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

In standard cosmology, the late Universe is assumed to be statistically homogeneous and isotropic. However, a recent study based on galaxy clusters by Migkas et al. (2021, arXiv:2103.13904) found an apparent spatial variation of approximately $9%$ in the Hubble constant, H₀, across the sky. 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 H₀ variations. In this study, we search for directional T measurement biases by examining the scaling relation between the member galaxy velocity dispersion and the gas temperature (σᵥ-T). Additionally, we search for apparent H₀ angular variations independently of T by analysing the relations between the X-ray luminosity and Sunyaev-Zeldovich signal with the velocity dispersion, LX-σᵥ and YSZ-σᵥ. We utilise Monte Carlo simulations of isotropic cluster samples to quantify the statistical significance of any observed anisotropies. We find no significant directional T measurement biases, and the probability that a directional T bias causes the previously observed H₀ anisotropy is only $0.002%$. On the other hand, from the joint analysis of the LX-σᵥ and YSZ-σᵥ relations, the maximum variation of H₀ is found in the direction of (295^∘±71^∘, -30^∘±71^∘) with a statistical significance of 3.64σ, fully consistent with arXiv:2103.13904. Our findings strongly corroborate the previously detected spatial anisotropy of galaxy cluster scaling relations using a new independent cluster property, σᵥ.