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

Context. 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% 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. Aims. In this work, we search for directional T measurement biases by examining the relationship between the member galaxy velocity dispersion and gas temperature ( σ 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 − σ v and Y SZ − σ v . Methods. 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 σ v − T relation, as well as the apparent H 0 variations using the L X − σ v and Y SZ − σ 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. Results. No significant directional T measurement biases are found from the σ v − T anisotropy study. The probability that the previously observed H 0 anisotropy is caused by a directional T bias is only 0.002%. On the other hand, from the joint analysis of the L X − σ v and Y SZ − σ v relations, the maximum variation of H 0 is found in the direction of (295 ° ±71 ° , − 30 ° ±71 ° ) with a statistical significance of 3.64 σ , fully consistent with our previous results. Conclusions. Our findings, based on the analysis of new scaling relations utilising a completely independent cluster property, σ 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.