We introduce a new test to study the cosmological principle with galaxy clusters. Galaxy clusters exhibit a tight correlation between the luminosity and temperature of the X-ray-emitting intracluster medium. While the luminosity measurement depends on cosmological parameters through the luminosity distance, the temperature determination is cosmology-independent. We exploit this property to test the isotropy of the luminosity distance over the full extragalactic sky, through the normalization a of the LX–T scaling relation and the cosmological parameters Ωm and H0. To this end, we use two almost independent galaxy cluster samples: the ASCA Cluster Catalog (ACC) and the XMM Cluster Survey (XCS-DR1). Interestingly enough, these two samples appear to have the same pattern for a with respect to the Galactic longitude. More specifically, we identify one sky region within l ~ (−15°, 90°) (Group A) that shares very different best-fit values for the normalization of the LX–T relation for both ACC and XCS-DR1 samples. We use the Bootstrap and Jackknife methods to assess the statistical significance of these results. We find the deviation of Group A, compared to the rest of the sky in terms of a, to be ~2.7σ for ACC and ~3.1σ for XCS-DR1. This tension is not significantly relieved after excluding possible outliers and is not attributed to different redshift (z), temperature (T), or distributions of observable uncertainties. Moreover, a redshift conversion to the cosmic microwave background (CMB) frame does not have an important impact on our results. Using also the HIFLUGCS sample, we show that a possible excess of cool-core clusters in this region, is not able to explain the obtained deviations. Furthermore, we tested for a dependence of the results on supercluster environment, where the fraction of disturbed clusters might be enhanced, possibly affecting the LX–T relation. We indeed find a trend in the XCS-DR1 sample for supercluster members to be underluminous compared to field clusters. However, the fraction of supercluster members is similar in the different sky regions, so this cannot explain the observed differences, either. Constraining Ωm and H0 via the redshift evolution of LX–T and the luminosity distance via the flux–luminosity conversion, we obtain approximately the same deviation amplitudes as for a. It is interesting that the general observed behavior of Ωm for the sky regions that coincide with the CMB dipole is similar to what was found with other cosmological probes such as supernovae Ia. The reason for this behavior remains to be identified.
Spherically averaging ellipsoidal galaxy clusters in X-ray and Sunyaev-Zel’dovich studies - I. Analytical relations