Velocity Dispersion Of Galaxy Clusters Research Articles

Examining the local Universe isotropy with galaxy cluster velocity dispersion scaling relations

In standard cosmology, the Universe is assumed to be statistically homogeneous and isotropic. This assumption suggests that the expansion rate of the Universe, as measured by the Hubble parameter, should be the same in all directions. However, our recent study based on galaxy clusters finds an apparent angular variation of approximately $9<!PCT!>$ in the Hubble constant, $H_0$, across the sky. In the study, the authors utilised galaxy cluster scaling relations between various cosmology-dependent cluster properties and a cosmology-independent property, i.e. the temperature of the intracluster gas ($T$). A position-dependent systematic bias of $T$ measurements can, in principle, result in an overestimation of apparent $H_0$ variations. Therefore, it is crucial to confirm or exclude this possibility. In this work, we search for directional $T$ measurement biases by examining the relationship between the member galaxy velocity dispersion and gas temperature ($ v -T$) of galaxy clusters. Both measurements are independent of any cosmological assumptions and do not suffer from the same potential systematic biases. Additionally, we search for apparent $H_0$ angular variations independently of $T$ by analysing the relations between the X-ray luminosity and Sunyaev-Zeldovich signal with the velocity dispersion, $L_ X v $ and $Y_ SZ v To study the angular variation of scaling relation parameters, we determined the latter for different sky patches across the extra-galactic sky. We constrained the possible directional $T$ bias using the $ v -T$ relation, as well as the apparent $H_0$ variations using the $L_ X v $ and $Y_ SZ v $ relations. We utilised Monte Carlo simulations of isotropic cluster samples to quantify the statistical significance of any observed anisotropies. We calculated and rigorously took into account a correlation of $L_ X $ and $Y_ SZ $ residuals. No significant directional $T$ measurement biases are found from the $ v -T$ anisotropy study. The probability that the previously observed $H_0$ anisotropy is caused by a directional $T$ bias is only $0.002<!PCT!>$. On the other hand, from the joint analysis of the $L_ X v $ and $Y_ SZ v $ relations, the maximum variation of $H_0$ is found in the direction of $(295^ with a statistical significance of $3.64 fully consistent with our previous results. Our findings, based on the analysis of new scaling relations utilising a completely independent cluster property, $ v $, strongly corroborate the previously detected anisotropy of galaxy cluster scaling relations. The underlying cause, for example, $H_0$ angular variation or large-scale bulk flows of matter, remains to be identified.

Correlation between centre offsets and gas velocity dispersion of galaxy clusters in cosmological simulations

The gas is the dominant component of baryonic matter in most galaxy groups and clusters. The spatial offsets of gas centre from the halo centre could be an indicator of the dynamical state of cluster. Knowledge of such offsets is important for estimate the uncertainties when using clusters as cosmological probes. In this paper, we study the centre offsets $r_{\rm off}$ between the gas and that of all the matter within halo systems in $\Lambda$CDM cosmological hydrodynamic simulations. We focus on two kinds of centre offsets: one is the three-dimensional PB offsets between the gravitational potential minimum of the entire halo and the barycentre of the ICM, and the other is the two-dimensional PX offsets between the potential minimum of the halo and the iterative centroid of the projected synthetic X-ray emission of the halo. Halos at higher redshifts tend to have larger values of rescaled offsets $r_{\rm off}/r_{200}$ and larger gas velocity dispersion $\sigma_{v}^{\rm gas}/\sigma_{200}$. For both types of offsets, we find that the correlation between the rescaled centre offsets $r_{\rm off}/r_{200}$ and the rescaled 3D gas velocity dispersion, $\sigma_v^{\rm gas}/\sigma_{200}$ can be approximately described by a quadratic function as $r_{{\rm off}}/r_{200} \propto (\sigma_{v}^{\rm gas}/\sigma_{200} - k_2)^{2}$. A Bayesian analysis with MCMC method is employed to estimate the model parameters. Dependence of the correlation relation on redshifts and the gas mass fraction are also investigated.

Probing screened modified gravity with nonlinear structure formation

We review the effects of modified gravity theories, in particular the symmetron and [Formula: see text] gravity, on the nonlinear regime of structure formation. In particular, we investigate the velocity dispersion of galaxy clusters as a function of the halo masses, how the matter power spectra depend on the coupling, range, and screening scale of the fifth force, and on possible ways of detecting violations of the equivalence principle using the mass inferred via lensing methods versus the mass inferred via dynamical methods. Furthermore, we show how one could use different voids statistics as one of the most promising probes of modified gravity.

Nonlinear structure formation in gravity theories beyond general relativity

We investigate the effects of modified gravity theories, in particular, the symmetron and f(R) gravity, on the nonlinear regime of structure formation. In particular, we investigate the velocity dispersion of galaxy clusters as a function of the halo masses, how the matter power spectra depend on the coupling, range and screening scale of the fifth force, and on possible ways of detecting violations of the equivalence principle using the mass inferred via lensing methods versus the mass inferred via dynamical methods.

A comparison between observed and analytical velocity dispersion profiles of 20 nearby galaxy clusters

We derive analytical expression for the velocity dispersion of galaxy clusters, using the statistical mechanical approach. We compare the observed velocity dispersion profiles for 20 nearby (z≤0.1) galaxy clusters with the analytical ones. It is interesting to find that the analytical results closely match with the observed velocity dispersion profiles only if the presence of the diffuse matter in clusters is taken into consideration. This takes us to introduce a new approach to detect the ratio of diffuse mass, Mdiff, within a galaxy cluster. For the present sample, the ratio f=Mdiff/M, where M the cluster’s total mass is found to has an average value of 45±12 %. This leads us to the result that nearly 45 % of the cluster mass is impeded outside the galaxies, while around 55 % of the cluster mass is settled in the galaxies.

Brighter galaxy bias: underestimating the velocity dispersions of galaxy clusters

We study the systematic bias introduced when selecting the spectroscopic redshifts of brighter cluster galaxies to estimate the velocity dispersion of galaxy clusters from both simulated and observational galaxy catalogues. We select clusters with Ngal > 50 at five low redshift snapshots from a semi-analytic model galaxy catalogue, and from a catalogue of SDSS DR8 groups and clusters across the redshift range 0.021<z<0.098. We employ various selection techniques to explore whether the velocity dispersion bias is simply due to a lack of dynamical information or is the result of an underlying physical process occurring in the cluster, for example, dynamical friction. The velocity dispersions and stacked particle velocity distributions of the parent dark matter (DM) halos are compared to the corresponding cluster dispersions and galaxy velocity distribution. We find a clear bias between the halo and the semi-analytic galaxy cluster velocity dispersion on the order of sigma gal / sigma DM = 0.87-0.95 and a distinct difference in the stacked galaxy and DM particle velocity distribution. We identify a systematic underestimation of the velocity dispersions when imposing increasing absolute I-band magnitude limits. This underestimation is enhanced when using only the brighter cluster members for dynamical analysis on the order of 5-35%, indicating that dynamical friction is a serious source of bias when using galaxy velocities as tracers of the underlying gravitational potential. In contrast to the literature we find that the resulting bias is not only halo mass-dependent but that the nature of the dependence changes according to the galaxy selection strategy. We make a recommendation that, in the realistic case of limited availability of spectral observations, a strictly magnitude-limited sample should be avoided to ensure an unbiased estimate of the velocity dispersion.

The virial theorem and the dark matter problem in hybrid metric-Palatini gravity

Hybrid metric-Palatini gravity is a recently proposed theory, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an f(ℛ) term constructed à la Palatini. The theory predicts the existence of a long-range scalar field, which passes the Solar System observational constraints, even if the scalar field is very light, and modifies the cosmological and galactic dynamics.Thus, the theory opens new possibilities to approach, in the same theoretical framework, the problems of both dark energy and dark matter.In this work, we consider the generalized virial theorem in the scalar-tensor representation of the hybrid metric-Palatini gravity. More specifically, taking into account the relativistic collisionless Boltzmann equation, we show that the supplementary geometric terms in the gravitational field equations provide an effective contribution to the gravitational potential energy. We show that the total virial mass is proportional to the effective mass associated with the new terms generated by the effective scalar field, and the baryonic mass. In addition to this, we also consider astrophysical applications of the model and show that the model predicts that the mass associated to the scalar field and its effects extend beyond the virial radius of the clusters of galaxies. In the context of the galaxy cluster velocity dispersion profiles predicted by the hybrid metric-Palatini model, the generalized virial theorem can be an efficient tool in observationally testing the viability of this class of generalized gravity models.

Virial mass in warped DGP-inspired $\mathcal{L}(R)$ gravity

A version of the virial theorem is derived in a brane-world scenario in the framework of a warped DGP model where the action on the brane is an arbitrary function of the Ricci scalar, \(\mathcal{L}(R)\). The extra terms in the modified Einstein equations generate an equivalent mass term (geometrical mass), which give an effective contribution to the gravitational energy and offer viable explanation to account for the virial mass discrepancy in clusters of galaxies. We also obtain the radial velocity dispersion of galaxy clusters and show that it is compatible with the radial velocity dispersion profile of such clusters. Finally, we compare the result of the model with \(\mathcal{L}(R)\) gravity theories.

Generalized virial theorem in warped DGP brane-world

We generalize the virial theorem to the warped DGP brane world scenario and consider its implications on the virail mass. In this theory the four dimensional scalar curvature term is included in the bulk action and the resulting four dimensional effective Einstein equation is augmented with extra terms which can be interpreted as geometrical mass, contributing to the gravitational energy. Estimating the geometrical mass using the observational data, we show that these geometric terms may account for the virial mass discrepancy in clusters of galaxies. Finally, we obtain the radial velocity dispersion of galaxy clusters and show that it is compatible with the radial velocity dispersion profle of such clusters.

Virial mass in DGP brane cosmology

We study the virial mass discrepancy in the context of a Dvali, Gabadadze and Poratti (DGP) brane-world scenario and show that such a framework can offer viable explanations to account for the mass discrepancy problem. This is done by defining a geometrical mass that we prove to be proportional to the virial mass. Estimating using observational data, we show that it behaves linearly with r and has a value of the order of M200, pointing to a possible resolution of the virial mass discrepancy. We also obtain the radial velocity dispersion of galaxy clusters and show that it is compatible with the radial velocity dispersion profile of such clusters. This velocity dispersion profile can be used to differentiate various models predicting the virial mass.

The generalized virial theorem inf(R) gravity

We generalize the virial theorem inf(R) modified gravity using the collisionless Boltzmann equation. We find supplementarygeometric terms in the modified Einstein equation providing an effective contribution tothe gravitational energy. The total virial mass is proportional to the effective massassociated with the new geometrical term, which may account for the well-known virialtheorem mass discrepancy in clusters of galaxies. The model predicts that thegeometric mass and its effects extend beyond the virial radius of the clusters.We also consider the behavior of the galaxy cluster velocity dispersion inf(R) models. The metric inside the galactic cluster, as well as the Lagrangian of the modifiedgravity model, are obtained in terms of quantities directly related to the physical propertiesof the clusters, and which can be determined from astrophysical observations. Thus, thef(R) virial theorem can be an efficient tool in observationally testing the viability of this class ofgeneralized gravity models.

Virial theorem and the dynamics of clusters of galaxies in the brane world models

A version of the virial theorem, which takes into account the effects of the noncompact extra dimensions, is derived in the framework of the brane world models. In the brane world scenario, the four-dimensional effective Einstein equation has some extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the 3-brane in the bulk. To derive the generalized virial theorem, we use a method based on the collisionless Boltzmann equation. The dark radiation term generates an equivalent mass term (the dark mass), which gives an effective contribution to the gravitational energy. This term may account for the well-known virial theorem mass discrepancy in actual clusters of galaxies. An approximate solution of the vacuum field equations on the brane, corresponding to weak gravitational fields, is also obtained, and the expressions for the dark radiation and dark mass are derived. The qualitative behavior of the dark mass is similar to that of the observed virial mass in clusters of galaxies. We compare our model with the observational data for galaxy clusters, and we express all the physical parameters of the model in terms of observable quantities. In particular, we predict that the dark mass must extend far more » beyond the presently considered virial radius. The behavior of the galaxy cluster velocity dispersion in brane world models is also considered. Therefore the study of the matter distribution and velocity dispersion at the extragalactic scales could provide an efficient method for testing the multidimensional physical models. « less