In conventional models of galactic and cluster cooling flows widespread cooling (mass dropout) is assumed to avoid accumulation of unacceptably large central masses. However, recent XMM observations have failed to find spectral evidence for locally cooling gas. This has revived the notion that cooling flows are heated by some process such as an intermittent, low-level AGN involving supermassive black holes in the central galaxy. To explore this hypothesis, we consider the gasdynamical consequences of galactic cooling flows heated by many different scenarios without specifying the detailed physics of the heating process. We are unable to find a single acceptable heated flow in reasonable agreement with well observed hot gas temperature and density profiles, even using finely tuned parameters. Idealized flows in which radiative cooling is perfectly balanced by global heating are grossly incompatible with observations. Flows heated by episodic central feedback generate quasi-cyclic changes in the hot gas density profile which are not supported by current observations. Paradoxically, centrally heated (or pressurized) cooling flows experience spontaneous non-linear compressions that result in spatially widespread cooling instabilities. Therefore, spectral evidence for cooling gas is difficult to avoid by central heating.

17 pages (emulateapj5) with 12 figures and Appendix; accepted by The Astrophysical Journal