The theoretical framework of cosmology is mainly defined by gravity, of which general relativity is the current model. Recent tests of general relativity within the Lambda Cold Dark Matter (ΛCDM) model have found a concordance between predictions and the observations of the growth rate and clustering of the cosmic web. General relativity has not hitherto been tested on cosmological scales independently of the assumptions of the ΛCDM model. Here we report an observation of the gravitational redshift of light coming from galaxies in clusters at the 99 per cent confidence level, based on archival data. Our measurement agrees with the predictions of general relativity and its modification created to explain cosmic acceleration without the need for dark energy (the f(R) theory), but is inconsistent with alternative models designed to avoid the presence of dark matter.

The mass measurement of galaxy clusters is an important tool for the determination of cosmological parameters describing the matter and energy content of the Universe. However, the standard methods rely on various assumptions about the shape or the level of equilibrium of the cluster. We present a novel method of measuring cluster masses. It is complementary to most of the other methods, since it only uses kinematical information from outside the virialized cluster. Our method identifies objects, as galaxy sheets or filaments, in the cluster outer region, and infers the cluster mass by modeling how the massive cluster perturbs the motion of the structures from the Hubble flow. At the same time, this technique allows to constrain the three-dimensional orientation of the detected structures with a good accuracy. We use a cosmological numerical simulation to test the method. We then apply the method to the Coma cluster, where we find two galaxy sheets, and measure the mass of Coma to be M vir = (9.2 ± 2.4) × 10 14 M ⊙ , in good agreement with previous measurements obtained with the standard methods.

We study the kinematics of satellites around isolated galaxies selected from the Sloan Digital Sky Survey (SDSS) spectroscopic catalog. Using a model of the phase-space density previously measured for the halos of ΛCDM dark matter cosmological simulations, we determine the properties of the halo mass distribution and the orbital anisotropy of the satellites as a function of the colour-based morphological type and the stellar mass of the central host galaxy. We place constraints on the halo mass and the concentration parameter of dark matter and the satellite number density profiles. We obtain a concentration-mass relation for galactic dark matter haloes that is consistent with predictions of a standard ΛCDM cosmological model. At given halo or stellar mass, red galaxies have more concentrated halos than their blue counterparts. The fraction of dark matter within a few effective radii is minimal for 11.25 < log M ⋆ < 11.5. The number density profile of the satellites appears to be shallower than of dark matter, with the scale radius typically 60 per cent larger than of dark matter. The orbital anisotropy around red hosts exhibits a mild excess of radial motions, in agreement with the typical anisotropy profiles found in cosmological simulations, whereas blue galaxies are found to be consistent with an isotropic velocity distribution. Our new constraints on the halo masses of galaxies are used to provide analytic approximations of the halo-to-stellar mass relation for red and blue galaxies.

The historic detection of gravitational waves from a binary neutron star merger (GW170817) and its electromagnetic counterpart led to the first accurate (sub-arcsecond) localization of a gravitational-wave event. The transient was found to be ∼10″ from the nucleus of the S0 galaxy NGC 4993. We report here the luminosity distance to this galaxy using two independent methods. (1) Based on our MUSE/VLT measurement of the heliocentric redshift (z helio =0.009783±0.000023), we infer the systemic recession velocity of the NGC 4993 group of galaxies in the cosmic microwave background (CMB) frame to be v CMB = 3231±53kms −1. Using constrained cosmological simulations we estimate the line-of-sight peculiar velocity to be v pec =307±230kms −1 , resulting in a cosmic velocity of v cosmic =2924±236 kms −1 (z cosmic =0.00980±0.00079) and a distance of D z =40.4±3.4 Mpc assuming a local Hubble constant of H 0 =73.24±1.74 kms −1 Mpc −1. (2) Using Hubble Space Telescope measurements of the effective radius (15 5±1 5) and contained intensity and MUSE/VLT measurements of the velocity dispersion, we place NGC 4993 on the Fundamental Plane (FP) of E and S0 galaxies. Comparing to a frame of 10 clusters containing 226 galaxies, this yields a distance estimate of D FP =44.0±7.5 Mpc. The combined redshift and FP distance is D NGC 4993 =41.0±3.1 Mpc. This "electromagnetic" distance estimate is consistent with the independent measurement of the distance to GW170817 as obtained from the gravitational-wave signal (D 43.8 GW 6.9 2.9 =-+ Mpc) and confirms that GW170817 occurred in NGC 4993.

We study the distribution function (DF) of dark matter particles in haloes of mass range 10^{14}--10^{15}\Msun. In the numerical part of this work we measure the DF for a sample of relaxed haloes formed in the simulation of a standard \LambdaCDM 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+L^{2}/(2L_{0}^{2})]^{-\beta_{\infty}+\beta_{0}}L^{-2\beta_{0}}. This formulation involves three parameters describing the anisotropy profile in terms of its asymptotic values (\beta_{0} and \beta_{\infty}) 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=\rho(r)/\sigma^{3}(r).Comment: 16 pages, 12 figures, final version accepted for publication in MNRA

Aims. The aim of this paper is to study the efficiency of different approaches to interloper treatment in dynamical modelling of galaxy clusters. Methods. Using cosmological N-body simulation of standard ΛCDM model, we select 10 massive dark matter haloes and use their particles to emulate mock kinematic data in terms of projected galaxy positions and velocities as they would be measured by a distant observer. Taking advantage of the full 3D information available from the simulation, we select samples of interlopers defined with different criteria. The interlopers thus selected provide means to assess the efficiency of different interloper removal schemes found in the literature. Results. We study direct methods of interloper removal based on dynamical or statistical restrictions imposed on ranges of positions and velocities available to cluster members. In determining these ranges, we use either the velocity dispersion criterion or a maximum velocity profile. We also generalize the common approaches taking into account both the position and velocity information. Another criterion is based on the dependence of the commonly used virial mass and projected mass estimators on the presence of interlopers. We find that the direct methods exclude on average 60-70 percent of unbound particles producing a sample with contamination as low as 2-4 percent. Next, we consider indirect methods of interloper treatment which are applied to the data stacked from many objects. In these approaches, interlopers are treated in a statistical way as a uniform background which modifies the distribution of cluster members. Using a Bayesian approach, we reproduce the properties of composite clusters and estimate the probability of finding an interloper as a function of distance from the object centre.

We study the mass distribution in six nearby (z<0.06) relaxed Abell clusters of galaxies A0262, A0496, A1060, A2199, A3158 and A3558. Given the dominance of dark matter in galaxy clusters we approximate their total density distribution by the NFW formula characterized by virial mass and concentration. We also assume that the anisotropy of galactic orbits is reasonably well described by a constant and that galaxy distribution traces that of the total density. Using the velocity and position data for 120-420 galaxies per cluster we calculate, after removal of interlopers, the profiles of the lowest-order even velocity moments, dispersion and kurtosis. We then reproduce the velocity moments by jointly fitting the moments to the solutions of the Jeans equations. Including the kurtosis in the analysis allows us to break the degeneracy between the mass distribution and anisotropy and constrain the anisotropy as well as the virial mass and concentration. The method is tested in detail on mock data extracted from N-body simulations of dark matter haloes. We find that the best-fitting galactic orbits are remarkably close to isotropic in most clusters. Using the fitted pairs of mass and concentration parameters for the six clusters we conclude that the trend of decreasing concentration for higher masses found in cosmological N-body simulations is consistent with the data. By scaling the individual cluster data by mass we combine them to create a composite cluster with 1465 galaxies and perform a similar analysis on such sample. The estimated concentration parameter then lies in the range 1.5 < c < 14 and the anisotropy parameter in the range -1.1 < \beta < 0.5 at the 95 percent confidence level.Comment: 11 pages, 9 figures, final version accepted for publication in MNRA

We analyse kinematic data of 41 nearby (z < 0.1) relaxed galaxy clusters in terms of the projected phase‐space density using a phenomenological, fully anisotropic model of the distribution function. We apply the Markov Chain Monte Carlo approach to place constraints on total mass distribution approximated by the universal Navarro, Frenk and White (NFW) profile and the profile of the anisotropy of galaxy orbits. We find the normalization of the mean mass–concentration relation is c= 6.9+0.6−0.7 at the virial mass Mv= 5 × 1014  M⊙. By comparison with the calibration from cosmological N‐body simulations it is demonstrated that this result is fully consistent with σ8 from 1‐yr Wilkinson Microwave Anisotropy Probe (WMAP1) data release and agrees at ∼ 1σ level with that from WMAP5. Assuming a one‐to‐one correspondence between σ8 and the normalization of the mass–concentration relation in the framework of the concordance model we estimate the normalization of the linear power spectrum to be σ8= 0.91+0.07−0.08. Our constraints on the parameters of the mass profile are compared with estimates from X‐ray observations and other methods based on galaxy kinematics. We also study correlations between the virial mass and different mass proxies including the velocity dispersion, the X‐ray temperature and the X‐ray luminosity. We demonstrate that the mass scaling relations with the velocity dispersion and the X‐ray temperature are fully consistent with the predictions of the virial theorem. We show that galaxy orbits are isotropic at the cluster centres (with the mean ratio of the radial‐to‐tangential velocity dispersions σr/σθ= 0.97 ± 0.04) and radially anisotropic at the virial sphere (with the mean ratio σr/σθ= 1.75+0.23−0.19). Although the value of the central anisotropy appears to be universal, the anisotropy at the virial radius differs between clusters within the range 1 ≲ (σr/σθ) ≲ 2. Utilizing the Bautz–Morgan morphological classification and information on the prominence of a cool core we select two subsamples of galaxy clusters corresponding to less and more advanced evolutionary states. It is demonstrated that less evolved clusters have shallower mass profiles and their galaxy orbits are more radially biased at the virial sphere. This property is consistent with the expected evolution of the mass profiles as well as with the observed orbital segregation of late‐ and early‐type galaxies.