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1.
We present a numerical study of rapid, so-called type III migration for Jupiter-sized planets embedded in a protoplanetary disc. We limit ourselves to the case of inward migration, and study in detail its evolution and physics, concentrating on the structure of the corotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using the results of global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. The initial conditions are chosen to satisfy the condition for rapid inward migration. We find that type III migration can be divided into two regimes, fast and slow. The structure of the co-orbital region, mass accumulation rate and migration behaviour differ between these two regimes. All our simulations show a transition from the fast to the slow regime, ending type III migration well before reaching the star. The stopping radius is found to be larger for more massive planets and less massive discs. A sharp density drop is also found to be an efficient stopping mechanism. In the fast migration regime the migration rate and induced eccentricity are lower for less massive discs, but almost do not depend on planet mass. Eccentricity is damped on the migration time-scale.  相似文献   

2.
We investigate the fast (type III) migration regime of high-mass protoplanets orbiting in protoplanetary discs. This type of migration is dominated by corotational torques. We study the details of flow structure in the planet's vicinity, the dependence of migration rate on the adopted disc model and the numerical convergence of models (independence of certain numerical parameters such as gravitational softening).
We use two-dimensional hydrodynamical simulations with adaptive mesh refinement, based on the flash code with improved time-stepping scheme. We perform global disc simulations with sufficient resolution close to the planet, which is allowed to freely move throughout the grid. We employ a new type of equation of state in which the gas temperature depends on both the distance to the star and planet, and a simplified correction for self-gravity of the circumplanetary gas.
We find that the migration rate in the type III migration regime depends strongly on the gas dynamics inside the Hill sphere (Roche lobe of the planet) which, in turn, is sensitive to the aspect ratio of the circumplanetary disc. Furthermore, corrections due to the gas self-gravity are necessary to reduce numerical artefacts that act against rapid planet migration. Reliable numerical studies of type III migration thus require consideration of both the thermal and the self-gravity corrections, as well as a sufficient spatial resolution and the calculation of disc–planet attraction both inside and outside the Hill sphere. With this proviso, we find type III migration to be a robust mode of migration, astrophysically promising because of a speed much faster than in the previously studied modes of migration.  相似文献   

3.
We study the torque on low-mass protoplanets on fixed circular orbits, embedded in a protoplanetary disc in the isothermal limit. We consider a wide range of surface density distributions including cases where the surface density increases smoothly outwards. We perform both linear disc response calculations and non-linear numerical simulations. We consider a large range of viscosities, including the inviscid limit, as well as a range of protoplanet mass ratios, with special emphasis on the co-orbital region and the corotation torque acting between disc and protoplanet.
For low-mass protoplanets and large viscosity, the corotation torque behaves as expected from linear theory. However, when the viscosity becomes small enough to enable horseshoe turns to occur, the linear corotation torque exists only temporarily after insertion of a planet into the disc, being replaced by the horseshoe drag first discussed by Ward. This happens after a time that is equal to the horseshoe libration period reduced by a factor amounting to about twice the disc aspect ratio. This torque scales with the radial gradient of specific vorticity, as does the linear torque, but we find it to be many times larger. If the viscosity is large enough for viscous diffusion across the co-orbital region to occur within a libration period, we find that the horseshoe drag may be sustained. If not, the corotation torque saturates leaving only the linear Lindblad torques. As the magnitude of the non-linear co-orbital torque (horseshoe drag) is always found to be larger than the linear torque, we find that the sign of the total torque may change even for mildly positive surface density gradients. In combination with a kinematic viscosity large enough to keep the torque from saturating, strong sustained deviations from linear theory and outward or stalled migration may occur in such cases.  相似文献   

4.
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   

5.
There is evidence for the existence of massive planets at orbital radii of several hundred au from their parent stars where the time-scale for planet formation by core accretion is longer than the disc lifetime. These planets could have formed close to their star and then migrated outwards. We consider how the transfer of angular momentum by viscous disc interactions from a massive inner planet could cause significant outward migration of a smaller outer planet. We find that it is in principle possible for planets to migrate to large radii. We note, however, a number of effects which may render the process somewhat problematic.  相似文献   

6.
Using 2D magnetohydrodynamic (MHD) numerical simulations performed with two different finite-difference Eulerian codes, we analyse the effect that a toroidal magnetic field has on low-mass planet migration in non-turbulent protoplanetary discs. The presence of the magnetic field modifies the waves that can propagate in the disc. In agreement with a recent linear analysis, we find that two magnetic resonances develop on both sides of the planet orbit, which contribute to a significant global torque. In order to measure the torque exerted by the disc on the planet, we perform simulations in which the latter is either fixed on a circular orbit or allowed to migrate. For a     planet, when the ratio β between the square of the sound speed and that of the Alfven speed at the location of the planet is equal to 2, we find inward migration when the magnetic field   B φ  is uniform in the disc, reduced migration when   B φ  decreases as   r −1  and outward migration when   B φ  decreases as   r −2  . These results are in agreement with predictions from the linear analysis. Taken as a whole, our results confirm that even a subthermal stable field can stop inward migration of an earth-like planet.  相似文献   

7.
We investigate the properties of circumplanetary discs formed in three-dimensional, self-gravitating radiation hydrodynamical models of gas accretion by protoplanets. We determine disc sizes, scaleheights, and density and temperature profiles for different protoplanet masses, in solar nebulae of differing grain opacities.
We find that the analytical prediction of circumplanetary disc radii in an evacuated gap  ( R Hill/3)  from Quillen & Trilling yields a good estimate for discs formed by high-mass protoplanets. The radial density profiles of the circumplanetary discs may be described by power laws between   r −2  and   r −3/2  . We find no evidence for the ring-like density enhancements that have been found in some previous models of circumplanetary discs. Temperature profiles follow a  ∼ r −7/10  power law regardless of protoplanet mass or nebula grain opacity. The discs invariably have large scaleheights  ( H / r > 0.2)  , making them thick in comparison with their encompassing circumstellar discs, and they show no flaring.  相似文献   

8.
In this paper we look at one of the effects of irradiation on a warped accretion disc in the context of active galactic nuclei (AGN). A warp will catch a substantial amount of the radiation emitted by the central object. We consider the fluid motions that may arise inside a warped disc when the surface is subject to a radiation stress, and also the net mass flows that result. We find that, to first order, we have a balance of the viscous and Coriolis-type forces. The radial radiation stress causes outward motion of the surface layer, but only the azimuthal Poynting–Robertson drag leads to an increase in the net accretion rate. We investigate the distribution of the velocity perturbations and find them to be significant in determining the local structure of the disc.
An unexpected result is that the picture changes significantly when we take into account the periodic illumination of the warped disc. A type of resonance at the local Keplerian rotation frequency causes a flow that penetrates the whole thickness of the disc; these flows are faster than the flows due to unchanging illumination. They totally dominate the induced flows in terms of sheer mass, but significant impact on disc structure still occurs only near the surface, where velocity perturbations typically go up to some kilometres per second.  相似文献   

9.
The migration and growth of protoplanets in protostellar discs   总被引：1，自引：0，他引：1  
We investigate the gravitational interaction of a Jovian-mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the protoplanetary disc from which it formed. Different disc surface density distributions are investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protoplanet. Non-linear two-dimensional hydrodynamic simulations are employed using three independent numerical codes.
A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches the central star in a near-circular orbit after a characteristic viscous time‐scale of ∼104 initial orbital periods. This is found to be independent of whether the protoplanet is allowed to accrete mass or not. Inward migration is helped by the disappearance of the inner disc, and therefore the positive torque it would exert, because of accretion on to the central star. Maximally accreting protoplanets reach about 4 Jovian masses on reaching the neighbourhood of the central star. Our results indicate that a realistic upper limit for the masses of closely orbiting giant planets is ∼5 Jupiter masses, if they originate in protoplanetary discs similar to the minimum-mass solar nebula. This is because of the reduced accretion rates obtained for planets of increasing mass.
Assuming that some process such as termination of the inner disc through a magnetospheric cavity stops the migration, the range of masses estimated for a number of close orbiting giant planets as well as their inward orbital migration can be accounted for by consideration of disc–protoplanet interactions during the late stages of giant planet formation.  相似文献   

10.
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   

11.
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   

12.
We present analytic models for the local structure of self-regulated self-gravitating accretion discs that are subject to realistic cooling. Such an approach can be used to predict the secular evolution of self-gravitating discs (which can usefully be compared with future radiation hydrodynamical simulations) and to define various physical regimes as a function of radius and equivalent steady state accretion rate. We show that fragmentation is inevitable, given realistic rates of infall into the disc, once the disc extends to radii >70 au (in the case of a solar mass central object). Owing to the outward redistribution of disc material by gravitational torques, we also predict fragmentation at >70 au even in the case of low angular momentum cores which initially collapse to a much smaller radius. We point out that 70 au is close to the median binary separation and propose that such delayed fragmentation, at the point that the disc expands to >70 au, ensures the creation of low mass ratio companions that can avoid substantial further growth and consequent evolution towards unit mass ratio. We thus propose this as a promising mechanism for producing low mass ratio binaries, which, while abundant observationally, are severely underproduced in hydrodynamical models.  相似文献   

13.
We study the effects of winds on the time evolution of isothermal, self-gravitating accretion discs by adopting a radius-dependent mass-loss rate because of the existence of the wind. Our similarity and semi-analytical solution describes time evolution of the system in the slow accretion limit. The disc structure is distinct in the inner and outer parts, irrespective of the existence of the wind. We show that the existence of wind will lead to a reduction of the surface density in the inner and outer parts of the disc in comparison to a no-wind solution. Also, the radial velocity significantly increases in the outer part of the disc, however, the accretion rate decreases due to the reduced surface density in comparison to the no-wind solution. In the inner part of the disc, mass loss due to the wind is negligible according to our solution. But the radial size of this no-wind inner region becomes smaller for stronger winds.  相似文献   

14.
The irradiation of protoplanetary discs by central stars is the main heating mechanism for discs, resulting in their flared geometric structure. In a series of papers, we investigate the deep links between two-dimensional self-consistent disc structure and planetary migration in irradiated discs, focusing particularly on those around M stars. In this first paper, we analyse the thermal structure of discs that are irradiated by an M star by solving the radiative transfer equation by means of a Monte Carlo code. Our simulations of irradiated hydrostatic discs are realistic and self-consistent in that they include dust settling with multiple grain sizes  ( N = 15)  , the gravitational force of an embedded planet on the disc and the presence of a dead zone (a region with very low levels of turbulence) within it. We show that dust settling drives the temperature of the mid-plane from an   r −3/5  distribution (well mixed dust models) towards an   r −3/4  . The dead zone, meanwhile, leaves a dusty wall at its outer edge because dust settling in this region is enhanced compared to the active turbulent disc at larger disc radii. The disc heating produced by this irradiated wall provides a positive gradient region of the temperature in the dead zone in front of the wall. This is crucially important for slowing planetary migration because Lindblad torques are inversely proportional to the disc temperature. Furthermore, we show that low turbulence of the dead zone is self-consistently induced by dust settling, resulting in the Kelvin–Helmholtz instability (KHI). We show that the strength of turbulence arising from the KHI in the dead zone is  α= 10−5  .  相似文献   

15.
Metallicity, planetary formation and migration   总被引：1，自引：0，他引：1  
Recent observations show a clear correlation between the probability of hosting a planet and the metallicity of the parent star. As radial velocity surveys are biased, however, towards detecting planets with short orbital periods, the probability–metallicity correlation could merely reflect a dependence of migration rates on metallicity. We investigated the possibility, but find no basis to suggest that the migration process is sensitive to the metallicity. The indication is, therefore, that a higher metallicity results in a higher probability for planet  formation .  相似文献   

16.
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17.
An explanation for the soft X-ray excess in active galactic nuclei   总被引：1，自引：0，他引：1  
We present a large sample of type 1 active galactic nuclei (AGN) spectra taken with XMM–Newton , and fit them with both the conventional model (a power law and blackbody) and the relativistically blurred photoionized disc reflection model of Ross & Fabian. We find that the disc reflection model is a better fit. The disc reflection model successfully reproduces the continuum shape, including the soft excess, of all the sources. The model also reproduces many features that would conventionally be interpreted as absorption edges. We are able to use the model to infer the properties of the sources, specifically that the majority of black holes in the sample are strongly rotating, and that there is a deficit in sources with an inclination >70°. We conclude that the disc reflection model is an important tool in the study of AGN X-ray spectra.  相似文献   

18.
We present a numerical model for the evolution of a protostellar disc that has formed self-consistently from the collapse of a molecular cloud core. The global evolution of the disc is followed for several million years after its formation. The capture of a wide range of spatial and temporal scales is made possible by use of the thin-disc approximation. We focus on the role of gravitational torques in transporting mass inward and angular momentum outward during different evolutionary phases of a protostellar disc with disc-to-star mass ratio of order 0.1. In the early phase, when the infall of matter from the surrounding envelope is substantial, mass is transported inward by the gravitational torques from spiral arms that are a manifestation of the envelope-induced gravitational instability in the disc. In the late phase, when the gas reservoir of the envelope is depleted, the distinct spiral structure is replaced by ongoing irregular non-axisymmetric density perturbations. The amplitude of these density perturbations decreases with time, though this process is moderated by swing amplification aided by the existence of the disc's sharp outer edge. Our global modelling of the protostellar disc reveals that there is typically a residual non-zero gravitational torque from these density perturbations, i.e. their effects do not exactly cancel out in each region. In particular, the net gravitational torque in the inner disc tends to be negative during first several million years of the evolution, while the outer disc has a net positive gravitational torque. Our global model of a self-consistently formed disc shows that it is also self-regulated in the late phase, so that it is near the Toomre stability limit, with a near-uniform Toomre parameter Q ≈ 1.5–2.0. Since the disc also has near-Keplerian rotation, and comparatively weak temperature variation, it maintains a near-power-law surface density profile proportional to r −3/2.  相似文献   

19.
We numerically study the tidal instability of accretion discs in close binary systems using a two-dimensional SPH code. We find that the precession rate of tidally unstable, eccentric discs does not only depend upon the binary mass ratio q . Although the (prograde) disc precession rate increases with the strength of the tidal potential, we find that increasing the shear viscosity ν also has a significant prograde effect. Increasing the disc temperature has a retrograde impact upon the precession rate.   We find that motion relative to the binary potential results in superhump-like, periodic luminosity variations in the outer reaches of an eccentric disc. The nature and location of the luminosity modulation are functions of ν. Light curves most similar to observations are obtained for ν values appropriate for a dwarf nova in outburst.   We investigate the thermal–tidal instability model for superoutburst. A dwarf nova outburst is simulated by instantaneously increasing ν, which causes a rapid radial expansion of the disc. Should the disc encounter the 3: 1 eccentric inner Lindblad resonance and become tidally unstable, then tidal torques become much more efficient at removing angular momentum from the disc. The disc then shrinks and M d increases. The resulting increase in disc luminosity is found to be consistent with the excess luminosity of a superoutburst.  相似文献   

20.
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