2018ApJ...862...39B

We present atmospheric gas entropy profiles for 40 early-type galaxies and 110 clusters spanning several decades of halo mass, atmospheric gas mass, radio jet power, and galaxy type. We show that within ∼0.1R₂₅₀₀ the entropy profiles of low-mass systems, including ellipticals, brightest cluster galaxies, and spiral galaxies, scale approximately as K ∝ R^2/3. Beyond ∼0.1R₂₅₀₀ entropy profiles are slightly shallower than the K ∝ R^1.1 profile expected from gravitational collapse alone, indicating that heating by active galactic nuclei (AGN) feedback extends well beyond the central galaxy. We show that the K ∝ R^2/3 entropy profile shape indicates that thermally unstable cooling is balanced by heating where the inner cooling and free-fall timescales approach a constant ratio. Hot atmospheres of elliptical galaxies have a higher rate of heating per gas particle compared to those of central cluster galaxies. This excess heating may explain why some central cluster galaxies are forming stars while most early-type galaxies have experienced no significant star formation for billions of years. We show that the entropy profiles of six lenticular and spiral galaxies follow the R^2/3 form. The continuity between central galaxies in clusters, giant ellipticals, and spirals suggests perhaps that processes heating the atmospheres of elliptical and brightest cluster galaxies are also active in spiral galaxies.