Title: Relativistic SZ temperatures and hydrostatic mass bias for massive clusters in the FLAMINGO simulations

Abstract: The relativistic Sunyaev-Zel'dovich (SZ) effect can be used to measure intracluster gas temperatures independently of X-ray spectroscopy. Here, we use the large-volume FLAMINGO simulation suite to determine whether SZ $y$-weighted temperatures lead to more accurate hydrostatic mass estimates in massive ($M_{\rm 500c} > 7.5\times 10^{14}\,{\rm M}_{\odot}$) clusters than when using X-ray spectroscopic-like temperatures. We find this to be the case, on average. The median bias in the SZ mass at redshift zero is $\left< b \right> \equiv 1-\left< M_{\rm 500c,hse}/M_{\rm 500c,true} \right> = -0.05 \pm 0.01$, over 4 times smaller in magnitude than the X-ray spectroscopic-like case, $\left< b \right> = 0.22 \pm 0.01$. However, the scatter in the SZ bias, $\sigma_{b} \approx 0.2$, is around 40 per cent larger than for the X-ray case. We show that this difference is strongly affected by clusters with large pressure fluctuations, as expected from shocks in ongoing mergers. Selecting the clusters with the best-fitting generalized NFW pressure profiles, the median SZ bias almost vanishes, $\left< b \right> = -0.009 \pm 0.005$, and the scatter is halved to $\sigma_{b} \approx 0.1$. We study the origin of the SZ/X-ray difference and find that, at $R_{\rm 500c}$ and in the outskirts, SZ weighted gas better reflects the hot, hydrostatic atmosphere than the X-ray weighted gas. The SZ/X-ray temperature ratio increases with radius, a result we find to be insensitive to variations in baryonic physics, cosmology and numerical resolution.