Local stability of self-gravitating fluid disks made of two components in relative motion (original) (raw)

ON THE DYNAMICS AND EVOLUTION OF GRAVITATIONAL INSTABILITY-DOMINATED DISKS

The Astrophysical Journal, 2010

We derive the evolution equations describing a thin axisymmetric disk of gas and stars with an arbitrary rotation curve that is kept in a state of marginal gravitational instability and energy equilibrium due to the balance between energy released by accretion and energy lost due to decay of turbulence. Rather than adopt a parameterized α prescription, we instead use the condition of marginal gravitational instability to self-consistently determine the position-and time-dependent transport rates. We show that there is a steady-state configuration for disks dominated by gravitational instability, and that this steady state persists even when star formation is taken into account if the accretion rate is sufficiently large. For disks in this state we analytically determine the velocity dispersion, surface density, and rates of mass and angular momentum transport as a function of the gas mass fraction, the rotation curve, and the rate of external accretion onto the disk edge. We show that disks that are initially out of steady state will evolve into it on the viscous timescale of the disk, which is comparable to the orbital period if the accretion rate is high. Finally, we discuss the implications of these results for the structure of disks in a broad range of environments, including high redshift galaxies, the outer gaseous disks of local galaxies, and accretion disks around protostars.

Nonaxisymmetric instabilities in self-gravitating disks. II. Linear and quasi-linear analyses

Astrophysics and Space Science, 2014

We studied global nonaxisymmetric hydrodynamic instabilities in an extensive collection of hot, self-gravitating polytropic disk systems, systems that covered a wide expanse of the parameter space relevant to protostellar and protoplanetary systems. We examined equilibrium disk models varying three parameters: the ratio of the inner to outer equatorial radii, the ratio of star mass to disk mass, and the rotation law exponent q. We took the polytropic index n = 1.5 and examined the exponents q = 1.5 and 2, and the transitional one q = 1.75. For each of these sets of parameters, we examined models with inner to outer radius ratios from 0.1 to 0.75, and star mass to disk mass ratios from 0 to 10 3. We numerically calculated the growth rates and oscillation frequencies of low-order nonaxisymmetric disk modes, modes with azimuthal dependence ∝ e imφ. Low-m modes are found to dominate with the character and strength of instability strongly dependent on disk self-gravity. Representatives of each mode type are examined in detail, and torques and mass transport rates are calculated.

1 Gravitational Instabilities in Two-Component Galaxy Disks with Gas Dissipation

2016

Growth rates for gravitational instabilities in a thick disk of gas and stars are determined for a turbulent gas that dissipates on the local crossing time. The scale heights are derived from vertical equilibrium. The accuracy of the usual thickness correction, (1 + kH) −1 , is better than 6% in the growth rate when compared to exact integrations for the gravitational acceleration in the disk. Gas dissipation extends the instability to small scales, removing the minimum Jeans length. This makes infinitesimally thin disks unstable for all Toomre-Q values, and reasonably thick disks stable at high Q primarily because of thickness effects. The conventional gas+star threshold, Q tot , increases from ∼ 1 without dissipation to 2 or 3 when dissipation has a rate equal to the crossing rate over a perturbation scale. Observations of Q tot ∼ 2 − 3 and the presence of supersonic turbulence suggest that disks are unstable over a wide range of scales. Such instabilities drive spiral structure if there is shear and clumpy structure if shear is weak; they may dominate the generation of turbulence. Feedback regulation of Q tot is complex because the stellar component does not cool; the range of spiral strengths from multiple arm to flocculent galaxies suggests that feedback is weak. Gravitational instabilities may have a connection to star formation even when the star formation rate scales directly with the molecular mass because the instabilities return dispersed gas to molecular clouds and complete the cycle of cloud formation and destruction. The mass flow to dense clouds by instabilities can be 10 times larger than the star formation rate.

Gravitational Instabilities in Two-Component Galaxy Disks with Gas Dissipation

The Astrophysical Journal, 2011

Instabilities of Galactic Disks in the Presence of Star Formation

Mon Notic Roy Astron Soc, 2005

We discuss the stability of galactic disks in which the energy of interstellar clouds is gained in encounters with expanding supernova remnants and lost in inelastic collisions. Energy gain and loss processes introduce a phase difference between the pressure and density perturbations, making disks unstable on small scales for several recipes of star formation. This is in contrast to the standard stability analysis in which small scale perturbations are stabilized by pressure. In the limit of small scales the dispersion relation for the growth rate reduces to that of thermal instabilities in a fluid without gravity. If instabilities lead to star formation, then our results imply a secondary mode of star formation which operates on small scales and feeds on the existence of a primary mode on intermediate scales. This may be interpreted as a positive feedback. Further, the standard stability criterion on intermediate scales is significantly modified.

Instability of counter-rotating stellar disks

Journal of Physics: Conference Series

We use an N-body simulation, constructed using GADGET-2, to investigate an accretion flow onto an astrophysical disk that is in the opposite sense to the disk's rotation. In order to separate dynamics intrinsic to the counter-rotating flow from the impact of the flow onto the disk, we consider an initial condition in which the counter-rotating flow is in an annular region immediately exterior the main portion of the astrophysical disk. Such counter-rotating flows are seen in systems such as NGC 4826 (known as the "Evil Eye Galaxy"). Interaction between the rotating and counter-rotating components is due to two-stream instability in the boundary region. A multi-armed spiral density wave is excited in the astrophysical disk and a density distribution with high azimuthal mode number is excited in the counter-rotating flow. Density fluctuations in the counter-rotating flow aggregate into larger clumps and some of the material in the counter-rotating flow is scattered to large radii. Accretion flow processes such as this are increasingly seen to be of importance in the evolution of multi-component galactic disks.

Instabilities of galactic discs in the presence of star formation

Monthly Notices of the Royal Astronomical Society, 2005

We discuss the stability of galactic discs in which the energy of interstellar clouds is gained in encounters with expanding supernova (SN) remnants and lost in inelastic collisions. Energy gain and loss processes introduce a phase difference between the pressure and density perturbations, making discs unstable on small scales for several recipes of star formation. This is in contrast to the standard stability analysis in which small-scale perturbations are stabilized by pressure. In the limit of small scales, the dispersion relation for the growth rate reduces to that of thermal instabilities in a fluid without gravity. If instabilities lead to star formation, then our results imply a secondary mode of star formation that operates on small scales and feeds on the existence of a primary mode on intermediate scales. This may be interpreted as positive feedback. Further, the standard stability criterion on intermediate scales is significantly modified.

Stability of general-relativistic accretion disks

Physical Review D, 2011

Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core-collapse of massive stars. We explore the stability of such disks against runaway and non-axisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the THOR code. We model the disk matter using the ideal fluid approximation with a Gamma\GammaGamma-law equation of state with Gamma=4/3\Gamma=4/3Gamma=4/3. We explore three disk models around non-rotating black holes with disk-to-black hole mass ratios of 0.24, 0.17 and 0.11. Due to metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable non-axisymmetric modes on a dynamical timescale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the non-axisymmetric mode with azimuthal number m = 1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m = 1 mode in some cases. Overall, our simulations show that the properties of the unstable non-axisymmetric modes in our disk models are qualitatively similar to those in Newtonian theory.

On the mechanism of self gravitating Rossby interfacial waves in proto-stellar accretion discs

Geophysical & Astrophysical Fluid Dynamics, 2016

The dynamical response of edge waves under the influence of self-gravity is examined in an idealized two-dimensional model of a proto-stellar disc, characterized in steady state as a rotating vertically infinite cylinder of fluid with constant density except for a single density interface at some radius r 0. The fluid in basic state is prescribed to rotate with a Keplerian profile Ω k (r) ∼ r −3/2 modified by some additional azimuthal sheared flow. A linear analysis shows that there are two azimuthally propagating edge waves, kin to the familiar Rossby waves and surface gravity waves in terrestrial studies, which move opposite to one another with respect to the local basic state rotation rate at the interface. Instability only occurs if the radial pressure gradient is opposite to that of the density jump (unstably stratified) where self-gravity acts as a wave stabilizer irrespective of the stratification of the system. The propagation properties of the waves are discussed in detail in the language of vorticity edge waves. The roles of both Boussinesq and non-Boussinesq effects upon the stability and propagation of these waves with and without the inclusion of self-gravity are then quantified. The dynamics involved with self-gravity non-Boussinesq effect is shown to be a source of vorticity production where there is a jump in the basic state density In addition, self-gravity also alters the dynamics via the radial main pressure gradient, which is a Boussinesq effect. Further applications of these mechanical insights are presented in the conclusion including the ways in which multiple density jumps or gaps may or may not be stable.

Local stability of self-gravitating fluid disks made of two components in relative motion (original) (raw)

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