arXiv subjects

Radoslaw Wojtak

Publications and source records attributed to Radoslaw Wojtak.

34 records · Page 2Linked to original sources

arXiv2011

Gravitational redshift of galaxies in clusters as predicted by general relativity

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 ΛCold Dark Matter (CDM) 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 independent of the assumptions of the ΛCDM model. Here we report observation of the gravitational redshift of light coming from galaxies in clusters at the 99 per cent confidence level, based upon archival data. The measurement agrees with the predictions of general relativity and its modification created to explain cosmic acceleration without the need for dark energy (f(R) theory), but is inconsistent with alternative models designed to avoid the presence of dark matter.

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arXiv2010

Statistical mechanics of collisionless orbits. III. Comparison with N-body simulations

We compare the DARKexp differential energy distribution, N(E) \propto \exp(ϕ_0-E)-1, obtained from statistical mechanical considerations, to the results of N-body simulations of dark matter halos. We first demonstrate that if DARKexp halos had anisotropic velocity distributions similar to those of N-body simulated halos, their density and energy distributions could not be distinguished from those of isotropic DARKexp halos. We next carry out the comparison in two ways, using (1) the actual energy distribution extracted from simulations, and (2) N-body fitting formula for the density distribution as well as N(E) computed from the density using the isotropic Eddington formula. Both the methods independently agree that DARKexp N(E) with ϕ_0\approx 4-5 is an excellent match to N-body N(E). Our results suggest (but do not prove) that statistical mechanical principles of maximum entropy can be used to explain the equilibrated final product of N-body simulations.

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arXiv2010

Mass profiles and galaxy orbits in nearby galaxy clusters from the analysis of the projected phase-space

We analyze 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 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_{-0.7}^{+0.6} at the virial mass M_v=5x10^{14}M_sun. Assuming a one-to-one correspondence between sigma_8 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 sigma_8=0.91_{-0.08}^{+0.07}. Our constraints on the parameters of the mass profile are compared with estimates from other methods. We show that galaxy orbits are isotropic at the cluster centres (with the mean ratio of the radial-to-tangential velocity dispersions sigma_r/sigma_theta=0.97+/-0.04) and radially anisotropic at the virial sphere (with the mean ratio sigma_r/sigma_theta=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<(sigma_r/sigma_theta)<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.

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arXiv2009

The mass and anisotropy profiles of galaxy clusters from the projected phase space density: testing the method on simulated data

We present a new method of constraining the mass and velocity anisotropy profiles of galaxy clusters from kinematic data. The method is based on a model of the phase space density which allows the anisotropy to vary with radius between two asymptotic values. The characteristic scale of transition between these asymptotes is fixed and tuned to a typical anisotropy profile resulting from cosmological simulations. The model is parametrized by two values of anisotropy, at the centre of the cluster and at infinity, and two parameters of the NFW density profile, the scale radius and the scale mass. In order to test the performance of the method in reconstructing the true cluster parameters we analyze mock kinematic data for 20 relaxed galaxy clusters generated from a cosmological simulation of the standard LCDM model. We use Bayesian methods of inference and the analysis is carried out following the Markov Chain Monte Carlo approach. The parameters of the mass profile are reproduced quite well, but we note that the mass is typically underestimated by 15 percent, probably due to the presence of small velocity substructures. The constraints on the anisotropy profile for a single cluster are in general barely conclusive. Although the central asymptotic value is determined accurately, the outer one is subject to significant systematic errors caused by substructures at large clustercentric distance. The anisotropy profile is much better constrained if one performs joint analysis of at least a few clusters. In this case it is possible to reproduce the radial variation of the anisotropy over two decades in radius inside the virial sphere.

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arXiv2008

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}\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})]^{-β_{\infty}+β_{0}}L^{-2β_{0}}. This formulation involves three parameters describing the anisotropy profile in terms of its asymptotic values (β_{0} and β_{\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=ρ(r)/σ^{3}(r).

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arXiv2007

Mass modelling of Abell 2634: avoiding the interloper bias

Using an example of the Abell 2634 galaxy cluster we discuss the effect of contamination of kinematic data by interlopers and its impact on mass modelling. The cluster data reveal rich substructure along the line of sight. We demonstrate that it is necessary to apply a few independent methods of interloper removal in order to obtain a reliable sample of cluster members. We present results of three such methods which are commonly used in the literature and have been recently extensively tested on simulated data. Only two of them lead to consistent and reliable samples of cluster galaxies. For both of them we provide parameters of the best-fitting NFW density profile by fitting an isotropic solution of the Jeans equation to the velocity dispersion profiles.

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arXiv2007

Mass modelling of galaxy clusters via velocity moments

We summarize the method of mass modelling of galaxy clusters based on reproducing the dispersion and kurtosis of the projected velocity distribution of galaxies. The models are parametrized within the framework of the NFW density profile, characterized by the virial mass and concentration, together with the constant anisotropy of galaxy orbits. The use of velocity dispersion alone does not allow to constrain all the three parameters from kinematic data due to the mass-anisotropy degeneracy. The degeneracy is broken by introducing the fourth velocity moment, the kurtosis. We tested the method based on fitting both moments on mock data sets drawn from simulated dark matter haloes and showed it to reproduce reliably the properties of the haloes. The method has been applied to estimate the mass, concentration and anisotropy of more than 20 clusters which allowed us to confirm, for the first time using kinematic data, the mass-concentration relation found in N-body simulations.

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arXiv2007

The effect of unbound stars on the mass modelling of the Fornax dwarf

We discuss how different approaches to selecting member stars in kinematic samples of dwarf spheroidal galaxies affect the estimates of their mass and anisotropy of stellar orbits. We demonstrate that the selection of members is an additional source of error compared to the usual uncertainties due to the sampling of velocity moments. As an example we use the kinematic data set for 202 stars in the Fornax dwarf galaxy for which we model the velocity dispersion profile and estimate the mass-to-light ratio and anisotropy assuming that mass follows light. We also show that stronger constraints on these parameters can be obtained if kurtosis of the velocity distribution is included in the analysis. Using the Besancon model of the Milky Way we demonstrate that the majority of contamination in Fornax probably comes from the Milky Way stars.

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arXiv2007

The importance of interloper removal in galaxy clusters: saving more objects for the Jeans analysis

We study the effect of contamination by interlopers in kinematic samples of galaxy clusters. We demonstrate that without the proper removal of interlopers the inferred parameters of the mass distribution in the cluster are strongly biased towards higher mass and lower concentration. The interlopers are removed using two procedures previously shown to work most efficiently on simulated data. One is based on using the virial mass estimator and calculating the maximum velocity available to cluster members and the other relies on the ratio of the virial and projected mass estimators. We illustrate the performance of the methods in detail using the example of A576, a cluster with a strong uniform background contamination, and compare the case of A576 to 15 other clusters with different degree of contamination. We model the velocity dispersion and kurtosis profiles obtained for the cleaned data samples of these clusters solving the Jeans equations to estimate the mass, concentration and anisotropy parameter. We present the mass-concentration relation for the total sample of 22 clusters.

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arXiv2007

Interloper treatment in dynamical modelling of galaxy clusters

The aim of this paper is to study the efficiency of different approaches to interloper treatment in dynamical modelling of galaxy clusters. Using cosmological N-body simulation of standard LCDM 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. 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.

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arXiv2006

Equation of state for Universe from similarity symmetries

In this paper we proposed to use the group of analysis of symmetries of the dynamical system to describe the evolution of the Universe. This methods is used in searching for the unknown equation of state. It is shown that group of symmetries enforce the form of the equation of state for noninteracting scaling multifluids. We showed that symmetries give rise the equation of state in the form $p=-Λ+w_{1}ρ(a)+w_{2}a^β+0$ and energy density $ρ=Λ+ρ_{01}a^{-3(1+w)}+ρ_{02}a^β+ρ_{03}a^{-3}$, which is commonly used in cosmology. The FRW model filled with scaling fluid (called homological) is confronted with the observations of distant type Ia supernovae. We found the class of model parameters admissible by the statistical analysis of SNIa data. We showed that the model with scaling fluid fits well to supernovae data. We found that $Ω_{\text{m},0} \simeq 0.4$ and $n \simeq -1$ ($β= -3n$), which can correspond to (hyper) phantom fluid, and to a high density universe. However if we assume prior that $Ω_{\text{m},0}=0.3$ then the favoured model is close to concordance $Λ$CDM model. Our results predict that in the considered model with scaling fluids distant type Ia supernovae should be brighter than in $Λ$CDM model, while intermediate distant SNIa should be fainter than in $Λ$CDM model. We also investigate whether the model with scaling fluid is actually preferred by data over $Λ$CDM model. As a result we find from the Akaike model selection criterion prefers the model with noninteracting scaling fluid.

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arXiv2005

Mass distribution in nearby Abell clusters

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 < β< 0.5 at the 95 percent confidence level.

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arXiv2005

Towards testing interacting cosmology by distant type Ia supernovae

We investigate the possibility of testing cosmological models with interaction between matter and energy sector. We assume the standard FRW model while the so called energy conservation condition is interpreted locally in terms of energy transfer. We analyze two forms of dark energy sectors: the cosmological constant and phantom field. We find a simple exact solution of the models in which energy transfer is described by a Cardassian like term in the relation of $H^{2}(z)$, where $H$ is Hubble's function and $z$ is redshift. The considered models have two additional parameters $(Ω_{\text{int}},n)$ (apart the parameters of the $Λ$CDM model) which can be tested using SNIa data. In the estimation of the model parameters Riess et al.'s sample is used. We also confront the quality of statistical fits for both the $Λ$CDM model and the interacting models with the help of the Akaike and Bayesian informative criteria. Our conclusion from standard best fit method is that the interacting models explains the acceleration of the Universe better but they give rise to a universe with high matter density. However, using the tools of information criteria we find that the two new parameters play an insufficient role in improving the fit to SNIa data and the standard $Λ$CDM model is still preferred. We conclude that high precision detection of high redshift supernovae could supply data capable of justifying adoption of new parameters.

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arXiv2005

The complex velocity distribution of galaxies in Abell 1689: implications for mass modelling

The Abell 1689 galaxy cluster has recently become a subject of intensive study. Thanks to its intermediate redshift (z=0.183) its mass distribution can be reconstructed using numerous methods including gravitational lensing, galaxy kinematics and X-ray imaging. The methods used to yield conflicting mass estimates in the past and recently the cluster mass distribution has been claimed to be in conflict with standard CDM scenarios due to rather large concentration and steep mass profile obtained from detailed studies of Broadhurst et al. using lensing. By studying in detail the kinematics of about 200 galaxies with measured redshifts in the vicinity of the cluster we show that the cluster is probably surrounded by a few structures, quite distant from each other, but aligned along the line of sight. We support our arguments by referring to cosmological N-body simulations and showing explicitly that distant, non-interacting haloes can produce entangled multi-peak line-of-sight velocity distributions similar to that in A1689. We conclude that it is difficult to estimate the cluster mass reliably from galaxy kinematics, but the value we obtain after applying a simple cut-off in velocity agrees roughly with the mass estimated from lensing. The complicated mass distribution around the cluster may however increase the uncertainty in the determination of the density profile shape obtained with weak lensing.

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arXiv2005

Velocity moments of dark matter haloes

Using cosmological N-body simulations we study the line-of-sight velocity distribution of dark matter haloes focusing on the lowest-order even moments, dispersion and kurtosis, and their application to estimate the mass profiles of cosmological structures. For each of the ten massive haloes selected from the simulation box we determine the virial mass, concentration and the anisotropy parameter. In order to emulate observations from each halo we choose randomly 300 particles and project their velocities and positions along the line of sight and on the surface of the sky, respectively. After removing interlopers we calculate the profiles of the line-of-sight velocity moments and fit them with the solutions of the Jeans equations. The estimates of virial mass, concentration parameter and velocity anisotropy obtained in this way are in good agreement with the values found from the full 3D analysis.

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arXiv2005

Radial velocity moments of dark matter haloes

Using cosmological N-body simulations we study the radial velocity distribution in dark matter haloes focusing on the lowest-order even moments, dispersion and kurtosis. We determine the properties of ten massive haloes in the simulation box approximating their density distribution by the NFW formula characterized by the virial mass and concentration. We also calculate the velocity anisotropy parameter of the haloes and find it mildly radial and increasing with distance from the halo centre. The radial velocity dispersion of the haloes shows a characteristic profile with a maximum, while the radial kurtosis profile decreases with distance starting from a value close to Gaussian near the centre. We therefore confirm that dark matter haloes possess intrinsically non-Gaussian, flat-topped velocity distributions. We find that the radial velocity moments of the simulated haloes are quite well reproduced by the solutions of the Jeans equations obtained for the halo parameters with the anisotropy measured in the simulations. We also study the radial velocity moments for a composite cluster made of ten haloes out to ten virial radii. In this region the velocity dispersion decreases systematically to reach the value of the background, while kurtosis increases from below to above the Gaussian value of 3 signifying a transition from a flat-topped to a strongly peaked velocity distribution with respect to the Gaussian, which can be interpreted as the dominance of ordered flow with a small dispersion. We illustrate the transition by showing explicitly the velocity distribution of the composite cluster in a few radial bins.

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