Global lopsided instability in a purely stellar galactic disc

It is shown that pure exponential discs in spiral galaxies are capable of supporting slowly varying discrete global lopsided modes, which can explain the observed features of lopsidedness in the stellar discs. Using linearized fluid dynamical equations with the softened self-gravity and pressure of the perturbation as the collective effect, we derive self-consistently a quadratic eigenvalue equation for the lopsided perturbation in the galactic disc. On solving this, we find that the ground-state mode shows the observed characteristics of the lopsidedness in a galactic disc, namely the fractional Fourier amplitude A ₁, increases smoothly with the radius. These lopsided patterns precess in the disc with a very slow pattern speed with no preferred sense of precession. We show that the lopsided modes in the stellar disc are long-lived because of a substantial reduction (approximately a factor of 10 compared to the local free precession rate) in the differential precession. The numerical solution of the equations shows that the ground-state lopsided modes are either very slowly precessing stationary normal mode oscillations of the disc or growing modes with a slow growth rate depending on the relative importance of the collective effect of the self-gravity. N -body simulations are performed to test the spontaneous growth of lopsidedness in a pure stellar disc. Both approaches are then compared and interpreted in terms of long-lived global   m = 1  instabilities, with almost zero pattern speed.     

Stability of power-law discs — II. The global spiral modes

This paper reports on the in-plane normal modes in the self-consistent and the cut-out power-law discs. Although the cut-out discs are remarkably stable to bisymmetric perturbations, they are very susceptible to one-armed modes. For this harmonic, there is no inner Lindblad resonance, thus removing a powerful stabilizing influence. A physical mechanism for the generation of the one-armed instabilities is put forward. Incoming trailing waves are reflected as leading waves at the inner cut-out, thus completing the feedback for the swing-amplifier. Growing three-armed and four-armed modes occur only at very low temperatures. However, neutral m  = 3 and m  = 4 modes are possible at higher temperatures for some discs. The rotation curve index β has a marked effect on stability. For all azimuthal wavenumbers, any unstable modes persist to higher temperatures and grow more vigorously if the rotation curve is rising (β < 0) than if the rotation curve is falling (β > 0). If the central regions or outer parts of the disc are carved out more abruptly, any instabilities become more virulent. The self-consistent power-law discs possess a number of unusual stability properties. There is no natural time-scale in the self-consistent disc. If a mode is admitted at some pattern speed and growth rate, then it must be present at all pattern speeds and growth rates. Our analysis — although falling short of a complete proof — suggests that such a two-dimensional continuum of non-axisymmetric modes does not occur and that the self-consistent power-law discs admit no global non-axisymmetric normal modes whatsoever. Without reflecting boundaries or cut-outs, there is no resonant cavity and no possibility of unstable growing modes. The self-consistent power-law discs certainly admit equi-angular spirals as neutral modes, together with a one-dimensional continuum of growing axisymmetric modes.     

Dynamical response to supernova-induced gas removal in spiral galaxies with dark matter halo

We investigate the dynamical response, in terms of disc size and rotation velocity, to mass loss by supernovae in the evolution of spiral galaxies. A thin baryonic disc having the Kuzmin density profile embedded in a spherical dark matter halo having a density profile proposed by Navarro, Frenk & White is considered. For the purpose of comparison, we also consider the homogeneous and   r ⁻¹  profiles for dark matter in a truncated spherical halo. Assuming for simplicity that the dark matter distribution is not affected by mass-loss from discs and the change of baryonic disc matter distribution is homologous, we evaluate the effects of dynamical response in the resulting discs. We found that the dynamical response only for an adiabatic approximation of mass-loss can simultaneously account for the rotation velocity and disc size as observed particularly in dwarf spiral galaxies, thus reproducing the Tully–Fisher relation and the size versus magnitude relation over the full range of magnitude. Furthermore, we found that the mean specific angular momentum in discs after the mass-loss becomes larger than that before the mass-loss, suggesting that the mass-loss would most likely occur from the central disc region where the specific angular momentum is low.     

The paradox of the scale-free discs

Scale-free discs have no preferred length or time-scale. The question has been raised whether such discs have a continuum of unstable linear modes or perhaps no unstable modes at all. We resolve this paradox by analysing the particular case of a gaseous, isentropic disc with a completely flat rotation curve (the Mestel disc) exactly . The heart of the matter is this: what are the correct boundary conditions to impose at the origin or central cusp? We argue that the linear stability problem is ill-posed and that similar ambiguities may afflict general disc models with power-law central cusps. From any finite radius, waves reach the origin after finite time but with logarithmically divergent phase. Instabilities exist, but their pattern speeds depend upon an undetermined phase with which waves are reflected from the origin. For any definite choice of this phase, there is an infinite but discrete set of growing modes. The ratio of growth rate to pattern speed is independent of the central phase. This ratio is derived in closed form for non-self-gravitating normal modes and is shown to agree with approximate results obtained from the shearing sheet in the short-wavelength limit. This provides the first exact, analytically solved stability analysis for a differentially rotating disc. For self-gravitating normal modes, the ratio of growth rate to pattern is found numerically by solving recurrence relations in Mellin-transform space.     

Formation of gas discs in merging galaxies

Observations indicate that much of the interstellar gas in merging galaxies may settle into extended gaseous discs. Here, I present simulations of disc formation in mergers of gas-rich galaxies. Up to half of the total gas settles into embedded discs; the most massive instances result from encounters in which both galaxies are inclined to the orbital plane. These discs are often warped, many have rather complex kinematics, and roughly a quarter have counter-rotating or otherwise decoupled central components. Discs typically grow from the inside out; infall from tidal tails may continue disc formation over long periods of time.     

The flattening and the orbital structure of early-type galaxies and collisionless N-body binary disc mergers

We use oblate axisymmetric dynamical models including dark haloes to determine the orbital structure of intermediate mass to massive early-type galaxies in the Coma galaxy cluster. We find a large variety of orbital compositions. Averaged over all sample galaxies the unordered stellar kinetic energy in the azimuthal and the radial direction are of the same order, but they can differ by up to 40 per cent in individual systems. In contrast, both for rotating and non-rotating galaxies the vertical kinetic energy is on average smaller than in the other two directions. This implies that even most of the rotating ellipticals are flattened by an anisotropy in the stellar velocity dispersions. Using three-integral axisymmetric toy models, we show that flattening by stellar anisotropy maximizes the entropy for a given density distribution. Collisionless disc merger remnants are radially anisotropic. The apparent lack of strong radial anisotropy in observed early-type galaxies implies that they may not have formed from mergers of discs unless the influence of dissipational processes was significant.     

Coupled galactic density-wave modes in a composite system of thin stellar and gaseous discs

A rotating disc galaxy is modelled as a composite system consisting of thin stellar and gaseous discs, which are described by a two-fluid modal formalism. The composite disc system is assumed to retain axisymmetry in the background equilibrium. General density-wave perturbations in the two discs are coupled through the mutual gravitational interaction. We study the basic properties of open and tight spiral density-wave modes in such a composite disc system. Within the Lindblad resonances, perturbation enhancements of surface mass density in stellar and gaseous discs are in phase; this is also true during the initial growth phase of density-wave perturbations. Outside the Lindblad resonances, there exists a possible spiral density-wave branch for which perturbation enhancements of surface mass density in stellar and gaseous discs are out of phase. We discuss implications of these results on the critical parameters for global star formation in barred and normal spiral galaxies and on magnetohydrodynamic density waves within the Lindblad resonances.     

Gas-driven evolution of stellar orbits in barred galaxies

We carry out a detailed orbit analysis of gravitational potentials selected at different times from an evolving self-consistent model galaxy consisting of a two-component disc (stars+gas) and a live halo. The results are compared with a pure stellar model, subject to nearly identical initial conditions, which are chosen so as to make the models develop a large-scale stellar bar. The bars are also subject to hose-pipe (buckling) instability which modifies the vertical structure of the disc. The diverging morphological evolution of both models is explained in terms of gas radial inflow, the resulting change in the gravitational potential at smaller radii, and the subsequent modification of the main families of orbits, both in and out of the disc plane.   We find that dynamical instabilities become milder in the presence of the gas component, and that the stability of planar and 3D stellar orbits is strongly affected by the related changes in the potential — both are destabilized, with the gas accumulation at the centre. This is reflected in the overall lower amplitude of the bar mode and in the substantial weakening of the bar, which appears to be a gradual process. The vertical buckling of the bar is much less pronounced and the characteristic peanut shape of the galactic bulge almost disappears when there is a substantial gas inflow towards the centre. Milder instability results in a smaller bulge, the basic parameters of which are in agreement with observations. We also find that the overall evolution in the model with a gas component is accelerated because of the larger central mass concentration and the resulting decrease in the characteristic dynamical time.     

Mass profiles and anisotropies of early-type galaxies

We discuss the problem of using stellar kinematics of early-type galaxies to constrain the orbital anisotropies and radial mass profiles of galaxies. We demonstrate that compressing the light distribution of a galaxy along the line of sight produces approximately the same signature in the line-of-sight velocity profiles as radial anisotropy. In particular, fitting spherically symmetric dynamical models to apparently round, isotropic face-on flattened galaxies leads to a spurious bias towards radial orbits in the models, especially if the galaxy has a weak face-on stellar disc. Such face-on stellar discs could plausibly be the cause of the radial anisotropy found in spherical models of intermediate luminosity ellipticals such as NGC 2434, 3379 and 6703.
In the light of this result, we use simple dynamical models to constrain the outer mass profiles of a sample of 18 round, early-type galaxies. The galaxies follow a Tully–Fisher relation parallel to that for spiral galaxies, but fainter by at least 0.8 mag ( I -band) for a given mass. The most luminous galaxies show clear evidence for the presence of a massive dark halo, but the case for dark haloes in fainter galaxies is more ambiguous. We discuss the observations that would be required to resolve this ambiguity.     

The formation and survival of discs in a ΛCDM universe

We study the formation of galaxies in a Λ cold dark matter (ΛCDM) universe using high-resolution hydrodynamical simulations with a multiphase treatment of gas, cooling and feedback, focusing on the formation of discs. Our simulations follow eight isolated haloes similar in mass to the Milky Way and extracted from a large cosmological simulation without restriction on spin parameter or merger history. This allows us to investigate how the final properties of the simulated galaxies correlate with the formation histories of their haloes. We find that, at   z = 0  , none of our galaxies contains a disc with more than 20 per cent of its total stellar mass. Four of the eight galaxies nevertheless have well-formed disc components, three have dominant spheroids and very small discs, and one is a spheroidal galaxy with no disc at all. The   z = 0  spheroids are made of old stars, while discs are younger and formed from the inside-out. Neither the existence of a disc at   z = 0  nor the final disc-to-total mass ratio seems to depend on the spin parameter of the halo. Discs are formed in haloes with spin parameters as low as 0.01 and as high as 0.05; galaxies with little or no disc component span the same range in spin parameter. Except for one of the simulated galaxies, all have significant discs at   z ≳ 2  , regardless of their   z = 0  morphologies. Major mergers and instabilities which arise when accreting cold gas is misaligned with the stellar disc trigger a transfer of mass from the discs to the spheroids. In some cases, discs are destroyed, while in others, they survive or reform. This suggests that the survival probability of discs depends on the particular formation history of each galaxy. A realistic ΛCDM model will clearly require weaker star formation at high redshift and later disc assembly than occurs in our models.     

A dynamical model for the extraplanar gas in spiral galaxies

Recent H  i observations reveal that the discs of spiral galaxies are surrounded by extended gaseous haloes. This extraplanar gas reaches large distances (several kiloparsecs) from the disc and shows peculiar kinematics (low rotation and inflow). We have modelled the extraplanar gas as a continuous flow of material from the disc of a spiral galaxy into its halo region. The output of our models is pseudo data cubes that can be directly compared to the H  i data. We have applied these models to two spiral galaxies (NGC 891 and NGC 2403) known to have a substantial amount of extraplanar gas. Our models are able to reproduce accurately the vertical distribution of extraplanar gas for an energy input corresponding to a small fraction (<4 per cent) of the energy released by supernovae. However, they fail in two important aspects: (1) they do not reproduce the right gradient in rotation velocity; (2) they predict a general outflow of the extraplanar gas, contrary to what is observed. We show that neither of these difficulties can be removed if clouds are ionized and invisible at 21 cm as they leave the disc but become visible at some point on their orbits. We speculate that these failures indicate the need for accreted material from the intergalactic medium that could provide the low angular momentum and inflow required.     

Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density which travels at a relevant radial group speed C _g. The wave energy surface density and the wave angular momentum surface density are related to by = and = m respectively, where is the angular frequency in an inertial frame of reference and the integer m , proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discussed.     

Central cusp caused by a supermassive black hole in axisymmetric models of elliptical galaxies

We use numerical simulations to investigate the cusp at the centre of elliptical galaxies caused by the slow growth of a supermassive black hole. We study this problem for axisymmetric models of galaxies with or without rotation. The numerical simulations are based on the 'perturbation particles' method, and use GRAPEs to compute the force arising from the cusp. We study the way in which the density cusp is affected by the initial flattening of the model, as well as the role played by initial rotation. The logarithmic slope of the density cusp is found to be very much insensitive to flattening; as a consequence, we deduce that tangential velocity anisotropy – which supports the flattening – is also of little influence on the final cusp. We investigate, via two different kinds of rotating models, the efficiency with which a rotation velocity component builds within the cusp. A cusp in rotation develops only for models where a net rotation component is initially present at high energy levels. The eventual observation of a central rotational velocity peak in elliptical galaxies has, therefore, some implications for the galaxy dynamical history.     

Large-scale galactic turbulence: can self-gravity drive the observed H i velocity dispersions?

Observations of turbulent velocity dispersions in the H  i component of galactic discs show a characteristic floor in galaxies with low star formation rates and within individual galaxies the dispersion profiles decline with radius. We carry out several high-resolution adaptive mesh simulations of gaseous discs embedded within dark matter haloes to explore the roles of cooling, star formation, feedback, shearing motions and baryon fraction in driving turbulent motions. In all simulations the disc slowly cools until gravitational and thermal instabilities give rise to a multiphase medium in which a large population of dense self-gravitating cold clouds are embedded within a warm gaseous phase that forms through shock heating. The diffuse gas is highly turbulent and is an outcome of large-scale driving of global non-axisymmetric modes as well as cloud–cloud tidal interactions and merging. At low star formation rates these processes alone can explain the observed H  i velocity dispersion profiles and the characteristic value of  ∼10 km s⁻¹  observed within a wide range of disc galaxies. Supernovae feedback creates a significant hot gaseous phase and is an important driver of turbulence in galaxies with a star formation rate per unit area  ≳10⁻³ M_⊙ yr⁻¹ kpc⁻²  .     

Numerical modelling of the vertical structure and dark halo parameters in disc galaxies

The non‐linear dynamics of bending instability and vertical structure of a galactic stellar disc embedded into a spherical halo are studied with N‐body numerical modelling. Development of the bending instability in stellar galactic disc is considered as the main factor that increases the disc thickness. Correlation between the disc vertical scale height and the halo‐to‐disc mass ratio is predicted from the simulations. The method of assessment of the spherical‐to‐disc mass ratio for edge‐on spiral galaxies with a small bulge is considered. Modelling of eight edge‐on galaxies: NGC 891, NGC 4738, NGC 5170, UGC 6080, UGC 7321, UGC 8286, UGC 9422 and UGC 9556 is performed. Parameters of stellar discs, dark haloes and bulges are estimated. The lower limit of the dark‐to‐luminous mass ratio in our galaxies is of the order of one within the limits of their stellar discs. The dark haloes dominate by mass in the galaxies with very thin stellar discs (NGC 5170, UGC 7321 and UGC 8286) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the origin of warps and the role of the intergalactic medium

There is still no consensus as to what causes galactic discs to become warped. Successful models should account for the frequent occurrence of warps in quite isolated galaxies, their amplitude as well as the observed azimuthal and vertical distributions of the H  i layer. Intergalactic accretion flows and intergalactic magnetic fields may bend the outer parts of spiral galaxies. In this paper we consider the viability of these non-gravitational torques to take the gas off the plane. We show that magnetically generated warps are clearly flawed because they would wrap up into a spiral in less than two or three galactic rotations. The inclusion of any magnetic diffusivity to dilute the wrapping effect causes the amplitude of the warp to damp. We also consider the observational consequences of the accretion of an intergalactic plane-parallel flow at infinity. We have computed the amplitude and warp asymmetry in the accretion model, for a disc embedded in a flattened dark matter halo, including self-consistently the contribution of the modes with azimuthal wavenumbers   m = 0  and   m = 1  . Since the m = 0 component, giving a U-shaped profile, is not negligible compared to the m = 1 component, this model predicts quite asymmetric warps, maximum gas displacements on the two sides in the ratio 3 : 2 for the preferred Galactic parameters, and the presence of a fraction ∼3.5 per cent of U-shaped warps, at least. The azimuthal dependence of the moment transfer by the ram pressure would produce a strong asymmetry in the thickness of the H  i layer and asymmetric density distributions in z , in conflict with observational data for the warp in our Galaxy and in external galaxies. The amount of accretion that is required to explain the Galactic warp would give gas scaleheights in the far outer disc that are too small. We conclude that accretion of a flow with no net angular momentum cannot be the main and only cause of warps.     

The onset of warps in Spitzer observations of edge-on spiral galaxies

We analyse warps in the nearby edge-on spiral galaxies observed in the Spitzer /Infrared Array Camera (IRAC) 4.5-μm band. In our sample of 24 galaxies, we find evidence of warp in 14 galaxies. We estimate the observed onset radii for the warps in a subsample of 10 galaxies. The dark matter distribution in each of these galaxies are calculated using the mass distribution derived from the observed light distribution and the observed rotation curves. The theoretical predictions of the onset radii for the warps are then derived by applying a self-consistent linear response theory to the obtained mass models for six galaxies with rotation curves in the literature. By comparing the observed onset radii to the theoretical ones, we find that discs with constant thickness can not explain the observations; moderately flaring discs are needed. The required flaring is consistent with the observations. Our analysis shows that the onset of warp is not symmetric in our sample of galaxies. We define a new quantity called the onset-asymmetry index and study its dependence on galaxy properties. The onset asymmetries in warps tend to be larger in galaxies with smaller disc scalelengths. We also define and quantify the global asymmetry in the stellar light distribution, that we call the edge-on asymmetry in edge-on galaxies. It is shown that in most cases the onset asymmetry in warp is actually anticorrelated with the measured edge-on asymmetry in our sample of edge-on galaxies and this could plausibly indicate that the surrounding dark matter distribution is asymmetric.     

Interface modes and their instabilities in accretion disc boundary layers

We study global non-axisymmetric oscillation modes trapped near the inner boundary of an accretion disc. Observations indicate that some of the quasi-periodic oscillations (QPOs) observed in the luminosities of accreting compact objects (neutron stars, black holes and white dwarfs) are produced in the innermost regions of accretion discs or boundary layers. Two simple models are considered in this paper. The magnetosphere–disc model consists of a thin Keplerian disc in contact with a uniformly rotating magnetosphere with and low plasma density, while the star–disc model involves a Keplerian disc terminated at the stellar atmosphere with high density and small density scaleheight. We find that the interface modes at the magnetosphere–disc boundary are generally unstable due to Rayleigh–Taylor and/or Kelvin–Helmholtz instabilities. However, differential rotation of the disc tends to suppress Rayleigh–Taylor instability, and a sufficiently high disc sound speed (or temperature) is needed to overcome this suppression and to attain net mode growth. On the other hand, Kelvin–Helmholtz instability may be active at low disc sound speeds. We also find that the interface modes trapped at the boundary between a thin disc and an unmagnetized star do not suffer Rayleigh–Taylor or Kelvin–Helmholtz instability, but can become unstable due to wave leakage to large disc radii and, for sufficiently steep disc density distributions, due to wave absorption at the corotation resonance in the disc. The non-axisymmetric interface modes studied in this paper may be relevant to the high-frequency QPOs observed in some X-ray binaries and in cataclysmic variables.     

Boxy/peanut 'bulges': comparing the structure of galaxies with the underlying families of periodic orbits

The vertical profiles of disc galaxies are built by the material trapped around stable periodic orbits, which form their 'skeletons'. Therefore, knowledge of the stability of the main families of periodic orbits in appropriate 3D models enables one to predict possible morphologies for edge-on disc galaxies. In a pilot survey we compare the orbital structures that lead to the appearance of 'peanut'- and 'X'-like features with the edge-on profiles of three disc galaxies (IC 2531, NGC 4013 and UGC 2048). The subtraction from the images of a model representing the axisymmetric component of the galaxies reveals the contribution of the non-axisymmetric terms. We find a direct correspondence between the orbital profiles of 3D bars in models and the observed main morphological features of the residuals. We also apply a simple unsharp masking technique in order to study the sharpest features of the images. Our basic conclusion is that the morphology of the boxy 'bulges' of these galaxies can be explained by considering disc material trapped around stable 3D periodic orbits. In most models, these building-block periodic orbits are bifurcated from the planar central family of a non-axisymmetric component, usually a bar, at low-order vertical resonances. In such a case, the boxy 'bulges' are parts of bars seen edge-on. For the three galaxies we study, the families associated with the 'peanut' or 'X'-shape morphology are probably bifurcations at the vertical 2/1 or 4/1 resonance.