Implications of SPT and eROSITA cosmologies for Planck cluster number counts and t-SZ power spectrum

Abstract

Comparison between cosmological studies is usually performed in a statistical manner at the level of the posteriors of cosmological parameters. In this Letter, we show how this approach poorly reflects the differences between cosmological analyses, when applied to cosmological studies using galaxy cluster abundances. We illustrate this by deriving the implications of the best-fit cosmologies from the recent SPT and eROSITA cluster number counts analyses on the Planck thermal Sunyaev-Zeldovich (t-SZ) probes. We first fix the mass calibration, and find that the Planck cluster sample would theoretically contain 498 clusters with the SPT cosmology, and 1098 clusters with the eROSITA cosmology, instead of the 439 clusters observed. We then fit the Planck number counts to both cosmologies, only varying the hydrostatic mass bias, and find required biases of $0.790 \pm 0.070$ and $0.630 \pm 0.034$ for SPT and eROSITA respectively, instead of the $0.844^{+0.055}_{-0.062}$ derived in Aymerich et al. (2025). Lastly, we compute the expected t-SZ power spectrum obtained from the SPT and eROSITA cosmologies, and compare these to the Planck measurement. While the predicted SPT angular power spectrum is in good agreement with the Planck measurements, the normalisation of the predicted eROSITA angular power spectrum is two times higher at all scales. These two tests highlight the power of comparing predicted cluster abundances and t-SZ power spectra to measured data in a physically interpretable way.

Figures (4)

• Figure 1: Comparison of the predicted number counts for the Planck sample for the cosmologies of eROSITA, SPT, and Planck.
• Figure 2: Comparison of eROSITA and Planck masses. In grey, Planck masses are computed with the best-fit mass bias from the Planck+DES analysis. In blue, Planck masses are computed with the mass bias required to obtain the eROSITA cosmology with the PSZ2 catalogue and population model.
• Figure 3: Comparison on t-SZ angular power spectra assuming the Planck, SPT, and eROSITA number counts cosmologies. The shaded area takes into account the uncertainties on the cosmological parameters for each analysis (and the trispectrum term of uncertainty for the Planck power spectrum). The data obtained from Planck$y$-map are plotted in black.
• Figure 4: Comparison of the biases obtained in Sect. \ref{['bias_NC']} with values from the literature. Two values for a single study indicate that it is subject to the X-ray temperature calibration differences. A dark blue diamond corresponds to a Chandra bias and a red diamond to an XMM-Newton bias. Crosses indicate Chandra-like or XMM-like biases, i.e. biases rescaled to the expected value with data from the other instrument. Light blue points correspond to analyses insensitive to the X-ray temperature calibration problem, with a diamond indicating an observational value and a dot indicating a value derived from simulations.