Morphology of Galaxy Clusters: A Cosmological Model-Independent Test of the Cosmic Distance-Duality Relation

Abstract

Aiming at comparing different morphological models of galaxy clusters, we use two new methods to make a cosmological model-independent test of the distance-duality (DD) relation. The luminosity distances come from Union2 compilation of Supernovae Type Ia. The angular diameter distances are given by two cluster models (De Filippis et al. and Bonamente et al.). The advantage of our methods is that it can reduce statistical errors. Concerning the morphological hypotheses for cluster models, it is mainly focused on the comparison between elliptical β-model and spherical β-model. The spherical β-model is divided into two groups in terms of different reduction methods of angular diameter distances, i.e. conservative spherical β-model and corrected spherical β-model. Our results show that the DD relation is consistent with the elliptical β-model at 1σ confidence level (CL) for both methods, whereas for almost all spherical β-model parameterizations, the DD relation can only be accommodated at 3σ CL, particularly for the conservative spherical β-model. In order to minimize systematic uncertainties, we also apply the test to the overlap sample, i.e. the same set of clusters modeled by both De Filippis et al. and Bonamente et al.. It is found that the DD relation is compatible with the elliptically modeled overlap sample at 1σ CL, however for most of the parameterizations, the DD relation can not be accommodated even at 3σ CL for any of the two spherical β-models. Therefore it is reasonable that the marked triaxial ellipsoidal model is a better geometrical hypothesis describing the structure of the galaxy cluster compared with the spherical β-model if the DD relation is valid in cosmological observations.

Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae

“…Yu et al [9] got α = 0.81 +0. 19 −0.20 at 1σ CL via the observational H(z) data, and Busti et al [10] got α ≥ 0.25 (2σ) using Union2 SNe Ia data. In this paper we use latest Union2.1 SNe Ia data which contains 580 SNe Ia to constrain α, and we get α = 0.92 +0.08 −0.32 (1σ) and 0.92 +0.08 −0.65 (2σ).…”

“…Therefore, their results just satisfy the DD relation at 2σ CL for elliptical model. In subsequent papers, Li et al [18] and Meng et al [19] obtained the conclusion that DD relation can be accommodated at the 1σ CL for the elliptical model. In short, these cosmological model-independent tests suggest that the deviation of η from 1 is minor.…”

“…2) and there are generally two ways to test it's validity. The first way to constrain η is to combine the observed results of D L and D A both from observations [14,[17][18][19]. This method is popular because it is cosmological model-independent.…”

Constraints on cosmic distance duality relation from cosmological observations

“…see refs. [4][5][6][7][8][9][10][11][12][13][14][15][16] and references * Electronic address: xiajq@bnu.edu.cn therein). If η obtained from the d L and d A datasets is different from the unity, the CDDR relation is violated.…”

Constraints on the duality relation from ACT cluster data

“…It is known, however, that the verification of the CDDR validity depends on the assumptions used to describe the galaxy clusters (Holanda et al 2010(Holanda et al , 2012aNair et al 2011;Li et al 2011;Meng et al 2012;Lima et al 2012;Xi et al 2013;Allen et al 2013). As an example, assuming the CDDR, Holanda et al (2012b) and Meng et al (2012) show that the elliptical β-model constitutes a better geometrical description of the galaxy cluster structure when compared to the spherical β-model. Following a different approach, Gonçalves et al (2012) show that measurements of the gas mass fraction ( f gas ) A&A 573, A88 (2015) of galaxy clusters depend on the validity of the CDDR and used a sample of 38 clusters along with SNe Ia observations to test the CDDR.…”