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.     

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.     

Orbits supporting bars within bars

High-resolution observations of the inner regions of barred disc galaxies have revealed many asymmetrical, small-scale central features, some of which are best described as secondary bars. Because orbital time-scales in the galaxy centre are short, secondary bars are likely to be dynamically decoupled from the main kiloparsec-scale bars. Here we show that regular orbits exist in such doubly barred potentials, and that they can support the bars in their motion. We find orbits in which particles remain on loops : closed curves which return to their original positions after two bars have come back to the same relative orientation. Stars trapped around stable loops could form the building blocks for a long-lived, doubly barred galaxy. Using the loop representation, we can find which orbits support the bars in their motion, and the constraints on the sizes and shapes of self-consistent double bars. In particular, it appears that a long-lived secondary bar may exist only when an inner Lindblad resonance is present in the primary bar, and that it would not extend beyond this resonance.     

Response of the integrals in the Tremaine–Weinberg method to multiple pattern speeds: a counter-rotating inner bar in NGC 2950?

When integrals in the standard Tremaine–Weinberg method are evaluated for the case of a realistic model of a doubly barred galaxy, their modifications introduced by the second rotating pattern are in accord with what can be derived from a simple extension of that method, based on separation of tracer's density. This extension yields a qualitative argument that discriminates between prograde and retrograde inner bars. However, the estimate of the value of inner bar's pattern speed requires further assumptions. When this extension of the Tremaine–Weinberg method is applied to the recent observation of the doubly barred galaxy NGC 2950, it indicates that the inner bar there is counter-rotating, possibly with the pattern speed of  −140 ± 50 km s⁻¹ arcsec⁻¹  . The occurrence of counter-rotating inner bars can constrain theories of galaxy formation.     

The clustering of barred galaxies in the local Universe

We study the clustering properties of barred galaxies using data from the Sloan Digital Sky Survey. We compute projected redshift-space two-point cross-correlation functions   w _p( r _p)  for a sample of nearly 1000 galaxies for which we have performed detailed structural decompositions using the methods described in Gadotti. The sample includes 286 barred galaxies. The clustering of barred and unbarred galaxies of similar stellar mass is indistinguishable over all the scales probed (∼20 kpc–30 Mpc). This result also holds even if the sample is restricted to bars with bluer   g − i   colours (and hence younger ages). Our result also does not change if we split our sample of barred galaxies according to bar-to-total luminosity ratio, bar boxyness, effective surface brightness, length or the shape of the surface density profile within the bar. There is a hint that red, elliptical bars are more strongly clustered than red and less elliptical bars, on scales  ≳1 Mpc  , although the statistical significance is not high. We conclude that there is no significant evidence that bars are a product of mergers or interactions. We tentatively interpret the stronger clustering of the more elliptical bars as evidence that they are located in older galaxies, which reside in more massive haloes.     

The effect of dust on Tremaine–Weinberg measurements

We investigate the effect of dust on the observed rotation rate of a stellar bar. The only direct way to measure this quantity relies on the Tremaine & Weinberg (TW) method which requires that the tracer satisfies the continuity equation. Thus, it has been applied largely to early-type barred galaxies. We show using numerical simulations of barred galaxies that dust attenuation factors typically found in these systems change the observed bar pattern speed by 20–40 per cent. We also address the effect of star formation on the TW method and find that it does not change the results significantly. The results presented here suggest that applications of the TW method can be extended to include barred galaxies covering the full range of Hubble type.     

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.     

Bars and the symmetry of star formation patterns in the discs of spiral galaxies

We present a test for the degree of symmetry in the distribution of the Hα brightness along the arms of a sample of spiral galaxies. The test consists of deriving the cross-correlation function of the Hα brightness as a function of curvilinear distance along pairs of opposed arms, after unfolding the arms geometrically. Our results reveal a significantly greater degree of symmetry in the non-barred population than in the barred. We derive parameters for both bar strength and bar ellipticity, and compare these with the derived cross-correlations to strengthen this conclusion. We suggest that density waves are a probable cause for the appearance of global, i.e. disc-wide, two-fold symmetry in spiral discs. Comparison with published work on abundance gradients in the discs of barred and non-barred galaxies indicates that, as for the abundances, mixing in the spiral disc as a result of the bar potential may well be responsible for our observation that stronger bars are related to reduced two-fold symmetry in the distribution of star-forming regions along the spiral arms.     

Broad-band and Hα surface photometry of the central regions of nearby active galaxies – I. Observations

Broad-band V , R and I and narrow-band H α CCD surface photometry of a sample of 24 active and three normal nearby galaxies is presented, in order to study their morphological and structural properties. This first paper presents the observations, data reduction and processing techniques used; the main characteristics of the central regions of the sample galaxies are derived from broad-band and H α images; broad-band surface brightness and colour profiles are presented; based on the inspection of individual images and the examination of the radial variation of ellipticity and polar angle, the morphological class of the sample objects is revised: several objects previously classified as non-barred or unclassified are found to be barred galaxies. A high fraction (∼71 per cent) of the objects that present any kind of nuclear activity are barred. This proportion is even higher (∼87 per cent) if only Seyfert galaxies are considered. This result can reinforce the clues about the connection between bars and nuclear activity as a fuelling mechanism that can trigger and sustain nuclear activity.     

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.     

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.     

Unravelling the mystery of the M31 bar

The inclination of M31 is too close to edge-on for a bar component to be easily recognized and is not sufficiently edge-on for a boxy/peanut bulge to protrude clearly out of the equatorial plane. Nevertheless, a sufficient number of clues allow us to argue that this galaxy is barred. We use fully self-consistent N -body simulations of barred galaxies and compare them with both photometric and kinematic observational data for M31. In particular, we rely on the near-infrared photometry presented in a companion paper. We compare isodensity contours to isophotal contours and the light profile along cuts parallel to the galaxy major axis and offset towards the north, or the south, to mass profiles along similar cuts on the model. All these comparisons, as well as position–velocity diagrams for the gaseous component, give us strong arguments that M31 is barred. We compare four fiducial N -body models to the data and thus set constraints on the parameters of the M31 bar, as its strength, length and orientation. Our 'best' models, although not meant to be exact models of M31, reproduce in a very satisfactory way the main relevant observations. We present arguments that M31 has both a classical and a boxy/peanut bulge. Its pseudo-ring-like structure at roughly 50 arcmin is near the outer Lindblad resonance of the bar and could thus be an outer ring, as often observed in barred galaxies. The shape of the isophotes also argues that the vertically thin part of the M31 bar extends considerably further out than its boxy bulge, that is, that the boxy bulge is only part of the bar, thus confirming predictions from orbital structure studies and from previous N -body simulations. It seems very likely that the backbone of M31's boxy bulge is families of periodic orbits, members of the x₁-tree and bifurcating from the x₁ family at its higher order vertical resonances, such as the x1v3 or x1v4 families.     

The morphology of galactic rings exterior to evolving bars: test-particle simulations

The morphology of the outer rings of early-type spiral galaxies is compared to integrations of massless collisionless particles initially in nearly circular orbits. Particles are perturbed by a quadrupolar gravitational potential corresponding to a growing and secularly evolving bar. We find that outer rings with R1R2 morphology and pseudo-rings are exhibited by the simulations even though they lack gaseous dissipation. Simulations with stronger bars form pseudo-rings earlier and more quickly than those with weaker bars. We find that the R1 ring, perpendicular to the bar, is fragile and dissolves after a few bar rotation periods if the bar pattern speed increases by more than ∼8 per cent, bar strength increases (by ≳140 per cent) after bar growth or the bar is too strong  ( Q_T > 0.3)  . If the bar slows down after formation, pseudo-ring morphology persists and the R2 ring perpendicular to the bar is populated due to resonance capture. The R2 ring remains misaligned with the bar and increases in ellipticity as the bar slows down. The R2 ring becomes scalloped and does not resemble any ringed galaxies if the bar slows down more than 3.5 per cent suggesting that bars decrease in strength before they slow down this much. We compare the morphology of our simulations to B -band images of nine ringed galaxies from the Ohio State University Bright Spiral Galaxy Survey, and we find a reasonable match in morphologies to R1R2' pseudo-rings seen within a few bar rotation periods of bar formation. Some of the features previously interpreted in terms of dissipative models may be due to transient structure associated with recent bar growth and evolution.     

A new challenge: Bar formation and secular evolution in lenticular galaxies

To further enhance our understanding on the formation and evolution of bars in lenticular (S0) galaxies, we are undertaking a detailed photometric and spectroscopic study on a sample of 22 objects. Here we report the results of a 2D structural analysis on two barred face-on S0's, which indicate that presently these galaxies do not possess disks. We discuss two possibilities to explain these surprising results, namely strong secular evolution and bar formation without disks. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

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.     

A new formula describing the scaffold structure of spiral galaxies

We describe a new formula capable of quantitatively characterizing the Hubble sequence of spiral galaxies including grand design and barred spirals. Special shapes such as ring galaxies with inward and outward arms are also described by the analytic continuation of the same formula. The formula is   r (φ) = A /log [ B tan   (φ/2 N )]  . This function intrinsically generates a bar in a continuous, fixed relationship relative to an arm of arbitrary winding sweep. A is simply a scale parameter while B , together with N , determines the spiral pitch. Roughly, greater N results in tighter winding. Greater B results in greater arm sweep and smaller bar/bulge, while smaller B fits larger bar/bulge with a sharper bar/arm junction. Thus B controls the 'bar/bulge-to-arm' size, while N controls the tightness much like the Hubble scheme. The formula can be recast in a form dependent only on a unique point of turnover angle of pitch – essentially a one-parameter fit, aside from a scalefactor. The recast formula is remarkable and unique in that a single parameter can define a spiral shape with either constant or variable pitch capable of tightly fitting Hubble types from grand design spirals to late-type large barred galaxies. We compare the correlation of our pitch parameter to Hubble type with that of the traditional logarithmic spiral for 21 well-shaped galaxies. The pitch parameter of our formula produces a very tight correlation with ideal Hubble type suggesting it is a good discriminator compared to logarithmic pitch, which shows poor correlation here similar to previous works. Representative examples of fitted galaxies are shown.     

Orbital dynamics of three-dimensional bars – I. The backbone of three-dimensional bars. A fiducial case

In this series of papers we investigate the orbital structure of three-dimensional (3D) models representing barred galaxies. In the present introductory paper we use a fiducial case to describe all families of periodic orbits that may play a role in the morphology of three-dimensional bars. We show that, in a 3D bar, the backbone of the orbital structure is not just the x1 family, as in two-dimensional (2D) models, but a tree of 2D and 3D families bifurcating from x1. Besides the main tree we have also found another group of families of lesser importance around the radial 3:1 resonance. The families of this group bifurcate from x1 and influence the dynamics of the system only locally. We also find that 3D orbits elongated along the bar minor axis can be formed by bifurcations of the planar x2 family. They can support 3D bar-like structures along the minor axis of the main bar. Banana-like orbits around the stable Lagrangian points build a forest of 2D and 3D families as well. The importance of the 3D x1-tree families at the outer parts of the bar depends critically on whether they are introduced in the system as bifurcations in z or in   z˙   .     

Bar dissolution in non-spherical halos

Dynamical evolution of N-body bars embedded in spherical and prolate dark matter halos is investigated. In particular, the configuration such that galactic disks are placed in the plane perpendicular to the equatorial plane of the prolate halos is considered. Such a configuration is frequently found in cosmological simulations. N-body disks embedded in a fixed external halo potential were simulated, so that the barred structure was formed via dynamical instability in initially cool disks. In the subsequent evolution, bars in prolate halos dissolved gradually with time, while the bar pattern in spherical halos remained almost unchanged until the end of simulations. The e-folding time of bars suggest that they could be destroyed in a time smaller than a Hubble time. This revised version was published online in August 2006 with corrections to the Cover Date.