Numerical simulations of interacting gas-rich barred galaxies: vertical impact of small companions

We investigate the dynamical effects of an interaction between an initially barred galaxy and a small spherical companion using an N -body/smoothed-particle-hydrodynamics algorithm. In the models described here the small companion passes through the disc of the larger galaxy nearly perpendicular to its plane. The impact positions and times are varied with respect to the phase of the bar and the dynamical evolution of the disc.
The interactions produce expanding ring structures, offset bars, spokes and other asymmetries in the stars and gas. These characteristic signatures of the interaction are present in the disc for about 1 Gyr. We find that in some cases it is possible to destroy the bar while keeping the disc structure. In general, the central impacts cause larger damage to the bar and the disc than the peripheral ones. The interaction tends to accelerate the transition from a strongly-barred galaxy to a weakly- or non-barred galaxy. The final disc morphology is determined more by the impact position relative to the bar rather than the impact time.     

Bar-induced evolution of dark matter cusps

The evolution of a stellar bar transforms not only the galactic disc, but also the host dark matter halo. We present high-resolution, fully self-consistent N -body simulations that clearly demonstrate that dark matter halo central density cusps flatten as the bar torques the halo. This effect is independent of the bar formation mode and occurs even for rather short bars. The halo and bar evolution is mediated by resonant interactions between orbits in the halo and the bar pattern speed, as predicted by linear Hamiltonian perturbation theory. The bar lengthens and slows as it loses angular momentum, a process that occurs even in rather warm discs. We demonstrate that the bar and halo response can be critically underestimated for experiments that are unable to resolve the relevant resonant dynamics; this occurs when the phase space in the resonant region is undersampled or plagued by noise.     

Evolution and destruction of bars

We summarize here some ongoing work by our group on the formation and evolution of barred galaxies. We first discuss the evolution of bars in isolated disc galaxies. Then we address the problem of bar destruction during interactions and mergers. Finally we describe work on generation and regeneration of bars in interactions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Model-based pattern speed estimates for 38 barred galaxies

We have modelled 38 barred galaxies by using near-infrared and optical data from the Ohio State University Bright Spiral Galaxy Survey. We constructed the gravitational potentials of the galaxies from H -band photometry, assuming a constant mass-to-light ratio. The halo component we choose corresponds to the so-called universal rotation curve. In each case, we used the response of gaseous and stellar particle disc to rigidly rotating potential to determine the pattern speed.
We find that the pattern speed of the bar depends roughly on the morphological type. The average value of corotation resonance radius to bar radius,     , increases from 1.15 ± 0.25 in types SB0/a–SBab to 1.44 ± 0.29 in SBb and 1.82 ± 0.63 in SBbc–SBc. Within the error estimates for the pattern speed and bar radius, all galaxies of type SBab or earlier have a fast bar     , whereas the bars in later type galaxies include both fast and slow rotators. Of 16 later type galaxies with a nominal value of     , there are five cases, where the fast-rotating bar is ruled out by the adopted error estimates.
We also study the correlation between the parameter     and other galactic properties. The clearest correlation is with the bar size: the slowest bars are also the shortest bars when compared to the galaxy size. A weaker correlation is seen with bar strength in a sense that slow bars tend to be weaker. These correlations leave room for a possibility that the determined pattern speed in many galaxies corresponds to actually that of the spiral, which rotates more slowly than the bar. No clear correlation is seen with either the galaxy luminosity or the colour.     

The pattern speed of the bar in NGC 4596

The pattern speed is a defining parameter of any barred galaxy. A large number of model-dependent techniques have therefore been developed to derive the pattern speed. However, the only model-independent technique for measuring this quantity – the Tremaine–Weinberg method – has hitherto been applied to just one case, the SB0 galaxy NGC 936. In this paper, we apply the technique to a second system, the SBa galaxy NGC 4596. The resulting estimate for the pattern speed is Ω_p=52±13 km s⁻¹ kpc⁻¹. This result is corroborated by a spectrum obtained along the major axis of the bar in this system. The corotation radius associated with this pattern speed lies just beyond the end of the bar indicating a fast bar. Combining the bar major-axis spectra with data obtained from a Hubble Space Telescope WFPC2 image, we also find strong evidence for a nuclear disc.     

Rotational mixing in early-type main-sequence stars

We present N -body simulations of galaxy groups embedded in a common halo of matter. We study the influence of the different initial conditions upon the evolution of the group and show that denser configurations evolve faster, as expected. We then concentrate on the influence of the initial radial density profile of the common halo and of the galaxy distribution. We select two kinds of density distributions, a singular profile (modelled by a Hernquist distribution) and a profile with a flat core (modelled by a Plummer sphere). In all cases we witness the formation of a central massive object owing to mergings of individual galaxies and to accretion of stripped material, but both its formation history and its properties depend heavily on the initial distribution. In Hernquist models the formation is caused by a 'burst' of mergings in the inner parts, owing to the large initial concentration of galaxies in the centre. The merging rate is much slower in the initial phases of the evolution of a Plummer distribution, where the contribution of accretion to the formation of the central object is much more important. The central objects formed within Plummer distributions have projected density profiles which are not in agreement with the radial profiles of observed brightest cluster members, unless the percentage of mass in the common halo is small. In contrast, the central object formed in initially cusped models has projected radial profiles in very good agreement with those of brightest cluster members, sometimes also showing luminosity excess over the r ^1/4 law in the outer parts, as is observed in cD galaxies.     

Dynamical Evolution of Barred Galaxies

Angular momentum redistribution within barred galaxies drives their dynamical evolution. Angular momentum is emitted mainly by near-resonant material in the bar region and absorbed by resonant material mainly in the outer disc and in the halo. This exchange determines the strength of the bar, the decrease of its pattern speed, as well as its morphology. If the galaxy has also a gaseous component and/or a companion or satellite, then these also take part in the angular momentum exchange. During the evolution a bar structure forms in the inner parts of the halo as well. This bar is shorter and fatter than the disc bar and stays so all through the simulation, although its length grows considerably with time. Viewed edge-on, the bar in the disc component acquires a boxy or peanut shape. I describe the families of periodic orbits that explain such structures and review the observations showing that boxy/peanut ‘bulges’ are in fact just bars seen edge-on.     

Formation of giant low surface brightness galaxies through disc instability

It is shown that the giant low surface brightness galaxies (GLSBs), characterized by a large but diffuse disc component, can result from ordinary spiral galaxies through dynamical evolution. Numerical simulations indicate that the formation of a bar in a gravitationally unstable disc with high surface density induces non-circular motions and radial mixing of disc matter, leading to the flattening of the disc density profile. The resulting decrease in the disc central surface brightness is ∼1.5 magnitude, while the disc scalelength is nearly doubled, transforming a typical high surface brightness galaxy to a GSLB. This scenario seems promising especially for the GSLBs possessing a significant bulge, which are difficult to incorporate into the traditional Hubble sequence. Namely, because this disc transmutation can operate even if a moderate bulge component exists, the GSLBs with a bulge are argued to have resulted from the high surface brightness galaxies which had already possessed a bulge. The current picture naturally explains other observed characteristics of the GSLBs as well, including the propensity for having grand-design spiral arms and a bar, a high incidence of active nuclei, and galaxy environments.     

Orbital dynamics of three-dimensional bars – II. Investigation of the parameter space

We investigate the orbital structure in a class of three-dimensional (3D) models of barred galaxies. We consider different values of the pattern speed, of the strength of the bar and of the parameters of the central bulge of the galactic model. The morphology of the stable orbits in the bar region is associated with the degree of folding of the x1 characteristic. This folding is larger for lower values of the pattern speed. The elongation of rectangular-like orbits belonging to x1 and to x1-originated families depends mainly on the pattern speed. A detailed investigation of the trees of bifurcating families in the various models shows that major building blocks of 3D bars can be supplied by families initially introduced as unstable in the system, but becoming stable at another energy interval. In some models without radial and vertical 2:1 resonances we find, except for the x1 and x1-originated families, also families related to the z -axis orbits, which support the bar. Bifurcations of the x2 family can build a secondary 3D bar along the minor axis of the main bar. This is favoured in the slowly rotating bar case.     

A bar in the inner halo of barred galaxies – I. Structure and kinematics of a representative model

N -body simulations argue that the inner haloes of barred galaxies should not be spherical, nor even axisymmetric, but triaxial. The departure from sphericity is the strongest near the centre and decreases outwards; typical axial ratios for the innermost parts are of the order of 0.8. The halo shape is prolate-like in the inner parts up to a certain radius and then turns to oblate-like. I call this inner halo structure the 'halo bar' and analyse here in depth its structure and kinematics in a representative model. It is always considerably shorter than the disc bar. It lags the disc bar by only a few degrees at all radii and the difference between the two bar phases increases with distance from the centre. The two bars turn with roughly the same pattern speed. This means that the halo bar is a slow bar, since its corotation radius is much larger than its length. The bisymmetric component in the halo continues well outside the halo bar in the form of an open spiral, trailing behind the disc bar. The inner parts of the halo display some mean rotation in the same sense as the disc rotation. This is more important for particles nearer to the equatorial plane and decreases with increasing distance from it, but is always much smaller than the disc rotation.     

Star formation and chemical evolution of damped Lyman α systems

In this paper, we investigate the star formation and chemical evolution of damped Lyman α systems (DLAs) based on the disc galaxy formation model developed by Mo, Mao & White. We propose that the DLAs are the central galaxies of less-massive dark haloes present at redshifts z ∼3, and they should inhabit haloes of moderately low circular velocity. The empirical Schmidt law of star formation rates, and closed box model of chemical evolution that an approximation known as instantaneous recycling is assumed, are adopted. In our models, when the predicted distribution of metallicity for DLAs is calculated, two cases are considered. One is that, using the closed-box model, empirical Schmidt law and star formation time, the distribution of metallicity can be directly calculated. The other is that, when the simple gravitational instability of a thin isothermal gas disc as first discussed by Toomre is considered, the star formation occurs only in the region where the surface density of gas satisfies the critical value, not everywhere of a gas disc. In this case, we first obtain the region where the star formation can occur by assuming that the disc has a flat rotation curve and rotational velocity is equal to the circular velocity of the surrounding dark matter halo, and then calculate the metallicity distribution as in case one. We assume that star formation in each DLA lasts for a period of 1 Gyr from redshifts z =3. There is only one output parameter in our models, i.e. the stellar yield, which relates to the time of star formation history and is obtained by normalizing the predicted distribution of metallicity to the mean value of 1/13 Z_⊙ as presented by Pettini et al.. The predicted metallicity distribution is consistent with the current (rather limited) observational data. A random distribution of galactic discs is taken into account.     

Storm fronts over galaxy discs: models of how waves generate extraplanar gas and its anomalous kinematics

The existence of partially ionized, diffuse gas and dust clouds at kiloparsec scale distances above the central planes of edge-on, galaxy discs was an unexpected discovery about 20 years ago. Subsequent observations showed that this extended or extraplanar diffuse interstellar gas (EDIG) has rotation velocities approximately 10–20 per cent lower than those in the central plane, and has been hard to account for. Here, we present results of hydrodynamic models, with radiative cooling and heating from star formation. We find that in models with star formation generated stochastically across the disc, an extraplanar gas layer is generated as long as the star formation is sufficiently strong. However, this gas rotates at nearly the same speed as the midplane gas. We then studied a range of models with imposed spiral or bar waves in the disc. EDIG layers were also generated in these models, but primarily over the wave regions, not over the entire disc. Because of this partial coverage, the EDIG clouds move radially, as well as vertically, with the result that observed kinematic anomalies are reproduced. The implication is that the kinematic anomalies are the result of three-dimensional motions when the cylindrical symmetry of the disc is broken. Thus, the kinematic anomalies are the result of bars or strong waves, and more face-on galaxies with such waves should have an asymmetric EDIG component. The models also indicate that the EDIG can contain a significant fraction of cool gas, and that some star formation can be triggered at considerable heights above the disc mid-plane. We expect all of these effects to be more prominent in young, forming discs, to play a role in rapidly smoothing disc asymmetries and in working to self-regulate disc structure.     

Barred galaxy resonance rings: analytically explaining morphology and predicting dissipative misalignment

Many barred disc galaxies show rings of gas clouds and young stars thought to be in periodic orbits near the two-fold inner and outer Lindblad resonances (ILR and OLR) plus a four-fold ultraharmonic resonance (UHR) of the turning bar with oscillations about the disc orbital motion. To confirm and extend simulations by Schwarz and by Byrd et al. of resonance ring formation, we present an analytical formulation of the clouds' orbital motion which includes dissipative damping of oscillations relative to the local interstellar medium plus the rotation curve, bar pattern speed, and strength. Observed ring morphology matches our plots of periodic orbits where the density is enhanced but clouds do not collide violently. Pairs of 'outer rings' bracket the OLR. Dimpled outer rings like that of ESO 507-16 can be matched by plots with strong bars. Slightly dimpled outer rings like that of ESO 509-98 can be matched by weak bar plots. For flat rotation curves, a pair of two-fold rings bracket the ILR; the smaller can be identified with the tiny 'nuclear rings'. We find narrow UHR rings just outside this pair as well as just inside the OLR pair. We confirm the identification of the larger ILR ring and the inner UHR ring with 'inner rings'. Disagreeing with the common identification, we associate the dimpled outer rings with the UHR just inside the OLR. See ESO 507-16 as an example. We predict that damping can misalign the ILR and OLR rings relative to the bar as seen in our match to ESO 507-16. We find that for weak bars, if the linearly rising portion of the rotation curve is a significant fraction of the corotation radius, nuclear and inner rings are absent with outer rings still present. We show this in a match to ESO 509-98. Success of the matches to ESO 507-16 and 509-98 shows how the analytic formulation can be used to estimate disc orientation and pattern speed if rotation curve observations are available.     

H i and CO observations of Arp 104: a spiral–elliptical interacting pair

We present data probing the spatial and kinematical distribution of both the atomic (H  i ) and molecular (CO) gas in NGC 5218, the late-type barred spiral galaxy in the spiral–elliptical interacting pair, Arp 104. We consider these data in conjunction with far-infrared and radio-continuum data, and N -body simulations, to study the galaxies interactions, and the star formation properties of NGC 5218. We use these data to assess the importance of the bar and tidal interaction on the evolution of NGC 5218, and the extent to which the tidal interaction may have been important in triggering the bar. The molecular gas distribution of NGC 5218 appears to have been strongly affected by the bar; the distribution is centrally condensed with a very large surface density in the central region. The N -body simulations indicate a time-scale since perigalacticon of  ∼3 × 10⁸ yr  , which is consistent with the interaction having triggered or enhanced the bar potential in NGC 5218, leading to inflow and the large central molecular gas density observed. Whilst NGC 5218 appears to be undergoing active star formation, its star formation efficiency is comparable to a 'normal' SBb galaxy. We propose that this system may be on the brink of a more active phase of star formation.     

Numerical simulations of the formation and chemical evolution of galaxies

We present the results of a set of three-dimensional SPH-Treecode simulations which model the formation and early evolution of disc galaxies, including the generation and return of heavy elements to the interstellar medium by star formation. Starting from simple initial conditions which are given by a uniform density sphere of gas which is embedded in a dark matter halo and in solid-body rotation, we are able to form realistic disc galaxies, and find that an exponential gas disc is quickly formed. Star formation within this exponential disc naturally leads to the formation of abundance gradients which are in broad agreement with those observed, although they are slightly shallower than some observations.
We investigate the systematic effects of variation of mass, rotation and star formation parameters on the abundance gradients. We find that the abundance gradients are most sensitive to changes in the star formation parameters or rotation. Including a critical-density cut-off in the star formation law causes abundance gradients to be steepened.
Analysis of gas flows within the models shows radial flows which are a function of angle of azimuth around the galaxies, with alternating inward and outward flows. This motion is linked to the presence of a bar, whose strength is related to the amount of star formation in the models, and there is a gentle drift of mass inwards. The shallow abundance gradients may be linked to these radial flows.     

Bar-driven evolution of S0s: the edge-on galaxy NGC 4570

We present circumstantial evidence that the central region of the edge-on S0 galaxy NGC 4570, which harbours a 150-pc scale nuclear disc in addition to its main outer disc, has been shaped under the influence of a small (∼ 500 pc) bar. This is based on the discovery of two edge-on rings, the locations of which are consistent with the inner Lindblad and ultraharmonic resonances of a rapidly tumbling triaxial potential. Observed features in the photometry and rotation curve correspond nicely with the positions of the main resonances, strengthening the case for a tumbling bar potential. The relative blue colour of the ILR ring, and the complete absence of any detected ISM, indicates that the nuclear ring is made of relatively young (≲ 2 Gyr) stars. We discuss a possible secular evolution scenario for this complex multicomponent galaxy, which may also apply to many other S0 galaxies with observed rings and/or multiple disc components.     

Tidal evolution of discy dwarf galaxies in the Milky Way potential: the formation of dwarf spheroidals

We conduct high-resolution collisionless N -body simulations to investigate the tidal evolution of dwarf galaxies on an eccentric orbit in the Milky Way (MW) potential. The dwarfs originally consist of a low surface brightness stellar disc embedded in a cosmologically motivated dark matter halo. During 10 Gyr of dynamical evolution and after five pericentre passages, the dwarfs suffer substantial mass loss and their stellar component undergoes a major morphological transformation from a disc to a bar and finally to a spheroid. The bar is preserved for most of the time as the angular momentum is transferred outside the galaxy. A dwarf spheroidal (dSph) galaxy is formed via gradual shortening of the bar. This work thus provides a comprehensive quantitative explanation of a potentially crucial morphological transformation mechanism for dwarf galaxies that operates in groups as well as in clusters. We compare three cases with different initial inclinations of the disc and find that the evolution is fastest when the disc is coplanar with the orbit. Despite the strong tidal perturbations and mass loss, the dwarfs remain dark matter dominated. For most of the time, the one-dimensional stellar velocity dispersion, σ, follows the maximum circular velocity, V _max, and they are both good tracers of the bound mass. Specifically, we find that   M _bound∝ V ^3.5_max  and     in agreement with earlier studies based on pure dark matter simulations. The latter relation is based on directly measuring the stellar kinematics of the simulated dwarf, and may thus be reliably used to map the observed stellar velocity dispersions of dSphs to halo circular velocities when addressing the missing satellites problem.     

The formation of the Hubble sequence of disc galaxies: the effects of early viscous evolution

We investigate a model of disc galaxies whereby viscous evolution of the gaseous disc drives material inwards to form a protobulge. We start from the standard picture of disc formation through the settling of gas into a dark halo potential well, with the disc initially coming into centrifugal equilibrium with detailed conservation of angular momentum. We derive generic analytic solutions for the disc–halo system after adiabatic compression of the dark halo, with free choice of the input virialized dark halo density profile and of the specific angular momentum distribution. We derive limits on the final density profile of the halo in the central regions. Subsequent viscous evolution of the disc is modelled by a variation of the specific angular momentum distribution of the disc, providing analytic solutions to the final disc structure. The assumption that the viscous evolution time-scale and the star formation time-scale are similar leads to predictions of the properties of the stellar components. Focusing on small 'exponential' bulges, i.e., ones that may be formed through a disc instability, we investigate the relationship between the assumed initial conditions, such as halo 'formation', or assembly, redshift z _f, spin parameter λ , baryonic fraction F , and final disc properties such as global star formation time-scale, gas fraction, and bulge-to-disc ratio. We find that the present properties of discs, such as the scalelength, are compatible with a higher initial formation redshift if the redistribution by viscous evolution is included than if it is ignored. We also quantify the dependence of final disc properties on the ratio F λ , thus including the possibility that the baryonic fraction varies from galaxy to galaxy, as perhaps may be inferred from the observations.     

The evolution of galactic discs

We use recent observations of high-redshift galaxies to study the evolution of galactic discs over the redshift range 0 <  z ≲1. The data are inconsistent with models in which discs were already assembled at z  = 1 and have evolved only in luminosity since that time. Assuming that disc properties change with redshift as powers of 1 +   z and analysing the observations assuming an Einstein–de Sitter universe, we find that for given rotation speed, disc scalelength decreases with z as ∼ (1 +  z )⁻¹, total B -band mass-to-light ratio decreases with z as ∼ (1 +  z )⁻¹, and disc luminosity (again in B ) depends only weakly on z . These scalings are consistent with current data on the evolution of disc galaxy abundance as a function of size and luminosity. Both the scalings and the abundance evolution are close to the predictions of hierarchical models for galaxy formation. If different cosmogonies are compared, the observed evolution in disc size and disc abundance favours a flat low-Ω₀ universe over an Einstein–de Sitter universe.     

Chemo-spectrophotometric evolution of spiral galaxies – V. Properties of galactic discs at high redshift

We explore the implications for the high-redshift universe of 'state-of-the-art' models for the chemical and spectrophotometric evolution of spiral galaxies. The models are based on simple 'scaling relations' for discs, obtained in the framework of cold dark matter models for galaxy formation, and were 'calibrated' so as to reproduce the properties of the Milky Way and of nearby discs (at redshift z ∼0) . In this paper, we compare the predictions of our 'hybrid' approach to galaxy evolution to observations at moderate and high redshift. We find that the models are in fairly good agreement with observations up to z ∼1 , while some problems appear at higher redshift (provided there is no selection bias in the data); these discrepancies may suggest that galaxy mergers (not considered in this work) played a non-negligible role at z >1 . We also predict the existence of a 'universal' correlation between abundance gradients and disc scalelengths, independent of redshift.