Are HI-deficient galaxies of the Coma supercluster deficient in moleculargas ?

We present the first ^12^CO(1 - 0) and ^12^CO(2 - 1) observations of spiral galaxies located in the clusters Abell 367 and Abell 1656 (Coma supercluster). Because of their strong X-ray emission and high galaxy density, these are among the best candidates to search for H_2_ deficient galaxies. Our sample is made of 18 galaxies selected from their far-infrared emission. Nine are strongly deficient in atomic gas, with H I contents more than three times lower than in isolated galaxies of the same luminosities and types, whereas the remaining nine display a normal H I content: the latter are used as a comparison subsample. With the IRAM 30 m telescope, we have detected all these galaxies except for one which is H I-deficient and one which is normal. From the measured CO(1-0) intensities, we derive the molecular mass inside the central 10 kpc of the detected galaxies. It ranges from 0.75 to 6.8 10^9^M_sun_. In H I-deficient galaxies, most of the gas is in molecular form, with H_2_ /H I mass ratios around 2 or even larger in some cases where H I is not detected. In order to reveal possible deficiencies in molecular matter, we compare our data to the results of the FCRAO extragalactic survey (Young et al. 1989). The molecular content of our sample galaxies referred to their blue luminosity, namely, the M (H_2_)/L_B_ ratio, is on the average similar to what has been found for this survey. It indicates that these galaxies are probably not deficient in molecular gas. As an additional clue, galaxies in both the H I-deficient and comparison subsamples have the same average values of M (H_2_)/L_B_. The star-formation activity of the Coma galaxies,as measured by the LFIR/M (H_2_ ) and LFIR/L_B_ ratios or Hα emission, is normal and independent of the H I deficiency. The inferred star-formation rates are in the range 0.1 to 2 M_sun_ yr^-1^. This leads to exhaustion time scales of about 4 10^9^ yr for the total gas content, a value similar to what is found for field galaxies. We discuss to which extent the apparent absence of H_2_ - deficient galaxies is due to our having selected the sample with an IR criterion - flux density at 60 microns > 0.15 Jy and detection at 100 microns. It appears that the sample is biased against galaxies with a low star- formation rate. Using a much larger sample of galaxies compiled by Gavazzi (1987), we however find that, on the average, H I-deficient galaxies do not have a lower star-formation activity than normal ones, as traced by their L_FIR_/L_B_ ratio. This suggests that although H_2_ -deficient objects could exist in the core of Coma, most galaxies that have lost their atomic gas have retained their molecular clouds and go on forming stars at a normal rate.