Characterizing hydrostatic mass bias with Mock-X
  Surveys in the next decade will deliver large samples of galaxy clusters that
transform our understanding of their formation. Cluster astrophysics and
cosmology studies will become systematics limited with samples of this
magnitude. With known properties, hydrodynamical simulations of clusters
provide a vital resource for investigating potential systematics. However, this
is only realized if we compare simulations to observations in the correct way.
Here we introduce the \textsc{Mock-X} analysis framework, a multiwavelength
tool that generates synthetic images from cosmological simulations and derives
halo properties via observational methods. We detail our methods for generating
optical, Compton-$y$ and X-ray images. Outlining our synthetic X-ray image
analysis method, we demonstrate the capabilities of the framework by exploring
hydrostatic mass bias for the IllustrisTNG, BAHAMAS and MACSIS simulations.
Using simulation derived profiles we find an approximately constant bias
$b\approx0.13$ with cluster mass, independent of hydrodynamical method or
subgrid physics. However, the hydrostatic bias derived from synthetic
observations is mass-dependent, increasing to $b=0.3$ for the most massive
clusters. This result is driven by a single temperature fit to a spectrum
produced by gas with a wide temperature distribution in quasi-pressure
equilibrium. The spectroscopic temperature and mass estimate are biased low by
cooler gas dominating the emission, due to its quadratic density dependence.
The bias and the scatter in estimated mass remain independent of the numerical
method and subgrid physics. Our results are consistent with current
observations and future surveys will contain sufficient samples of massive
clusters to confirm the mass dependence of the hydrostatic bias.
