Intracluster Medium Fluctuations on Scales up to 1 Mpc: A Combined eROSITA and SPT/Planck Analysis of Abell 3266

Galaxy clusters form through hierarchical assembly, where smaller substructures merge to build the largest gravitationally bound objects in the universe. These mergers, combined with feedback from AGN, filamentary accretion, and other energy injection processes, generate turbulence and perturbations within the intra-cluster medium (ICM). X-ray and Sunyaev-Zel'dovich (SZ) observations can be utilized to measure these ICM density and pressure inhomogeneities, in turn providing constraints on the effective Equation of State (EOS) of the perturbations and ICM velocities. In this work, we analyze deep SRG-eROSITA and Planck/SPT observations of Abell 3266 (A3266), a dynamically complex merging cluster with elongated morphology and significant substructure. We measure pressure and density fluctuations, and compute the power spectra and deprojected 3D amplitudes of these perturbations. We estimate the ratio of pressure-to-density fluctuation amplitudes as $1.00 \pm 0.55$ and non-thermal pressure support $0.068 \pm 0.050$. Density fluctuations are found to be stronger in the northern sector of the cluster compared to the south, consistent with ongoing accretion along a filamentary structure revealed by eROSITA. Further, we find the amplitude of density fluctuations increases with radius, qualitatively consistent with the trend found in cosmological simulations. Uncertainties in our results are dominated by the relatively low sensitivity of current Planck/SPT data, suggesting that improvements in SZ data quality could substantially improve our understanding of ICM energy injection, transport, and dissipation from this technique.