CHEX-MATE: Relationship between X-ray and millimetre inferences of galaxy cluster temperature profiles

Thermodynamic profiles from X-ray and millimetre observations of galaxy clusters are often compared under the simplifying assumptions of smooth, spherically symmetric intracluster medium. These approximations lead to expected discrepancies in the inferred profiles, which can provide insights about the cluster structure or cosmology. Motivated by this, we present a joint XMM-$\mathit{\text{Newton}}$ and $\mathit{\text{Planck}}$ analysis of 116 CHEX-MATE clusters to measure ${\eta }_T=T_X\mathrm{/}{T}_{SZ,X}$, the ratio between spectroscopic X-ray temperatures and a temperature proxy derived from Sunyaev-Zel’dovich (SZ) pressures and X-ray densities. We considered relativistic corrections to the thermal SZ signal and implemented X-ray absorption by Galactic molecular hydrogen. The ${\eta }_T$ distribution has a mean of $1.01\pm 0.03$, with average changes of $8.1\mathrm{\%}$ and $2.7\mathrm{\%}$ when relativistic corrections and molecular hydrogen absorption are not included, respectively. The ${\eta }_T$ distribution is positively skewed, with the scatter mostly affected by cluster morphology: relaxed clusters are closer to unity and less scattered than mixed and disturbed systems. We find little or no correlation with redshift, mass, or temperature.