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

TL;DR

This study probes cosmic isotropy by testing directional variations in galaxy-cluster scaling relations against ΛCDM using FLAMINGO hydrodynamical simulations. It implements two complementary analyses (M21-style sky patches and full MCMC likelihood) on 1728 simulated lightcones, with scatter and instrumental uncertainties matched to observations, to quantify the frequency of M21-like anisotropies. The results show that most apparent anisotropies arise from statistical noise, but a residual tension remains, particularly in the joint $L_X{-}T$ and $Y_{SZ}{-}T$ analysis, at roughly $2.3$–$3.6\sigma$ depending on method and scatter treatment. The work highlights the critical role of scaling-relation scatter, offers guidance on selecting low-scatter observables (e.g., $M_{gas}{-}T$), and underscores the importance of simulations for interpreting potential cosmological anisotropies in cluster data. It also points to future pathways, including applying the method to new cluster catalogs (eRASS1) and performing signal-injection tests to calibrate methodology and robustness against systematics.

Abstract

The standard cosmological model, $Λ$CDM, assumes isotropy on large cosmic scales. However, recent studies using galaxy cluster scaling relations have reported an apparent $H_0$ anisotropy at $5.4σ$ that could be attributed to large bulk flows extending beyond ${500}\,\mathrm{Mpc}$, which is in disagreement with $Λ$CDM. To quantify the statistical tension of the observational galaxy cluster data used in past studies with $Λ$CDM, we utilised the isotropic (${2.8}\,\mathrm{Gpc})^3$ run of the FLAMINGO ($Λ$CDM) simulations, the largest hydrodynamical cosmological simulation available to date. We created 1728 simulated lightcones and studied 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 the past study. We find the probability of such apparent anisotropies randomly emerging in cluster scaling relations within a $Λ$CDM universe to be $0.12\%\, (3.2σ)$. The discrepancy goes up to $\sim 3.6σ$ when modelled as a bulk flow at $z < 0.1$. We also 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 the past results and $Λ$CDM persists, albeit at a lower significance than previously reported.

Figures (18)

• Figure 1: Average cluster redshift distribution of the 1728 $(2.8Gpc)^3$ lightcones (red) compared with two runtime $(1.0Gpc)^3$ lightcones (purple, orange) and the M21 sample (blue). The most X-ray concentrated clusters from the simulation were selected to match the M21 sample size ($N = 313$).
• Figure 2: Mock instrumental uncertainties for one lightcone in $T$ (top left), $L_\mathrm{X}$ (top right), and $Y_\mathrm{SZ}$ (bottom right) compared with the M21 sample. The bottom-left panel shows the correlation between $Y_\mathrm{SZ}$ and its uncertainty $eY_\mathrm{SZ}$. In each panel, the mock uncertainty (green) represents one realisation drawn from the fitted distribution (red).
• Figure 3: Distribution of $H_0$ variation and its statistical significance from 1728 lightcones using the M21 scanning method (left) and the MCMC method (right) with (bottom) and without (top) mock scatter. The blue solid, red dashed, and green dash-dotted contours correspond to constraints from the $L_\mathrm{X}\text{--} T$, $Y_\mathrm{SZ}\text{--} T$, and $M_\mathrm{gas}\text{--} T$ relations, respectively. Contour levels indicate 39%, 86%, and 98.9% probability regions (equivalent to 1, 2, and 3$\sigma$ in two dimensions). Blue (red) squares mark the M21 results from $L_\mathrm{X}\text{--} T$ ($Y_\mathrm{SZ}\text{--} T$), including their measured statistical significance. Blue (red) circles show the M21 results obtained from isotropic Monte Carlo realisations for $L_\mathrm{X}\text{--} T$ ($Y_\mathrm{SZ}\text{--} T$). While the $L_\mathrm{X}\text{--} T$ results fall within the $3\sigma$ contours in every configuration, the $Y_\mathrm{SZ}\text{--} T$ results fall well outside the contours for the no-scatter case, and roughly at the $3\sigma$ limit for the matched scatter case.
• Figure 4: Joint MCMC constraint from the $L_\mathrm{X}\text{--} T$ and $Y_\mathrm{SZ}\text{--} T$ relations compared to the combined M21 result (red dot). The orange contour includes injected scatter, while the grey does not. Contours show the 39%, 86%, and 98.9% confidence regions.
• Figure 5: Extreme value statistics analyses of joint $H_0$ anisotropy in the FLAMINGO lightcones using the MCMC (left) and M21 (right) methods without (top) and with (bottom) matched scatter. Grey and orange histograms show the lower-bound projection of all 1728 lightcones without and with scatter, respectively. The red vertical line marks the M21 result under the same projection. The blue dashed line indicates the GPD threshold (90th or 95th percentile), above which the tail is modelled by a GDP, shown in green. The small shaded green region around the best fit line represents the 16th to 84th percentile region of bootstrapping error of the fit. Annotated in red is the EVS probability of obtaining the M21 result in FLAMINGO.