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Register a new userVortices in self-gravitating disks
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Added by
George Mamatsashvili
Publication date
2008
fields
Physics
and research's language is
English
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Vortices are believed to greatly help the formation of km sized planetesimals by collecting dust particles in their centers. However, vortex dynamics is commonly studied in non-self-gravitating disks. The main goal here is to examine the effects of disk self-gravity on the vortex dynamics via numerical simulations. In the self-gravitating case, when quasi-steady gravitoturbulent state is reached, vortices appear as transient structures undergoing recurring phases of formation, growth to sizes comparable to a local Jeans scale, and eventual shearing and destruction due to gravitational instability. Each phase lasts over 2-3 orbital periods. Vortices and density waves appear to be coupled implying that, in general, one should consider both vortex and density wave modes for a proper understanding of self-gravitating disk dynamics. Our results imply that given such an irregular and rapidly changing, transient character of vortex evolution in self-gravitating disks it may be difficult for such vortices to effectively trap dust particles in their centers that is a necessary process towards planet formation.
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The mechanism through which meter-sized boulders grow to km-sized planetesimals in protoplanetary discs is a subject of active research, since it is critical for planet formation. To avoid spiralling into the protostar due to aerodynamic drag, objects must rapidly grow from cm-sized pebbles, which are tightly coupled to the gas, to large boulders of 1-100m in diameter. It is already well known that over-densities in the gaseous component of the disc provide potential sites for the collection of solids, and that significant density structures in the gaseous component of the disc (e.g., spiral density waves) can trap solids efficiently enough for the solid component of the disc to undergo further gravitational collapse due to their own self-gravity. In this work, we employ the PENCIL CODE to conduct local shearing sheet simulations of massive self-gravitating protoplanetary discs, to study the effect of anticyclonic transient vortices, or eddies, on the evolution of solids in these discs. We find that these types of structures are extremely efficient at concentrating small and intermediate-sized dust particles with friction times comparable to, or less than, the local orbital period of the disc. This can lead to significant over-densities in the solid component of the disc, with density enhancements comparable to, and even higher, than those within spiral density waves; increasing the rate of gravitational collapse of solids into bound structures.
The long wavelength emission of protostellar objects is commonly attributed to a disk of gas and dust around the central protostar. In the first stages of disk accretion or in the case of high mass protostars, the disk mass is likely to be sufficiently large, so that the disk self-gravity may have an impact on the dynamics and the emission properties of the disk. In this paper we describe the spectral energy distribution (SED) produced by a simple, non-flaring, self-gravitating accretion disk model. Self-gravity is included in the calculation of the rotation curve of the disk and in the energy balance equation, as a term of effective heating related to Jeans instability. In order to quantify in detail the requirements on the mass of the disk and on the accretion rate posed on the models by realistic situations, we compare the SEDs produced by these models with the observed SEDs of a small sample of well-studied protostellar objects. We find that relatively modest disks - even lighter than the central star - can lead to an interesting fit to the infrared SED of the FU Orionis objects considered, while in the case of T Tauri stars the required parameters fall outside the range suggested as acceptable by the general theoretical and observational scenario. On the basis of the present results, we may conclude that the contribution of a self-gravitating disk is plausible in several cases (in particular, for FU Orionis objects) and that, in the standard irradiation dominated disk scenario, it would help softening the requirements encountered by Keplerian accretion models.
We give a complete solution to the existence problem for gravitating vortices with non-negative topological constant $c geqslant 0$. Our first main result builds on previous results by Yang and establishes the existence of solutions to the Einstein-Bogomolnyi equations, corresponding to $c=0$, in all admissible Kahler classes. Our second main result completely solves the existence problem for $c>0$. Both results are proved by the continuity method and require that a GIT stability condition for an effective divisor on the Riemann sphere is satisfied. For the former, the continuity path starts from a given solution with $c = 0$ and deforms the Kahler class. For the latter result we start from the established solution in any fixed admissible Kahler class and deform the coupling constant $alpha$ towards $0$. A salient feature of our argument is a new bound $S_g geqslant c$ for the curvature of gravitating vortices, which we apply to construct a limiting solution along the path via Cheeger-Gromov theory.
We introduce the notion of twisted gravitating vortex on a compact Riemann surface. If the genus of the Riemann surface is greater than 1 and the twisting forms have suitable signs, we prove an existence and uniqueness result for suitable range of the coupling constant generalizing the result of arXiv:1510.03810v2 in the non twisted setting. It is proved via solving a continuity path deforming the coupling constant from 0 for which the system decouples as twisted Kahler-Einstein metric and twisted vortices. Moreover, specializing to a family of twisting forms smoothing delta distribution terms, we prove the existence of singular gravitating vortices whose Kahler metric has conical singularities and Hermitian metric has parabolic singularities. In the Bogomolnyi phase, we establish an existence result for singular Einstein-Bogomolnyi equations, which represents cosmic strings with singularities.
Observations suggest that protoplanetary disks have moderate accretion rates onto the central young star, especially at early stages (e.g. HL Tau), indicating moderate disk turbulence. However, recent ALMA observations suggest that dust is highly settled, implying weak turbulence. Motivated by such tension, we carry out 3D stratified local simulations of self-gravitating disks, focusing on settling of dust particles in actively accreting disks. We find that gravitationally unstable disks can have moderately high accretion rates while maintaining a relatively thin dust disk for two reasons. First, accretion stress from the self-gravitating spirals (self-gravity stress) can be stronger than the stress from turbulence (Reynolds stress) by a factor of 5-20. Second, the strong gravity from the gas to the dust decreases the dust scale height by another factor of $sim 2$. Furthermore, the turbulence is slightly anisotropic, producing a larger Reynolds stress than the vertical dust diffusion coefficient. Thus, gravitoturbulent disks have unusually high vertical Schmidt numbers ($Sc_z$) if we scale the total accretion stress with the vertical diffusion coefficient (e.g. $Sc_zsim$ 10-100). The reduction of the dust scale height by the gas gravity, should also operate in gravitationally stable disks ($Q>$1). Gravitational forces between particles become more relevant for the concentration of intermediate dust sizes, forming dense clouds of dust. After comparing with HL Tau observations, our results suggest that self-gravity and gravity among different disk components could be crucial for solving the conflict between the protoplanetary disk accretion and dust settling, at least at the early stages.
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