The constraints placed by these observations and existing data on the massive cooling flow scenario are examined. Contrary to some claims, the covering fraction of neutral gas has been found to be much less than unity in all cooling flows where the necessary data are available. As the cooling gas presumably forms low-mass stars or sub-stellar objects, the possibility of large masses of neutral gas escaping detection is investigated in detail. The gas, with or without dust, should not cool down to K as has been claimed but should remain K through X-ray heating at column densities up to . Greater column densities may be physically reasonable if the magnetic field is strong enough to support the cloud against fragmentation. In this case, ambipolar diffusion or magnetic slip-ion heating becomes important and should maintain the temperature . If the clouds contain dust, then although the dust radiates away most of the energy, the absorbed starlight keeps the temperature . Lack of CO or very broad lines do not appear to be feasible means of reconciling large molecular (or atomic) gas masses with the global lack of detections and tight upper limits. The primary conclusion is that the real mass inflow rates must be much lower that frequently claimed. It should then be noted that present-day cooling flows, if not so massive, lose much of their cosmological importance.
The FIR and CO emission from NGC 1275 correspond exactly to what is found in gas-rich spirals. Rather than a massive cooling flow, the gas may come from accretion of one or more gas-rich galaxies. Since, however, at least 14 other central galaxies would have been detected in CO if they contained similar quantities of gas, such events must be quite rare, very roughly if the time required for a large fraction of the gas to disappear is yr. cm