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Mechanical feedback from active galactic nuclei (AGN) is thought to be thedominant feedback mechanism quenching cooling flows and star formation ingalaxy cluster cores. However, the mechanisms by which AGN couple to theintracluster medium (ICM) are not well understood. The nature of pressuresupporting the cavities is not known. Using the MUSTANG-2 instrument on theGreen Bank Telescope (GBT), we aimed to measure thermal Sunyaev-Zeldovich (SZ)effect signals associated with the X-ray cavities in MS0735.6+7421, a moderatemass cluster hosting one of the most energetic AGN outbursts known. We usethese measurements to infer the level of non-thermal sources of pressure, suchas magnetic fields and turbulence, as well as relativistic and cosmic raycomponents, supporting the cavities. We used preconditioned gradient descent tofit a model for the cluster, cavities, and central point source directly to thetime ordered data of the MUSTANG-2 signal. We use this model to probe thethermodynamic state of the cavities. We have shown that the SZ signalassociated with the cavities is suppressed compared to the expectations for athermal plasma with the temperature $\sim$few tens keV. The smallest value ofthe suppression factor $f$ that is consistent with the data is $\sim$0.4, lowerthan inferred in earlier work. Larger values of $f$ are possible once thecontribution of the cocoon shock surrounding the bubbles is taken into account.The baseline model with this particular geometrical setup yields best-fittingvalue f~0.5, which at face value implies a mix of thermal and non-thermalpressure support. Larger values of $f$ (up to 1, i.e. no tSZ signal from thebubbles) are still possible when allowing for variations in the line-of-sightgeometry.

GBT/MUSTANG-2 9" resolution imaging of the SZ effect in MS0735.6+7421: Confirmation of the SZ Cavities through direct imaging