Forecasting constraints from surface brightness fluctuations in galaxy clusters

Studies of surface brightness (SB) fluctuations in the intracluster medium (ICM) present an indirect estimate of turbulent pressure support and associated Mach numbers. While high resolution X-ray spectroscopy offer means to directly constrain line of sight gas motions, including those due to turbulence, such observations are relatively expensive and will be limited to nearby, bright clusters. In this respect, SB fluctuations are the most economical means to constrain turbulent motions at large cluster radii across a range of redshifts and masses. To forecast what current and future X-ray and SZ facilities may achieve in SB fluctuation studies, I review and synthesize matters of accuracy and precision with respect to calculating power spectra of SB fluctuations, from which turbulent properties are derived. Balance concerns of power spectrum accuracy and precision across a range of spatial scales, I propose the use of three annuli with: [0,0.4] $R_{500}$, [0.4,1] $R_{500}$, and [1,1.5] $R_{500}$. Adopting these three regions, I calculate the uncertainty in the hydrostatic mass bias, $\sigma_{b_{\mathcal{M}}}$, can be achieved for various instruments in several scenarios. I find that $\textit{Lynx}$ and AtLAST are competitive in their constraints at $R_{500}$, while AtLAST should perform better when constraining $\sigma_{b_{\mathcal{M}}}$ at $R_{200}$.