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The failure of the XMM-Newton and Chandra X-ray telescopes to detect coolinggas in elliptical galaxies and clusters of galaxies has led many to adopt theposition that the gas is not cooling at all and that heating by an activenucleus in the central E or cD galaxy is sufficient to offset radiativecooling. In this paper we explore an idealized limiting example of this pointof view in which hot, buoyant bubbles formed near the center return theinflowing, radiatively cooling gas to distant regions in the flow. We show thatidealized steady state, centrally heated non-cooling flows can indeed beconstructed. In addition, the emission-weighted temperature profiles in thesecirculating flows resemble those of normal cooling flows. However, thesesolutions are valid only (1) for a range of bubble parameters for which thereis no independent justification, (2) for a limited spatial region in thecooling flow and (3) for a limited period of time after which cooling seemsinevitable. Our exploration of non-cooling flows is set in the context ofgalaxy/group flows.Comment: 10 pages (emulateapj5) with 4 figures; accepted by The Astrophysical  Journa

Circulation Flows: Cooling Flows with Bubble Return