We analyze the gas accretion flow through a planet-produced gap in a protoplanetary disk. We adopt the a-disk model and ignore effects of planetary migration. We develop a semianalytic, ...one-dimensional model that accounts for the effects of the planet as a mass sink and also carry out two-dimensional hydrodynamic simulations of a planet embedded in a disk. The predictions of the mass flow rate through the gap based on the semianalytic model generally agree with the hydrodynamic simulations at the 25% level. Through these models, we are able to explore steady state disk structures and over large spatial ranges. The presence of an accreting 61M sub(J) planet significantly lowers the density of the disk within a region of several times the planet's orbital radius. The mass flow rate across the gap (and onto the central star) is typically 10%-25% of the mass accretion rate outside the orbit of the planet, for planet-to-star mass ratios that range from 5 x 10 super(-5) to 1 x 10 super(-3).
We describe two-dimensional hydrodynamic simulations of the migration of low-mass planets (<=30 M {circled plus}) in nearly laminar disks (viscosity parameter alpha < 10-3) over timescales of several ...thousand orbit periods. We consider disk masses of 1, 2, and 5 times the minimum mass solar nebula, disk thickness parameters of H/r = 0.035 and 0.05, and a variety of alpha values and planet masses. Disk self-gravity is fully included. Previous analytic work has suggested that Type I planet migration can be halted in disks of sufficiently low turbulent viscosity, for alpha ~ 10-4. The halting is due to a feedback effect of breaking density waves that results in a slight mass redistribution and consequently an increased outward torque contribution. The simulations confirm the existence of a critical mass (M cr ~ 10M {circled plus}) beyond which migration halts in nearly laminar disks. For alpha 10-3, density feedback effects are washed out and Type I migration persists. The critical masses are in good agreement with the analytic model of Rafikov. In addition, for alpha 10-4 steep density gradients produce a vortex instability, resulting in a small time-varying eccentricity in the planet's orbit and a slight outward migration. Migration in nearly laminar disks may be sufficiently slow to reconcile the timescales of migration theory with those of giant planet formation in the core accretion model.
Evolution of Giant Planets in Eccentric Disks D’Angelo, Gennaro; Lubow, Stephen H; Bate, Matthew R
Astrophysical journal/The Astrophysical journal,
12/2006, Letnik:
652, Številka:
2
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We investigate the interaction between a giant planet and a viscous circumstellar disk by means of high-resolution, two-dimensional hydrodynamic simulations. We consider planetary masses that range ...from 1 to 3 Jupiter masses (M sub(J)) and initial orbital eccentricities that range from 0 to 0.4. We find that a planet can cause eccentricity growth in a disk region adjacent to the planet's orbit, even if the planet's orbit is circular. Disk-planet interactions lead to growth in a planet's orbital eccentricity. The orbital eccentricities of a 2M sub(J) and a 3M sub(J) planet increase from 0 to 0.11 within about 3000 orbits. Over a similar time period, the orbital eccentricity of a 1M sub(J) planet grows from 0 to 0.02. For a case of a 1M sub(J) planet with an initial eccentricity of 0.01, the orbital eccentricity grows to 0.09 over 4000 orbits. Radial migration is directed inward but slows considerably as a planet's orbit becomes eccentric. If a planet's orbital eccentricity becomes sufficiently large, e 0.02, migration can reverse and so be directed outward. The accretion rate toward a planet depends on both the disk and the planetary orbital eccentricity and is pulsed over the orbital period. Planetary mass growth rates increase with planetary orbital eccentricity. For e 6 0.2, the mass growth rate of a planet increases by 630% above the value for e = 0. For e 0.1, most of the accretion within the planet's Roche lobe occurs when the planet is near the apocenter. Similar accretion modulation occurs for flow at the inner disk boundary, which represents accretion toward the star.
Aligning spinning black holes and accretion discs King, A. R.; Lubow, S. H.; Ogilvie, G. I. ...
Monthly Notices of the Royal Astronomical Society,
10/2005, Letnik:
363, Številka:
1
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We consider the alignment torque between a spinning black hole and an accretion disc whose angular momenta are misaligned. This situation must hold initially in almost all gas accretion events on to ...supermassive black holes, and may occur in binaries where the black hole receives a natal supernova kick. We show that the torque always acts to align the hole's spin with the total angular momentum without changing its magnitude. The torque acts dissipatively on the disc, reducing its angular momentum, and aligning it with the hole if and only if the angle θ between the angular momenta Jd of the disc and Jh of the hole satisfy the inequality cos θ > −Jd/2Jh. If this condition fails, which requires both θ > π/2 and Jd < 2Jh, the disc counteraligns.
Standard, planar accretion discs operate through a dissipative mechanism, usually thought to be turbulent, and often modelled as a viscosity. This acts to take energy from the radial shear, enabling ...the flow of mass and angular momentum in the radial direction. In a previous paper, we discussed observational evidence for the magnitude of this viscosity, and pointed out discrepancies between these values and those obtained in numerical simulations. In this paper, we discuss the observational evidence for the magnitude of the dissipative effects which act in non-planar discs, both to transfer and to eliminate the non-planarity. Estimates based on the model by Ogilvie, which assumes a small-scale, isotropic viscosity, give alignment time-scales for fully ionized discs which are apparently too short by a factor of a few compared with observations, although we emphasize that more detailed computations as well as tighter observational constraints are required to verify this conclusion. For discs with low temperature and conductivity, we find that the time-scales for disc alignment based on isotropic viscosity are too short by around two orders of magnitude. This large discrepancy suggests that our understanding of viscosity in quiescent discs is currently inadequate.
Previous theoretical studies have found that repeating outbursts can occur in certain regions of an accretion disk due to sudden transitions in time from gravitationally produced turbulence to ...magnetically produced turbulence. We analyze the disk evolution in a state diagram that plots the mass accretion rate versus disk surface density. We determine steady state accretion branches that involve gravitational and magnetic sources of turbulence. Using time-dependent numerical disk simulations, we show that cases having outbursts track along a nonsteady 'dead zone' branch and some steady state accretion branches. The outburst is the result of a rapid inter-branch transition. The gravo-magneto outbursts are then explained on this diagram as a limit cycle that is analogous to the well-known S-curve that has been applied to dwarf nova outbursts. The diagram and limit cycle provide a conceptual framework for understanding the nature of the outbursts that may occur in accretion disks of all scales, from circumplanetary to protoplanetary to active galactic nucleus accretion disks.
On the wake generated by a planet in a disc Ogilvie, G. I.; Lubow, S. H.
Monthly Notices of the Royal Astronomical Society,
03/2002, Letnik:
330, Številka:
4
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A planet of low mass orbiting in a two-dimensional gaseous disc generates a one-armed spiral wake. We explain this phenomenon as the result of constructive interference between wave modes in the ...disc, somewhat similar to the Kelvin wedge produced in the wake of a ship. The same feature is not expected in a three-dimensional disc with thermal stratification.
We carry out two-dimensional high-resolution numerical simulations of type I planet migration with different disk viscosities. We find that the planet migration is strongly dependent on disk ...viscosities. Two kinds of density wave damping mechanisms are discussed. Accordingly, the angular momentum transport can be either viscosity dominated or shock dominated, depending on the disk viscosities. The long-term migration behavior is different as well. Influences of the Rossby vortex instability on planet migration are also discussed. In addition, we investigate very weak shock generation in inviscid disks by small mass planets and compare the results with prior analytic results.
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