Outbursts from active galactic nuclei (AGN) can inflate cavities in the intracluster medium (ICM) of galaxy clusters and are believed to play the primary role in offsetting radiative cooling in the ICM. However, the details of how the energy from AGN feedback thermalizes to heat the ICM is not well understood, partly due to the unknown composition and energetics of the cavities. The Sunyaev-Zeldovich (SZ) effect, a measure of the integrated pressure along the line of sight, provides a means of measuring the thermal contents of the cavities, to discriminate between thermal, nonthermal, and other sources of pressure support. Here we report measurements of the SZ effect at 30 GHz toward the galaxy cluster MS 0735.6+7421 (MS0735), using the Combined Array for Research in Millimeter-wave Astronomy (CARMA). MS0735 hosts the most energetic AGN outburst known and lobes of radio synchrotron emission coincident with a pair of giant X-ray cavities $sim 200$ across. Our CARMA maps show a clear deficit in the SZ signal coincident with the X-ray identified cavities, when compared to a smooth X-ray derived pressure model. We find that the cavities have very little SZ-contributing material, suggesting that they are either supported by very diffuse thermal plasma with temperature in excess of hundreds of keV, or are not supported thermally. Our results represent the first detection (with $4.4 sigma$ significance) of this phenomenon with the SZ effect.
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