Standard Cold Dark Matter Model Research Articles

A Universal Temperature Profile for Galaxy Clusters

We investigate the predicted present-day temperature profiles of the hot, X-ray-emitting gas in galaxy clusters for two cosmological models—a current best-guess ΛCDM model and a standard cold dark matter (SCDM) model. Our numerically simulated catalogs of clusters are derived from high-resolution (15 h-1 kpc) simulations which make use of a sophisticated, Eulerian-based, adaptive mesh-refinement code that faithfully captures the shocks that are essential for correctly modeling cluster temperatures. We show that the temperature structure on Mpc scales is highly complex and non-isothermal. However, the temperature profiles of the simulated ΛCDM and SCDM clusters are remarkably similar and drop off as T ∝ (1 + r/ax)-δ, where ax ~ rvir/1.5 and δ ~ 1.6. This decrease is in good agreement with the observational results of Markevitch et al. but diverges, primarily in the innermost regions, from their fit which assumes a polytropic equation of state. Our result is also in good agreement with a recent sample of clusters observed by BeppoSAX, though there is some indication of missing physics at small radii (r 0.2 rvir, our universal temperature profile is consistent with our most recent simulations, which include both radiative cooling and supernovae feedback.

Three-Dimensional Genus Statistics of Galaxies in the SDSS Early Data Release

Abstract We present the first analysis of three-dimensional genus statistics for the SDSS EDR galaxy sample. Due to the complicated survey volume and the selection function, analytic predictions of the genus statistics for this sample are not feasible; therefore, we construct extensive mock catalogs from $ N$-body simulations in order to compare the observed data with model predictions. This comparison allows us to evaluate the effects of a variety of observational systematics on the estimated genus for the SDSS sample, including the shape of the survey volume, the redshift distortion effect, and the radial selection function due to the magnitude limit. The observed genus for the SDSS EDR galaxy sample is consistent with that predicted by simulations of a $ \Lambda$-dominated spatially-flat cold dark matter model. Standard ($ \Omega_0=1$) cold dark matter model predictions do not match the observations. We discuss how future SDSS galaxy samples will yield improved estimates of the genus.

The Effect of Merger Boosts on the Luminosity, Temperature, and Inferred Mass Functions of Clusters of Galaxies

In the standard cold dark matter model of structure formation, massive clusters form via the merger of smaller clusters. N-body/hydrodynamical simulations of merging galaxy clusters have shown that mergers can temporarily boost the X-ray luminosity and temperature of the merged cluster above the equilibrium values for the merged system. The cumulative effect of these "merger boosts" will affect the observed X-ray luminosity functions (XLFs) and temperature functions (TFs) of clusters. One expects this effect to be most important for the most luminous and hottest clusters. XLFs and TFs of clusters provide some of the strongest constraints on cosmological and large-scale structure parameters, such as the mean fluctuation parameter σ8 and the matter density divided by the critical density Ω0. Merger boosts may bias the values of σ8 and Ω0 inferred from cluster XLFs and TFs if virial equilibrium is assumed. We use a semianalytic technique to estimate the effect of merger boosts on the XLFs and TFs. The boosts from individual mergers are derived from N-body/hydrodynamical simulations of mergers. The statistics of the merger histories of clusters are determined from extended Press-Schechter (PS) merger trees. We find that merger boosts can increase the apparent number of hot, luminous clusters. For example, in a universe with Ω0 = 0.3 and ΩΛ = 0.7 at a redshift of z = 1, the number of clusters with temperatures T > 10 keV is increased by a factor of 9.5, and the number of clusters with luminosities LX > 5 × 1044 h-2 ergs s-1 is increased by a factor of 8.9. We have used our merger-boosted TFs and XLFs to derive the cosmological structure parameters σ8 and Ω0 by fitting PS equilibrium relations to local (z = 0) and distant (either z = 0.5 or z = 1) cluster samples. Merger boosts cause σ8 to be overestimated by about 20%. The matter density parameter Ω0 may be underestimated by about 20%, although this result is less clear. If the parameters of the fluctuation spectrum are derived from the observed TF or XLF (e.g., from a low-redshift sample), then this removes most of the boost effect on Ω0. However, larger merger boost effects may appear when cluster XLFs and TFs are compared to cosmological structure parameters derived by other techniques (e.g., cosmic microwave background fluctuations or the brightness of distant supernovae).

An analytical model for the non-linear redshift-space power spectrum

We use N-body simulations to test the predictions of the redshift distortion in the power spectrum given by the halo model in which the clustering of dark matter particles is considered as a result both of the clustering of dark halos in space and of the distribution of dark matter particles in individual dark halo. The predicted redshift distortion depends sensitively on several model parameters in a way different from the real-space power spectrum. An accurate model of the redshift distortion can be constructed if the following properties of the halo population are modelled accurately: the mass function of dark halos, the velocity dispersion among dark halos, and the non-linear nature of halo bias on small scales. The model can be readily applied to interpreting the clustering properties and velocity dispersion of different populations of galaxies once a cluster-weighted bias (or equivalently an halo occupation number model) is specified for the galaxies. Some non-trivial bias features observed from redshift surveys of optical galaxies and of IRAS galaxies relative to the standard low-density cold dark matter model can be easily explained in the cluster weighted bias model. The halo model further indicates that a linear bias can be a good approximation only on for k <= 0.1 hMpc^{-1}.

The three-point function in large-scale structure – I. The weakly non-linear regime in N-body simulations

ABSTRA C T This paper presents a comparison of the predictions for the two- and three-point correlation functions of density fluctuations, j and z, in gravitational perturbation theory (PT) against large cold dark matter (CDM) simulations. This comparison is made possible for the first time on large weakly non-linear scales (. 10 h 21 Mpc) thanks to the development of a new algorithm for estimating correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the three-point statistics with simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as those presented here, were limited to small scales where leading-order PT gives a poor approximation. Here we also propose and apply a method for separating the first-order and subsequent contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime where simulations do reproduce the leading-order (tree-level) predictions of PT for the reduced three-point function Q3 , z/j 2 . For steeply decreasing correlations (such as the standard CDM model) deviations from the tree-level results are important even at relatively large scales, . 20 Mpc h 21 . On larger scales j goes to zero and the results are dominated by sampling errors. In more realistic models (such as the LCDM cosmology) deviations from the leading-order PT become important at smaller scales r . 10 Mpc h 21 , although this depends on the particular three-point configuration. We characterize the range of validity of this agreement and show the behaviour of the next-order (one-loop) corrections.

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

ABSTRA C T 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 constantdensity cores to r 22 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 21 cusps. We show that the dwarf galaxies analysed here are consistent with CDM haloes in a LCDM 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 21.5 . 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.

Further analysis of a cosmological model with quintessence and scalar dark matter

We present the complete solution to a $95%$ scalar field cosmological model in which the dark matter is modeled by a scalar field $\ensuremath{\Phi}$ with the scalar potential $V(\ensuremath{\Phi}{)=V}_{0}[\mathrm{cosh}(\ensuremath{\lambda}\sqrt{{\ensuremath{\kappa}}_{0}}\ensuremath{\Phi})\ensuremath{-}1]$ and the dark energy is modeled by a scalar field \ensuremath{\Psi}, endowed with the scalar potential $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}(\ensuremath{\Psi})={V}_{0}[\mathrm{sinh}(\ensuremath{\alpha}\sqrt{{\ensuremath{\kappa}}_{0}}\ensuremath{\Psi}){]}^{\ensuremath{\beta}}.$ This model has only two free parameters, \ensuremath{\lambda} and the equation of state ${\ensuremath{\omega}}_{\ensuremath{\Psi}}.$ With these potentials, the fine-tuning and cosmic coincidence problems are ameliorated for both dark matter and dark energy and the model agrees with astronomical observations. For the scalar dark matter, we clarify the meaning of a scalar Jeans length and then the model predicts a suppression of the mass power spectrum for small scales having a wave number $k&gt;{k}_{\mathrm{min},\ensuremath{\Phi}},$ where ${k}_{\mathrm{min},\ensuremath{\Phi}}\ensuremath{\simeq}4.5h$ ${\mathrm{Mpc}}^{\ensuremath{-}1}$ for $\ensuremath{\lambda}\ensuremath{\simeq}20.28.$ This last fact could help to explain the death of dwarf galaxies and the smoothness of galaxy core halos. From this, all parameters of the scalar dark matter potential are completely determined. The dark matter consists of an ultralight particle, whose mass is ${m}_{\ensuremath{\Phi}}\ensuremath{\simeq}1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}$ eV and all the success of the standard cold dark matter model is recovered. This implies that a scalar field could also be a good candidate the dark matter of the Universe.

Properties of Cosmic Shock Waves in Large‐Scale Structure Formation

We have examined the properties of shock waves in simulations of large-scale structure formation. Two cosmological scenarios have been considered: a standard cold dark matter model with ΩM = 1 (SCDM), and a cold dark matter model with cosmological constant and ΩM + ΩΛ = 1 (ΛCDM) having ΩΛ = 0.55. Large-scale shocks result from accretion onto sheets, filaments, and knots of mass distribution on a scale of the order of ~5 h-1 Mpc in both scenarios. Energetic motions, partly residuals of past accretion processes and partly caused by current asymmetric inflow along filaments, end up generating additional shocks. These extend on a scale of the order of ~1 h-1 Mpc and envelop and penetrate deep inside the clusters. Collisions between substructures inside clusters also form merger shocks. Consequently, the topology of the shocks is very complex and highly connected. During cosmic evolution the comoving shock surface density decreases, reflecting the ongoing structure merger process in both scenarios. Accretion shocks have very high Mach numbers, typically between 10 and a few ×103, when photoheating of the preshock gas is not included. The characteristic shock velocity is of the order of vsh(z) = H(z)λnl(z), where λnl(z) is the wavelength scale of the nonlinear perturbation at the given epoch. However, the Mach number for merger and flow shocks (which occur within clusters) is usually smaller, in the range of ~3-10, corresponding to the fact that the intracluster gas is hot (i.e., already shock heated). Statistical fits of shock velocities around clusters as a function of cluster temperature give power-law functions in accord with those predicted by one-dimensional solutions. On the other hand, a very different result is obtained for the shock radius, reflecting extremely complex shock structures surrounding clusters of galaxies in three-dimensional simulations. The amount of inflowing kinetic energy across the shocks around clusters, which represents the power available for cosmic-ray acceleration, is comparable to the cluster X-ray luminosity emitted from a central region of radius 0.5 h-1 Mpc. Considering their large size and long lifetimes, those shocks are potentially interesting sites for cosmic-ray acceleration, if modest magnetic fields exist within them.

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 mx is the mass of the dark matter particle: σmx≈4×10−25 (100 km s−1v−1) cm2 GeV−1.

Topology of the Las Campanas Redshift Survey

The topology of the Las Campanas Redshift Survey is analyzed using Minkowski functional statistics, taking into account the selection effects of the survey. The results are compared with the predictions of some toy models of structure formation, including the Standard Cold Dark Matter Model and topological defect-based models. All of the toy models have a scale invariant primordial spectrum of perturbations, but quite different topologies. The statistics can discriminate between the predictions of the models with high significance. Amongst the four Minkowski functionals, the integrated mean curvature statistic appears to be the most powerful discriminant, followed by the genus statistic. None of the models considered gives an acceptable fit to the data.

What if dark matter is bosonic and self-interacting

Recently the problem of singular galactic cores and over-abundant formation of dwarf galaxies, inherent to the standard cold dark matter model, had attracted a great deal of attention. One scenario which may be free of these problems invokes a self-interacting Bose-field. We find the limiting core density in this model due to the self-annihilation of the scalar field into its own relativistic quanta. The limiting density may correspond to the observable one if there is only one dark matter component. Alternatively, there may be more than one dark matter species and the annihilation of one species may be very efficient with subsequent expansion of the other, thus avoiding the problem of singular cores.

Gravitational Lensing by NFW Halos

We investigate the gravitational lensing properties of dark matter halos with Navarro, Frenk & White (NFW) density profiles and derive an analytic expression for the radial dependence of the shear, γ(x), due to these objects. In addition, we derive an expression for the mean shear interior to a given radius, (x), and use this to quantify systematic errors that will arise in weak-lensing mass estimates of astronomical objects in cases where the mass estimate is based on an a priori assumption that the underlying potential is that of a singular isothermal sphere when in fact the potential is that of an NFW-type object. On mass scales of 1011 M☉ M200 1015 M☉, the assumption of an isothermal sphere potential results in an overestimate of the halo mass, and the amount by which the mass is overestimated increases linearly with the value of the NFW concentration parameter. Considerable overestimates of the mass (~60%) can occur for galaxy-sized halos, but for rich clusters the mass overestimate is small. The degree to which the mass is systematically in error depends on the cosmology adopted, with a COBE-normalized standard cold dark matter (CDM) model yielding the largest systematic errors for a given true value of the halo mass.

The Evolution of the Galaxy Sizes in the New Technology Telescope Deep Field: A Comparison with Cold Dark Matter Models

The sizes of the field galaxies with I ≤ 25 have been measured in the New Technology Telescope (NTT) Deep Field. Intrinsic sizes have been obtained after deconvolution of the point-spread function with a multi-Gaussian method. The reliability of the method has been tested using both simulated data and Hubble Space Telescope (HST) observations of the same field. The distribution of the half-light radii is peaked at rhl 03, in good agreement with that derived from HST images at the same magnitude. An approximate morphological classification has been obtained using the asymmetry and concentration parameters. The intrinsic sizes of the galaxies are shown as a function of their redshifts and absolute magnitudes using photometric redshifts derived from the multicolor catalog. While the brighter galaxies with morphological parameters typical of the normal spirals show a flat distribution in the range rd = 1 - 6 kpc, the fainter population at 0.4 < z < 0.8 dominates at small sizes. To explore the significance of this behavior, an analytical rendition of the standard cold dark matter model for the disk size evolution has been computed. The model showing the best fit to the local luminosity function and the Tully-Fisher relation is able to reproduce at intermediate redshifts a size distribution in general agreement with the observations, although it tends to underestimate the number of galaxies fainter than MB ~ -19 with disk sizes rd ~ 1-2 kpc.

The Galaxy‐weighted Small‐Scale Velocity Dispersion of the Las Campanas Redshift Survey

The pair-weighted relative velocity dispersion of galaxies provides a measure of the thermal energy of fluctuations of the observed galaxy distribution, but the measure is difficult to interpret and is very sensitive to the existence of rare, rich clusters of galaxies. Several alternative statistical procedures have recently been suggested to relieve these problems. We apply a variant of the object-weighted statistical method of Davis, Miller, & White (1997) to the Las Campanas Redshift Survey (LCRS), which is the largest and deepest existing redshift survey that is nearly fully sampled. The derived one-dimensional dispersion on scales ~ 1 Mpc/h is quite low: sigma_1 = 126 +/- 10 km/s, with a modest decrease at larger scales. The statistic is very stable; the six independent slices of the LCRS all yield consistent results. We apply the same statistical procedure to halos in numerical simulations of an open cosmological model and flat models with and without a cosmological constant. In contrast to the LCRS, all the models show a dispersion which increases for scales > 1 Mpc/h; it is uncertain whether this is a numerical artifact or a real physical effect. The standard cluster-normalized Cold Dark Matter model with Omega_m = 1 as well as a tilted variant with n = 0.8 yield dispersions substantially hotter than the LCRS value, while models with low matter density (Omega_m = 0.3) are broadly consistent with the LCRS data. Using a filtered cosmic energy equation, we measure Omega_m ~ 0.2, with small-scale bias factors b = 1.0--1.5 for high-density models and b = 0.7--1.1 for low-density models.

Breaking Degeneracy of Dark Matter Models by the Scale‐Scale Correlations of Galaxies

Recently, scale-scale correlations have been detected in the distributions of quasars' Lyα absorption lines and the maps of cosmic temperature fluctuations. This paper investigates the scale-scale correlations in galaxy distributions. Using samples of mass field given by N-body simulation, we first show that the scale-scale correlation of two-dimensional and three-dimensional mass distributions at present day are capable of breaking the degeneracy between the SCDM (standard cold dark matter model) and OCDM (open CDM model) or LCDM (flat CDM model) and even show the difference between the OCDM and LCDM. Using biased galaxy samples produced in an appropriate bias model, we show that the scale-scale correlation of galaxy distribution at zero redshift is still a powerful tool to break the degeneracy in the parameter space, including both cosmological and biasing parameters. We analyze the scale-scale correlations of the APM bright galaxy catalog and compare it with the mock catalog in the SCDM, OCDM, and LCDM models. We find that all the spectra of local and nonlocal scale-scale correlations predicted by the OCDM model are in excellent agreement with those of the APM-BGC sample, while the SCDM and LCDM mock catalog appear to have somewhat weaker scale-scale correlations than the observation.

The Projected Three-Point Correlation Function: Theory and Observations

We report results for the angular three-point galaxy correlation function in the APM survey and compare them with theoretical expectations. For the first time, these measurements extend to sufficiently large scales to probe the weakly non-linear regime. On large scales, the results are in good agreement with the predictions of non-linear cosmological perturbation theory, for a model with initially Gaussian fluctuations and linear power spectrum $P(k)$ consistent with that inferred from the APM survey. These results reinforce the conclusion that large-scale structure is driven by non-linear gravitational instability and that APM galaxies are relatively unbiased tracers of the mass on large scales; they also provide stringent constraints upon models with non-Gaussian initial conditions and strongly exclude the standard cold dark matter model.

Cosmic microwave background observations with the Jodrell Bank-IAC interferometer at 33 GHz

This paper presents the first results obtained with the Jodrell Bank–IAC two-element 33-GHz interferometer. The instrument was designed to measure the level of the cosmic microwave background (CMB) fluctuations at angular scales of 1°–2°. The observations analysed here were taken in a strip of the sky at Dec.=+41° with an element separation of 16.7λ, which gives a maximum sensitivity to ∼16 structures on the sky. The data processing and calibration of the instrument are described. The sensitivity achieved in each of the two channels is 7 μK per resolution element. A reconstruction of the sky at Dec.=+41° using a maximum entropy method shows the presence of structure at a high level of significance. A likelihood analysis, assuming a flat CMB spatial power spectrum, gives a best estimate of the level of CMB fluctuations of for the range l=109±19; the main uncertainty in this result arises from sample variance. We consider that the contamination from the Galaxy is small. These results represent a new determination of the CMB power spectrum on angular scales at which previous results show a large scatter; our new results are in agreement with the theoretical predictions of the standard inflationary cold dark matter models.

Tensor-induced CMB temperature-polarization correlation in reionized universes

We reexamine the temperature-polarization correlation function of the cosmic microwave background induced by a tensor mode with a scale-invariant spectrum in reionized standard cold dark matter models. It is found that the sign of the correlation function is positive on all angular scales even in a model with substantial reionization.

Wavelets applied to cosmic microwave background maps: a multiresolution analysis for denoising

Analysis and denoising of cosmic microwave background (CMB) maps are performed using wavelet multiresolution techniques. The method is tested on 12.8×12.8 deg2 maps, with the resolution resembling the experimental one expected for future high-resolution space observations. Semi-analytic formulae of the variance of wavelet coefficients are given for the Haar and Mexican Hat wavelet bases. Results are presented for the standard cold dark matter (CDM) model. Denoising of simulated maps is carried out by removal of wavelet coefficients dominated by instrumental noise. CMB maps with a signal-to-noise ratio, SN∼1, are denoised with an error improvement factor between 3 and 5. Moreover, we have also tested how well the CMB temperature power spectrum is recovered after denoising. We are able to reconstruct the Cℓs up to l∼1500 with errors always below 20 per cent in cases with SN1.

Resolving the Lyα Forest

In this paper we critically examine predictions of the Ly? forest within the standard cold dark matter (SCDM) model, paying particular attention to the low end of the column-density distribution. We show in particular that the width of these lines, typically measured by the b-parameter of a Voigt profile, is sensitive to spatial resolution in numerical simulations and has previously been overestimated. The new result, which predicts a distribution with a median b of around 20-22 km s-1 at z=3, is substantially below that observed. We examine a number of possible causes of this discrepancy and argue that it is unlikely to be rectified by an increase in the thermal broadening of the absorbing gas but is instead telling us something about the distribution of matter on these scales. Although the median differs, the shape of the b-parameter distribution agrees quite well with that observed, and the high-end tail is naturally produced by the filamentary nature of gravitational collapse in these models. In particular, we demonstrate that lines of sight that obliquely intersect filaments or sheets tend to produce absorption lines with larger b parameters. We also examine the physical nature of the gas that is responsible for the forest, showing that for lines with neutral column densities below N~10 cm-2 (for this model at z=3), the peculiar infall velocity is actually slower than the Hubble flow, while larger lines have, on average, turned around and are collapsing.