The Bullet Cluster 1E0657-558 evidence shows modified gravity in the absence of dark matter

A detailed analysis of the 2006 November 15 data release X-ray surface density Σ-map and the strong and weak gravitational lensing convergence κ-map for the Bullet Cluster 1E0657-558 is performed and the results are compared with the predictions of a modified gravity (MOG) and dark matter. Our surface density Σ-model is computed using a King β-model density, and a mass profile of the main cluster and an isothermal temperature profile are determined by the MOG. We find that the main cluster thermal profile is nearly isothermal. The MOG prediction of the isothermal temperature of the main cluster is   T = 15.5 ± 3.9 keV  , in good agreement with the experimental value   T = 14.8^+2.0_−1.7 keV  . Excellent fits to the 2D convergence κ-map data are obtained without non-baryonic dark matter, accounting for the 8σ spatial offset between the Σ-map and the κ-map reported in Clowe et al. The MOG prediction for the κ-map results in two baryonic components distributed across the Bullet Cluster 1E0657-558 with averaged mass fraction of 83 per cent intracluster medium (ICM) gas and 17 per cent galaxies. Conversely, the Newtonian dark matter κ-model has on average 76 per cent dark matter (neglecting the indeterminant contribution due to the galaxies) and 24 per cent ICM gas for a baryon to dark matter mass fraction of 0.32, a statistically significant result when compared to the predicted Λ-cold dark matter cosmological baryon mass fraction of 0.176^+0.019_−0.012.     

Possible indication for non-zero neutrino mass and additional neutrino species from cosmological observations

The constraints on total neutrino mass and effective number of neutrino species based on CMB anisotropy power spectrum, Hubble constant, baryon acoustic oscillations and galaxy cluster mass function data are presented. It is shown that discrepancies between various cosmological data in Hubble constant and density fluctuation amplitude, measured in standard ΛCDM cosmological model, can be eliminated if more than standard effective number of neutrino species and non-zero total neutrino mass are considered. This extension of ΛCDM model appears to be ≈3σ significant when all cosmological data are used. The model with approximately one additional neutrino type, N _eff ≈ 4, and with non-zero total neutrino mass, Σmν ≈ 0.5 eV, provide the best fit to the data. In the model with only one massive neutrino the upper limits on neutrino mass are slightly relaxed. It is shown that these deviations from ΛCDM model appearmainly due to the usage of recent data on the observations of baryon acoustic oscillations. The larger than standard number of neutrino species is measured mainly due to the comparison of the BAO data with direct measurements of Hubble constant, which was already noticed earlier. As it is shown below, the data on galaxy cluster mass function in this case give the measurement of non-zero neutrino mass.     

CMB Comptonization in clusters: spectral and angular power from evolving polytropic gas

The angular power spectrum of the Sunyaev–Zeldovich (SZ) effect is calculated in the ΛCDM cosmological model with the aim of investigating its detailed dependence on the cluster population, gas morphology, and gas evolution. We calculate the power spectrum for three different mass functions, compute it within the framework of isothermal and polytropic gas distributions, and explore the effect of gas evolution on the magnitude and shape of the power spectrum. We show that it is indeed possible to explain the ‘excess’ power measured by the CBI experiment on small angular scales as originating from the SZ effect without (arbitrary) rescaling the value of σ₈, the mass variance parameter. The need for a self-consistent choice of the basic parameters characterizing the cluster population is emphasized. In particular, we stress the need for a consistent choice of the value of σ₈ extracted from fitting theoretical models for the mass function to the observed cluster X-ray temperature function, such that it agrees with the mass–temperature relation used to evaluate the cluster Comptonization parameter. Our treatment includes the explicit spectral dependence of the thermal component of the effect, which we calculate at various frequencies. We find appreciable differences between the nonrelativistic and relativistic predictions for the power spectrum even for this superposed contribution from clusters at the full range of gas temperatures.     

A scaling relation between the SZ decrement and the Thomson depth in clusters of galaxies

In a recent study of dark mater N-body simulations, a scaling relation between the SZ decrement and the Thomson depth of a cluster of galaxies of the form ΔT _r ∝τ _T ² has been found (Diaferio et al. 2000). In this paper, it will be shown that such a scaling relation arises if the intracluster gas is distributed similar to the dark matter density described by the NFW-profile and the finite spatial resolution of the numerical simulation is taken into account. It is furthermore investigated whether the ΔT _r ∝τ _T ² relation holds for analytical models of an isothermal gas sphere in the gravitational potential of a dark matter halo distributed according to the NFW-profile, the available experimental data of SZE observations, and recent results from cosmological gas-dynamical simulations of clusters of galaxies. Combining such a relation with temperature estimates from X-ray observations would provide information about a dependence of T _e on τ_T. The Thomson depth might therefore emerge as another important scaling parameter in studies of clusters of galaxies.     

X-ray temperature spectroscopy of simulated cooling clusters

Results from a large sample of hydrodynamical/N-body simulations of galaxy clusters in a ΛCDM cosmology are used to simulate cluster X-ray observations. The physical modeling of the gas includes radiative cooling, star formation, energy feedback, and metal enrichment that follow from supernova explosions. Mock cluster samples are constructed grouping simulation data according to a number of constraints which would be satisfied by a data set of X-ray measurements of cluster temperatures as expected from Chandra observations. The X-ray spectra from simulated clusters are fitted into different energy bands using the XSPEC mekal model. The biasing of spectral temperatures with respect to mass-weighted temperatures is found to be influenced by two independent processes. The first scale dependency is absent in adiabatic runs and is due to cooling, whose efficiency to transform cold gas into stars is higher for cool clusters and this in turn implies a strong dependency of the spectral versus mass-weighted temperature relation on the cluster mass. The second dependency is due to photon emission because of cool gas which is accreted during merging events and biases the spectral fits. These events have been quantified according to the power ratio method and a robust correlation is found to exist between the spectral bias and the amount of cluster substructure.The shape of the simulated temperature profiles is not universal and it is steeper at the cluster center for cool clusters than for the massive ones. This follows owing to the scale dependency introduced by cooling which implies for cool clusters higher central temperatures, in scaled units, than for massive clusters. The profiles are in good agreement with data in the radial range between ∼0.1r_vir and ∼0.4r_vir; at small radii (r ≲ 0.1r_vir) the cooling runs fail to reproduce the shape of the observed profiles. The fit is improved if one considers a hierarchical merging scenario in which cluster cores can accrete cooler gas through merging with cluster subclumps, though the shape of the temperature profiles is modified in a significant way only in the regime where the mass of the substructure is a large fraction of the cluster mass.     

Constraints the properties of neutron star matter from the mass of neutron star PSR J1614-2230

The constraints on the properties of neutron star matter from the mass of neutron star PSR J1614-2230 are examined in the framework of the relativistic mean field theory. We find that there are little differences between the σ potentials of large mass neutron star and those of canonnical mass neutron star. For potentials of ω, ρ, neutrons and electrons, the values corresponding to the large mass neutron star are larger than those to the canonnical mass neutron star as the baryon number density is more than a certain value. We also find that for the relative particle number density of electrons, muons, neutrons and protons and the pressure of the neutron star, the values corresponding to the large mass neutron star are far larger than those to the canonnical mass neutron star. For the relative particle number density of hyperons Λ, Σ^?, Σ⁰, Σ⁺ and Ξ^?, the values corresponding to the large mass neutron star are far smaller than those to the canonnical mass neutron star. These mean that the larger mass of neutron star is more advantageous to the production of protons but is not advantageous to the production of hyperons.     

Physical properties of X-ray gas in galaxy cluster CL0024+17

We analyzed the X-ray data obtained by the Chandra telescope for the galaxy cluster CL0024+17 (z = 0.39). The mean temperature of the cluster is estimated (kT = 4.35 _?0.44 ^+0.51 keV) and the surface brightness profile is derived. We generated the mass and density profiles for dark matter and gas using numerical simulations and the Navarro-Frenk-White dark matter density profile (Navarro et al., 1995) for a spherically symmetric cluster in which gas is in hydrostatic equilibrium with the cluster field. The total mass of the cluster is estimated to be M ₂₀₀ = 3.51 _?0.47 ^+0.38 × 10 _Sun ¹⁴ within a radius of R ₂₀₀ = 1.24 _?0.17 ^+0.12 Mpc of the cluster center. The contribution of dark matter to the total mass of the cluster is estimated as ${{M_{200_{DM} } } \mathord{\left/ {\vphantom {{M_{200_{DM} } } {M_{tot} }}} \right. \kern-0em} {M_{tot} }} = 0.89$ .     

Neutron stars in generalized f(R) gravity

A gravity theory is considered with the Einstein-Hilbert Lagrangean R+aR ²+bR _μν R ^μν , R _μν being Ricci’s tensor and R the curvature scalar. The parameters a and b are taken of order 1 km². Arguments are given which suggest that the effective theory so obtained might be a fair approximation of a viable theory. A numerical integration is performed of the field equations for a free neutron gas. The result is that the star mass increases with increasing central density until about 1 solar mass and then decreases. The baryon number increases monotonically, which suggests that the theory allows stars in equilibrium with arbitrary baryon number, no matter how large.     

On the detectability of turbulence and bulk flows in X-ray clusters

Coolingflows, cluster mergers, and the motions of galaxies through cluster gas with supersonic and sonic velocities must lead to large scale motions of the intracluster medium (ICM). A high-resolution numerical simulation of X-ray cluster formation by Norman and Bryan (1999) predicts cluster-wide turbulence with ν_turb ≈300–600 km s^?1 and eddy scales l_outer ≈100–500 kpc, the larger numbers being characteristic of turbulence near the virial radius, while the smaller numbers pertain to the core. The simulation also predicts the existence of ordered bulk flows in the core with v≈400 km s^?1 on scales of several hundred kpc. In this paper, we consider the observability of such fluid motions via the distortions they induce in the CMB via the kinematic SZ effect, as well as via Doppler broadening and shifting of metal lines in the X-ray spectrum. We estimate |ΔT/T|_kinematic?6—at or below current limits of detectability. However, we find that an energy resolution of a few eV is sufficient to detect several Doppler shifted components in the 6.7 keV Fe line in the cluster core.     

Impact of a non-Gaussian density field on Sunyaev–Zeldovich observables

The main statistical properties of the Sunyaev–Zeldovich (S–Z) effect – the power spectrum, cluster number counts and angular correlation function – are calculated and compared within the framework of two density fields which differ in their predictions of the cluster mass function at high redshifts. We do so for the usual Press & Schechter mass function, which is derived on the basis of a Gaussian density fluctuation field, and for a mass function based on a  χ²  distributed density field. These three S–Z observables are found to be very significantly dependent on the choice of the mass function. The different predictions of the Gaussian and non-Gaussian density fields are probed in detail by investigating the behaviour of the three S–Z observables in terms of cluster mass and redshift. The formation time distribution of clusters is also demonstrated to be sensitive to the underlying mass function. A semiquantitative assessment is given of its impact on the concentration parameter and the temperature of intracluster gas.     

The distant galaxy cluster XLSSJ022403.9-041328 on the L X –T X –M scaling relations using Chandra and XMM–Newton observations

We present a very detailed analysis of Chandra and XMM–Newton observations of XLSSJ022403.9-041328 galaxy cluster of z=1, which was detected during the XMM-Newton Large Scale Structure survey. To define the “luminosity-temperature-mass”, L _X –T _X –M, scaling relations we built temperature, surface brightness, density, and mass profiles. The total gravitational mass of this cluster was taken within the scaled radius, R ₅₀₀, was determined under the assumption of hydrostatic equilibrium for intercluster gas and spherical symmetry of a cluster. The temperature of XLSSJ022403.9-041328 was found to be 4.5±0.7 keV from the Chandra data, and 3.8±0.3 from the XMM–Newton data. The total gravitational mass is equal to 1.44±0.23×10¹⁴ M _⊙ at the corresponding radius, while the fraction of gas is equal to 15 % of a total mass. These values were used to define the XLSSJ022403.9-041328 galaxy cluster at the L _X –T _X –M _g scaling relations, and for all of these cases we got agreement which fitting well with self-similar model. This research permits us to use L _X –T _X –M relations for galaxy clusters at a highest redshift in the cosmological probes.     

The Sunyaev–Zel'dovich temperature of the intracluster medium

The relativistic Sunyaev–Zel'dovich (SZ) effect offers a method, independent of X-ray, for measuring the temperature of the intracluster medium (ICM) in the hottest systems. Here, using N -body/hydrodynamic simulations of three galaxy clusters, we compare the two quantities for a non-radiative ICM, and for one that is subject both to radiative cooling and to strong energy feedback from galaxies. Our study has yielded two interesting results. First, in all cases, the SZ temperature is hotter than the X-ray temperature and is within 10 per cent of the virial temperature of the cluster. Secondly, the mean SZ temperature is less affected by cooling and feedback than the X-ray temperature. Both these results can be explained by the SZ temperature being less sensitive to the distribution of cool gas associated with cluster substructure. A comparison of the SZ and X-ray temperatures (measured for a sample of hot clusters) would therefore yield interesting constraints on the thermodynamic structure of the intracluster gas.     

Measurements of the Matter Density Perturbation Amplitude from Cosmological Data

The various measurements of the linear matter density perturbation amplitude obtained from the observations of the cosmic microwave background (CMB) anisotropy, weak gravitational lensing, galaxy cluster mass function, matter power spectrum, and redshift space distortions are compared. The Planck data on the CMB temperature anisotropy spectrum at high multipoles, ? > 1000 (where the effect of gravitational lensing is most significant), are shown to give a measurement of the matter density perturbation amplitude that contradicts all other measurements of this quantity from both Planck CMB anisotropy data and other data at a significance level of about 3.7σ. Thus, at present these data should not be combined together for the calculations of constraints on cosmological parameters. Except for the Planck data on the CMB temperature anisotropy spectrum at high multipoles, all the remaining measurements of the density perturbation amplitude agree well between themselves and give the following constraints: σ₈ = 0.792± 0.006 on the linear matter density perturbation amplitude, Ω_m = 0.287± 0.007 on the matter density parameter, and H₀ = 69.4 ± 0.6 km s^?1 Mpc^?1 on the Hubble constant. Various constraints on the sum of neutrino masses and the number of neutrino flavors can be obtained by additionally taking into account the data on baryon acoustic oscillations and (or) direct Hubble constant measurements in the local Universe.     

The role of dark matter in the galaxy mass-size relationship

The observed relationship between stellar mass and effective radius for early type galaxies, pointed out by many authors, is interpreted in the context of Clausius’ virial maximum theory. In this view, it is strongly underlined that the key of the above mentioned correlation is owing to the presence of a deep link between cosmology and the existence of the galaxy Fundamental Plane. Then the ultimate meaning is: understanding visible mass-size correlation and/or Fundamental Plane means understanding how galaxies form. The mass-size relationship involves baryon (mainly stellar) mass and its typical dimension related to the light, but it gets memory of the cosmological mass variance at the equivalence epoch. The reason is that the baryonic component virializes by sharing virial energy in about equal amount between baryons and dark matter, this sharing depending, in turn, on the steepness of the dark matter distribution. The general strategy consists in using the two-component tensor virial theorem for determining the virialized baryonic configurations. A King and a Zhao density profile are assumed for the inner baryonic and the outer dark matter component, respectively, at the end of the relaxation phase. All the considerations are restricted to spherical symmetry for simplicity. The effect of changing the dark-to-baryon mass ratio, m, is investigated inside a ΛCDM scenario. A theoretical mass-size relation is expressed for the baryonic component, which fits fairly well to the data from a recently studied galaxy sample. Finally, the play of intrinsic dispersion on the mass ratio, m, is discussed in the light of the cusp/core problem and some consequences are speculated about the existence of a limit m_l expected by the theory.     

The mass distribution in the galaxy cluster Abell 2744

The mass distribution for the galaxy cluster Abell 2744 (z = 0.308) is investigated on the base of the archival X-ray data of the Chandra observatory. The temperature of the hot gas in the cluster (kT = 9.82_−0.41^+0.43 keV) and the cluster total mass (M ₂₀₀ = 2.22_−0.12^+0.13 × 10¹⁵ M _⊙) for the radius R ₂₀₀ = 2.38_−0.31^+0.36 Mpc are estimated. The density and mass profiles for the intergalactic gas and dark matter are obtained. The fractions of the intergalactic gas and dark matter in the total mass of the cluster are 15.4_−1.3^+1.3% and 84.6_−1.3^+1.4%, respectively.     

How do binaries affect the derived dynamical mass of a star cluster?

The dynamical mass of a star cluster can be derived from the virial theorem, using the measured half-mass radius and line-of-sight velocity dispersion of the cluster. However, this dynamical mass may be a significant overestimation of the cluster mass if the contribution of the binary orbital motion is not taken into account. Here, we describe the mass overestimation as a function of cluster properties and binary population properties, and briefly touch on the issue of selection effects. We find that for clusters with a measured velocity dispersion of σ _los?10 km?s^?1 the presence of binaries does not affect the dynamical mass significantly. For clusters with σ _los?1 km?s^?1 (i.e., low-density clusters), the contribution of binaries to σ _los is significant, and may result in a major dynamical mass overestimation. The presence of binaries may introduce a downward shift of Δlog?(L _V /M _dyn)=0.05–0.4 (in solar units) in the log?(L _V /M _dyn) versus age diagram.     

Cosmological constraints on the neutrino mass from CMB anisotropy and large-scale structure of the Universe

Using cosmological data on the CMB anisotropy and large-scale structure of the Universe, we have obtained new constraints on the sum of the masses of three generations of active neutrinos: Σm _ν < 1.05 eV (95% confidence level). Data of the third year of the WMAP mission served as the source of CMB anisotropy data. The mass functions of X-ray clusters of galaxies were taken as the data on the large-scale structure of the Universe. The observational properties of the clusters were obtained during the ROSAT mission and the assumption that the baryon fraction is universal in the Universe was used to determine the total cluster mass.     

The origin of the correlation between the spin parameter and the baryon fraction of galactic disks

The puzzling correlation between the spin parameter λ of galactic disks and the disk-to-halo mass fraction f _disk is investigated. It is shown that such a correlation arises naturally from large uncertainties in determining the virial masses of dark matter halos. This result indicates that halo properties derived from fits to observed rotation curves are still very uncertain. An analysis of λ versus f _disk as function of the adopted halo virial mass shows that for reasonable halo concentrations f _disk ≈ 0.01 - 0.07 which is significantly smaller than the universal baryon fraction. Most of the available gas either never settled into the galactic disks or was ejected subsequently. This revised version was published online in August 2006 with corrections to the Cover Date.     

X-ray observations of the galaxy cluster PKS 0745−191: to the virial radius, and beyond

We measure X-ray emission from the outskirts of the cluster of galaxies PKS 0745−191 with Suzaku , determining radial profiles of density, temperature, entropy, gas fraction and mass. These measurements extend beyond the virial radius for the first time, providing new information about cluster assembly and the diffuse intracluster medium out to  ∼1.5  r ₂₀₀( r ₂₀₀≃ 1.7 Mpc ≃ 15 arcmin  ). The temperature is found to decrease by roughly 70 per cent from 0.3 to  1 r ₂₀₀  . We also see a flattening of the entropy profile near the virial radius and consider the implications this has for the assumption of hydrostatic equilibrium when deriving mass estimates. We place these observations in the context of simulations and analytical models to develop a better understanding of non-gravitational physics in the outskirts of the cluster.