New constraints on cosmic anisotropy from galaxy clusters using an improved dipole fitting method

In this work, we attempted to apply the dipole fitting (DF) method to galaxy clusters to search for cosmic anisotropic signals, and to construct a statistical isotropic analysis scheme for them. Compared to Type Ia supernova (SNe Ia), the galaxy clusters offer a significant advantage in terms of spatial distribution. This advantage makes the anisotropic signals obtained from them more reliable. From 313 galaxy clusters (Chandra + XMM-Newton), we find two preferred directions (l, b) = (${257.82^{\circ}}{-52.88}^{+58.01}$, $-31.30{^{\circ}}{-39.46}^{+35.92}$) and ($80.89{^{\circ}}{-52.46}^{+60.97}$, $31.75{^{\circ}}{-40.16}^{+35.19}$). The former to a direction where the universe is expanding at a faster rate than the surrounding area, while the latter to a slower rate of expansion. The corresponding magnitude of anisotropy is $|A|$ = 5.2 $\sim$ 5.4 $\times$ 10$^{-4}$. The results of statistical isotropy analyses give $\sim$1.0$σ$ confidence level. From the reanalyses based on the subsamples including Chandra, XMM-Newton, low reshift (LR, $z < 0.10$), high redshift (HR, $z > 0.10$) datasets, we find that the observation equipment and sample redshift can affect the preferred direction, anisotropic magnitude, and statistical significance of anisotropy. The XMM-Newton dataset gives a statistical significance of 2.26$σ$ (Mock) and 2.86$σ$ (Iso) which are much higher than that from Chandra and the total datasets. The magnitude of anisotropy $|A|$ from HR dataset is larger than that from LR dataset. Overall, our results indicate the presence of anisotropic signals in galaxy clusters, which must be taken seriously. Further test is still needed to better understand these signals.

💡 Research Summary

In this work the authors investigate whether the large‑scale Universe is truly isotropic by applying a dipole‑fitting (DF) technique to a sample of 313 galaxy clusters observed with the Chandra and XMM‑Newton X‑ray telescopes. Galaxy clusters are advantageous for such tests because their X‑ray luminosity–temperature (L_X–T) scaling relation depends on the luminosity distance, which in turn is sensitive to the underlying cosmology. By fitting the L_X–T relation in a flat ΛCDM background (Ω_m = 0.30, Ω_Λ = 0.70, H_0 = 70 km s⁻¹ Mpc⁻¹) the authors first determine the correlation parameters (normalisation k, slope s, intrinsic scatter σ_int). They then introduce a dipole + monopole correction to the theoretical luminosity: Δlog L_X / log L_X,th = A cos θ + B, where θ is the angle between a trial dipole direction (l, b) and the line‑of‑sight to each cluster. The seven free parameters (k, s, σ_int, l, b, A, B) are simultaneously constrained by minimizing a modified χ² that incorporates the dipole term.

The analysis yields two nearly antipodal preferred directions, as expected for a dipole model. The first direction lies at Galactic coordinates (l ≈ 257.8°, b ≈ −31.3°) with a positive dipole amplitude A ≈ +5.3 × 10⁻⁴, indicating that clusters in this region appear slightly brighter (hence a locally faster expansion) than the average. The opposite direction (l ≈ 80.9°, b ≈ 31.8°) shows a negative amplitude of similar magnitude, implying a comparatively slower expansion. The magnitude of the anisotropy is modest, |A| ≈ 5.2–5.4 × 10⁻⁴.

To assess the statistical significance of these findings, the authors generate 10⁴ mock catalogues that preserve the sky distribution but assume isotropy, as well as 10⁴ fully isotropic simulations. For the full combined sample the dipole amplitude is consistent with isotropy at roughly the 1σ level (≈ 1.0 σ). However, when the data are split by instrument, the XMM‑Newton subsample (76 clusters) shows a stronger signal: 2.26 σ in the mock test and 2.86 σ in the isotropic simulation, suggesting that instrumental systematics or selection effects may enhance the apparent anisotropy. A further split by redshift (low‑z < 0.10, high‑z > 0.10) reveals that the high‑redshift subset exhibits a larger dipole magnitude than the low‑redshift one, indicating a possible redshift dependence of the effect.

The paper emphasizes several key points. First, galaxy clusters provide a more uniform sky coverage than Type Ia supernovae, reducing biases associated with uneven sampling. Second, the detected anisotropy is small and only marginally significant for the full sample, but the elevated significance in the XMM‑Newton subset warrants caution and further investigation. Third, the dependence of the dipole direction and amplitude on instrument and redshift suggests that systematic uncertainties (e.g., calibration differences, selection functions, evolution of the L_X–T relation) could mimic or amplify genuine cosmological anisotropy. Finally, the authors acknowledge that the current sample size and the limited redshift range restrict the robustness of the conclusions and call for larger, higher‑quality cluster catalogs (e.g., from eROSITA, LSST, Euclid) and more sophisticated statistical tools (Bayesian model comparison, machine‑learning pattern detection) to either confirm or refute the tentative anisotropic signals reported here.

In summary, the study provides the first application of dipole fitting to galaxy‑cluster X‑ray data, finds a low‑level dipole‑like anisotropy with opposite fast‑/slow‑expansion directions, and demonstrates that the significance of this signal is sensitive to the data subset used. While the results do not yet constitute decisive evidence against the cosmological principle, they highlight the importance of using uniformly distributed probes and of carefully accounting for instrumental and redshift‑dependent systematics in future anisotropy searches.