  The Voit et al. (2020) black hole feedback valve model predicts relationships
between stellar velocity dispersion and atmospheric structure among massive
early-type galaxies. In this work, we test that model using the Chandra
archival sample of 49 early-type galaxies from Lakhchaura et al. (2018). We
consider relationships between stellar velocity dispersion and entropy profile
slope, multiphase gas extent, and the ratio of cooling time to freefall time.
We also define subsamples based on data quality and entropy profile properties
that clarify those relationships and enable more specific tests of the model
predictions. We find that the atmospheric properties of early-type galaxies
generally align with the predictions of the Voit et al. (2020) model, in that
galaxies with greater stellar velocity dispersion tend to have radial profiles
of pressure, gas density, and entropy with steeper slopes and less extended
multiphase gas. Quantitative agreement with the model predictions improves when
the sample is restricted to have low central entropy and stellar velocity
dispersion of between 220 and 300 km/s.
