Characterising galaxy cluster scaling relations as cosmic isotropy tracers using the FLAMINGO simulations

The standard cosmological model, $\Lambda$CDM, assumes isotropy on large cosmic scales. However, recent studies using galaxy cluster scaling relations reported an apparent $H_0$ anisotropy at $5.4\sigma$ that could be attributed to large bulk flows extending beyond $500\,\mathrm{Mpc}$, in disagreement with $\Lambda$CDM. To quantify the statistical tension of the observational galaxy cluster data used in past studies with $\Lambda$CDM, we utilise the isotropic ($2.8\,\mathrm{Gpc})^3$ run of the FLAMINGO ($\Lambda$CDM) simulations, the largest hydrodynamical cosmological simulation available to date. We create 1728 simulated lightcones and study the apparent level of anisotropy traced by X-ray and thermal Sunyaev-Zeldovich scaling relations in the same cluster sample selection and methodology as in Migkas et al. (2021, arXiv:2103.13904). We find the probability of such apparent anisotropies randomly emerging in cluster scaling relations within a $\Lambda$CDM universe to be $0.12\%\, (3.2\sigma)$. The discrepancy goes up to $\sim 3.6\sigma$ when modelled as a bulk flow at $z < 0.1$. We find that statistical noise accounts for over $80\%$ of the anisotropy amplitude in each lightcone, with large peculiar velocities contributing less than $20\%$. We also show that anisotropy amplitudes are highly sensitive to the intrinsic scatter in the scaling relations, with tighter relations providing stronger constraints. Nevertheless, the tension between Migkas et al. (2021, arXiv:2103.13904) and $\Lambda$CDM persists, however, at a lower significance than previously reported.