Dwarf galaxy rotation curves and the core problem of dark matter haloes

The standard cold dark matter (CDM) model has recently been challenged by the claim that dwarf galaxies have dark matter haloes with constant-density cores, whereas CDM predicts haloes with steeply cusped density distributions. Consequently, numerous alternative dark matter candidates have recently been proposed. In this paper we scrutinize the observational evidence for the incongruity between dwarf galaxies and the CDM model. To this end, we analyse the rotation curves of 20 late-type dwarf galaxies studied by Swaters. Taking the effects of beam smearing and adiabatic contraction into account, we fit mass models to these rotation curves with dark matter haloes with different cusp slopes, ranging from constant-density cores to r ⁻² cusps. Even though the effects of beam smearing are small for these data, the uncertainties in the stellar mass-to-light ratio and the limited spatial sampling of the halo's density distribution hamper a unique mass decomposition. Consequently, the rotation curves in our sample cannot be used to discriminate between dark haloes with constant-density cores and r ⁻¹ cusps. We show that the dwarf galaxies analysed here are consistent with CDM haloes in a ΛCDM cosmology, and that there is thus no need to abandon the idea that dark matter is cold and collisionless. However, the data are also consistent with any alternative dark matter model that produces dark matter haloes with central cusps less steep than r ^−1.5. In fact, we argue that based on existing H  i rotation curves alone, at best weak limits can be obtained on cosmological parameters and/or the nature of the dark matter. In order to make progress, rotation curves with higher spatial resolution and independent measurements of the mass-to-light ratio of the disc are required.     

Dynamical friction in dwarf galaxies

We present a simplified analytic approach to the problem of the spiralling of a massive body orbiting within the dark halo of a dwarf galaxy. This dark halo is treated as the core region of a King distribution of dark matter particles, in consistency with the observational result of dwarf galaxies having solid-body rotation curves. Thus we derive a simple formula which provides a reliable and general first-order solution to the problem, totally analogous to the one corresponding to the dynamical friction problem in an isothermal halo. This analytic approach allows a clear handling and a transparent understanding of the physics and the scaling of the problem. A comparison with the isothermal case shows that in the core regions of a King sphere, dynamical friction proceeds at a different rate, and is sensitive to the total core radius. Thus, in principle, observable consequences may result. In order to illustrate the possible effects, we apply this formula to the spiralling of globular cluster orbits in dwarf galaxies, and show how present-day globular cluster systems could, in principle, be used to derive better limits on the structure of dark haloes around dwarf galaxies, when the observational situation improves. As a second application, we study the way a massive black hole population forming a fraction of these dark haloes would gradually concentrate towards the centre, with a consequent deformation of an originally solid-body rotation curve. This effect allows us to set limits on the fraction/mass of any massive black hole minority component of the dark haloes of dwarf galaxies. In essence, we take advantage of the way the global matter distribution fixes the local distribution function for the dark matter particles, which in turn determines the dynamical friction problem.     

Evolution of dwarf early-type galaxies – I. Spatially resolved stellar populations and internal kinematics of Virgo cluster dE/dS0 galaxies

Understanding the origin and evolution of dwarf early-type galaxies remains an important open issue in modern astrophysics. Internal kinematics of a galaxy contains signatures of violent phenomena which may have occurred, e.g. mergers or tidal interactions, while stellar population keeps a fossil record of the star formation history; therefore studying connection between them becomes crucial for understanding galaxy evolution. Here, in the first paper of the series, we present the data on spatially resolved stellar populations and internal kinematics for a large sample of dwarf elliptical (dE) and lenticular (dS0) galaxies in the Virgo cluster. We obtained radial velocities, velocity dispersions, stellar ages and metallicities out to 1–2 half-light radii by reanalysing already published long-slit and integral-field spectroscopic data sets using the nbursts full spectral fitting technique. Surprisingly, bright representatives of the dE/dS0 class (   M_B =−18.0  to −16.0 mag) look very similar to intermediate-mass and giant lenticulars and ellipticals: (1) their nuclear regions often harbour young metal-rich stellar populations always associated with the drops in the velocity dispersion profiles; (2) metallicity gradients in the main discs/spheroids vary significantly from nearly flat profiles to −0.9 dex   r ⁻¹_e  , i.e. somewhat three times steeper than for typical bulges; (3) kinematically decoupled cores were discovered in four galaxies, including two with very little, if any, large-scale rotation. These results suggest similarities in the evolutionary paths of dwarf and giant early-type galaxies and call for reconsidering the role of major mergers in the dE/dS0 evolution.     

The high-mass end of the Tully–Fisher relation

We study the location of massive disc galaxies on the Tully–Fisher (TF) relation. Using a combination of K -band photometry and high-quality rotation curves, we show that in traditional formulations of the TF relation (using the width of the global H  i profile or the maximum rotation velocity), galaxies with rotation velocities larger than 200 km s⁻¹ lie systematically to the right of the relation defined by less massive systems, causing a characteristic 'kink' in the relations. Massive, early-type disc galaxies in particular have a large offset, up to 1.5 mag, from the main relation defined by less massive and later-type spirals.
The presence of a change in slope at the high-mass end of the TF relation has important consequences for the use of the TF relation as a tool for estimating distances to galaxies or for probing galaxy evolution. In particular, the luminosity evolution of massive galaxies since z ≈ 1 may have been significantly larger than estimated in several recent studies.
We also show that many of the galaxies with the largest offsets have declining rotation curves and that the change in slope largely disappears when we use the asymptotic rotation velocity as kinematic parameter. The remaining deviations from linearity can be removed when we simultaneously use the total baryonic mass (stars + gas) instead of the optical or near-infrared luminosity. Our results strengthen the view that the TF relation fundamentally links the mass of dark matter haloes with the total baryonic mass embedded in them.     

Probing the 2D kinematic structure of early-type galaxies out to three effective radii

We detail an innovative new technique for measuring the two-dimensional (2D) velocity moments (rotation velocity, velocity dispersion and Gauss–Hermite coefficients h ₃ and h ₄) of the stellar populations of galaxy haloes using spectra from Keck DEIMOS (Deep Imaging Multi-Object Spectrograph) multi-object spectroscopic observations. The data are used to reconstruct 2D rotation velocity maps.
Here we present data for five nearby early-type galaxies to ∼three effective radii. We provide significant insights into the global kinematic structure of these galaxies, and challenge the accepted morphological classification in several cases. We show that between one and three effective radii the velocity dispersion declines very slowly, if at all, in all five galaxies. For the two galaxies with velocity dispersion profiles available from planetary nebulae data we find very good agreement with our stellar profiles. We find a variety of rotation profiles beyond one effective radius, i.e. rotation speed remaining constant, decreasing and increasing with radius. These results are of particular importance to studies which attempt to classify galaxies by their kinematic structure within one effective radius, such as the recent definition of fast- and slow-rotator classes by the Spectrographic Areal Unit for Research on Optical Nebulae project. Our data suggest that the rotator class may change when larger galactocentric radii are probed. This has important implications for dynamical modelling of early-type galaxies. The data from this study are available on-line.     

Gas in early-type galaxies: cross-fuelling in late-type–early-type pairs?

We present  ¹²CO ( J = 1–0)  and  ¹²CO ( J = 2–1)  observations of eight early-type galaxies, forming part of a sample of interacting galaxies, each consisting of one late- and one early-type system. All of the early-type galaxies observed are undetected in CO to low levels, allowing us to place tight constraints on their molecular gas content. Additionally, we present H  i absorption data for one system. The implications for possible gas transfer from the late- to the early-type galaxy during the interaction are discussed.     

The HST/ACS Coma Cluster Survey – V. Compact stellar systems in the Coma Cluster

The Hubble Space Telescope /Advanced Camera for Surveys ( HST /ACS) Coma Cluster Treasury Survey is a deep two-passband imaging survey of the nearest very rich cluster of galaxies, covering a range of galaxy density environments. The imaging is complemented by a recent wide field redshift survey of the cluster conducted with Hectospec on the 6.5-m Monolithic Mirror Telescope (MMT). Among the many scientific applications for these data is the search for compact galaxies. In this paper, we present the discovery of seven compact (but quite luminous) stellar systems, ranging from M32-like galaxies down to ultra-compact dwarfs (UCDs)/dwarf to globular transition objects (DGTOs).
We find that all seven compact galaxies require a two-component fit to their light profile and have measured velocity dispersions that exceed those expected for typical early-type galaxies at their luminosity. From our structural parameter analysis, we conclude that three of the samples should be classified as compact ellipticals or M32-like galaxies, and the remaining four being less extreme systems. The three compact ellipticals are all found to have old luminosity weighted ages (≳12 Gyr), intermediate metallicities  (−0.6 < [Fe/H] < −0.1)  and high [Mg/Fe] (≳0.25).
Our findings support a tidal stripping scenario as the formation mode of compact galaxies covering the luminosity range studied here. We speculate that at least two early-type morphologies may serve as the progenitor of compact galaxies in clusters.     

GHASP: an Hα kinematic survey of spiral and irregular galaxies – IV. 44 new velocity fields. Extension, shape and asymmetry of Hα rotation curves

We present Fabry–Perot observations obtained in the frame of the GHASP survey (Gassendi HAlpha survey of SPirals). We have derived the Hα map, the velocity field and the rotation curve for a new set of 44 galaxies. The data presented in this paper are combined with the data published in the three previous papers providing a total number of 85 of the 96 galaxies observed up to now. This sample of kinematical data has been divided into two groups: isolated (ISO) and softly interacting (SOFT) galaxies. In this paper, the extension of the Hα discs, the shape of the rotation curves, the kinematical asymmetry and the Tully–Fisher relation have been investigated for both ISO and SOFT galaxies. The Hα extension is roughly proportional to R₂₅ for ISO as well as for SOFT galaxies. The smallest extensions of the ionized disc are found for ISO galaxies. The inner slope of the rotation curves is found to be correlated with the central concentration of light more clearly than with the type or the kinematical asymmetry, for ISO as well as for SOFT galaxies. The outer slope of the rotation curves increases with the type and with the kinematical asymmetry for ISO galaxies but shows no special trend for SOFT galaxies. No decreasing rotation curve is found for SOFT galaxies. The asymmetry of the rotation curves is correlated with the morphological type, the luminosity, the  ( B − V )  colour and the maximal rotational velocity of galaxies. Our results show that the brightest, the most massive and the reddest galaxies, which are fast rotators, are the least asymmetric, meaning that they are the most efficient with which to average the mass distribution on the whole disc. Asymmetry in the rotation curves seems to be linked with local star formation, betraying disturbances of the gravitational potential. The Tully–Fisher relation has a smaller slope for ISO than for SOFT galaxies.     

Modelling the number counts of early-type galaxies by pure luminosity evolution

In this paper, we explore the plausible luminosity evolution of early-type galaxies in different cosmological models by constructing a set of pure luminosity evolution (PLE) models via the choices of the star-formation rate (SFR) parameters and formation redshift z _f of galaxies, with the observational constraints derived from the Hubble Space Telescope ( HST  ) morphological number counts for elliptical and S0 galaxies of the Medium Deep Survey (MDS) and the Hubble Deep Field (HDF). We find that the number counts of early-type galaxies can be explained by the pure luminosity evolution models, without invoking exotic scenarios such as merging or introducing an additional population, but the evolution should be nearly passive, with a high z _f assumed. The conclusion is valid in all of the three cosmological models we adopt in this paper. We also present the redshift distributions for three bins of observed magnitudes in the F814w passband, to show the redshift at which the objects that dominate the counts at a given magnitude may be found. The predictions of the redshift distribution of 22.5 <  b _j  < 24.0 are also presented for comparison with future data.     

Recovering the intrinsic shape of early-type galaxies

We investigate how well the intrinsic shape of early-type galaxies can be recovered when both photometric and two-dimensional stellar kinematic observations are available. We simulate these observations with galaxy models that are representative of observed oblate fast-rotator to triaxial slow-rotator early-type galaxies. By fitting realistic triaxial dynamical models to these simulated observations, we recover the intrinsic shape (and mass-to-light ratio), without making additional (ad hoc) assumptions on the orientation.
For (near) axisymmetric galaxies, the dynamical modelling can strongly exclude triaxiality, but the regular kinematics do not further tighten the constraint on the intrinsic flattening significantly, so that the inclination is nearly unconstrained above the photometric lower limit even with two-dimensional stellar kinematics. Triaxial galaxies can have additional complexity in both the observed photometry and kinematics, such as twists and (central) kinematically decoupled components, which allows the intrinsic shape to be accurately recovered. For galaxies that are very round or show no significant rotation, recovery of the shape is degenerate, unless additional constraints such as from a thin disc are available.     

Globular cluster systems in nearby dwarf galaxies – I. HST/ACS observations and dynamical properties of globular clusters at low environmental density

We investigate the old globular cluster (GC) population of 68 faint  ( M _V > −16 mag)  dwarf galaxies located in the halo regions of nearby (≲12 Mpc) loose galaxy groups and in the field environment based on archival Hubble Space Telescope ( HST )/Advanced Camera for Surveys (ACS) images in F606W and F814W filters. The combined colour distribution of 175 GC candidates peaks at  ( V − I ) = 0.96 ± 0.07 mag  and the GC luminosity function turnover for the entire sample is found at   M _{V ,TO}=−7.6 ± 0.11 mag  , similar to the old metal-poor Large Magellanic Cloud (LMC) GC population. Our data reveal a tentative trend of   M _{V ,TO}  becoming fainter from late- to early-type galaxies. The luminosity and colour distributions of GCs in dIrrs show a lack of faint blue GCs (bGCs). Our analysis reveals that this might reflect a relatively younger GC system than typically found in luminous early-type galaxies. If verified by spectroscopy, this would suggest a later formation epoch of the first metal-poor star clusters in dwarf galaxies. We find several bright (massive) GCs which reside in the nuclear regions of their host galaxies. These nuclear clusters have similar luminosities and structural parameters as the peculiar Galactic clusters suspected of being the remnant nuclei of accreted dwarf galaxies, such as M54 and ωCen. Except for these nuclear clusters, the distribution of GCs in dIrrs in the half-light radius versus cluster mass plane is very similar to that of Galactic young halo clusters, which suggests comparable formation and dynamical evolution histories. A comparison with theoretical models of cluster disruption indicates that GCs in low-mass galaxies evolve dynamically as self-gravitating systems in a benign tidal environment.     

Inferring dark halo structure from observed scaling laws of late-type galaxies and LSBs

We re-examine the Fall & Efstathiou scenario for galaxy formation, including the dark halo gravitational reaction to the formation of the baryon disc, as well as continuous variations in the intrinsic halo density profile. The recently published rotation curves of low surface brightness (LSB) and dwarf galaxies together with previously known scaling relations provide sufficient information on the present-day structure of late-type disc galaxies to invert the problem. By requiring that the models reproduce all the observational restrictions we can fully constrain the initial conditions of galaxy formation, with a minimum of assumptions, in particular without the need to specify a cold dark matter (CDM) halo profile. This allows one to solve for all the initial conditions, in terms of the halo density profile, the baryon fraction and the total angular momentum. We find that a unique initial halo shape is sufficient to accurately reproduce the rotation curves of both LSB and normal late-type spiral galaxies. This unique halo profile differs substantially from that found in standard CDM models. A galactic baryon fraction of 0.065 is found. The initial value of the dimensionless angular momentum is seen to be the principal discriminator between the galaxy classes we examine. The present-day scalings between structural parameters are seen to originate in the initial conditions.     

The galaxy population of Cl 1601+42 at z=0.54

Photometric redshifts are used to determine the rest-frame luminosity function (LF) of both early- and late-type galaxies to  M_B∼−17.6  for the cluster Cl 1601+42 at  z=0.54  . The total LF shows a steep faint-end slope   α ∼−1.4  , indicating the existence of a population of numerous dwarf galaxies. Luminous galaxies, with  M_B≲−19.5  are mostly red, early-type galaxies, with a LF best described by a Gaussian. Faint galaxies are predominantly blue, late-type galaxies, well fitted by a Schechter function with   α ∼−1.7  . Compared with clusters at lower redshift, the steepening of the faint end starts at brighter magnitudes for Cl 1601+42, which may indicate a brightening of the present-day dwarf population relative to the giant population with increasing redshift. Early-type galaxies are centrally concentrated, and dominate the core region, implying that the radial gradient of early-type galaxies seen in local clusters is already established at  z∼0.5  . Bright, late-type galaxies are rare, consistent with a decrease in star formation in field galaxies as they are accreted on to the cluster, while faint, blue galaxies are evenly distributed across the cluster, except for a depletion in the core region. The blue fraction is  f_B∼0.15  , which is somewhat lower than the Butcher–Oemler average at  z∼0.5  . The value of f _B is found to increase with limiting magnitude and with radius from the centre.     

Kinematic properties and stellar populations of faint early-type galaxies – I. Velocity dispersion measurements of central Coma galaxies

We present velocity dispersion measurements for 69 faint early-type galaxies in the core of the Coma cluster, spanning  −22.0 ≲ M_R ≲−17.5 mag  . We examine the   L –σ  relation for our sample and compare it to that of bright elliptical galaxies (Es) from the literature. The distribution of the the faint early-type galaxies in the   L –σ  plane follows the relation   L ∝σ^2.01±0.36  , which is significantly shallower from   L ∝σ⁴  as defined for the bright Es. While increased rotational support for fainter early-type galaxies could account for some of the difference in slope, we show that it cannot explain it. We also investigate the colour–σ relation for our Coma galaxies. Using the scatter in this relation, we constrain the range of galaxy ages as a function of their formation epoch for different formation scenarios. Assuming a strong coordination in the formation epoch of faint early-type systems in Coma, we find that most had to be formed at least 6 Gyr ago and over a short 1-Gyr period.     

Scalar fields as dark matter in spiral galaxies: comparison with experiments

We present an exact solution for a static and axially symmetric spacetime, which is obtained from a scalar-tensor theory that comes from unification theories. As an attempt to model the dark matter (DM) in spiral galaxies we find that an exponential scalar potential is enough to explain the rotation curves in such galaxies. We also present the fitting to the rotation curve of six spiral galaxies and we find an excellent agreement between observational data and the results of our model.     

Scaling relations of the colour-detected cluster RzCS 052 at z= 1.016 and some other high-redshift clusters

This paper investigates the possibility that ultra-compact dwarf (UCD) galaxies in the Fornax cluster are formed by the threshing of nucleated, early-type dwarf galaxies (hereafter dwarf galaxies).
Similar to the results of Côté et al. for the Virgo cluster, we show that the Fornax cluster observations are consistent with a single population in which all dwarfs are nucleated, with a ratio of nuclear to total magnitude that varies slowly with magnitude. Importantly, the magnitude distribution of the UCD population is similar to that of the dwarf nuclei in the Fornax cluster.
The joint population of UCDs and the dwarfs from which they may originate is modelled and shown to be consistent with a Navarro, Frenk & White (NFW) profile with a characteristic radius of 5 kpc. Furthermore, a steady-state dynamical model reproduces the known mass profile of Fornax. However, there are a number of peculiarities in the velocity dispersion data that remain unexplained.
The simplest possible threshing model is tested, in which dwarf galaxies move on orbits in a static cluster potential and are threshed if they pass within a radius at which the tidal force from the cluster exceeds the internal gravity at the core of their dark matter halo. This fails to reproduce the observed fraction of UCDs at radii greater than 30 kpc from the core of Fornax.     

X-ray luminosities of galaxies in groups

We have derived the X-ray luminosities of a sample of galaxies in groups, making careful allowance for contaminating intragroup emission. The L _X: L _B and L _X: L _FIR relations of spiral galaxies in groups appear to be indistinguishable from those in other environments, however the elliptical galaxies fall into two distinct classes. The first class is central-dominant group galaxies, which are very X-ray luminous and may be the focus of group cooling flows. All other early-type galaxies in groups belong to the second class, which populates an almost constant band of L _X/ L _B over the range 9.8< log  L _B<11.3 . The X-ray emission from these galaxies can be explained by a superposition of discrete galactic X-ray sources together with a contribution from hot gas lost by stars, which varies a great deal from galaxy to galaxy. In the region where the optical luminosity of the non-central group galaxies overlaps with the dominant galaxies, the dominant galaxies are over an order of magnitude more luminous in X-rays.
We also compared these group galaxies with a sample of isolated early-type galaxies, and used previously published work to derive L _X: L _B relations as a function of environment. The non-dominant group galaxies have mean L _X/ L _B ratios very similar to those of isolated galaxies, and we see no significant correlation between L _X/ L _B and environment. We suggest that previous findings of a steep L _X: L _B relation for early-type galaxies result largely from the inclusion of group-dominant galaxies in samples.     

Kinematics and stellar populations of 17 dwarf early-type galaxies

We present kinematics and stellar population properties of 17 dwarf early-type galaxies in the luminosity range -14 ≥ M _B ≥ -19. Our sample fills the gap between the intensively studied giant elliptical and Local Group dwarf spheroidal galaxies. The dwarf ellipticals of the present sample have constant velocity dispersion profiles within their effective radii and do not show significant rotation, hence are clearly anisotropic. The dwarf lenticulars, instead, rotate faster and are, at least partially, supported by rotation. From optical Lick absorption indices, we derive metallicities and element abundances. Combining our sample with literature data of the Local Group dwarf spheroidals and giant ellipticals, we find a surprisingly tight linear correlation between metallicity and luminosity over a wide range: -8 ≥ M _B ≥ -22. The α/Fe ratios of our dwarf ellipticals are significantly lower than the ones of giant elliptical galaxies, which is in agreement with spectroscopy of individual stars in Local Group dwarf spheroidals. Our results suggest the existence of a clear kinematic and stellar population dichotomy between dwarf and giant elliptical galaxies. This result is important for theories of galaxy formation, because it implies that present-day dwarf ellipticals are not the fossiled building blocks of giant ellipticals. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mass-to-light ratio gradients in early-type galaxy haloes

Owing to the fact that the near future should see a rapidly expanding set of probes of the halo masses of individual early-type galaxies, we introduce a convenient parameter for characterizing the halo masses from both observational and theoretical results:  ∇_ℓϒ  , the logarithmic radial gradient of the mass-to-light ratio. Using halo density profiles from Λ-cold dark matter (CDM) simulations, we derive predictions for this gradient for various galaxy luminosities and star formation efficiencies  ε_SF  . As a pilot study, we assemble the available  ∇_ℓϒ  data from kinematics in early-type galaxies – representing the first unbiased study of halo masses in a wide range of early-type galaxy luminosities – and find a correlation between luminosity and  ∇_ℓϒ  , such that the brightest galaxies appear the most dark-matter dominated. We find that the gradients in most of the brightest galaxies may fit in well with the ΛCDM predictions, but that there is also a population of fainter galaxies whose gradients are so low as to imply an unreasonably high star formation efficiency  ε_SF > 1  . This difficulty is eased if dark haloes are not assumed to have the standard ΛCDM profiles, but lower central concentrations.     

Exploring disc galaxy dynamics using integral field unit data

In order to test the basic equations believed to dictate the dynamics of disc galaxies, we present and analyse deep two-dimensional spectral data obtained using the PPAK integral field unit for the early-type spiral systems NGC 2273, NGC 2985, NGC 3898 and NGC 5533. We describe the care needed to obtain and process such data to a point where reliable kinematic measurements can be obtained from these observations, and a new more optimal method for deriving the rotational motion and velocity dispersions in such disc systems. The data from NGC 2273 and NGC 2985 show systematic variations in velocity dispersion with azimuth, as one would expect if the shapes of their velocity ellipsoids are significantly anisotropic, while the hotter discs in NGC 3898 and NGC 5533 appear to have fairly isotropic velocity dispersions. Correcting the rotational motion for asymmetric drift using the derived velocity dispersions reproduces the rotation curves inferred from emission lines reasonably well, implying that this correction is quite robust, and that the use of the asymmetric drift equation is valid. NGC 2985 is sufficiently close to face on for the data, combined with the asymmetric drift equation, to determine all three components of the velocity ellipsoid. The principal axes of this velocity ellipsoid are found to be in the ratio  σ _z : σ_φ : σ _R ≈ 0.7 : 0.7 : 1  , which shows unequivocally that this disc distribution function respects a third integral of motion. The ratio is also consistent with the predictions of epicyclic theory, giving some confidence in the application of this approximation to even fairly early-type disc galaxies.