A Universal Entropy Profile for the Hot Atmospheres of Galaxies and
  Clusters within $R_{2500}$
  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 $\sim 0.1R_{2500}$ the entropy
profiles of low-mass systems, including ellipticals, brightest cluster
galaxies, and spiral galaxies, scale approximately as $K\propto R^{2/3}$.
Beyond $\sim 0.1R_{2500}$ entropy profiles are slightly shallower than the $K
\propto R^{1.1}$ profile expected from gravitational collapse alone, indicating
that heating by AGN feedback extends well beyond the central galaxy. We show
that the $K\propto R^{2/3}$ 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 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.
