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.     

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.     

Regularized orbit models unveiling the stellar structure and dark matter halo of the Coma elliptical NGC 4807

This is the second in a series of papers dedicated to unveiling the mass structure and orbital content of a sample of flattened early-type galaxies in the Coma cluster. The ability of our orbit libraries to reconstruct internal stellar motions and the mass composition of a typical elliptical in the sample is investigated by means of Monte Carlo simulations of isotropic rotator models. The simulations allow a determination of the optimal amount of regularization needed in the orbit superpositions. It is shown that under realistic observational conditions and with the appropriate regularization, internal velocity moments can be reconstructed to an accuracy of ≈15 per cent; the same accuracy can be achieved for the circular velocity and dark matter fraction. In contrast, the flattening of the halo remains unconstrained. Regularized orbit superpositions are applied to a first galaxy in our sample, NGC 4807, for which stellar kinematical observations extend to  3  r _eff  . The galaxy seems dark-matter dominated outside   r > 2  r _eff  . Logarithmic dark matter potentials are consistent with the data, as well as NFW profiles, mimicking logarithmic potentials over the observationally sampled radial range. In both cases, the derived stellar mass-to-light ratio ϒ agrees well with independently obtained mass-to-light ratios from stellar population analysis. The achieved accuracy is  Δϒ≈ 0.5  . Kinematically, NGC 4807 is characterized by mild radial anisotropy outside   r > 0.5  r _eff  , becoming isotropic towards the centre. Our orbit models hint at either a distinct stellar component or weak triaxiality in the outer parts of the galaxy.     

The peculiar motions of early-type galaxies in two distant regions – VI. The maximum-likelihood Gaussian algorithm

The EFAR project is designed to measure the properties and peculiar motions of early-type galaxies in two distant regions. Here we describe the maximum-likelihood algorithm we developed to investigate the correlations between the parameters of the EFAR data base. One-, two- and three-dimensional Gaussian models are constructed to determine the mean value and intrinsic spread of the parameters, and the slopes and intrinsic parallel and orthogonal spread of the Mg₂–Mg b ', Mg₂– σ , Mg b '– σ relations, and the Fundamental Plane. In the latter case, the cluster peculiar velocities are also determined. We show that this method is superior to 'canonical' approaches of least-squares type, which give biased slopes and biased peculiar velocities. We test the algorithm with Monte Carlo simulations of mock EFAR catalogues, and derive the systematic and random errors on the estimated parameters. We find that random errors are always dominant. We estimate the influence of systematic errors resulting from the way clusters were selected, and the hard limits and uncertainties in the selection function parameters for the galaxies. We explore the influence of uniform distributions in the Fundamental Plane parameters and the errors. We conclude that the mean peculiar motions of the EFAR clusters can be determined reliably. In particular, the placement of the two EFAR sample regions relative to the Lauer & Postman dipole allows us to constrain strongly the amplitude of the bulk motion in this direction. We justify a posteriori the use of a Gaussian modelling for the galaxy distribution in the Fundamental Plane space, by showing that the mean likelihood of the EFAR sample is obtained in 10 to 30 per cent of our simulations. We derive the analytical solution for the maximum-likelihood Gaussian problem in N dimensions in the presence of small errors.     

The haloes of merger remnants

We perform collisionless N -body simulations of 1:1 galaxy mergers, using models which include a galaxy halo, disc and bulge, focusing on the behaviour of the halo component. The galaxy models are constructed without recourse to a Maxwellian approximation. We investigate the effect of varying the galaxies' orientation, their mutual orbit and the initial velocity anisotropy or cusp strength of the haloes upon the remnant halo density profiles and shape, as well as on the kinematics. We observe that the halo density profile (determined as a spherical average, an approximation we find appropriate) is exceptionally robust in mergers, and that the velocity anisotropy of our remnant haloes is nearly independent of the orbits or initial anisotropy of the haloes. The remnants follow the halo anisotropy – local density slope (β–γ) relation suggested by Hansen & Moore in the inner parts of the halo, but β is systematically lower than this relation predicts in the outer parts. Remnant halo axis ratios are strongly dependent on the initial parameters of the haloes and on their orbits. We also find that the remnant haloes are significantly less spherical than those described in studies of simulations which include gas cooling.     

Disc heating in NGC 2985

Various processes have been proposed to explain how galaxy discs acquire their thickness. A simple diagnostic for ascertaining this 'heating' mechanism is provided by the ratio of the vertical to radial velocity dispersion components. In a previous paper we have developed a technique for measuring this ratio, and demonstrated its viability on the Sb system NGC 488. Here we present follow-up observations of the morphologically similar Sab galaxy NGC 2985, still only the second galaxy for which this ratio has been determined outside the solar neighbourhood. The result is consistent with simple disc-heating models that predict ratios of σ _z σ _R less than one.     

The Planetary Nebula Spectrograph elliptical galaxy survey: the dark matter in NGC 4494

We present new Planetary Nebula Spectrograph observations of the ordinary elliptical galaxy NGC 4494, resulting in positions and velocities of 255 planetary nebulae out to seven effective radii (25 kpc). We also present new wide-field surface photometry from MMT/Megacam, and long-slit stellar kinematics from VLT/FORS2. The spatial and kinematical distributions of the planetary nebulae agree with the field stars in the region of overlap. The mean rotation is relatively low, with a possible kinematic axis twist outside  1 R _e  . The velocity dispersion profile declines with radius, though not very steeply, down to  ∼70 km s⁻¹  at the last data point.
We have constructed spherical dynamical models of the system, including Jeans analyses with multi-component Λ cold dark matter (CDM) motivated galaxies as well as logarithmic potentials. These models include special attention to orbital anisotropy, which we constrain using fourth-order velocity moments. Given several different sets of modelling methods and assumptions, we find consistent results for the mass profile within the radial range constrained by the data. Some dark matter (DM) is required by the data; our best-fitting solution has a radially anisotropic stellar halo, a plausible stellar mass-to-light ratio and a DM halo with an unexpectedly low central density. We find that this result does not substantially change with a flattened axisymmetric model.
Taken together with other results for galaxy halo masses, we find suggestions for a puzzling pattern wherein most intermediate-luminosity galaxies have very low concentration haloes, while some high-mass ellipticals have very high concentrations. We discuss some possible implications of these results for DM and galaxy formation.     

How special are brightest group and cluster galaxies?

We use the Sloan Digital Sky Survey (SDSS) to construct a sample of 625 brightest group and cluster galaxies (BCGs) together with control samples of non-BCGs matched in stellar mass, redshift and colour. We investigate how the systematic properties of BCGs depend on stellar mass and on their privileged location near the cluster centre. The groups and clusters that we study are drawn from the C4 catalogue of Miller et al. but we have developed improved algorithms for identifying the BCG and for measuring the cluster velocity dispersion. Since the SDSS photometric pipeline tends to underestimate the luminosities of large galaxies in dense environments, we have developed a correction for this effect which can be readily applied to the published catalogue data. We find that BCGs are larger and have higher velocity dispersions than non-BCGs of the same stellar mass, which implies that BCGs contain a larger fraction of dark matter. In contrast to non-BCGs, the dynamical mass-to-light ratio of BCGs does not vary as a function of galaxy luminosity. Hence BCGs lie on a different Fundamental Plane than ordinary elliptical galaxies. BCGs also follow a steeper Faber–Jackson relation than non-BCGs, as suggested by models in which BCGs assemble via dissipationless mergers along preferentially radial orbits. We find tentative evidence that this steepening is stronger in more massive clusters. BCGs have similar mean stellar ages and metallicities to non-BCGs of the same mass, but they have somewhat higher α/Fe ratios, indicating that star formation may have occurred over a shorter time-scale in the BCGs. Finally, we find that BCGs are more likely to host radio-loud active galactic nuclei than other galaxies of the same mass, but are less likely to host an optical active galactic nucleus (AGN). The differences we find are more pronounced for the less massive BCGs, i.e. they are stronger at the galaxy group level.     

The peculiar motions of early-type galaxies in two distant regions – VII. Peculiar velocities and bulk motions

We present peculiar velocities for 85 clusters of galaxies in two large volumes at distances between 6000 and 15 000 km s⁻¹ in the directions of Hercules–Corona Borealis and Perseus–Pisces–Cetus (the EFAR sample). These velocities are based on Fundamental Plane (FP) distance estimates for early-type galaxies in each cluster. We fit the FP using a maximum likelihood algorithm which accounts for both selection effects and measurement errors, and yields FP parameters with smaller bias and variance than other fitting procedures. We obtain a best-fitting FP with coefficients consistent with the best existing determinations. We measure the bulk motions of the sample volumes using the 50 clusters with the best-determined peculiar velocities. We find that the bulk motions in both regions are small, and consistent with zero at about the 5 per cent level. The EFAR results are in agreement with the small bulk motions found by Dale et al. on similar scales, but are inconsistent with pure dipole motions having the large amplitudes found by Lauer & Postman and Hudson et al. The alignment of the EFAR sample with the Lauer & Postman dipole produces a strong rejection of a large-amplitude bulk motion in that direction, but the rejection of the Hudson et al. result is less certain because their dipole lies at a large angle to the main axis of the EFAR sample. We employ a window function covariance analysis to make a detailed comparison of the EFAR peculiar velocities with the predictions of standard cosmological models. We find that the bulk motion of our sample is consistent with most cosmological models that approximately reproduce the shape and normalization of the observed galaxy power spectrum. We conclude that existing measurements of large-scale bulk motions provide no significant evidence against standard models for the formation of structure.     

Central mass-to-light ratios and dark matter fractions in early-type galaxies

Dynamical studies of local elliptical galaxies and the Fundamental Plane point to a strong dependence of the total mass-to-light ratio ( M / L ) on luminosity with a relation of the form   M / L ∝ L ^γ  . The 'tilt'γ may be caused by various factors, including stellar population properties (metallicity, age and star formation history), initial mass function, rotational support, luminosity profile non-homology and dark matter (DM) fraction. We evaluate the impact of all these factors using a large uniform data set of local early-type galaxies from Prugniel & Simien. We take particular care in estimating the stellar masses, using a general star formation history, and comparing different population synthesis models. We find that the stellar M / L contributes little to the tilt. We estimate the total M / L using simple Jeans dynamical models, and find that adopting accurate luminosity profiles is important but does not remove the need for an additional tilt component, which we ascribe to DM. We survey trends of the DM fraction within one effective radius, finding it to be roughly constant for galaxies fainter than   M _B∼−20.5  , and increasing with luminosity for the brighter galaxies; we detect no significant differences between S0s and fast- and slow-rotating ellipticals. We construct simplified cosmological mass models and find general consistency, where the DM transition point is caused by a change in the relation between luminosity and effective radius. A more refined model with varying galaxy star formation efficiency suggests a transition from total mass profiles (including DM) of faint galaxies distributed similarly to the light to near-isothermal profiles for the bright galaxies. These conclusions are sensitive to various systematic uncertainties which we investigate in detail, but are consistent with the results of dynamical studies at larger radii.     

Do galaxy mergers form elliptical galaxies? A comparison of kinematic and photometric properties

We present near-infrared K -band imaging and spectroscopy of a sample of galaxy mergers, which we use to derive light profile indices, absolute magnitudes and central velocity dispersions. We find that the light distributions of mergers more nearly resemble those of ellipticals than those of bulges, but that the mergers lie well away from the Fundamental Plane defined by the ellipticals. We interpret this as being due to enhancement of the K -band surface brightness of the mergers by a significant population of supergiant stars, and independent evidence for such a population is inferred from measurements of the depth of the 2.3-μm CO absorption feature.     

Multiwavelength observations of an evolved galaxy group: an end-point of galaxy merging?

The group of galaxies RXJ1340.6+4018 has approximately the same bolometric X-ray luminosity as other bright galaxy groups and poor clusters such as the Virgo cluster. However, 70 per cent of the optical luminosity of the group comes from a dominant giant elliptical galaxy, compared with 5 per cent from M87 in Virgo.The second brightest galaxy in RXJ1340.6+4018 is a factor of 10 fainter (Δ m ₁₂=2.5 mag) than the dominant elliptical, and the galaxy luminosity function has a gap at about L *.
We interpret the properties of the system as a result of galaxy merging within a galaxy group. We find that the central galaxy lies on the Fundamental Plane of ellipticals, has an undisturbed, non-cD morphology, and has no spectral features indicative of recent star formation, suggesting that the last major merger occurred ≳4 Gyr ago. The deviation of the system from the cluster L _X− T relation in the opposite sense to most groups may be caused by an early epoch of formation of the group or a strong cooling flow.
The unusual elongation of the X-ray isophotes and the similarity between the X-ray and optical ellipticities at large radii (∼230 kpc) suggest that both the X-ray gas and the outermost stars of the dominant galaxy are responding to an elongated dark matter distribution. RXJ1340.6+4018 may be part of a filamentary structure related to infall in the outskirts of the cluster A1774.     

Invariant manifolds, phase correlations of chaotic orbits and the spiral structure of galaxies

In the presence of a strong   m = 2  component in a rotating galaxy, the phase-space structure near corotation is shaped to a large extent by the invariant manifolds of the short-period family of unstable periodic orbits terminating at L ₁ or L ₂. The main effect of these manifolds is to create robust phase correlations among a number of chaotic orbits large enough to support a spiral density wave outside corotation. The phenomenon is described theoretically by soliton-like solutions of a Sine–Gordon equation. Numerical examples are given in an N -body simulation of a barred spiral galaxy. In these examples, we demonstrate how the projection of unstable manifolds in configuration space reproduces essentially the entire observed bar–spiral pattern.     

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.     

Two-component galaxy models: the effect of density profile at large radii on the phase-space consistency

It is well known that the density and anisotropy profile in the inner regions of a stellar system with positive phase-space distribution function (DF) are not fully independent. Here, we study the interplay between density profile and orbital anisotropy at large radii in physically admissible (consistent) stellar systems. The analysis is carried out by using two-component  ( n - γ, γ₁)  spherical self-consistent galaxy models, in which one density distribution follows a generalized γ profile with external logarithmic slope n , and the other a standard  γ₁  profile (with external slope 4). The two density components have different 'core' radii, the orbital anisotropy is controlled with the Osipkov–Merritt recipe, and for simplicity we assume that the mass of the  γ₁  component dominates the total potential everywhere. The necessary and sufficient conditions for phase-space consistency are determined analytically, also in the presence of a dominant massive central black hole, and the analytical phase-space DF of (   n - γ  ,1) models, and of   n - γ  models with a central black hole, is derived for  γ= 0, 1, 2  . It is found that the density slope in the external regions of a stellar system can play an important role in determining the amount of admissible anisotropy: in particular, for fixed density slopes in the central regions, systems with a steeper external density profile can support more radial anisotropy than externally flatter models. This is quantified by an inequality formally identical to the 'cusp slope-central anisotropy' theorem by An & Evans, relating at all radii (and not just at the centre) the density logarithmic slope and the anisotropy indicator in all Osipkov–Merritt systems.     

Spectroscopic constraints on the stellar population of elliptical galaxies in the Coma cluster

Near-infrared spectra for a sample of 31 elliptical galaxies in the Coma cluster are obtained. The galaxies are selected to be ellipticals (no lenticulars), with a large spatial distribution, covering both the core and outskirts of the cluster (i.e. corresponding to regions with large density contrasts). CO_sp (2.3-μm) absorption indices, measuring the contribution from intermediate-age red giant and supergiant stars to the near-infrared light of the ellipticals, are then estimated.
It is found that the strength of CO_sp features in elliptical galaxies increases from the core ( r <02) to the outskirts ( r >02) of the Coma cluster. Using the Mg₂ strengths, it is shown that the observed effect is not caused by metallicity and is mostly caused by the presence of a younger population (giant and supergiant stars) in ellipticals in the outskirts (low-density region) of the cluster.
Using the CO_sp features, the origin of the scatter on the near-infrared Fundamental Plane (the relation between the effective diameter, effective surface brightness and velocity dispersion) of elliptical galaxies is studied. Correcting this relation for contributions from the red giant and supergiant stars, the rms scatter reduces from 0.077 to 0.073 dex. Although measurable, the contribution from these intermediate-age stars to the scatter on the near-infrared Fundamental Plane of ellipticals is only marginal.
A relation is found between the CO_sp and V − K colours of ellipticals, corresponding to a slope of 0.036±0.016, significantly shallower than that from the Mg₂–( V − K ) relation. This is studied using stellar synthesis models.     

Stellar and gas dynamics of late-type barred-spiral galaxies: NGC 3359, a test case

We study the dynamics of a model for the late-type barred-spiral galaxy NGC 3359 by using both observational and numerical techniques. The results of our modelling are compared with photometric and kinematical data. The potential used is estimated directly from observations of the galaxy. It describes with a single potential function, a barred-spiral system with an extended spiral structure. Thus, the study of the dynamics in this potential has an interest by itself. We apply orbital theory and response models for the study of the stellar component, and smoothed particle hydrodynamics for modelling the gas. In particular, we examine the pattern speed of the system and the orbital character (chaotic or ordered) of the spiral arms. We conclude that the spiral pattern rotates slowly, in the sense that its corotation is close to or even beyond the end of the arms. Although a single, slow pattern speed could, under certain assumptions, characterize the whole disc, the comparison with the observational data indicates that probably the bar and the spirals have different angular velocities. In our two pattern speeds model, the best fit is obtained with a bar ending close to its 4:1 resonance and a more slowly rotating spiral. Assuming an 11 Mpc distance to the galaxy, a match of our models with the observed data indicates a pattern speed of about  39 km s⁻¹ kpc⁻¹  for the bar and about  15 km s⁻¹ kpc⁻¹  for the spiral. We do not find any indication for a chaotic character of the arms in this barred-spiral system. The flow in the region of the spirals can best be described as a regular 'precessing-ellipses flow'.     

The effect of dwarf galaxy disruption in semi-analytic models

We present results for a galaxy formation model that includes a simple treatment for the disruption of dwarf galaxies by gravitational forces and galaxy encounters within galaxy clusters. This is implemented a posteriori in a semi-analytic model by considering the stability of cluster dark matter subhaloes at   z = 0  . We assume that a galaxy whose dark matter substructure has been disrupted will itself disperse, while its stars become part of the population of intracluster stars responsible for the observed intracluster light. Despite the simplicity of this assumption, our results show a substantial improvement over previous models and indicate that the inclusion of galaxy disruption is indeed a necessary ingredient of galaxy formation models. We find that galaxy disruption suppresses the number density of dwarf galaxies by about a factor of 2. This makes the slope of the faint end of the galaxy luminosity function shallower, in agreement with observations. In particular, the abundance of faint, red galaxies is strongly suppressed. As a result, the luminosity function of red galaxies and the distinction between the red and the blue galaxy populations in colour–magnitude relationships are correctly predicted. Finally, we estimate a fraction of intracluster light comparable to that found in clusters of galaxies.     

The global structure of galactic discs

A statistical study of global galaxy parameters can help to improve our understanding of galaxy formation processes. In this paper we present the analysis of global galaxy parameters based on optical and near-infrared observations of a large sample of edge-on disc galaxies. We found a correlation between the ratio of the radial to vertical scale parameter and galaxy type: galaxies become systematically thinner when going from type S0 to type Sc, whereas the distribution seems to level off for later types. The observed scalelength ratios (and thus the radial colour gradients) largely represent the dust content of the galaxies. On average, the colour gradients indicated by the scalelength ratios increase from type Sa to at least type Sc. For galaxy types later than Sc, the average colour gradient seems to decrease again. The distribution of K -band (edge-on) disc central surface brightnesses is rather flat, although with a large scatter. However, the latest-type sample galaxies ( T  > 6) show an indication that their average disc central surface brightnesses may be fainter than those of the earlier types. This effect is probably not the result of dust extinction.     

A grid of chemical evolution models as a tool to interpret spiral and irregular galaxies data

We present a generalization of the multiphase chemical evolution model (CEM) applied to a wide set of theoretical galaxies with different masses and evolutionary rates. This generalized set of models has been computed using the so-called universal rotation curve from Persic, Salucci & Steel to calculate the radial mass distribution of 44 theoretical protogalaxies. This distribution is a fundamental input which, besides its own effect on the galaxy evolution, defines the characteristic collapse time-scale or gas infall rate on to the disc. We have adopted 10 sets of values, between 0 and 1, for the molecular cloud and star formation efficiencies, as corresponding to their probability nature, for each one of the radial distributions of total mass. Thus, we have constructed a biparametric grid of models, depending on those efficiency sets and on the rotation velocity, whose results are valid in principle for any spiral or irregular galaxy. The model results provide the time-evolution of different regions of the disc and the halo along galactocentric distance, measured by the gas (atomic and molecular) and stellar masses, the star formation rate (SFR) and chemical abundances of 14 elements, for a total of 440 models. This grid may be used to estimate the evolution of a given galaxy for which only present time information, such as radial distributions of elemental abundances, gas densities and/or star formation, which are the usual observational constraints of chemical evolution models (CEMs), is available.