| Summary: | We provide the first combined cosmological analysis of South Pole Telescope (SPT) and Planck cluster catalogs. The aim is to provide an independent calibration for Planck scaling relations, exploiting the cosmological constraining power of the SPT-SZ cluster catalog and its dedicated weak lensing (WL) and X-ray follow-up observations. We build a new version of the Planck cluster likelihood. In the $\nu \Lambda$CDM scenario, focusing on the mass slope and mass bias of Planck scaling relations, we find $\alpha_{\text{SZ}} = 1.49 _{-0.10}^{+0.07}$ and $(1-b)_{\text{SZ}} = 0.69 _{-0.14}^{+0.07}$ respectively. The results for the mass slope show a $\sim 4 \, \sigma$ departure from the self-similar evolution, $\alpha_{\text{SZ}} \sim 1.8$. This shift is mainly driven by the matter density value preferred by SPT data, $\Omega_m = 0.30 \pm 0.03$, lower than the one obtained by Planck data alone, $\Omega_m = 0.37 _{-0.06}^{+0.02}$. The mass bias constraints are consistent both with outcomes of hydrodynamical simulations and external WL calibrations, $(1-b) \sim 0.8$, and with results required by the Planck cosmic microwave background cosmology, $(1-b) \sim 0.6$. From this analysis, we obtain a new catalog of Planck cluster masses $M_{500}$. We estimate the relation between the published Planck derived $M_{\text{SZ}}$ masses and our derived masses, as a measured mass bias. We analyse the mass, redshift and detection noise dependence of this quantity, finding an increasing trend towards high redshift and low mass. These results mimic the effect of departure from self-similarity in cluster evolution, showing different dependencies for the low-mass high-mass, low-z high-z regimes.
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