Measuring the Three‐dimensional Structure of Galaxy Clusters. I. Application to a Sample of 25 Clusters

Abstract

We discuss a method to constrain the intrinsic shapes of galaxy clusters by combining X-ray and SunyaevZel'dovich observations. The method is applied to a sample of 25 X-ray-selected clusters, with measured SunyaevZel'dovich temperature decrements. The sample turns out to be slightly biased, with strongly elongated clusters preferentially aligned along the line of sight. This result demonstrates that X-ray-selected cluster samples may be affected by morphological and orientation effects, even if a relatively high threshold signal-to-noise ratio is used to select the sample. A large majority of the clusters in our sample exhibit a marked triaxial structure; the spherical hypothesis is strongly rejected for most sample members. Cooling-flow clusters do not show preferentially regular morphologies. We also show that identification of multiple gravitationally lensed images, together with measurements of the Sunyaev-Zel'dovich effect and X-ray surface brightness, can provide a simultaneous determination of the three-dimensional structure of a cluster, of the Hubble constant, and of the cosmological energy density parameters.

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

“…This method is popular because it is cosmological model-independent. Holanda et al [14] artificially assumed that η(z) takes two forms, i.e., η(z) = 1 + η 0 z or η(z) = 1 + η 0 z/(1 + z), and got η 0 = −0.28 +0.44 −0.44 (2σ CL) for the D A samples of elliptical model [20]. Therefore, their results just satisfy the DD relation at 2σ CL for elliptical model.…”

Improved constraints on violations of the Einstein equivalence principle in the electromagnetic sector with complementary cosmic probes

“…The distance modulusμ 1 (i), µ 2 (i) andμ 3 (i) correspond to weighted averages from the SNe Ia data for each i-galaxy cluster in samples present in Refs. [30,31,35] (see Eq. 50).…”

“…The second one is that presented by the Ref. [30], where the X-ray surface brightness was described by an elliptical isothermal β-model. In this case, the galaxy clusters are distributed over the redshift interval 0.023 ≤ z ≤ 0.784.…”

“…Then, we end up with 40, 29 and 25μ i and σ 2 µi measurements when the sample from [35], [31] and [30] is considered, respectively. Following [32] we added quadratically a 0.15 systematic error to each SNe Ia distance modulus error.…”

“…The authors have used angular diameter distances (ADD) of galaxy clusters obtained via their X-ray surface brightness jointly with observations of the Sunyaev-Zel'dovich effect (SZE) [30,31], SNe Ia samples [32], CMB temperature in different redshifts, T CMB (z) [33,34] and the most recent X-ray gas mass fraction (GMF) data with galaxy clusters in the redshift range 0.078 ≤ z ≤ 1.063 [35]. In the Ref.…”