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.
We derive a viscosity from gravitational instability in self-gravitating accretion disks, which has the required properties to account for the observed fast formation of the first super-massive black holes in highly redshifted quasars and for the cosmological evolution of the black hole-mass distribution.
The steady-state structure of self-gravitating, magnetized accretion disks is studied using a set of self-similar solutions which are appropriate in the outer regions. The disk is assumed to be isothermal and the magnetic field outside of the disk is treated in a phenomenological way. However, the internal field is determined self-consistently. The behaviour of the solutions are investigated by changing the input parameters of the model, i.e. mass accretion rate, coefficients of viscosity and resistivity, and the magnetic field configuration.
In the dynamics of accretion disks, the presence of collective effects associated with the self-gravity of the disk is expected to affect not only the momentum transport, but also the relevant energy balance equations, which could differ substantially from the non-self-gravitating case. Here we follow the picture that, when the disk is sufficiently cold, the stirring due to Jeans-related instabilities acts as a source of effective heating. The corresponding reformulation of the energy equations allows us to: ({\it i}) demonstrate how self-regulation can be established, so that the stability pa…
We present the first global simulations of self-gravitating magnetized tori. The simulations are performed with Zeus-2D and GLOBAL. We find the magnetorotational instability (MRI) to behave similarly in a self-gravitating environment as in previous simulations of non self-gravitating systems: enhancement of turbulent angular momentum transport follows the linear phase. The torus quickly develops a two component structure composed of an inner thick disk in Keplerian rotation and an outer massive disk. We compare this result with zero mass global simulations in 2D, and also present preliminary r…
We consider a class of steady-state self-gravitating accretion disks for which efficient cooling mechanisms are assumed to operate so that the disk is self-regulated at a condition of approximate marginal Jeans stability. In an earlier paper, this scenario had been shown to lead naturally, in the absence of a central point mass, to a self-similar solution characterized by a flat rotation curve. In this article we investigate the entire parameter space available for such self-regulated accretion disks and provide two non-trivial extensions of the model. The first extension is that of a bimodal …
In this paper and a companion work, we report on the first global numerical simulations of self-gravitating magnetized tori, subject in particular to the influence of the magnetorotational instability (MRI). In this work, paper I, we restrict our calculations to the study of the axisymmetric evolution of such tori. Our goals are twofold: (1) to investigate how self-gravity influences the global structure and evolution of the disks; and (2) to determine whether turbulent density inhomogeneities can be enhanced by self-gravity in this regime. As in non self-gravitating models, the linear growth …
In the borders of the dead zones of protoplanetary disks, the inflow of gas produces a local density maximum that triggers the Rossby wave instability. The vortices that form are efficient in trapping solids. We aim to assess the possibility of gravitational collapse of the solids within the Rossby vortices. We perform global simulations of the dynamics of gas and solids in a low mass non-magnetized self-gravitating thin protoplanetary disk with the Pencil code. We use multiple particle species of radius 1, 10, 30, and 100 cm. The dead zone is modeled as a region of low viscosity. The Rossby v…
(highly abridged) We define three requirements for accurate simulations that attempt to model circumstellar disks and the formation of collapsed objects (e.g. planets) within them. First, we define a resolution requirement based on the wavelength for neutral stability of self gravitating waves in the disk. For particle based or grid based simulations, this criterion takes the form, respectively, of a minimum number of particles per critical (`Toomre') mass or maximum value of a `Toomre number', $T= δx/λ_T$, where the wavelength, $λ_T$, is the wavelength for neutral stability for waves in disks…
We introduce exact analytical solutions of the steady-state hydrodynamic equations of scale-free, self-gravitating gaseous disks with flat rotation curves. We express the velocity field in terms of a stream function and obtain a third-order ordinary differential equation (ODE) for the angular part of the stream function. We present the closed-form solutions of the obtained ODE and construct hydrodynamical counterparts of the power-law and elliptic disks, for which self-consistent stellar dynamical models are known. We show that the kinematics of the Large Magellanic Cloud can well be explained…
Using 2D nonlinear simulations, we study the generation and nonlinear evolution of spiral structure in a star-forming multi-component gravitating disk. We confirm in agreement with previous studies the destabilizing role of a cold gaseous component and extend this conclusion for multi-component star-forming disks exchanging mass and momentum between its components. We show that the spiral structure growing on a non-stationary multi-phase background reaches its saturation in a similar manner like the one-component disks. The spiral structure survives even if most of the gas is transformed into …
We carry out the effect of $β$-prescription for viscosity which introduced by Duschel et al. 2000 & Hure, Richard & Zhan 2001, in a standard self-gravitating thin disks. We were predicted in a self-gravitating thin disk the $β$-model will have different dynamical behavior compare the well known $α$-prescriptions. We used self-similar methods for solving the integrated equations which govern the dynamical behavior of the thin disks. We present the results of self-similar solutions of the time evolution of axisymmetric, polytropic, self-gravitating viscous disks around a new born central object.…
We have constructed general relativistic models of a stationary, axially symmnetric, Keplerian thin disk around a rotating black hole. We computed profiles of a spectral line, emitted in the inner region of the disk. In our models we have taken into account also the self-gravity of the disk. The aim of this work is to study gravitational effects on the line profiles in connection with the X-ray features observed in spectra of active galactic nuclei. In some cases, the calculated profiles are clearly affected by the disk gravity but relativistic dragging effects are found to be negligible.
Effects of gravitational softening on the global structure of self-gravitating disks in centrifugal equillibrium are examined in relation to hydrodynamical/gravitational simulations. The one-parameter spline softening proposed by Hernquist & Katz is used. It is found that if the characteristic size of a disk, r, is comparable or less than the gravitational softening length, epsilon, then the cross section of the simulated disk is significantly larger than that of a no-softening (Newtonian) disk with the same mass and angular momentum. We furthermore demonstrate that if r is less than or about …
We investigate the tidal interaction between a low-mass planet and a self-gravitating protoplanetary disk, by means of two-dimensional hydrodynamic simulations. We first show that considering a planet freely migrating in a disk without self-gravity leads to a significant overestimate of the migration rate. The overestimate can reach a factor of two for a disk having three times the surface density of the minimum mass solar nebula. Unbiased drift rates may be obtained only by considering a planet and a disk orbiting within the same gravitational potential. In a second part, the disk self-gravit…
We consider the effects of eccentricity on the fragmentation of gravitationally unstable accretion disks, using numerical hydrodynamics. We find that eccentricity does not affect the overall stability of the disk against fragmentation, but significantly alters the manner in which such fragments accrete gas. Variable tidal forces around an eccentric orbit slow the accretion process, and suppress the formation of weakly-bound clumps. The "stellar" mass function resulting from the fragmentation of an eccentric disk is found to have a significantly higher characteristic mass than that from a corre…
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…
The stability of a rotating fluid disk to the formation of spiral arms is studied in the tightwinding approximation in the linear regime. The dispersion relation for spirals that was derived by Bertin et al. is shown to contain a new, acoustic instability beyond the Lindblad resonances that depends only on pressure and rotation. In this regime, pressure and gravity exchange roles as drivers and inhibitors of spiral wave structures. Other instabilities that are enhanced by pressure are also found in the general dispersion relation by including higher order terms in the small parameter 1/kr for …
Using high resolution, two-dimensional hydrodynamical simulations, we investigate the evolution of a self-gravitating multi-phase interstellar medium in the central kiloparsec region of a galactic disk. We find that a gravitationally and thermally unstable disk evolves, in a self-stabilizing manner, into a globally quasi-stable disk that consists of cold (T < 100 K), dense clumps and filaments surrounded by hot (T > 10^4 K), diffuse medium. The quasi-stationary, filamentary structure of the cold gas is remarkable. The hot gas, characterized by low-density holes and voids, is produced by shock …
We simulate planet migration caused by interactions between planets and a planetesimal disk. We use an N-body integrator optimized for near-Keplerian motion that runs in parallel on a video graphics card, and that computes all pair-wise gravitational interactions. We find that the fraction of planetesimals found in mean motion resonances is reduced and planetary migration rates are on average about 50% slower when gravitational interactions between the planetesimals are computed than when planetesimal self-gravity is neglected. This is likely due to gravitational stirring of the planetesimal d…
Following Toomre & Kalnajs (1991), local models of slightly dissipative self-gravitating disks show how inhomogeneous structures can be maintained over several galaxy rotations. Their basic physical ingredients are self-gravity, dissipation and differential rotation. In order to explore the structures resulting from these processes on the kpc scale, local simulation of self-gravitating disks are performed in this paper in 2D as well as in 3D. The third dimension becomes a priori important as soon as matter clumping causes a tight coupling of the 3D equations of motion. The physically simple an…
Context. We consider a simple self-gravitating disk, made of two fluid components characterized by different effective thermal speeds and interacting with one another only through gravity; two-component models of this type have often been considered in order to estimate the impact of the cold interstellar medium on gravitational instabilities in star-dominated galaxy disks. Aims. This simple model allows us to produce a unified description of instabilities in non-viscous self-gravitating disks, some originating from Jeans collapse, and others from the relative motion between the two components…
We discuss the physics of vortices in the circumstellar disks associated with young stellar objects. We elucidate the basic physical properties of these localized storm systems. In particular, we consider point vortices, linear vortices, the effects of self-gravity, magnetic fields, and nonlinear aspects of the problem. We find that these vortices can exist in many different forms in the disks of young stellar objects and may play a role in the formation of binary companions and/or giant planets. Vortices may enhance giant planet formation via gravitational instability by allowing dust grains …
A self-similar solution for time evolution of isothermal, self-gravitating viscous disks is found under the condition that $α' \equiv α(H/r)$ is constant in space (where $α$ is the viscosity parameter and $H/r$ is the ratio of a half-thickness to radius of the disk). This solution describes a homologous collapse of a disk via self-gravity and viscosity. The disk structure and evolution is distinct in the inner and outer parts. There is a constant mass inflow in the outer portions so that the disk has flat rotation velocity, constant accretion velocity, and surface density decreasing outward as…
We use a high order accuracy spectral code to carry out two-dimensional time-dependent numerical simulations of vortices in accretion disks. In particular, we examine the stability and the life time of vortices in circumstellar disks around young stellar objects. The results show that cyclonic vortices dissipate quickly, while anticyclonic vortices can survive in the flow for many orbits. When more than one vortex is present, the anticyclonic vortices interact through vorticity waves and merge together to form larger vortices. The decay time of anticyclonic vortices is of the order of 30-60 or…
Linear theory is used to determine the stability of the self-gravitating, rapidly (and nonuniformly) rotating, two-dimensional, and collisional particulate disk against small-amplitude gravity perturbations. A gas-kinetic theory approach is used by exploring the combined system of the Boltzmann and the Poisson equations. The effects of physical collisions between particles are taken into account by using in the Boltzmann kinetic equation a Krook model integral of collisions modified to allow collisions to be inelastic. It is shown that as a direct result of the classical Jeans instability and …
Isolated low-mass stars are formed, in the standard picture, from the collapse of dense cores condensed out of strongly magnetized molecular clouds. The dynamically collapsing inflow traps nearly half of the critical magnetic flux needed for the core support and deposits it in a small region surrounding the protostar. It has been argued previously that the deposited flux can slow down the inflow, allowing matter to pile up and settle along field lines into a magnetically supported, circumstellar disk. Here we show that the disk typically contains $\sim 10%$ of the stellar mass, and that it cou…
The interstellar medium (ISM) reveals strongly inhomogeneous structures at every scale. These structures do not seem completely random since they obey certain power laws. Larson's law (\citeyear{Larson81}) $σ\propto R^δ$ and the plausible assumption of virial equilibrium justify to consider fractals as a possible description of the ISM. In the following we investigate how self-gravitation, differential rotation and dissipation affect the matter distribution in galaxies. To this end we have performed 3D-simulations for self-gravitating local boxes embedded in a larger disk, extending the 2D-met…
Accretion disks are three-dimensional, turbulent, often self-gravitating, magnetohydrodynamic flows, which can be modeled in detail with numerical simulations. In this paper, we present a new algorithm that is based on a spectral decomposition method to simulate such flows. Because of the high order of the method, we can solve the induction equation in terms of the magnetic potential and, therefore, ensure trivially that the magnetic fields in the numerical solution are divergence free. The spectral method also suffers minimally from numerical dissipation and allows for an easy implementation …
We examine the effect of self-gravity in a rotating thick-disk equilibrium in the presence of a dipolar magnetic field. In the first part, we find a self-similar solution for non-self-gravitating disks. The solution that we have found shows that the pressure and density equilibrium profiles are strongly modified by a self-consistent toroidal magnetic field. We introduce 3 dimensionless variables $C_B$, $C_c$, $C_t$ that indicate the relative importance of toroidal component of magnetic field ($C_B$), centrifugal ($C_c$) and thermal ($C_t$) energy with respect to the gravitational potential ene…
We carry out a two-dimensional, compressible, simulation of a disk, including dust particles, to study the formation and role of vortices in protoplanetary disks. We find that anticyclonic vortices can form out of an initial random perturbation of the vorticity field. Vortices have a typical decay time of the order of 50 orbital periods (for a viscosity parameter alpha=0.0001 and a disk aspect ratio of H/r = 0.15). If vorticity is continuously generated at a constant rate in the flow (e.g. by convection), then a large vortex can form and be sustained (due to the merger of vortices). We find th…
We present new dynamical models of weakly self-gravitating, finite dispersion eccentric stellar disks around central black holes for the double nucleus of M31. The disk is fixed in a frame rotating at constant precession speed, and is populated by stars on quasi-periodic orbits whose parents are numerically integrated periodic orbits in the total potential. A distribution of quasi-periodic orbits about a given parent is approximated by a distribution of Kepler orbits dispersed in eccentricity and orientation, using an approximate phase-space distribution function written in terms of the integr…
The present work represents an attempt to understand the `rules of behavior' of observed warps in the HI disks of spiral galaxies found by Briggs (1990). In contrast with most earlier theoretical work, the present study investigates different initial value problems of a warped disk in an oblate (or prolate) halo potential, and it represents the disk warp in terms of $N$ independently tilted, self-gravitating, concentric rings. This representation gives new insight into the disk warping. A new constant of the motion of $N$ tilted rings is identified (in addition to the energy). The phenomenon o…
Two dimensional hydrodynamical disks are nonlinearly unstable to the formation of vortices. Once formed, these vortices essentially survive forever. What happens in three dimensions? We show with pseudospectral simulations that in 3D a vortex in a short box forms and survives just as in 2D. But a vortex in a tall box is unstable and is destroyed. In our simulation, the unstable vortex decays into a transient turbulent-like state that transports angular momentum outward at a nearly constant rate for hundreds of orbital times. The 3D instability that destroys vortices is a generalization of the …
We report on the results of novel global high-resolution three-dimensional simulations of disk-planet interaction which incorporate simultaneously realistic radiation physics and the self-gravity of the gas, as well as allowing the planet to move. We find that thermodynamics and radiative physics have a remarkable effect on both migration and accretion of Jupiter mass planets. In simulations with radiative transfer adopting flux-limited diffusion, inward migration can be decreased by about 30% relative to the isothermal case, while in adiabatic runs migration nearly shuts off after a few tens …
Models of the accretion disks of Young Stellar Objects show that they should not be ionized at a few AU from the star, and thus not subject to the MHD turbulence believed to cause accretion. This has been suggested to create a 'Dead Zone' where accretion remains unexplained. Here we show that the existence of the Dead Zone self-consistently creates a density profile favorable to the Rossby Wave Instability of Lovelace et al. (1999). This instability will create and sustain Rossby vortices in the disk which could lead to enhanced planet formation.
We consider the formation and evolution of vortices in a hydrodynamic shearing-sheet model. The evolution is done numerically using a version of the ZEUS code. Consistent with earlier results, an injected vorticity field evolves into a set of long-lived vortices, each of which has a radial extent comparable to the local scale height. But we also find that the resulting velocity field has a positive shear stress, <Sigma delta v_r delta v_phi>. This effect appears only at high resolution. The transport, which decays with time as t^-1/2, arises primarily because the vortices drive compressive mot…
We present the results of high-resolution, three-dimensional (3D) hydrodynamic simulations of the dynamics and formation of coherent, long-lived vortices in stably-stratified protoplanetary disks. Tall, columnar vortices that extend vertically through many scale heights in the disk are unstable to small perturbations; such vortices cannot maintain vertical alignment over more than a couple scale heights and are ripped apart by the Keplerian shear. Short, finite-height vortices that extend only one scale height above and below the midplane are also unstable, but for a different reason: we have …
A linear stability analysis has been performed onto a self-gravitating magnetized gas disk bounded by external pressure. The resulting dispersion relation is fully explained by three kinds of instability: a Parker-type instability driven by self-gravity, usual Jeans gravitational instability and convection. In the direction parallel to the magnetic fields, the magnetic tension completely suppresses the convection. If the adiabatic index $γ$ is less than a certain critical value, the perturbations trigger the Parker as well as the Jeans instability in the disk. Consequently, the growth rate cur…
We investigate the problem of self-gravitating dust disk dynamics in a static state taking into account nonlinear effects. For this purpose Schrodinger-type equation including the mass conservation law is used for the whole description of hydrodynamic flows of self-gravitating dust. We have shown a purely hydrodynamic mechanism of ring formation in the radial direction by taking into account nonlinearity in the lowest order of expansion parameter, which determines an order of magnitude of flow.
Sgr A* is extra-ordinarily dim in all wavelengths requiring a very low accretion rate at the present time. However, at a radial distance of a fraction of a parsec from Sgr A*, two rings populated by young massive stars suggest a recent burst of star formation in a rather hostile environment. Here we explore two ways of creating such young stellar rings with a gaseous accretion disk: by self-gravity in a massive disk, and by capturing "old" low mass stars and growing them via gas accretion in a disk. The minimum disk mass is above 10^4 Msun for the first mechanism and is few tens times larger f…
We present 3D magnetohydrodynamic (MHD) numerical simulations of the evolution of self--gravitating and weakly magnetized disks with an adiabatic equation of state. Such disks are subject to the development of both the magnetorotational and gravitational instabilities, which transport angular momentum outward. As in previous studies, our hydrodynamical simulations show the growth of strong m=2 spiral structure. This spiral disturbance drives matter toward the central object and disappears when the Toomre parameter Q has increased well above unity. When a weak magnetic field is present as well,…
We investigate the possibility of mapping large-scale anti-cyclonic vortices, resulting from a global baroclinic instability, as pre-cursors of planet formation in proto-planetary disks with the planned Atacama Large Millimeter Array (ALMA). On the basis of three-dimensional radiative transfer simulations, images of a hydrodynamically calculated disk are derived which provide the basis for the simulation of ALMA. We find that ALMA will be able to trace the theoretically predicted large-scale anti-cyclonic vortex and will therefore allow testing of existing models of this very early stage of pl…
Gravity is scale free. Thus gravity may form similar structures in self-gravitating systems on different scales. Indeed, observations of the interstellar medium, spiral disks and cosmic structures, reveal similar characteristics. The structures in these systems are very lumpy and inhomogeneous. Moreover some of these structures do not seem to be of random nature, but obey certain power laws. Models of slightly dissipative self-gravitating disks show how such inhomogeneous structures can be maintained on the kpc-scale. The basic physical processes in these models are self-gravity, dissipation a…
Centimeter and meter sized solid particles in protoplanetary disks are trapped within long lived high pressure regions, creating opportunities for collapse into planetesimals and planetary embryos. We study the accumulations in the stable Lagrangian points of a giant planet, as well as in the Rossby vortices launched at the edges of the gap it carves. We employ the Pencil Code, tracing the solids with a large number of interacting Lagrangian particles, usually 100,000. For particles of 1 cm to 10 cm radii, gravitational collapse occurs in the Lagrangian points in less than 200 orbits. For 5 cm…
We carry out three-dimensional, high resolution (up to $1024^2\times 256$) hydrodynamic simulations of the evolution of vortices in vertically unstratified Keplerian disks using the shearing sheet approximation. The transient amplification of incompressible, linear amplitude leading waves (which has been proposed as a possible route to nonlinear hydrodynamical turbulence in disks) is used as one test of our algorithms; our methods accurately capture the predicted amplification, converges at second-order, and is free from aliasing. Waves expected to reach nonlinear amplitude at peak amplificati…
We analyze stability conditions of "Maclaurin flows" (self-gravitating, barotropic, two dimensional, stationary streams moving in closed loops around a point) by minimizing their energy, subject to fixing all the constants of the motion including mass and circulations. Necessary and sufficient conditions of stability are obtained when gyroscopic terms in the perturbed Lagrangian are zero. To illustrate and check the properties of this new energy principle, we have calculated the stability limits of an ordinary Maclaurin disk whose dynamical stability limits are known. Perturbations are in the …
To be a formation mechanism of such large-scale structures as giant molecular clouds (GMCs) and HI superclouds, the classical Parker instability driven by external gravity has to overcome three major obstacles: The convective motion accompanying the instability generates thin sheets than large condensations. The degree of density enhancement achieved by the instability is too low to make dense interstellar clouds. The time and the length scales of the instability are significantly longer and larger than the estimated formation time and the observed mean separation of the GMCs, respectively. Th…
We have mapped, for the first time, the full velocity extent of the water maser emission in NGC 3079. The largely north-south distribution of emission, aligned with a kpc-scale molecular disk, and the segregation of blue- and red-shifted emission on the sky are suggestive of a nearly edge-on molecular disk on pc-scales. Positions and line-of-sight velocities of blue- and red-shifted maser emission are consistent with a central mass of ~2 x 10^6 Msun enclosed within a radius of ~0.4 pc. The corresponding mean mass density of 10^6.8 Msun pc^-3 is suggestive of a central black hole, which is cons…
We investigate the susceptibility of gaseous, magnetized galactic disks to formation of self-gravitating condensations using two-dimensional, local models. We focus on two issues: (1) determining the threshold condition for gravitational runaway, taking into account nonlinear effects, and (2) distinguishing the magneto-Jeans instability (MJI) that arises under inner-galaxy rotation curves from the modified swing amplification (MSA) that arises under outer-galaxy rotation curves. For axisymmetric density fluctuations, instability is known to require a Toomre parameter Q<1. For nonaxisymmetric f…
We find that nuclear rings in barred galaxies can be subject to a new type of non-self-gravitational dynamical instability. The instability leads to the formation of gaseous molecular bars with pattern speeds which are substantially slower than speeds of the primary stellar bars. This spectacular decoupling of nuclear bars from the underlying gravitational potential is triggered but is not driven by the gas viscosity. We find that low-viscosity systems can spend a substantial period of time in a fully decoupled state, with the nuclear bar slowly tumbling in the gravitational field of the prima…
Both core accretion and disk instability appear to be required as formation mechanisms in order to explain the entire range of giant planets found in extrasolar planetary systems. Disk instability is based on the formation of clumps in a marginally-gravitationally unstable protoplanetary disk. These clumps can only be expected to contract and survive to become protoplanets if they are able to lose thermal energy through a combination of convection and radiative cooling. Here we present several new three dimensional, radiative hydrodynamics models of self-gravitating protoplanetary disks, where…
(abridged) We study the nonlinear evolution of the Rossby wave instability in thin disks using global 2D hydrodynamic simulations. The key questions we are addressing in this paper are: (1) What happens when the instability becomes nonlinear? Specifically, does it lead to vortex formation? (2) What is the detailed behavior of a vortex? (3) Can the instability sustain itself and can the vortex last a long time? Among various initial equilibria that we have examined, we generally find that there are three stages of the disk evolution: (1) The exponential growth of the initial small amplitude per…
Rotating, turbulent cosmic fluids are generally pervaded by coherent structures such as vortices and magnetic flux tubes. The formation of such structures is a robust property of rotating turbulence as has been confirmed in computer simulations and laboratory experiments. We defend here the notion that accretion disks share this feature of rotating cosmic bodies. In particular, we show that the intense shears of Keplerian flows do not inhibit the formation of vortices. Given suitable initial disturbances and high enough Reynolds numbers, long-lived vortices form in Keplerian shear flows and an…
We address the generalized thermodynamics and the collapse of a system of self-gravitating Langevin particles exhibiting anomalous diffusion in a space of dimension D. The equilibrium states correspond to polytropic distributions. The index n of the polytrope is related to the exponent of anomalous diffusion. We consider a high-friction limit and reduce the problem to the study of the nonlinear Smoluchowski-Poisson system. We show that the associated Lyapunov functional is the Tsallis free energy. We discuss in detail the equilibrium phase diagram of self-gravitating polytropes as a function o…
We have computed line profiles from self-gravitating toroids around black holes. The specific angular momentum of the toroids is assumed to be constant in space. The images of the toroids show peculiar feature in the rear side of the black holes. Concerning the line profiles, the red wing extends to the very small frequency region because the location of the inner edge is rather near the event horizon of the black hole and consequently the velocity of the inner edge of toroids can be faster than that of the Kepler disks.
