Self-gravitating warped discs around supermassive black holes

We consider warped equilibrium configurations for stellar and gaseous discs in the Keplerian force field of a supermassive black hole, assuming that the self-gravity of the disc provides the only acting torques. Modelling the disc as a collection of concentric circular rings and computing the torques in the non-linear regime, we show that stable, strongly warped precessing equilibria are possible. These solutions exist for a wide range of disc-to-black-hole mass ratios   M _d/ M _bh  , can span large warp angles of up to  ±∼120°  , have inner and outer boundaries, and extend over a radial range of a factor of typically two to four. These equilibrium configurations obey a scaling relation such that in good approximation     where     is the (retrograde) precession frequency and Ω is a characteristic orbital frequency in the disc. Stability was determined using linear perturbation theory and, in a few cases, confirmed by numerical integration of the equations of motion. Most of the precessing equilibria are found to be stable, but some are unstable. The main result of this study is that highly warped discs near black holes can persist for long times without any persistent forcing other than by their self-gravity. The possible relevance of this to galactic nuclei is briefly discussed.     

Lopsided galaxies: the case of NGC 891

It has been known for a long time that a large fraction of disc galaxies are lopsided. We simulate three different mechanisms that can induce lopsidedness: flyby interactions, gas accretion from cosmological filaments and ram pressure from the intergalactic medium. Comparing the morphologies, H  i spectrum, kinematics and   m = 1  Fourier components, we find that all of these mechanisms can induce lopsidedness in galaxies, although in different degrees and with observable consequences. The time-scale over which lopsidedness persists suggests that flybys can contribute to ∼20 per cent of lopsided galaxies. We focus our detailed comparison on the case of NGC 891, a lopsided, edge-on galaxy with a nearby companion (UGC 1807). We find that the main properties of NGC 891 (morphology, H  i spectrum, rotation curve, existence of a gaseous filament pointing towards UGC 1807) favour a flyby event for the origin of lopsidedness in this galaxy.     

Global m= 1 instabilities and lopsidedness in disc galaxies

Lopsidedness is common in spiral galaxies. Often, there is no obvious external cause, such as an interaction with a nearby galaxy, for such features. Alternatively, the lopsidedness may have an internal cause, such as a dynamical instability. In order to explore this idea, we have developed a computer code that searches for self-consistent perturbations in razor-thin disc galaxies and performed a thorough mode-analysis of a suite of dynamical models for disc galaxies embedded in an inert dark matter halo with varying amounts of rotation and radial anisotropy.
Models with two equal-mass counter-rotating discs and fully rotating models both show growing lopsided modes. For the counter-rotating models, this is the well-known counter-rotating instability, becoming weaker as the net rotation increases. The m = 1 mode of the maximally rotating models, on the other hand, becomes stronger with increasing net rotation. This rotating m = 1 mode is reminiscent of the eccentricity instability in near-Keplerian discs.
To unravel the physical origin of these two different m = 1 instabilities, we studied the individual stellar orbits in the perturbed potential and found that the presence of the perturbation gives rise to a very rich orbital behaviour. In the linear regime, both instabilities are supported by aligned loop orbits. In the non-linear regime, other orbit families exist that can help support the modes. In terms of density waves, the counter-rotating m = 1 mode is due to a purely growing Jeans-type instability. The rotating m = 1 mode, on the other hand, grows as a result of the swing amplifier working inside the resonance cavity that extends from the disc centre out to the radius where non-rotating waves are stabilized by the model's outwardly rising Q profile.     

Gravitational loss-cone instability in stellar systems with retrograde orbit precession

We study spherical and disc clusters in a near-Keplerian potential of galactic centres or massive black holes. In such a potential orbit precession is commonly retrograde, that is, the direction of the orbit precession is opposite to the orbital motion. It is assumed that stellar systems consist of nearly-radial orbits. We show that if there is a loss-cone at low angular momentum (e.g. due to consumption of stars by a black hole), an instability similar to loss-cone instability in plasma may occur. The gravitational loss-cone instability is expected to enhance black hole feeding rates. For spherical systems, the instability is possible for the number of spherical harmonics   l ≥ 3  . If there is some amount of counter-rotating stars in flattened systems, they generally exhibit the instability independent of azimuthal number m . The results are compared with those obtained recently by Tremaine for distribution functions monotonically increasing with angular momentum.
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems.     

Self-consistent response of a galactic disc to vertical perturbations

We study the self-consistent, linear response of a galactic disc to vertical perturbations, as induced, say, by a tidal interaction. We calculate the self-gravitational potential corresponding to a non-axisymmetric, self-consistent density response of the disc using the Green's function method. The response potential is shown to oppose the perturbation potential because the self-gravity of the disc resists the imposed potential, and this resistance is stronger in the inner parts of a galactic disc. For the   m = 1  azimuthal wavenumber, the disc response opposes the imposed perturbation up to a radius that spans a range of 4–6 disc scalelengths, so that the disc shows a net warp only beyond this region. This physically explains the well known but so far unexplained observation that warps typically set in beyond this range of radii. We show that the inclusion of a dark matter halo in the calculation only marginally changes (by ∼10 per cent) the radius for the onset of warps. For perturbations with higher azimuthal wavenumbers, the net signature of the vertical perturbations can only be seen at larger radii – for example, beyond 7 exponential disc scalelengths for   m = 10  . Also, for the high- m cases, the magnitude of the negative disc response due to the disc self-gravity is much smaller. This is shown to result in corrugations of the mid-plane density, which explains the puzzling scalloping with   m = 10  detected in H  i in the outermost regions ∼30 kpc in the Galaxy.     

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.     

Gauss's method for secular dynamics, softened

We show that the algorithm proposed by Gauss to compute the secular evolution of gravitationally interacting Keplerian rings extends naturally to softened gravitational interactions. The resulting tool is ideal for the study of the secular dynamical evolution of nearly Keplerian systems such as stellar clusters surrounding black holes in galactic nuclei, cometary clouds or planetesimal discs. We illustrate its accuracy, efficiency and versatility on a variety of configurations. In particular, we examine a secularly unstable system of counterrotating discs, and follow the unfolding and saturation of the instability into a global, uniformly precessing, lopsided  ( m = 1)  mode.     

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)     

Phase-space density constraints on the formation of bulges from discs

The colours of stellar bulges and of inner stellar discs are comparable, and consistent with rather similar mean metallicities and ages. Indeed, the mean chemical abundances of the Milky Way bulge and old disc are approximately equal. Further, the scalelengths of discs and bulges are correlated. These observations imply a close relationship between discs and bulges, and may support models in which stellar bulges form from stellar discs. The present paper discusses constraints on this scenario from the stellar phase-space density of bulges and of discs. Phase-space density cannot increase in the absence of collisional processes. We show here that the maximum phase-space density of galactic bulges is higher than that of inner discs, arguing that instabilities of purely stellar discs cannot form bulges. Rather, the high densities of bulges probably reflect gaseous dissipation. Gas inflow from the disc would complicate the interpretation of the similarities in stellar colours between discs and bulges. Gas inflow from the stellar halo, if one exists, may be favoured on angular momentum grounds, but this means of formation of the bulge would provide no explanation for the relationships between disc and bulge in any one galaxy. At least in the Milky Way, the metallicity distribution of the bulge is not consistent with the bulge being built up from the dense regions of accreted satellite galaxies and/or globular clusters.     

Vertical distribution of Galactic disc stars and gas constrained by a molecular cloud complex

We investigate the dynamical effects of a molecular cloud complex with a mass ∼ 10⁷ M_⊙ and a size ∼ a few 100 pc on the vertical distribution of stars and atomic hydrogen gas in a spiral galactic disc. Such massive complexes have now been observed in a number of spiral galaxies. The extended mass distribution in a complex, with an average mass density 6 times higher than the Oort limit, is shown to dominate the local gravitational field. This results in a significant redistribution or clustering of the surrounding disc components towards the mid-plane, with a resulting decrease in their vertical scaleheights.
The modified, self-consistent stellar density distribution is obtained by solving the combined Poisson equation and the force equation along the z -direction for an isothermal stellar disc on which the complex is imposed. The effect of the complex is strongest at its centre, where the stellar mid-plane density increases by a factor of 2.6 and the vertical scaleheight decreases by a factor of 3.4 compared with the undisturbed stellar disc. A surprising result is the large radial distance of ∼ 500 pc from the complex centre over which the complex influences the disc; this is due to the extended mass distribution in a complex. The complex has a comparable effect on the vertical distribution of the atomic hydrogen gas in the galactic disc. This 'pinching' or constraining effect should be detectable in the nearby spiral galaxies, as for example has been done for NGC 2403 by Sicking. Thus the gravitational field of a complex results in local corrugations of the stellar and H  i vertical scaleheights, and the galactic disc potential is highly non-uniform on scales of the intercomplex separation of ∼ 1 kpc.     

The kinematics of lopsided galaxies

Lopsidedness is a common feature in galaxies, both in the distribution of light and in the kinematics. We investigate the kinematics of a model for lopsided galaxies that consists of a disc lying off-centre in a dark halo, and circling around the halo centre. We search for families of stable, closed, non-crossing orbits, and assume that gas in our galaxies moves on these orbits. Several of our models show strong lopsided gas kinematics, especially those in which the disc spins around its axis in a retrograde sense compared with its motion around the halo centre. We are able to reproduce the H  i velocity map of the kinematically lopsided galaxy NGC 4395.
The lopsidedness in our models is most pronounced in the models where the halo provides a relatively large fraction of the total mass at small radii. This may explain why the gas shows lopsidedness more frequently in late-type galaxies, which are dominated by dark matter. Surfaces of section show large regions of irregular orbits in the models where the halo density is low. This may indicate that these models are unstable.     

Time evolution of galactic warps in prolate haloes

A recent observation with the Hipparcos satellite and some numerical simulations imply that the interaction between an oblate halo and a disc is inappropriate for the persistence of galactic warps. Following on from this , we have compared the time evolution of galactic warps in a prolate halo with that in an oblate halo. The haloes were approximated as fixed potentials, while the discs were represented by N -body particles. We have found that the warping in the oblate halo continues to wind up, and finally disappears. On the other hand, for the prolate halo model, the precession rate of the outer disc increases when the precession of the outer disc recedes from that of the inner disc, and vice versa. Consequently, the warping in the prolate halo persisted to the end of the simulation by retaining the alignment of the line of nodes of the warped disc. Therefore, our results suggest that prolate haloes could sustain galactic warps. The physical mechanism of the persistence of warp is discussed on the basis of the torque between a halo and a disc and that between the inner and outer regions of the disc.     

Dynamical stability and evolution of the discs of Sc galaxies

We examine the local stability of galactic discs against axisymmetric density perturbations with special attention to the different dynamics of the stellar and gaseous components. In particular, the discs of the Milky Way and of NGC 6946 are studied. The Milky Way is shown to be stable, whereas the inner parts of NGC 6946, a typical Sc galaxy from the Kennicutt sample, are dynamically unstable. The ensuing dynamical evolution of the composite disc is studied by numerical simulations. The evolution is so fierce that the stellar disc heats up dynamically on a short time-scale to such a high degree, which seems to contradict the morphological appearance of the galaxy. The star formation rate required to cool the disc dynamically is estimated. Even if the star formation rate in NGC 6946 is at present high enough to meet this requirement, it is argued that the discs of Sc galaxies cannot sustain such a high star formation rate for extended periods.     

Origin of disc lopsidedness in the Eridanus group of galaxies

The H  i surface density maps for a sample of 18 galaxies in the Eridanus group are Fourier analysed. This analysis gives the radial variation of the lopsidedness in the H  i spatial distribution. The lopsidedness is quantified by the Fourier amplitude A ₁ of the m = 1 component normalized to the average value. It is also shown that in the radial region where the stellar disc and H  i overlap, their A ₁ coefficients are comparable. All the galaxies studied show significant lopsidedness in H  i . The mean value of A ₁ in the inner regions of the galaxies (1.5–2.5 scalelengths) is ≥ 0.2. This value of A ₁ is twice the average value seen in the field galaxies. Also, the lopsidedness is found to be smaller for late-type galaxies; this is opposite to the trend seen in the field galaxies. These two results indicate a different physical origin for disc lopsidedness in galaxies in a group environment compared to the field galaxies. Further, a large fraction (∼30 per cent) shows a higher degree of lopsidedness ( A ₁≥ 0.3). It is also seen that the disc lopsidedness increases with the radius as demonstrated in earlier studies, but over a radial range that is two times larger than done in the previous studies. The average lopsidedness of the halo potential is estimated to be ∼10 per cent, assuming that the lopsidedness in H  i disc is due to its response to the halo asymmetry.     

Nuclear stellar discs in early-type galaxies — II. Photometric properties

Hubble Space Telescope images of two early-type galaxies harbouring both nuclear and outer stellar discs are studied in detail. By means of a photometric decomposition, the images of NGC 4342 and 4570 are analysed and the photometric properties of the nuclear discs investigated. We find a continuity of properties in the parameter space defined by the central surface brightness μ₀ and the scalelength R _d of discs in spirals, S0s and embedded discs in ellipticals, in the sense that the nuclear discs extend the observed disc properties even further towards smaller scalelengths and brighter central surface brightnesses. When including the nuclear discs, disc properties span more than four orders of magnitude in both scalelength and central surface brightness. The nuclear discs studied here are the smallest and brightest stellar discs known, and as such, they are as extreme in their photometric properties as Malin I, when compared with typical galactic discs that obey Freeman's law. We discuss a possible formation scenario in which the double-disc structure observed in these galaxies has been shaped by now dissolved bars. Based on the fact that the black holes known to exist in some of these galaxies have masses comparable to those of the nuclear discs, we explore a possible link between the black holes and the nuclear discs.     

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  .     

Period changes in the pulsating extreme helium stars V652 Her and BX Cir

A new statement of the eigenvalue problem of studying small perturbations in arbitrary integrable self-gravitating systems is presented. An example of such a system, a 2D stellar disc, is considered in detail. The theory, based on the general equation for disc eigenmodes, reveals mechanisms for the formation and growth of global galactic structures. This new point of view specifies the limits of the unified theory of bar-like and spiral modes that was based on the assumption that global galactic structures could be understood in terms of low-frequency disc modes.     

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.