Unraveling Baroclinicity in Black Hole Weather Storms

In the intracluster, intragroup, and circumgalactic medium (ICM, IGrM, CGM), turbulence plays a vital role in the self-regulated feedback and feeding cycle of central supermassive black holes (SMBHs). Here we continue our systematic dissection of the turbulent "weather" in high-resolution hydrodynamical simulations of feedback driven by active galactic nuclei (AGN). In non-barotropic and stratified atmospheres, baroclinicity is expected to generate fresh turbulence via misaligned gradients of density and pressure - such as in cyclonic storms on Earth. In this work, we dissect for the first time baroclinicity and its components in the astrophysical halo weather. Over the macro-scale galaxy cluster, baroclinicity tends to be dynamically subdominant for the enstrophy amplification. However, at and below the meso scale near the SMBH (r<10 kpc; t<20 Myr), baroclinicity is important to seed the initial enstrophy during active periods of AGN jet feedback. We find that baroclinicity shows stronger correlation with the density rather than pressure gradients. Despite the density-pressure gradient misalignment being often below 45{\deg}, their amplitudes boosted by mechanical AGN feedback are sufficient to enable key enstrophy/turbulence generation. Our study provides a novel step forward in understanding astrophysical atmospheres toward a unified BlackHoleWeather framework, akin to the complexity of Earth's weather.