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This is the third paper in a series analyzing X-ray emission from the hotinterstellar medium in a sample of 54 normal elliptical galaxies observed byChandra, focusing on 36 galaxies with sufficient signal to compute radialtemperature profiles. We distinguish four qualitatively different types ofprofile: positive gradient (outwardly rising), negative gradients (falling),quasi-isothermal (flat) and hybrid (falling at small radii, then rising). Wemeasure the mean logarithmic temperature gradients in two radial regions: from0--2 $J$-band effective radii $R_J$ (excluding the central point source), andfrom 2--$4R_J$. We find the outer gradient to be uncorrelated with intrinsichost galaxy properties, but strongly influenced by the environment: galaxies inlow-density environments tend to show negative outer gradients, while those inhigh-density environments show positive outer gradients, suggesting influenceof circumgalactic hot gas. The inner temperature gradient is unaffected by theenvironment but strongly correlated with intrinsic host galaxy characteristics:negative inner gradients are more common for smaller, optically faint, lowradio-luminosity galaxies, whereas positive gradients are found in brightgalaxies with stronger radio sources. There is no evidence for bimodality inthe distribution of inner or outer gradients. We propose three scenarios toexplain the inner temperature gradients: (1) Weak AGN heat the ISM locally,higher-luminosity AGN heat the system globally through jets inflating cavitiesat larger radii; (2) The onset of negative inner gradients indicates adeclining importance of AGN heating relative to other sources, such ascompressional heating or supernovae; (3) The variety of temperature profilesare snapshots of different stages of a time-dependent flow.

The Hot Interstellar Medium in Normal Elliptical Galaxies III: The Thermal Structure of the Gas