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1.
We study protoplanetary disc evolution assuming that angular momentum transport is driven by gravitational instability at large radii, and magnetohydrodynamic (MHD) turbulence in the hot inner regions. At radii of the order of 1 au such discs develop a magnetically layered structure, with accretion occurring in an ionized surface layer overlying quiescent gas that is too cool to sustain MHD turbulence. We show that layered discs are subject to a limit cycle instability, in which accretion on to the protostar occurs in ∼104-yr bursts with ̇ ∼10−5 M⊙ yr−1, separated by quiescent intervals lasting ∼105 yr where ̇ ≈10−8 M⊙ yr−1. Such bursts could lead to repeated episodes of strong mass outflow in young stellar objects. The transition to this episodic mode of accretion occurs at an early epoch ( t ≪1 Myr), and the model therefore predicts that many young pre-main-sequence stars should have low rates of accretion through the inner disc. At ages of a few Myr, the discs are up to an order of magnitude more massive than the minimum-mass solar nebula, with most of the mass locked up in the quiescent layer of the disc at r ∼1 au. The predicted rate of low-mass planetary migration is reduced at the outer edge of the layered disc, which could lead to an enhanced probability of giant planet formation at radii of 1–3 au.  相似文献   

2.
We study the viscous evolution of protoplanetary discs driven by the combined action of magnetohydrodynamic turbulence, resulting from the magneto-rotational instability (MRI), self-gravity torques, parametrized in terms of an effective viscosity and an additional viscous agent of unspecified origin. The distribution of torques driving the evolution of the disc is calculated by analysing where in the disc the MRI develops and, to incorporate the effect of self-gravity, calculating the Toomre parameter. We find that, generally, discs rapidly evolve towards a configuration where the intermediate regions, from a fraction of an au to a few au, are stable against the MRI due to their low-ionization degree. As an additional source of viscosity is assumed to operate in those regions, subsequent evolution of the disc is eruptive. Brief episodes of high mass accretion ensue as the criterion for the development of the MRI is met in the low-ionization region. The radial distribution of mass and temperature in the disc differs considerably from disc models with constant α parameter or layered accretion models, with potentially important consequences on the process of planet formation.  相似文献   

3.
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   

4.
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   

5.
Dynamical relaxation and the orbits of low-mass extrasolar planets   总被引：1，自引：0，他引：1  
We consider the evolution of a system containing a population of massive planets formed rapidly through a fragmentation process occurring on a scale on the order of 100 au and a lower mass planet that assembles in a disc on a much longer time-scale. During the formation phase, the inner planet is kept on a circular orbit owing to tidal interaction with the disc, while the outer planets undergo dynamical relaxation. Interaction with the massive planets left in the system after the inner planet forms may increase the eccentricity of the inner orbit to high values, producing systems similar to those observed.  相似文献   

6.
We show that the dearth of brown dwarfs in short-period orbits around Solar-mass stars – the brown dwarf desert – can be understood as a consequence of inward migration within an evolving protoplanetary disc. Brown dwarf secondaries forming at the same time as the primary star have masses which are comparable to the initial mass of the protoplanetary disc. Subsequent disc evolution leads to inward migration, and destruction of the brown dwarf, via merger with the star. This is in contrast with massive planets, which avoid this fate by forming at a later epoch when the disc is close to being dispersed. Within this model, a brown dwarf desert arises because the mass at the hydrogen-burning limit is coincidentally comparable to the initial disc mass for a Solar mass star. Brown dwarfs should be found in close binaries around very low mass stars, around other brown dwarfs, and around Solar-type stars during the earliest phases of star formation.  相似文献   

7.
Detectable debris discs are thought to require dynamical excitation ('stirring'), so that planetesimal collisions release large quantities of dust. We investigate the effects of the secular perturbations of a planet, which may lie at a significant distance from the planetesimal disc, to see if these perturbations can stir the disc, and if so over what time-scale. The secular perturbations cause orbits at different semimajor axes to precess at different rates, and after some time   t cross  initially non-intersecting orbits begin to cross. We show that   t cross∝ a 9/2disc/( m pl e pl a 3pl)  , where   m pl, e pl  and   a pl  are the mass, eccentricity and semimajor axis of the planet, and   a disc  is the semimajor axis of the disc. This time-scale can be faster than that for the growth of planetesimals to Pluto's size within the outer disc. We also calculate the magnitude of the relative velocities induced among planetesimals and infer that a planet's perturbations can typically cause destructive collisions out to 100 s of au. Recently formed planets can thus have a significant impact on planet formation in the outer disc which may be curtailed by the formation of giant planets much closer to the star. The presence of an observed debris disc does not require the presence of Pluto-sized objects within it, since it can also have been stirred by a planet not in the disc. For the star ε Eridani, we find that the known radial velocity planet can excite the planetesimal belt at 60 au sufficiently to cause destructive collisions of bodies up to 100 km in size, on a time-scale of 40 Myr.  相似文献   

8.
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   

9.
We investigate the migration of massive extrasolar planets caused by gravitational interaction with a viscous protoplanetary disc. We show that a model in which planets form at 5 au at a constant rate, before migrating, leads to a predicted distribution of planets that is a steeply rising function of log( a ), where a is the orbital radius. Between 1 and 3 au, the expected number of planets per logarithmic interval in a roughly doubles. We demonstrate that, once selection effects are accounted for, this is consistent with current data, and then extrapolate the observed planet fraction to masses and radii that are inaccessible to current observations. In total, approximately 15 per cent of stars targeted by existing radial velocity searches are predicted to possess planets with masses  0.3< M p sin( i )<10 M J  and radii  0.1< a <5 au  . A third of these planets (around 5 per cent of the target stars) lie at the radii most amenable to detection via microlensing. A further  5–10  per cent of stars could have planets at radii of  5< a <8 au  that have migrated outwards. We discuss the probability of forming a system (akin to the Solar system) in which significant radial migration of the most massive planet does not occur. Approximately  10–15  per cent of systems with a surviving massive planet are estimated to fall into this class. Finally, we note that a smaller fraction of low-mass planets than high-mass planets is expected to survive without being consumed by the star. The initial mass function for planets is thus predicted to rise more steeply towards small masses than the observed mass function.  相似文献   

10.
Young massive stars in the central parsec of our Galaxy are best explained by star formation within at least one, and possibly two, massive self-gravitating gaseous discs. With help of numerical simulations, we here consider whether the observed population of young stars could have originated from a large angle collision of two massive gaseous clouds at   R ≃ 1 pc  from Sgr A*. In all the simulations performed, the post-collision gas flow forms an inner, nearly circular gaseous disc and one or two eccentric outer filaments, consistent with the observations. Furthermore, the radial stellar mass distribution is always very steep,  Σ*∝ R −2  , again consistent with the observations. All of our simulations produce discs that are warped by between 30° and 60°, in accordance with the most recent observations. The three-dimensional velocity structure of the stellar distribution is sensitive to initial conditions (e.g. the impact parameter of the clouds) and gas cooling details. For example, the runs in which the inner disc is fed intermittently with material possessing fluctuating angular momentum result in multiple stellar discs with different orbital orientations, contradicting the observed data. In all the cases the amount of gas accreted by our inner boundary condition is large, enough to allow Sgr A* to radiate near its Eddington limit over ∼105 yr. This suggests that a refined model would have physically larger clouds (or a cloud and a disc such as the circumnuclear disc) colliding at a distance of a few parsecs rather than 1 pc as in our simulations.  相似文献   

11.
The possibility that protoplanetary gaseous discs are dynamically unstable to axisymmetric and non-axisymmetric gravity perturbations (e.g. those produced by spontaneous disturbances) with characteristic scales larger than the vertical scale height is discussed analytically, using a local Wentzel–Kramers–Brillouin (WKB) approach. It is shown that such discs might be clumpy, and these gravitationally bound clumps may later collapse to become giant planets ('hot Jupiters'). The chief aim in this paper is to underscore a fact of vital importance for application in the planetary formation process: gravitationally unstable non-axisymmetric (spiral) perturbations can effectively transport both the angular momentum and the mass in a spatially inhomogeneous disc.  相似文献   

12.
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   

13.
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   

14.
It appears that most stars are born in clusters, and that at birth most stars have circumstellar discs which are comparable in size to the separations between the stars. Interactions between neighbouring stars and discs are therefore likely to play a key role in determining disc lifetimes, stellar masses, and the separations and eccentricities of binary orbits. Such interactions may also cause fragmentation of the discs, thereby triggering the formation of additional stars.   We have carried out a series of simulations of star–disc interactions using an SPH code which treats self-gravity, hydrodynamic and viscous forces. We find that interactions between discs and stars provide a mechanism for removing energy from, or adding energy to, the orbits of the stars, and for truncating the discs. However, capture during such encounters is unlikely to be an important binary formation mechanism.   A more significant consequence of such encounters is that they can trigger fragmentation of the disc, via tidally and compressionally induced gravitational instabilities, leading to the formation of additional stars and substellar objects. When the disc spins and stellar orbits are randomly oriented, encounters lead to the formation of new companions to the original star in 20 per cent of encounters. If most encounters are prograde and coplanar, as suggested by simulations of dynamically triggered star formation, then new companions are formed in approximately 50 per cent of encounters.  相似文献   

15.
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   

16.
We present a submillimetre continuum survey for accretion discs around seven embedded protostars in the Perseus and Serpens molecular clouds. Observations were made at frequencies between 339 and 357 GHz using the James Clerk Maxwell Telescope–Caltech Submillimeter Observatory single-baseline interferometer on Mauna Kea, Hawaii. All the objects in our survey show compact dust emission on scales ≲1 arcsec, assumed to arise in a circumstellar accretion disc. We compare the properties of this compact component with evolutionary indicators, such as the ratio of compact to extended emission, and bolometric temperature. We find that discs of mass ∼0.01 M⊙ have formed by the Class 0 stage, and that similar mass discs are observed in Class I and Class II sources. A trend is observed whereby the ratio of compact to extended emission in our sources increases from Class 0 to Class II sources. For three of the objects in the survey, NGC 1333 IRAS2:CR1 and SVS13 in Perseus, and FIRS1 in Serpens, the signal-to-noise ratio is sufficient to allow us to model the brightness distributions with elliptical Gaussian and power-law disc models. The Gaussian fits give semimajor half-power radii of approximately 90 to 140 au, at the assumed distance of 350 pc to the Perseus and Serpens clouds.  相似文献   

17.
It is expected that an average protostar will undergo at least one impulsive interaction with a neighbouring protostar whilst a large fraction of its mass is still in a massive, extended disc. Such interactions must have a significant impact upon the evolution of the protostars and their discs.   We have carried out a series of simulations of coplanar encounters between two stars, each possessing a massive circumstellar disc, using an SPH code that models gravitational, hydrodynamic and viscous forces. We find that during a coplanar encounter, disc material is swept up into a shock layer between the two interacting stars, and the layer then fragments to produce new protostellar condensations. The truncated remains of the discs may subsequently fragment; and the outer regions of the discs may be thrown off to form circumbinary disc-like structures around the stars. Thus coplanar disc–disc encounters lead efficiently to the formation of multiple star systems and small- N clusters, including substellar objects.  相似文献   

18.
We present models in which the photoevaporation of discs around young stars by an external ultraviolet source (as computed by Adams et al.) is coupled with the internal viscous evolution of the discs. These models are applied to the case of the Orion Nebula Cluster (ONC), where the presence of a strong ultraviolet field from the central OB stars, together with a detailed census of circumstellar discs and photoevaporative flows, is well established. In particular we investigate the constraints that are placed on the initial disc properties in the ONC by the twin requirement that most stars possess a disc on a scale of a few astronomical unit (au), but that only a minority (<20 per cent) are resolved by Hubble Space Telescope ( HST ) at a scale of 50 au. We find that these requirements place very weak constraints on the initial radius distribution of circumstellar discs: the resulting size distribution readily forgets the initial radius distribution, owing to the strong positive dependence of the photoevaporation rate on disc radius. Instead, the scarcity of large discs reflects the relative scarcity of initially massive discs (with mass  >0.1 M⊙  ). The ubiquity of discs on a small scale, on the other hand, mainly constrains the time-span over which the discs have been exposed to the ultraviolet field (<2 Myr). We argue that the discs that are resolved by HST represent a population of discs in which self-gravity was important at the time that the dominant central OB star switched on, but that, according to our models, self-gravity is unlikely to be important in these discs at the present time. We discuss the implications of our results for the so-called proplyd lifetime problem.  相似文献   

19.
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   

20.
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   

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