Wave propagation in protoplanetary disks: Formation of twin planets by ‘disk-brown dwarf’ collisions?

In this paper we derive a special linear non-vortical wave propagation solution in the shearing sheet, a model of a compressible two-dimensional fluid system with constant density, constant shear and constant Coriolis force, but without self-gravity. The linear analysis of the shearing sheet leads to a single differential equation for the azimuthal velocity perturbation. A detailed derivation of a special solution with a prescribed azimuthal wavenumber k is presented. More general wave solutions, eventually excited by large local ‘impacts’, can be derived by superimposing all k-modes. The special wave functions so obtained describe the formation of two independent spiral wave arms originating out of a ring-shaped structure. The motivation for this investigation lies in the fact that similar wave propagators can be excited by the transit of a solid or ‘clumpy’ object through a protoplanetary disk. We speculate that a disk-brown dwarf collision can produce in the disk a pair of two spiral density wave fragments triggering the rapid accretion of two giant planets by a gravitational shear instability simultaneously (Hypothesis of a mechanism for the production of giant planets in pairs).     

Density wave formation in differentially rotating disk galaxies: Hydrodynamic simulation of the linear regime

Most rapidly and differentially rotating disk galaxies, in which the sound speed (thermal velocity dispersion) is smaller than the orbital velocity, display graceful spiral patterns. Yet, over almost 240 yr after their discovery in M51 by Charles Messier, we still do not fully understand how they originate. In this first paper of a series, the dynamical behavior of a rotating galactic disk is examined numerically by a high-order Godunov hydrodynamic code. The code is implemented to simulate a two-dimensional flow driven by an internal Jeans gravitational instability in a nonresonant wave–“fluid” interaction in an infinitesimally thin disk composed of stars or gas clouds. A goal of this work is to explore the local and linear regimes of density wave formation, employed by Lin, Shu, Yuan and many others in connection with the problem of spiral pattern of rotationally supported galaxies, by means of computer-generated models and to compare those numerical results with the generalized fluid-dynamical wave theory. The focus is on a statistical analysis of time-evolution of density wave structures seen in the simulations. The leading role of collective processes in the formation of both the circular and spiral density waves (“heavy sound”) is emphasized. The main new result is that the disk evolution in the initial, quasilinear stage of the instability in our global simulations is fairly well described using the local approximation of the generalized wave theory. Certain applications of the simulation to actual gas-rich spiral galaxies are also explored.     

Origin of the Cartwheel Galaxy: Disk Instability?

The linear theory and N-body simulations are used to present a new, alternative model of the galaxy A0035-324 (the “Cartwheel”), which is the most striking example of the relatively small class of ring galaxies. The model is based on the gravitational Jeans-type instability of both axisymmetric (radial) and nonaxisymmetric (spiral) small-amplitude gravity perturbations (e.g., those produced by spontaneous disturbances) of a dynamically cold subsystem (identified as the gaseous component) of an isolated disk galaxy. The simplified model of a galaxy is used in which stars (and a dark matter, if it exists at all) do not participate in the disk collective oscillations and just form a background charge. In the theory presented here, a case for both purely radial solutions and purely spiral solutions to the equations of motion of an infinitesimally thin gaseous disk is made, which is associated with both a radial density wave and a dominant spiral density wave which propagate outwards creating a rough ring and a number of spiral arms. Through three-dimensional numerical simulation of a collisionless set of many particles, I associate these gravitationally unstable axisymmetric waves and nonaxisymmetric waves with growing clumps of matter which take on the appearance of a ring and spokes of mass blobs.     

Polygonal structures in a gaseous disk: Numerical simulations

The results of numerical simulations of a gaseous disk in the potential of a stellar spiral density wave are presented. The conditions under which straightened spiral arm segments (rows) form in the gas component are studied. These features of the spiral structure were identified in a series of works by A.D. Chernin with coauthors. Gas-dynamic simulations have been performed for a wide range of model parameters: the pitch angle of the spiral pattern, the amplitude of the stellar spiral density wave, the disk rotation speed, and the temperature of the gas component. The results of 2D- and 3D-disk simulations are compared. The rows in the numerical simulations are shown to be an essentially nonstationary phenomenon. A statistical analysis of the distribution of geometric parameters for spiral patterns with rows in the observed galaxies and the constructed hydrodynamic models shows good agreement. In particular, the numerical simulations and observations of galaxies give 〈α〉 }~ 120° for the average angles between straight segments.     

Does each spiral Galaxy house a slowly growing elliptical one?

N-body simulations performed by us suggest a mechanism for the generation of spiral waves in galaxies in which a mutual quasi-ellipsoidal rotating equilibrium configuration increasing slowly by accretion from the surrounding disk influences the density distribution of stars in the disk such as to give rise to a trailing spiral density wave. Interaction of the spiral wave with the viscous interstellar gas and mutual gravitation between the stars in the disk are believed to influence the form of the spiral. Nevertheless the basic assumption of conventional density wave theory according to which the mutual interaction of stars in the disk is essential for the formation of spirals may not be true.     

Detecting ionized bubbles in redshifted 21-cm maps

Linear transient phenomena induced by flow non-normality in thin self-gravitating astrophysical discs are studied using the shearing sheet approximation. The considered system includes two modes of perturbations: vortex and (spiral density) wave. It is shown that self-gravity considerably alters the vortex mode dynamics; its transient (swing) growth may be several orders of magnitude stronger than in the non-self-gravitating case and two to three times larger than the transient growth of the wave mode. Based on this finding, we comment on the role of vortex mode perturbations in a gravitoturbulent state. We also describe the linear coupling of the perturbation modes, caused by the differential character of disc rotation. The coupling is asymmetric: vortex mode perturbations are able to excite wave mode perturbations, but not vice versa. This asymmetric coupling lends additional significance to the vortex mode as a participant in spiral density waves and shock manifestations in astrophysical discs.     

Instabilities in a nonstationary model of self-gravitating disks. III. The phenomenon of lopsidedness and a comparison of perturbation modes

This is an examination of the gravitational instability of the major large-scale perturbation modes for a fixed value of the azimuthal wave number m = 1 in nonlinearly nonstationary disk models with isotropic and anisotropic velocity diagrams for the purpose of explaining the displacement of the nucleus away from the geometric center (lopsidedness) in spiral galaxies. Nonstationary analogs of the dispersion relations for these perturbation modes are obtained. Critical diagrams of the initial virial ratio are constructed from the rotation parameters for the models in each case. A comparative analysis is made of the instability growth rates for the major horizontal perturbation modes in terms of two models, and it is found that, on the average, the instability growth rate for the m = 1 mode with a radial wave number N = 3 almost always has a clear advantage relative to the other modes. An analysis of these results shows that if the initial total kinetic energy in an isotropic model is no more than 12.4% of the initial potential energy, then, regardless of the value of the rotation parameter Ω, an instability of the radial motions always occurs and causes the nucleus to shift away from the geometrical center. This instability is aperiodic when Ω = 0 and is oscillatory when Ω ≠ 0 . For the anisotropic model, this kind of structure involving the nucleus develops when the initial total kinetic energy in the model is no more than 30.6% of the initial potential energy.     

星系盘厚度效应的研究

在三维引力Poisson方程严格解基础上，探讨了有限厚星系盘基盘的动力学性质，并进一步讨论了盘的厚度效应对银河系所需晕质量的影响。研究了扰动盘的动力学性质，通过将扰动引力势Poisson方程的严格解与林家翘、徐遐生提出的自维持密度波理论相结合，建立了三维旋涡星系有限厚盘上密度波的色散关系。在此色散关系的基础上讨论了盘的局域稳定性，研究了旋涡星系旋臂的形态、三维盘状星系密度波的群速度。研究表明厚度是星系盘研究中不容忽略的重要参量。另外在有限厚盘星系密度波色散关系的基础上还探讨了一种确定星系厚度的新方法。     

On the Interaction of Spiral Density Waves with Stars near the Inner Lindblad Resonance in Galactic Disks

The interaction of a spiral wave with stars near the inner Lindblad resonance in a galactic disk has been investigated. The dispersion relation describing the behavior of the complex wave number of the spiral wave as a function of the distance to the resonance has been derived within the framework of a purely linear problem and in the leading orders of the epicyclic and WKB approximations. We also have improved the result of Mark (1971) concerning behavior of the amplitude of leading spiral wave near the resonance circle. We have studied the consequences following from the hypothesis that weak nonlinearity in a narrow resonance region changes the standard rule of bypassing the pole in the complex plane, known as the Landau–Lin bypass rule, to taking the corresponding principal value integral. By analogy with hydrodynamics, where such a problem arises when analyzing the resonant interaction of waves with shear flows, we expect that a small, but finite amplitude can lead to a modification of the bypass rule and, as a consequence, to the elimination of the effect of spiral wave absorption at the resonance and its reflection. We have shown that under some assumptions the presumed picture actually takes place, but the detailed situation looks quite unexpected: near the resonance the regions where stars cause wave attenuation alternate with the regions where the wave is amplified. At the same time, there is no wave absorption effect when integrated over the resonance region.     

旋涡星系颜色梯度的研究进展

旋涡星系的颜色梯度反映了其星族构成沿径向的分布,包含了星系恒星形成历史的信息.因此,对旋涡星系颜色梯度的研究有助于理解星系的形成和演化过程.大部分旋涡星系存在负的颜色梯度,其主要原因是旋涡星系存在星族梯度.颜色梯度与星系的面亮度之间存在内禀的相关,表明质量面密度在星系的形成和演化过程中具有重要作用.     

Spiral-Vortex Structure in the Gaseous Disks of Galaxies

General ideas, as well as experimental and theoretical efforts concerning the prediction and discovery of new structures in the disks of spiral galaxies – giant anticyclones - are reviewed. A crucial point is the development of a new method to restore the full vector velocity field of the galactic gas from the line-of-sight velocity field. This method can be used to get self-consistent solutions for the following problems: 1) determination of non-circular velocities associated with spiral-vortex structure; 2) determination of fundamental parameters of this structure: pattern speed, corotation radius, location of giant anticyclones; 3) refinement of galactic rotation curves taking into account regular non-circular motion in the spiral density wave, which makes it possible to build more accurate models of the mass distribution in the galaxy; 4) refinement of parameters of the rotating gaseous disk: inclination angle, center of rotation and position angle of the major dynamical axis, systematic velocity. The method is demonstrated using the restoration of the velocity field of the galaxy NGC 157 as an example. Results for this and some other spiral galaxies suggest that giant anticyclones are a universal property of galaxies with grand design structure.     

Global stability of disk-bulge systems: Spiral structure of disk galaxies

The spiral arms of disk galaxies are very sensitive to various morphological properties, such as, the gas content, the disk-to-bulge ratioetc. Here, the stability of self-gravitating annular disks surrounding the central rigid bulge component has been studied in order to explain the transition from the tight spiral arms in Sa galaxies to rather open patterns in Sc galaxies as the central amorphous component diminishes. Smooth spiral patterns are found associated with the dominant (or the fastest growing) modes of the system. When the disk-to-bulge mass ratio is small, a tight pattern results restricted to the inner regions of the disk. This pattern opens up and occupies larger disk areas as the disk component becomes comparable to the bulge. It is found here that the ‘explosive’ instabilities of the global density waves do not occur in the presence of a massive bulge. The growth-rates of the eigen-modes decrease as the disk-to-bulge mass ratio decreases. It is also found that unstable modes of the annular disk can be suppressed by increasing the thermal pressure sufficiently.     

Vorontsov-Velyaminov rows: Straight segments in the spiral arms of galaxies

The phenomenon of rows—straight features in the spiral patterns of galaxies, which was discovered by Vorontsov-Velyaminov, is investigated. The rows are not artifacts; in several cases, they outline regular spiral arms almost over their entire lengths. The galaxies M 101, M 51, and a number of more distant spirals are used as examples to demonstrate major geometrical and physical properties of these structures. It is shown that the row lengths increase nearly linearly with distance from the disk center, and that the angle between adjacent rows is almost always close to 2π/3. The galaxies with rows generally belong to moderate-luminosity Sbc-Sc systems with low rotational velocities, regular spiral patterns (Grand Design), and an H I content normal for these types of galaxies. Two types of rows are shown to exist, which differ in thickness and appear to be evolutionarily related. The formation mechanism of the rows should probably be sought in the peculiar behavior of the gas-compression wave in spiral density waves.     

The excitation of spiral density waves through turbulent fluctuations in accretion discs – I. WKBJ theory

We study and elucidate the mechanism of spiral density wave excitation in a differentially rotating flow with turbulence which could result from the magneto-rotational instability. We formulate a set of wave equations with sources that are only non-zero in the presence of turbulent fluctuations. We solve these in a shearing box domain, subject to the boundary conditions of periodicity in shearing coordinates, using a WKBJ method. It is found that, for a particular azimuthal wavelength, the wave excitation occurs through a sequence of regularly spaced swings during which the wave changes from leading to trailing form. This is a generic process that is expected to occur in shearing discs with turbulence. Trailing waves of equal amplitude propagating in opposite directions are produced, both of which produce an outward angular momentum flux that we give expressions for as functions of the disc parameters and azimuthal wavelength.
By solving the wave amplitude equations numerically, we justify the WKBJ approach for a Keplerian rotation law for all parameter regimes of interest. In order to quantify the wave excitation completely, the important wave source terms need to be specified. Assuming conditions of weak non-linearity, these can be identified and are associated with a quantity related to the potential vorticity, being the only survivors in the linear regime. Under the additional assumption that the source has a flat power spectrum at long azimuthal wavelengths, the optimal azimuthal wavelength produced is found to be determined solely by the WKBJ response and is estimated to be  2π H   , with H being the nominal disc scaleheight. In a following paper by Heinemann & Papaloizou, we perform direct three-dimensional simulations and compare results manifesting the wave excitation process and its source with the assumptions made and the theory developed here in detail, finding excellent agreement.     

On spiral structure formation in a galaxy with a bar-like nucleus

A new approach to the problem of the formation of galaxy spiral structures having a rotating bar-like nucleus is offered. The process of disk formation due to matter accretion onto the disk is considered in terms of the solution of the key problem on the motion of the matter element in the equatorial plane of the galaxy in the corotation resonance region. It is shown that in the vicinity of unstable libration points high-density regions are formed, which elongate with time following the separatrix shape and forming thereby spiral arms.     

Evolutionary processes in protoplanetary accretion disks: the propagation of axisymmetric shock waves

In this paper we investigate both the global and the local hydrodynamics of axisymmetric accretion disks around young stellar objects under the simultaneous action of viscosity, self-gravity and pressure forces. For simplicity, we take for the global model a polytropic equation of state, make the infinitely thin disk approximation and characterize the surface density and temperature profiles in the disk as power laws in the radial distance r from the protostar. We solve the problem of the general density profile of a Keplerian disk showing that self-gravity could not be an important factor for the fast formation of the rocky cores of giant gaseous planets in our solar system. Under the hypothesis that the unperturbed rotation curve of the disk is nearly Keplerian throughout the radial extent, we can estimate with our polytropic model a lower limit for the resulting masses M_d(r) of stable disks up to 100 AU. These masses are in the range of the so-called minimum mass solar nebular (_d/M_s ≈ 0.01–0.02).By adopting a simplified viscosity model, where the height-integrated turbulent dynamical viscosity ν is a function of the surface density σ like η ∝ σ^Γ, we derive in the local shearing sheet model linearized evolution equations for small density perturbations describing both a diffusion process and the propagation of acoustic density waves. We solve a special initial value problem and calculate the appropriate Green's function. The analytical solutions so obtained describe in the case Γ < 0 the successive formation of quasi-stationary ring-shaped density structures in a disk with a definite mode of maximum instability, whereas in the case Γ > Γ_c the density wave equation describes the propagation of an “overstable” ring-shaped acoustic density wavelet to the outer ranges of the accretion disk. Whereas the group velocity of the wave packet is subsonic, the phase velocities of individual wave crests in the wave packet are supersonic. The mode of maximum instability, the growth rate and the number of growing waves in the wavelet are controlled by Γ and α. Our present knowledge concerning turbulent viscosity in protoplanetary disks is not sufficient to decide whether or not the case Γ > Γ_c is realized.The suggested structuring processes in the linear theory should initiate in the non-linear regime the formation of narrow ring-shaped density shock waves moving through the protoplanetary disk. These non-linear waves could produce extremely spatially and temporally heterogeneous temperature regions in the disk. We speculate that ring-shaped density waves, excited by inner boundary conditions and which have dominated the disk's evolution at early times, are responsible both for the fast growth of dust to planetesimals and at least for the rapid accretion of the rocky cores of giant gaseous planets in the protoplanetary accretion disk (shock wave trigger hypothesis). We derive provisional scaling rules for planetary systems regarding the spacing of orbits as a function of the mass ratio of the protoplanetary disk to the protostar. However, further analytical work and linear as well as nonlinear numerical simulations of density waves excited by inner boundary conditions are needed to consolidate the results and speculations of our linear wave mechanics in the future.     

Inversions for axisymmetric galactic disks

We use two models for the distribution function to solve an inverse problem for axisymmetric disks. These systems may be considered - under certain assumptions - as galactic disks. In some cases the solutions of the resulting integral equations are simple, which allows the determination of the kinematic properties of self-consistent models for these systems. These properties for then = 1 Toomre disk are presented in this study.     

A hybrid scenario for gas giant planet formation in rings

The core-accretion mechanism for gas giant formation may be too slow to create all observed gas giant planets during reasonable gas disk lifetimes, but it has yet to be firmly established that the disk instability model can produce permanent bound gaseous protoplanets under realistic conditions. Based on our recent simulations of gravitational instabilities in disks around young stars, we suggest that, even if instabilities due to disk self-gravity do not produce gaseous protoplanets directly, they may create persistent dense rings that are conducive to accelerated growth of gas giants through core accretion. The rings occur at and near the boundary between stable and unstable regions of the disk and appear to be produced by resonances with discrete spiral modes on the unstable side.     

The effect of projection on the observed gas velocity fields in barred galaxies

The problem of determining the pattern of gas motions in the central regions of disk spiral galaxies is considered. Two fundamentally different cases—noncircular motions in the triaxial bar potential and motions in circular orbits but with orientation parameters different from those of the main disk—are shown to have similar observational manifestations in the line-of-sight velocity field of the gas. A reliable criterion is needed for the observational data to be properly interpreted. To find such a criterion, we analyze two-dimensional nonlinear hydrodynamic models of gas motions in barred disk galaxies. The gas line-of-sight velocity and surface brightness distributions in the plane of the sky are constructed for various inclinations of the galactic plane to the line of sight and bar orientation angles. We show that using models of circular motions for inclinations i>60° to analyze the velocity field can lead to the erroneous conclusions of a “tilted (polar) disk” at the galaxy center. However, it is possible to distinguish bars from tilted disks by comparing the mutual orientations of the photometric and dynamical axes. As an example, we consider the velocity field of the ionized gas in the galaxy NGC 972.