Inferences from surface brightness fluctuations of Zwicky 3146 via the Sunyaev-Zeldovich effect and X-ray observations

The galaxy cluster Zwicky 3146 is a sloshing cool core cluster at $z{=}0.291$ that in SZ imaging does not appear to exhibit significant pressure substructure in the intracluster medium (ICM). We perform a surface brightness fluctuation analysis via Fourier amplitude spectra on SZ (MUSTANG-2) and X-ray (XMM-Newton) images of this cluster. These surface brightness fluctuations can be deprojected to infer pressure and density fluctuations from the SZ and X-ray data, respectively. In the central region (Ring 1, $r < 100^{\prime\prime} = 440$ kpc, in our analysis) we find fluctuation spectra that suggest injection scales around 200 kpc ($\sim 140$ kpc from pressure fluctuations and $\sim 250$ kpc from density fluctuations). When comparing the pressure and density fluctuations in the central region, we observe a change in the effective thermodynamic state from large to small scales, from isobaric (likely due to the slow sloshing) to adiabatic (due to more vigorous motions). By leveraging scalings from hydrodynamical simulations, we find an average 3D Mach number $\approx0.5$. We further compare our results to other studies of Zwicky 3146 and, more broadly, to other studies of fluctuations in other clusters.