DEEP CO OBSERVATIONS OF DOMINANT CLUSTER GALAXIES WITH REPORTED COOLING FLOWS

X-ray observations of galaxy clusters have been interpreted as reveali ng massive cooling flows in many of them. Whatever the final sink (sta rs, planets, etc.), the cooling gas is bound to pass through a molecul ar phase. We have used the IRAM 30 m millimeter-wave telescope to obse rve eight cluster dominant galaxies with high reported gas inflow rate s in the (CO)-C-12 (1-0) and (CO)-C-12 (2-1) lines. Despite low noise levels, none of the galaxies were detected in either line with 1 sigma limits to M(H2) ranging between 4 10(7) and 1.3 10(9) M.. These value s are two orders of magnitude below values expected from the reported accretion rates (often M greater-than-or-equal-to 100 M. yr-1) and the measured star-formation time in spirals and ellipticals (tau(SF) appr oximately 1 Gyr). Even supposing that the whole process of star format ion - from recombination of ionized gas into atoms and molecules to cl oud gravitational condensation - is governed by the collapse time (app roximately 4 10(7) yr) and that only part of the cold gas is included in the IRAM beam, our detection limits rule out the high values of M p roposed by the ''standard model'' of cooling flows by a factor 5 on av erage. These results add to the other observational and theoretical pr oblems faced by the standard interpretation of X-ray data. We conclude that a revision of the traditional picture appears necessary.