A Cold Dark Matter Research Articles

Crawling the cosmic network: exploring the morphology of structure in the galaxy distribution

Although coherent large-scale structures such as filaments and walls are apparent to the eye in galaxy redshift surveys, they have so far proven difficult to characterize with computer algorithms. This paper presents a procedure that uses the eigenvalues and eigenvectors of the Hessian matrix of the galaxy density field to characterize the morphology of large-scale structure. By analysing the smoothed density field and its Hessian matrix, we can determine the types of structure – walls, filaments or clumps – that dominate the large-scale distribution of galaxies as a function of scale. We have run the algorithm on mock galaxy distributions in a Λcold dark matter cosmological N-body simulation and the observed galaxy distributions in the Sloan Digital Sky Survey. The morphology of structure is similar between the two catalogues, both being filament-dominated on 10–20 h−1 Mpc smoothing scales and clump-dominated on 5 h−1 Mpc scales. There is evidence for walls in both distributions, but walls are not the dominant structures on scales smaller than ∼ 25 h−1 Mpc. Analysis of the simulation suggests that, on a given comoving smoothing scale, structures evolve with time from walls to filaments to clumps, where those found on smaller smoothing scales are further in this progression at a given time.

Are fossil groups a challenge of the cold dark matter paradigm?

We study six groups and clusters of galaxies suggested in the literature to be 'fossil' systems (i.e. to have luminous diffuse X-ray emission and a magnitude gap of at least 2 mag R between the first and the second ranked member within half of the virial radius), each having good quality X-ray data and Sloan Digital Sky Survey (SDSS) spectroscopic or photometric coverage out to the virial radius. The poor cluster AWM 4 is clearly established as a fossil system, and we confirm the fossil nature of four other systems (RX J1331.5+1108, RX J1340.6+4018, RX J1256.0+2556 and RX J1416.4+2315), while the cluster RX J1552.2+2013 is disqualified as fossil system. For all systems, we present the luminosity functions within 0.5 and 1 virial radius that are consistent, within the uncertainties, with the universal luminosity function of clusters. For the five bonafide fossil systems, having amass range 2 x 10 13 -3 x 10 14 M ⊙, we compute accurate cumulative substructure distribution functions (CSDFs) and compare them with the CSDFs of observed and simulated groups/clusters available in the literature. We demonstrate that the CSDFs of fossil systems are consistent with those of normal observed clusters and do not lack any substructure with respect to simulated galaxy systems in the cosmological A cold dark matter (ACDM) framework. In particular, this holds for the archetype fossil group RX J1340.6+4018 as well, contrary to earlier claims.

Large Einstein radii: a problem for ΛCDM

The Einstein radius of a cluster provides a relatively model-independent measure of the mass density of a cluster within a projected radius of ∼150 kpc, large enough to be relatively unaffected by gas physics. We show that the observed Einstein radii of four well-studied massive clusters, for which reliable virial masses are measured, lie well beyond the predicted distribution of Einstein radii in the standard A cold dark matter (ACDM) model. Based on large samples of numerically simulated cluster-sized objects with virial masses ∼10 15 M O , the predicted Einstein radii are only 15-25 arcsec, a factor of 2 below the observed Einstein radii of these four clusters. This is because the predicted mass profile is too shallow to exceed the critical surface density for lensing at a sizable projected radius. After carefully accounting for measurement errors as well as the biases inherent in the selection of clusters and the projection of mass measured by lensing, we find that the theoretical predictions are excluded at a 4σ significance. Since most of the free parameters of the ACDM model now rest on firm empirical ground, this discrepancy may point to an additional mechanism that promotes the collapse of clusters at an earlier time thereby enhancing their central mass density.

Merger and ring galaxy formation rates atz≤ 2

We compare the observed merger rate of galaxies over cosmic time and the frequency of collisional ring galaxies (CRGs), with analytic models and halo merger and collision rates from a large cosmological simulation. In the A cold dark matter (ACDM) model, we find that the cosmic merger fraction does not evolve strongly between 0.2 < z ≤2, implying that the observed decrease in the cosmic star formation rate since z ∼ 1 might not be tied to a disappearing population of major mergers. Haloes hosting massive galaxies undergo on average ∼ 2 mergers from z ≤ 2 up to present day, reflecting the late assembly time for the massive systems and the related down-sizing problem. The cosmic merger rate declines with redshift: at the present time, it is of a factor of 10 lower than at z ∼ 2 in reasonable agreement with the current available data. The rate of CRG formation derived from the interactions between halo progenitors up to z = 2 is found to be a good tracer of the cosmic merger rate. In the ACDM model, the rate of CRGs as well as the merger rate do not scale as (1 + z) m as suggested by previous models. Our predictions of cosmic merger and CRG rates may be applied to forthcoming surveys such as GOODS and zCOSMOS.

A revised Λ CDM mass model for the Andromeda Galaxy

We present an updated mass model for M31 that makes use of a Spitzer 3.6-μm image, a mass-to-light ratio gradient based on the galaxy's B - R colour profile, and observed rotation curve data from a variety of sources. We examine cases where the dark matter follows a pure Navarro, Frenk & White (NFW) profile and where an initial NFW halo contracts adiabatically in response to the formation of the galaxy. We find that both of these scenarios can produce a reasonable fit to the observed rotation curve data. However, a pure NFW model requires a concentration c vir = 51 which is well outside the range predicted in Acold dark matter cosmology and is therefore disfavoured. An adiabatically contracted NFW halo favours an initial concentration c vir = 20 and virial mass 8.2 x 10 11 M ⊙ , and this is in line with the cosmological expectations for a galaxy of the size of M31. The best-fitting mass is consistent with published estimates from Andromeda Stream kinematics, satellite galaxy radial velocities and planetary nebulae studies. Finally, using the known linear correlation between rotation curve shear and spiral arm pitch angle, we show that the stellar spiral arm pitch angle of M31 (which cannot be deduced from imaging data due to the galaxy's inclination) is P = 24°7 ± 4°4.

Simulations of baryon acoustic oscillations - I. Growth of large-scale density fluctuations

We critically examine how well the evolution of large-scale density perturbations is followed in cosmological N-body simulations. We first run a large volume simulation and perform a mode-by-mode analysis in three-dimensional Fourier space. We show that the growth of large-scale fluctuations significantly deviates from linear-theory predictions. The deviations are caused by non-linear coupling with a small number of modes at largest scales owing to finiteness of the simulation volume. We then develop an analytic model based on second-order perturbation theory to quantify the effect. Our model accurately reproduces the simulation results. For a single realization, the second-order effect appears typically as 'zig-zag' patterns around the linear-theory prediction, which imprints artificial 'oscillations' that lie on the real baryon acoustic oscillations. Although an ensemble average of a number of realizations approaches the linear-theory prediction, the dispersions of the realizations remain large even for a large simulation volume of several hundred megaparsecs on a side. For the standard A cold dark matter (ACDM) model, the deviations from linear growth rate are as large as 10 per cent for a simulation volume with L = 500 h -1 Mpc and for a bin width in wavenumber of Δk = 0.005 h Mpc -1 , which are comparable to the intrinsic variance of Gaussian random realizations. We find that the dispersions scales as α L -3/2 Δk -1/2 and the mean dispersion amplitude can be made smaller than a per cent only if we use a very large volume of L > 2 h -1 Gpc. The finite box size effect needs to be appropriately taken into account when interpreting results from large-scale structure simulations for future dark energy surveys using baryon acoustic oscillations.

Angular momentum-large-scale structure alignments in ΛCDM models and the SDSS

We study the alignments between the angular momentum of individual objects and the large-scale structure in cosmological numerical simulations and real data from the Sloan Digital Sky Survey, Data Release 6 (SDSS-DR6). To this end, we measure anisotropies in the two point cross-correlation function around simulated haloes and observed galaxies, studying separately the one- and two-halo regimes. The alignment of the angular momentum of dark-matter haloes in A cold dark matter (ACDM) simulations is found to be dependent on scale and halo mass. At large distances (two-halo regime), the spins of high-mass haloes are preferentially oriented in the direction perpendicular to the distribution of matter; lower mass systems show a weaker trend that may even reverse to show an angular momentum in the plane of the matter distribution. In the one-halo term regime, the angular momentum is aligned in the direction perpendicular to the matter distribution; the effect is stronger than for the one-halo term and increases for higher mass systems. On the observational side, we focus our study on galaxies in the SDSS-DR6 with elongated apparent shapes, and study alignments with respect to the major semi-axis. We study five samples of edge-on galaxies; the full SDSS-DR6 edge-on sample, bright galaxies, faint galaxies, red galaxies and blue galaxies (the latter two consisting mainly of ellipticals and spirals, respectively). Using the two-halo term of the projected correlation function, we find an excess of structure in the direction of the major semi-axis for all samples; the red sample shows the highest alignment (2.7 ± 0.8 per cent) and indicates that the angular momentum of flattened spheroidals tends to be perpendicular to the large-scale structure. These results are in qualitative agreement with the numerical simulation results indicating that the angular momentum of galaxies could be built up as in the Tidal Torque scenario. The one-halo term only shows a significant alignment for blue spirals (1.0 ± 0.4 per cent), consistent with the one-halo results from the simulation but with a lower amplitude. This could indicate that even though the structure traced by galaxies is adequate to study large-scale structure alignments, this would not be the case for the inner structure of low-mass haloes, M ≤ 10 13 h -1 M ⊙ , an effect apparently more important around red g - r > 0.7 galaxies.

Thin, thick and dark discs in ΛCDM

In acold dark matter (� CDM) cosmology, the Milky Way accretes satellites into the stellar disc. We use cosmological simulations to assess the frequency of near disc plane and higher inclination accretion events, and collisionless simulations of satellite mergers to quantify the final state of the accreted material and the effect on the thin disc. On average, a Milky Way-sized galaxy has three subhaloes with vmax > 80 km s −1 ; seven with vmax > 60 km s −1 and 15 with vmax > 40 km s −1 merge at redshift z 1. Assuming isotropic accretion, a third of these merge at an impact angle θ 20 ◦ are twice as likely as low-inclination ones. These lead to structures that closely resemble the recently discovered inner and outer stellar haloes. They also do more damage to the Milky Way stellar disc creating a more pronounced flare, and warp; both long-lived and consistent with current observations. The most massive mergers (vmax 80 km s −1 ) heat the thin disc enough to produce a thick disc. These heated thin-disc stars are essential for obtaining a thick disc as massive as that seen in the Milky Way; they likely comprise some ∼50-90 per cent of the thick disc stars. The Milky Way thin disc must reform from fresh gas after z = 1. Only one in four of our sample Milky Way haloes experiences mergers massive and late enough to fully destroy the thin disc. We conclude that thick, thin and dark discs occur naturally within aCDM cosmology.

Is an 11 eV sterile neutrino consistent with clusters, the cosmic microwave background and modified Newtonian dynamics?

In this paper, we show that if a single sterile neutrino exists such that m vs ∼ 11 eV, it can serendipitously solve all outstanding issues of the Modified Newtonian Dynamics. We focus on fitting the angular power spectrum of the cosmic microwave background (CMB) in detail which is possible using a flat Universe with Ω vs ∼ 0.23 and the usual baryonic and dark energy components. One cannot match the CMB if there is more than one massive sterile neutrino, nor with three active neutrinos of 2 eV. This model has the same expansion history as the A cold dark matter (ACDM) model and only differs at the galactic scale, where the modified dynamics outperform ACDM comprehensively. We discuss how an 11 eV sterile neutrino can explain the dark matter of galaxy clusters without influencing individual galaxies and potentially match the matter power spectrum.

The distribution function of dark matter in massive haloes

We study the distribution function (DF) of dark matter particles in haloes of mass range 10 14 -10 15 M ⊙ . In the numerical part of this work we measure the DF for a sample of relaxed haloes formed in the simulation of a standard A cold dark matter (ACDM) model. The DF is expressed as a function of energy E and the absolute value of the angular momentum L, a form suitable for comparison with theoretical models. By proper scaling we obtain the results that do not depend on the virial mass of the haloes. We demonstrate that the DF can be separated into energy and angular momentum components and propose a phenomenological model of the DF in the form f E (E)[1 + L2/(2L 2 0 )] -β ∞ +β 0L -2β 0. This formulation involves three parameters describing the anisotropy profile in terms of its asymptotic values (β 0 and β ∞ ) and the scale of transition between them (L 0 ). The energy part f E (E) is obtained via inversion of the integral for spatial density. We provide a straightforward numerical scheme for this procedure as well as a simple analytical approximation for a typical halo formed in the simulation. The DF model is extensively compared with the simulations: using the model parameters obtained from fitting the anisotropy profile, we recover the DF from the simulation as well as the profiles of the dispersion and kurtosis of radial and tangential velocities. Finally, we show that our DF model reproduces the power-law behaviour of phase-space density Q = ρ(r)σ 3 (r).

The age dependence of galaxy clustering

We construct mock galaxy catalogues to analyse clustering properties of acold dark matter (�CDM) universe within a cosmological dark matter simulation of suffi- cient resolution to resolve structure down to the scale of dwarfs. We show that there is a strong age-clustering correlation for objects likely to host luminous galaxies, which includes the satellite halo (subhalo) population. Older mock galaxies are significantly more clustered in our catalog, which consists of satellite haloes as well as the central peaks of discrete haloes, selected solely by peak circular velocity. This age dependence is caused mainly by the age-clustering relation for discrete haloes, recently found by Gao et al. , acting mostly on field members, combined with the tendency for older mock galaxies to lie within groups and clusters, where galaxy clustering is enhanced. Our results suggest that the clustering age dependence is manifested in real galaxies. At small scales (less than �5 h 1 Mpc), the very simple assumption that galaxy colour depends solely on halo age is inconsistent with the strength of the observed cluster- ing colour trends, where red galaxies become increasingly more clustered than blue galaxies toward smaller scales, suggesting that luminosity weighted galaxy ages do not closely trace the assembly epoch of their dark matter hosts. The age dependence is present but is much weaker for satellite haloes lying within groups and clusters than for the global population.

ΛCDM halo density profiles: where do actual halos converge to NFW ones?

Aims. We present an analysis of 37 high-quality extended rotation curves that highlight the existence of a new discrepancy (or a new aspect of an old discrepancy) between the density profiles predicted by the A cold dark matter (ACDM) theory and the actual distribution of dark matter in galaxies. Methods. We compare the predicted face-value density vs. enclosed mass relationship, at large distances, to the observational data at the last measured radii of the rotation curves and in two whole rotation curves of high quality. A further analysis is performed by studying a relation, inbuilt in ACDM, that links, at radius R, the enclosed halo mass MNFW(R) and its density p(R) in a way that is independent of the mass of the virialised object. Results. We find that the predicted density vs. enclosed mass relationship has a systematic offset with respect to the observational data. In test case extended rotation curves, at their last measured point, the predicted NFW densities are up to a factor 3 lower than those derived from the kinematics. Moreover, the abovementioned relation, inbuilt in ACDM, does not hold for the objects of our sample. Such a new outer discrepancy is different and maybe complementary with respect to the core/cusp issue, for which the NFW densities turn out to be higher than those observed, and it seems to imply a global mass rearrangement of a pristine NFW-ACDM halo.

Deuterated hydrogen molecule and search for early structure-formation signatures in the Universe

Possible detection of signatures of structure formation at the end of the 'dark age' epoch (z ∼ 40-20) is examined. We discuss the spectral-spatial fluctuations in the cosmic microwave background radiation (CMBR) temperature produced by elastic resonant scattering of CMBR photons on deuterated hydrogen (HD) molecules located in protostructures moving with peculiar velocity. Detailed chemical kinematic evolution of HD molecules in the expanding homogeneous medium is calculated. Then, the HD abundances are linked to protostructures at their maximum expansion, whose properties are estimated by using the top-hat spherical approach and the A cold dark matter (ACDM) cosmology. We find that the optical depths in the HD three lowest pure rotational lines for high-peak protohaloes at their maximum expansion are much higher than those in LiH molecule. The corresponding spectral-spatial fluctuation amplitudes, however, are probably too weak to be detected by current and forthcoming millimetre telescope facilities. We extend our estimates of spectral-spatial fluctuations to gas clouds inside collapsed CDM haloes by using results from a crude model of HD production in these clouds. The fluctuations for the highest peak CDM haloes at redshifts ∼20-30 could be detected in the future. Observations will be important to test model predictions of early structure formation in the Universe.

The effect of low-mass substructures on the cusp lensing relation

It has been argued that the flux anomalies detected in gravitationally lensed QSOs are evidence for substructures in the foreground lensing haloes. In this paper we investigate this issue in greater detail focusing on the Cusp relation which corresponds to images of a source located to the cusp of the inner caustic curve. We use numerical simulations combined with a Monte Carlo approach to study the effects of the expected power law distribution of substructures within LCDM haloes on the multiple images. Generally, the high number of anomalous flux ratios in the cusp configurations is unlikely explained by 'simple' perturbers (subhaloes) inside the lensing galaxy, either modeled by point masses or extended NFW subhaloes. We considered in our analysis a mass range of 10^5-10^7 Msun for the subhaloes. We also demonstrate that including the effects of the surrounding mass distribution, such as other galaxies close to the primary lens, does not change the results. We conclude that triple images of lensed QSOs do not show any direct evidence for dark dwarf galaxies such as cold dark matter substructure.

Spatial fluctuations in the spectral shape of the ultraviolet background at 2 &gt; z &gt; 3 and the reionization of helium

The low-density hydrogen and helium in the intergalactic medium (IGM) probed by quasi- stellar object (QSO) absorption lines is sensitive to the amplitude and spectral shape of the metagalactic ultraviolet (UV) background. We use realistic H I and He II Lyα forest spectra, constructed from state-of-the-art hydrodynamical simulations of acold dark matter (�CDM) universe to confirm the reliability of using line profile fitting techniques to infer the ratio of the metagalactic H I and He II ionization rates. We further show that the large spatial variations and the anticorrelation with H I absorber density observed in the ratio of the measured He II to H I column densities can be explained in a model where the H I ionization rate is dominated by the combined UV emission from young star-forming galaxies and QSOs and the He II ionization rate is dominated by emission from QSOs only. In such a model the large fluctuations in the column density ratio are due to the small number of QSOs expected to contribute at any given point to the He II ionization rate. A significant contribution to UV emission at the He II photoelectric edge from hot gas in galaxies and galaxy groups would decrease the expected fluctuations in the column density ratio. Consequently, this model appears difficult to reconcile with the large increase in He II opacity fluctuations towards higher redshift. Our results further strengthen previous suggestions that observed He II Lyα forest spectra at z ∼ 2-3.5 probe the tail end of the reionization of He II by QSOs.

Hot and cooled baryons in smoothed particle hydrodynamic simulations of galaxy clusters: physics and numerics

We discuss an extended set of Tree+SPH (smoothed particle hydrodynamics) simulations of the formation of clusters of galaxies, with the goal of investigating the interplay between numerical resolution effects and star formation/feedback processes. Our simulations were all carried out in a concordance A cold dark matter (ACDM) cosmology and include radiative cooling, star formation and energy feedback from galactic winds. The simulated clusters span the mass range M vir ≃ (0.1-2.3) x 10 15 h -1 M ⊙ , with mass resolution varying by several decades. At the highest achieved resolution, the mass of gas particles is m gas ≃ 1.5 x 10 7 h -1 M ⊙ , which allows us to resolve the virial region of a Virgo-like cluster with more than two million gas particles and with at least as many dark matter (DM) particles. Our resolution study confirms that, in the absence of an efficient feedback mechanism, runaway cooling leads to about 35 per cent of baryons in clusters to be locked up in long lived stars at our highest resolution, with no evidence of convergence. However, including feedback causes the fraction of cooled baryons to converge at about 15 per cent already at modest resolution, which is much closer to the typical values inferred from observational data. Feedback also stabilizes other gas-related quantities, such as radial profiles of entropy, gas density and temperature, against variations due to changes in resolution. Besides the effects of mass resolution, we also investigate the influence of the gravitational force softening length and that of numerical heating of the gas induced by two-body encounters between DM and lighter gas particles. We also show that simulations where more DM than gas particles are used, such that m gas ≃ m DM , show a significantly enhanced efficiency of star formation at z ≥ 3, but they accurately reproduce at z = 0 the fraction of cooled gas and the thermodynamic properties of the intracluster gas. Our results are important for establishing and delineating the regime of numerical reliability of the present generation of hydrodynamical simulations of galaxy clusters.

The 2-Micron All-Sky Survey galaxy angular power spectrum: probing the galaxy distribution to gigaparsec scales

We present an angular power spectrum analysis of the 2-Micron All-Sky Survey (2MASS) full release extended source catalogue. The main sample used includes 518 576 galaxies below an extinction-corrected magnitude of K s = 13.5 and limited to |b| > 20°. The power spectrum results provide an estimate of the galaxy density fluctuations at extremely large scales, r? 1000 h -1 Mpc. We compare this with mock predictions constructed from the A cold dark matter (ACDM) Hubble Volume mock catalogue. At small scales, we find that the 2MASS C l is steeper than that for the Hubble Volume model. However, in the linear regime (l ≤ 30) there is good agreement between the two. We investigate in detail the effects of possible sources of systematic error. Converting linear power spectrum predictions for the form of the three-dimensional matter power spectrum, P(k), and assuming a flat CDM cosmology, a primordial n s = 1 spectrum and negligible neutrino mass, we perform fits to the galaxy angular power spectrum at large linear scales (l ≤ 30, corresponding to r? 50 h -1 Mpc). We obtain constraints on the galaxy power spectrum shape of Γ eff = 0.14 ± 0.02, in good agreement with previous estimates inferred at smaller scales. We also constrain the galaxy power spectrum normalization to (σ 8 b K ) 2 = 1.36 ± 0.1(1; in combination with previous constraints on σ 8 we infer a K,-band bias of b K = 1.39 ± 0.12. We are also able to provide weak constraints on Ω m h and Ω b /Ω m . These results are based on the usual assumption that the errors derived from the Hubble Volume mocks are applicable to all other models. If we instead assume that the error is proportional to the C l amplitude then the constraints weaken; for example it becomes more difficult to reject cosmologies with lower Γ eff .

Simulating galaxy clusters - II. Global star formation histories and the galaxy populations

We performed N-body + hydrodynamical simulations of the formation and evolution of galaxy groups and clusters in acold dark matter cosmology. The simulations invoke star forma- tion, chemical evolution with non-instantaneous recycling, metal-dependent radiative cooling, strong starbursts and (optionally) active galactic nucleus (AGN) driven galactic superwinds, effects of a meta-galactic ultraviolet field and thermal conduction. The properties of the galaxy populations in two clusters, one Virgo-like (T ∼ 3k eV) and one (sub)Coma-like (T ∼ 6k eV), are discussed. The global star formation rates of the cluster galaxies are found to decrease very significantly from redshift z = 2t o0 ,i nagreement with observations. The total K-band luminosity of the cluster galaxies correlates tightly with total cluster mass, and for models without additional AGN feedback, the zero-point of the relation matches the observed one fairly well. Compared to the observed galaxy luminosity function (LF), the simulations nicely match the number of intermediate-mass galaxies (−20 MB −17, smaller galaxies being affected by resolution limits) but they show a deficiency of bright galaxies in favour of an overgrown central dominant (cD) galaxy. High-resolution tests indicate that this deficiency is not simply due to numerical 'overmerging'. The redshift evolution of the LFs from z = 1t o0i smainly driven by luminosity evolution, but also by merging of bright galaxies with the cD. The colour-magnitude relation of the cluster galaxies matches the observed 'red sequence', although with a large scatter, and on average galaxy metallicity increases with luminosity. As the brighter galaxies are essentially coeval, the colour-magnitude relation results from metallicity rather than age effects, as observed. On the whole, a top-heavy initial mass function appears to be preferably required to reproduce also the observed colours and metallicities of the stellar populations. Ke yw ords: methods: N-body simulations - methods: numerical - galaxies: clusters: general -g alaxies: evolution - galaxies: formation - cosmology: theory.

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 character­ izing the halo masses from both observational and theoretical results: ∇ eϒ , the logarithmic radial gradient of the mass-to-light ratio. Using halo density profiles from A-cold dark matter (CDM) simulations, we derive predictions for this gradient for various galaxy luminosities and star formation efficiencies E SF .A s a pilot study, we assemble the available ∇ eϒ 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 ∇ eϒ , 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 ACDM 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 E SF > 1. This difficulty is eased if dark haloes are not assumed to have the standard ACDM profiles, but lower central concentrations. Ke yw ords: galaxies: evolution – galaxies: fundamental parameters – galaxies: haloes – galax­ ies: kinematics and dynamics – dark matter.

Cosmological parameter estimation using Very Small Array data out to ℓ= 1500

We estimate cosmological parameters using data obtained by the Very Small Array (VSA) in its extended configuration, in conjunction with a variety of other cosmic microwave background (CMB) data and external priors. Within the flat Λ cold dark matter (ΛCDM) model, we find that the inclusion of high-resolution data from the VSA modifies the limits on the cosmological parameters as compared to those suggested by the Wilkinson Microwave Anisotropy Probe (WMAP) alone, while still remaining compatible with their estimates. We find that Ωbh2= 0.0234+0.0012−0.0014, Ωdmh2= 0.111+0.014−0.016, h= 0.73+0.09−0.05, nS= 0.97+0.06−0.03, 1010AS= 23+7−3 and τ= 0.14+0.14−0.07 for WMAP and VSA when no external prior is included. On extending the model to include a running spectral index of density fluctuations, we find that the inclusion of VSA data leads to a negative running at a level of more than 95 per cent confidence (nrun=−0.069 ± 0.032), something that is not significantly changed by the inclusion of a stringent prior on the Hubble constant. Inclusion of prior information from the 2dF galaxy redshift survey reduces the significance of the result by constraining the value of Ωm. We discuss the veracity of this result in the context of various systematic effects and also a broken spectral index model. We also constrain the fraction of neutrinos and find that fν < 0.087 at 95 per cent confidence, which corresponds to mν < 0.32 eV when all neutrino masses are equal. Finally, we consider the global best fit within a general cosmological model with 12 parameters and find consistency with other analyses available in the literature. The evidence for nrun < 0 is only marginal within this model.