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.     

The radial Tully–Fisher relation for spiral galaxies – I

We find a new Tully–Fisher-like relation for spiral galaxies holding at different galactocentric radii. This radial Tully–Fisher relation allows us to investigate the distribution of matter in the optical regions of spiral galaxies. This relation, applied to three different samples of rotation curves of spiral galaxies, directly proves that: (i) the rotation velocity of spirals is a good measure of their gravitational potential and both the rotation curve's amplitudes and profiles are well predicted by galaxy luminosity, (ii) the existence of a dark component, less concentrated than the luminous one, and (iii) a scaling law, according to which, inside the disc optical size:   M _dark/ M _lum= 0.5( L _B /10¹¹ L _{B ⊙})^−0.7  .     

Dynamical response to supernova-induced gas removal in spiral galaxies with dark matter halo

We investigate the dynamical response, in terms of disc size and rotation velocity, to mass loss by supernovae in the evolution of spiral galaxies. A thin baryonic disc having the Kuzmin density profile embedded in a spherical dark matter halo having a density profile proposed by Navarro, Frenk & White is considered. For the purpose of comparison, we also consider the homogeneous and   r ⁻¹  profiles for dark matter in a truncated spherical halo. Assuming for simplicity that the dark matter distribution is not affected by mass-loss from discs and the change of baryonic disc matter distribution is homologous, we evaluate the effects of dynamical response in the resulting discs. We found that the dynamical response only for an adiabatic approximation of mass-loss can simultaneously account for the rotation velocity and disc size as observed particularly in dwarf spiral galaxies, thus reproducing the Tully–Fisher relation and the size versus magnitude relation over the full range of magnitude. Furthermore, we found that the mean specific angular momentum in discs after the mass-loss becomes larger than that before the mass-loss, suggesting that the mass-loss would most likely occur from the central disc region where the specific angular momentum is low.     

The dark matter distribution in disc galaxies

We use high-quality optical rotation curves of nine low-luminosity disc galaxies to obtain the velocity profiles of the surrounding dark matter haloes. We find that they increase linearly with radius at least out to the edge of the stellar disc, implying that, over the entire stellar region, the density of the dark halo is about constant.
The properties of the mass structure of these haloes are similar to those found for a number of dwarf and low surface brightness galaxies, but provide a more substantial evidence of the discrepancy between the halo mass distribution predicted in the cold dark matter scenario and those actually detected around galaxies. We find that the density law proposed by Burkert reproduces the halo rotation curves, with halo central densities ( ρ ₀∼1–4×10⁻²⁴ g cm⁻³) and core radii ( r ₀∼5–15 kpc) scaling as ρ ₀∝ r ₀^−2/3.     

Constraints on dark matter physics from dwarf galaxies through galaxy cluster haloes

One of the predictions of the standard cold dark matter model is that dark haloes have centrally divergent density profiles. An extensive body of rotation curve observations of dwarf and low surface brightness galaxies shows the dark haloes of those systems to be characterized by soft constant-density central cores. Several physical processes have been proposed to produce soft cores in dark haloes, each one with different scaling properties. With the aim of discriminating among them we have examined the rotation curves of dark-matter-dominated dwarf and low surface brightness galaxies and the inner mass profiles of two clusters of galaxies lacking a central cD galaxy and with evidence of soft cores in the centre. The core radii and central densities of these haloes scale in a well-defined manner with the depth of their potential wells, as measured through the maximum circular velocity. As a result of our analysis we identify self-interacting cold dark matter as a viable solution to the core problem, where a non-singular isothermal core is formed in the halo centre surrounded by a Navarro, Frenk & White profile in the outer parts. We show that this particular physical situation predicts core radii in agreement with observations. Furthermore, using the observed scalings, we derive an expression for the minimum cross-section ( σ ) which has an explicit dependence with the halo dispersion velocity ( v ). If m _x is the mass of the dark matter particle: σ m _x ≈4×10⁻²⁵ (100 km s⁻¹  v ⁻¹) cm² GeV⁻¹.     

A robust method for measuring the Hubble parameter

We obtain a robust, non-parametric, estimate of the Hubble constant from the linear diameters and rotation velocities of galaxies in the recent KLUN sample, calibrated using Cepheid distances to Hubble Space Telescope Key Project galaxies. There are two key features that make our analysis considerably more robust than previous work. First, the method is independent of the spatial distribution of galaxies and is insensitive to Malmquist bias. It may, therefore, be applied to more distant samples than so-called 'plateau' methods – making it much less vulnerable to the impact of peculiar motions in the Local Supercluster. Secondly, we include information on the galaxy rotation velocities in a fully non-parametric manner: unlike the conventional Tully–Fisher relation we reconstruct a robust estimate of the cumulative distribution function of galaxy diameter at given rotation velocity, without requiring the assumption of, for example, a linear Tully–Fisher relation with symmetric Gaussian residuals.
Using this robust method we find H ₀=65±6 km s⁻¹ Mpc⁻¹ from our analysis – in excellent agreement with many recent determinations of the Hubble parameter, although somewhat larger than previous results using galaxy diameters.     

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.     

Semi-analytic modelling of galaxy formation: the local Universe

Using semi-analytic models of galaxy formation, we investigate galaxy properties such as the Tully–Fisher relation, the B - and K -band LFs, cold gas contents, sizes, metallicities and colours, and compare our results with observations of local galaxies. We investigate several different recipes for star formation and supernova feedback, including choices that are similar to the treatment by Kauffmann, White & Guiderdoni and Cole et al., as well as some new recipes. We obtain good agreement with all of the key local observations mentioned above. In particular, in our best models, we simultaneously produce good agreement with both the observed B - and K -band LFs and the I -band Tully–Fisher relation. Improved cooling and supernova feedback modelling, inclusion of dust extinction and an improved Press–Schechter model all contribute to this success. We present results for several variants of the CDM family of cosmologies, and find that models with values of Ω₀≃0.3–0.5 give the best agreement with observations.     

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.     

Halo masses for optically selected and for radio-loud AGN from clustering and galaxy–galaxy lensing

We compute two-point correlation functions and measure the shear signal due to galaxy–galaxy lensing for 80 000 optically identified and 5700 radio-loud active galactic nuclei (AGN) from Data Release 4 of the Sloan Digital Sky Survey. Halo occupation models are used to estimate halo masses and satellite fractions for these two types of AGN. The large sample size allows us to separate AGN according to the stellar mass of their host galaxies. We study how the halo masses of optical and radio AGN differ from those of the parent population at fixed   M _*  . Halo masses deduced from clustering and from lensing agree satisfactorily. Radio AGN are found in more massive haloes than optical AGN: in our samples, their mean halo masses are  1.6 × 10¹³  and  8 × 10¹¹  h ⁻¹ M_⊙  , respectively. Optical AGN follow the same relation between stellar mass and halo mass as galaxies selected without regard to nuclear properties, but radio-loud AGN deviate significantly from this relation. The dark matter haloes of radio-loud AGN are about twice as massive as those of control galaxies of the same stellar mass. This boost is independent of radio luminosity, and persists even when our analysis is restricted to field galaxies. The large-scale gaseous environment of the galaxy clearly plays a crucial role in producing observable radio emission. The dark matter halo masses that we derive for the AGN in our two samples are in good agreement with recent models in which feedback from radio AGN becomes dominant in haloes where gas cools quasi-statically.     

Large-scale galactic turbulence: can self-gravity drive the observed H i velocity dispersions?

Observations of turbulent velocity dispersions in the H  i component of galactic discs show a characteristic floor in galaxies with low star formation rates and within individual galaxies the dispersion profiles decline with radius. We carry out several high-resolution adaptive mesh simulations of gaseous discs embedded within dark matter haloes to explore the roles of cooling, star formation, feedback, shearing motions and baryon fraction in driving turbulent motions. In all simulations the disc slowly cools until gravitational and thermal instabilities give rise to a multiphase medium in which a large population of dense self-gravitating cold clouds are embedded within a warm gaseous phase that forms through shock heating. The diffuse gas is highly turbulent and is an outcome of large-scale driving of global non-axisymmetric modes as well as cloud–cloud tidal interactions and merging. At low star formation rates these processes alone can explain the observed H  i velocity dispersion profiles and the characteristic value of  ∼10 km s⁻¹  observed within a wide range of disc galaxies. Supernovae feedback creates a significant hot gaseous phase and is an important driver of turbulence in galaxies with a star formation rate per unit area  ≳10⁻³ M_⊙ yr⁻¹ kpc⁻²  .     

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.     

Peculiar velocities and the mean density parameter

We study the peculiar velocity field inferred from the Mark III spirals using a new method of analysis. We estimate optimal values of Tully–Fisher scatter and zero-point offset, and we derive the three-dimensional rms peculiar velocity ( σ _v ) of the galaxies in the samples analysed. We check our statistical analysis using mock catalogues derived from numerical simulations of cold dark matter (CDM) models considering measurement uncertainties and sampling variations. Our best determination for the observations is σ _v =(660±50) km s⁻¹. We use the linear theory relation between σ _v , the density parameter Ω, and the galaxy correlation function ξ ( r ) to infer the quantity     , where b is the linear bias parameter of optical galaxies and the uncertainties correspond to bootstrap resampling and an estimated cosmic variance added in quadrature. Our findings are consistent with the results of cluster abundances and redshift-space distortion of the two-point correlation function. These statistical measurements suggest a low value of the density parameter Ω∼0.4 if optical galaxies are not strongly biased tracers of mass.     

Dynamical friction and galaxy merging time-scales

The time-scale for galaxies within merging dark matter haloes to merge with each other is an important ingredient in galaxy formation models. Accurate estimates of merging time-scales are required for predictions of astrophysical quantities such as black hole binary merger rates, the build-up of stellar mass in central galaxies and the statistical properties of satellite galaxies within dark matter haloes. In this paper, we study the merging time-scales of extended dark matter haloes using N -body simulations. We compare these results to standard estimates based on the Chandrasekhar theory of dynamical friction. We find that these standard predictions for merging time-scales, which are often used in semi-analytic galaxy formation models, are systematically shorter than those found in simulations. The discrepancy is approximately a factor of 1.7 for M _sat/ M _host≈ 0.1 and becomes larger for more disparate satellite-to-host mass ratios, reaching a factor of ∼3.3 for M _sat/ M _host≈ 0.01. Based on our simulations, we propose a new, easily implementable fitting formula that accurately predicts the time-scale for an extended satellite to sink from the virial radius of a host halo down to the halo's centre for a wide range of M _sat/ M _host and orbits. Including a central bulge in each galaxy changes the merging time-scale by ≲10 per cent. To highlight one concrete application of our results, we show that merging time-scales often used in the literature overestimate the growth of stellar mass by satellite accretion by ≈40 per cent, with the extra mass gained in low mass ratio mergers.     

Satellite kinematics – II. The halo mass–luminosity relation of central galaxies in SDSS

The kinematics of satellite galaxies reflect the masses of the extended dark matter haloes in which they orbit, and thus shed light on the mass–luminosity relation (MLR) of their corresponding central galaxies. In this paper, we select a large sample of centrals and satellites from the Sloan Digital Sky Survey and measure the kinematics (velocity dispersions) of the satellite galaxies as a function of the r -band luminosity of the central galaxies. Using the analytical framework presented in More, van den Bosch & Cacciato, we use these data to infer both the mean and the scatter of the MLR of central galaxies, carefully taking account of selection effects and biases introduced by the stacking procedure. As expected, brighter centrals on average reside in more massive haloes. In addition, we find that the scatter in halo masses for centrals of a given luminosity,  σ_{log  M}   , also increases with increasing luminosity. As we demonstrate, this is consistent with  σ_{log  L}   , which reflects the scatter in the conditional probability function   P ( L _c| M )  , being independent of halo mass. Our analysis of the satellite kinematics yields  σ_{log  L} = 0.16  ±  0.04  , in excellent agreement with constraints from clustering and group catalogues, and with predictions from a semi-analytical model of galaxy formation. We thus conclude that the amount of stochasticity in galaxy formation, which is characterized by  σ_{log  L}   , is well constrained, independent of halo mass and in a good agreement with current models of galaxy formation.     

The tightening of wide binaries in dSph galaxies through dynamical friction as a test of the dark matter hypothesis

We estimate the time-scales for orbital decay of wide binaries embedded within dark matter haloes, due to dynamical friction against the dark matter particles. We derive analytical scalings for this decay and calibrate and test them through the extensive use of N -body simulations, which accurately confirm the predicted temporal evolution. For density and velocity dispersion parameters as inferred for the dark matter haloes of local dSph galaxies, we show that the decay time-scales become shorter than the ages of the dSph stellar populations for binary stars composed of  1 M_⊙  stars, for initial separations larger than 0.1 pc. Such wide binaries are conspicuous and have been well measured in the solar neighbourhood. The prediction of the dark matter hypothesis is that they should now be absent from stellar populations embedded within low velocity dispersion, high-density dark mater haloes, as currently inferred for the local dSph galaxies, having since evolved into tighter binaries. Relevant empirical determinations of this will become technically feasible in the near future, and could provide evidence to discriminate between dark matter particle haloes or modified gravitational theories, to account for the high dispersion velocities measured for stars in local dSph galaxies.     

Dark matter in elliptical galaxies – I. Is the total mass density profile of the NFW form or even steeper?

Elliptical galaxies are modelled as Sérsic luminosity distributions with density profiles (DPs) for the total mass adopted from the DPs of haloes within dissipationless ΛCDM (cold dark matter) N -body simulations. Ellipticals turn out to be inconsistent with cuspy low-concentration NFW models representing the total mass distribution, neither are they consistent with a steeper −1.5 inner slope, nor with the shallower models proposed by Navarro et al., nor with NFW models 10 times more concentrated than predicted, as deduced from several X-ray observations – the mass models, extrapolated inwards, lead to local mass-to-light ratios that are smaller than the stellar value inside an effective radius ( R _e), and to central aperture velocity dispersions that are much smaller than observed. This conclusion remains true as long as there is no sharp steepening (slope < −2) of the dark matter DPs just inside 0.01 virial radii.
The very low total mass and velocity dispersion produced within R _e by an NFW-like total mass profile suggests that the stellar component should dominate the dark matter component out to at least R _e. It should then be difficult to kinematically constrain the inner slope of the DP of ellipticals. The high-concentration parameters deduced from X-ray observations appear to be a consequence of fitting an NFW model to the total mass DP made up of a stellar component that dominates inside and a dark matter component that dominates outwards.
An appendix gives the virial mass dependence of the concentration parameter, central density and total mass of the Navarro et al. model. In a second appendix are given single integral expressions for the velocity dispersions averaged along the line of sight, in circular apertures and in thin slits, for general luminosity density and mass distributions, with isotropic orbits.     

Numerical simulations of hot halo gas in galaxy mergers

Galaxy merger simulations have explored the behaviour of gas within the galactic disc, yet the dynamics of hot gas within the galaxy halo have been neglected. We report on the results of high-resolution hydrodynamic simulations of colliding galaxies with metal-free hot halo gas. To isolate the effect of the halo gas, we simulate only the dark matter halo and the hot halo gas over a range of mass ratios, gas fractions and orbital configurations to constrain the shocks and gas dynamics within the progenitor haloes. We find that (i) a strong shock is produced in the galaxy haloes before the first passage, increasing the temperature of the gas by almost an order of magnitude to   T ∼ 10^6.3 K  . (ii) The X-ray luminosity of the shock is strongly dependent on the gas fraction; it is  ≳10³⁹ erg s⁻¹  for halo gas fractions larger than 10 per cent. (iii) The hot diffuse gas in the simulation produces X-ray luminosities as large as  10⁴² erg s⁻¹  . This contributes to the total X-ray background in the Universe. (iv) We find an analytic fit to the maximum X-ray luminosity of the shock as a function of merger parameters. This fit can be used in semi-analytic recipes of galaxy formation to estimate the total X-ray emission from shocks in merging galaxies. (v) ∼10–20 per cent of the initial gas mass is unbound from the galaxies for equal-mass mergers, while 3–5 per cent of the gas mass is released for the 3:1 and 10:1 mergers. This unbound gas ends up far from the galaxy and can be a feasible mechanism to enrich the intergalactic medium with metals.     

Velocity dispersions of dwarf spheroidal galaxies: dark matter versus MOND

We present predictions for the line-of-sight velocity dispersion profiles of dwarf spheroidal galaxies and compare them to observations in the case of the Fornax dwarf. The predictions are made in the framework of standard dynamical theory of spherical systems with different velocity distributions. The stars are assumed to be distributed according to Sérsic laws with parameters fitted to observations. We compare predictions obtained assuming the presence of dark matter haloes (with density profiles adopted from N -body simulations) with those resulting from Modified Newtonian Dynamics (MOND). If the anisotropy of velocity distribution is treated as a free parameter, observational data for Fornax are reproduced equally well by models with dark matter and with MOND. If stellar mass-to-light ratio of 1 M_⊙/L_⊙ is assumed, the required mass of the dark halo is     , two orders of magnitude larger than the mass in stars. The derived MOND acceleration scale is     . In both cases a certain amount of tangential anisotropy in the velocity distribution is needed to reproduce the shape of the velocity dispersion profile in Fornax.