection sensitivity by orders of magnitude over the TTV measurement. We find that TDV measurements over a approximately 4 yr period can typically detect the precession rate to a precision well exceeding the level predicted by general relativity.  相似文献   

19.
We investigate the distribution of mass M and orbital period P of extrasolar planets, taking account of selection effects caused by the limited velocity precision and duration of existing surveys. We fit the data on 72 planets to a power-law distribution of the form  d n = CM −α P −β(d M / M )(d P / P )  , and find  α= 0.11 ± 0.10  ,  β=−0.27 ± 0.06  for   M ≲ 10 M J  , where   M J  is the mass of Jupiter. The correlation coefficient between these two exponents is −0.31, indicating that uncertainties in the two distributions are coupled. We estimate that 4 per cent of solar-type stars have companions in the range  1 M J < M < 10 M J  ,  2d < P < 10 yr  .  相似文献   

20.
Dynamical relaxation and massive extrasolar planets   总被引：1，自引：0，他引：1  
Following the suggestion of Black that some massive extrasolar planets may be associated with the tail of the distribution of stellar companions, we investigate a scenario in which 5 N 100 planetary mass objects are assumed to form rapidly through a fragmentation process occuring in a disc or protostellar envelope on a scale of 100 au. These are assumed to have formed rapidly enough through gravitational instability or fragmentation that their orbits can undergo dynamical relaxation on a time-scale of ∼100 orbits.
Under a wide range of initial conditions and assumptions, the relaxation process ends with either (i) one potential 'hot Jupiter' plus up to two 'external' companions, i.e. planets orbiting near the outer edge of the initial distribution; (ii) one or two 'external' planets or even none at all; (iii) one planet on an orbit with a semi-major axis of 10 to 100 times smaller than the outer boundary radius of the inital distribution together with an 'external' companion. Most of the other objects are ejected and could contribute to a population of free-floating planets. Apart from the potential 'hot Jupiters', all the bound objects are on orbits with high eccentricity, and also with a range of inclination with respect to the stellar equatorial plane. We found that, apart from the close orbiters, the probability of ending up with a planet orbiting at a given distance from the central star increases with the distance. This is because of the tendency of the relaxation process to lead to collisions with the central star. The scenario we envision here does not impose any upper limit on the mass of the planets. We discuss the application of these results to some of the more massive extrasolar planets.  相似文献   

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