7 Discussion

7.1 The molecular gas content of late-type galaxies

The molecular gas content of our sample galaxies, normalized to the total mass of galaxies, is plotted in Figs. 6a and b as a function of the H luminosity and the morphological type. To avoid any systematic environmental effect, only unperturbed galaxies with an HI-deficiency $\leq$0.3 (defined as in Sect. 5.1) are considered.

Figure 6: The relationship between the normalised molecular gas mass of unperturbed galaxies (HI-deficiency $\leq$ 0.3) and a) the H band luminosity, b) the morphological type; the relationship between the H2 to HI gas ratio and c) the H band luminosity, d) the morphological type. All quantities are in solar units. Open triangles are upper limits to the molecular gas mass. To avoid overplotting, a random number between -0.4 and 0.4 was added to each half Hubble class bin taken as unity.

Figure 6 shows a strong anticorrelation between the normalized molecular gas mass and the total mass of galaxies, as traced by the H luminosity. The relationship with the morphological type is significantely weaker, even though it seems that early spirals have a lower normalized amount of molecular gas than late-type ones. Figures 6c and d show that the molecular to atomic hydrogen ratio is roughly constant in galaxies spanning a large range in luminosity and morphological type. The average value is M(H₂)/M(HI)=0.14 (with upper limits treated as detections).

The weak trends of the molecular gas content (per unit mass) with the morphological type and with the H luminosity as well as the constant molecular to atomic gas fraction observed by Boselli et al. (1997b) on a small, optically selected sample of Sa-Sc galaxies in the Coma supercluster is confirmed here with higher statistical significance and extended to lower luminosities, including Im and BCDs. The decrease of the molecular hydrogen to dynamical mass ratio or to the atomic hydrogen ratio claimed by Casoli et al. (1998), Sage (1993), Young & Knezek (1989) and Kenney & Young (1988b) for Scd-Sm-Im galaxies is probably due to a systematic underestimate of the total M(H₂) in low mass galaxies when derived assuming a constant X conversion factor.

7.2 The effect of the environment on the molecular gas

The available data can be used to analyse the effects of environment on the molecular gas content of normal galaxies. Following Boselli et al. (1997b) an H₂ deficiency parameter can be defined once the relationship between the molecular gas content and the H luminosity is calibrated on the unperturbed sample:

$$\log M({\rm H}_2)=3.28(\pm0.39)+0.51(\pm0.05)\log L_H$$ (8)

where M(H₂) and L_H are expressed in solar units. We can thus define the H₂ deficiency parameter as:

$${\rm H}_2-{\rm deficiency}=\log M({\rm H}_2)_{\rm e} - \log M({\rm H}_2)_{\rm o}$$ (9)

where M(H $_2)_{\rm e}$ is the expected molecular gas mass of a galaxy of a given H luminosity as determined from Eq. (8) and M(H $_2)_{\rm o}$ is the observed molecular gas mass. The H₂ deficiency parameter determined for the whole sample is plotted in Fig. 7 versus the HI-deficiency parameter.

Figure 7: The relationship between the H2 and the HI-deficiency parameter; filled dots are for the isolated galaxies sample. Triangles indicate lower limits to the H2 ($\triangle$), HI ( $\triangleright$) or both gas deficiency.

Figure 8: The relationship between the normalized star formation index H$\alpha +[$NII]EW (see text) and a) the molecular, b) the atomic and c) the total gas mass normalized to the H luminosity (in solar units). Filled symbols are for the unperturbed sample ( ${\rm HI}-{\rm deficiency}$ $\leq$ 0.3). Triangles indicate upper limits to the molecular hydrogen mass. The dashed line is the best fit to the whole sample, the dashed-dotted line the best fit to the unperturbed sample.

The present work confirms the lack of molecular-gas deficient galaxies in clusters such as Coma (Boselli et al. 1997b; Casoli et al. 1991) or Virgo (Kenney & Young 1989; Boselli 1994), extending previous results to lower luminosities. This analysis suggests that the low luminosity, CO deficient spiral galaxies observed in Virgo by Kenney & Young (1988b) are not necessarily deficient in molecular hydrogen.

7.3 The relationship between the molecular gas content and star formation

The atomic gas has to condense into molecular clouds to form new stars. A strong relationship between any tracer of star formation and the molecular gas content of late-type galaxies is thus expected.

 

 

Table 6: The relationships between the $\log {\rm H}\alpha+[$NII]EW and the atomic, molecular and total gas phases for the whole sample and for the unperturbed sample (bisector fit, with upper limits treated as detections).

Whole sample
Variable	slope	constant	scatter
$\log M($HI)/LH	0.797	2.184	0.603
$\log M($H2)/LH	1.005	3.042	0.723
$\log M({\rm HI}+{\rm H}_2)/L_H$	0.938	2.214	0.554

Unperturbed sample ( ${\rm HI}-{\rm def}$ $\leq$ 0.3)
Variable	slope	constant	scatter
$\log M($HI)/LH	1.078	2.300	0.902
$\log M($H2)/LH	0.896	2.944	0.741
$\log M({\rm HI}+{\rm H}_2)/L_H$	1.116	2.251	0.792

The relationship between the normalized star formation index H$\alpha +[$NII]EW and the molecular gas content (per unit mass) observed in bright galaxies by Boselli et al. (1995b, 1997b) extends to low luminosity galaxies ( $8 \leq \log L_H \leq 12~L_{H\odot}$) (see Fig. 8a) once their molecular gas mass is estimated using a luminosity-dependent X conversion factor. The best fits to the data along with the scatter from the linear fit are given in Table 6 for the whole sample and for the unperturbed sample ( ${\rm HI}-{\rm def} \leq 0.3$). This observational evidence confirms that the lack of a strong relationship between any star formation tracer and the molecular gas mass when determined assuming a constant value of Xis due to a systematic underestimate of the total molecular gas mass of low luminosity galaxies. Figure 8 shows that the relationship between the star formation activity and the total gas (HI + H₂) content of galaxies is stronger and less dispersed than for the individual gas components. This relationship is shared by normal and gas deficient galaxies, even though unperturbed galaxies have on average higher values of H$\alpha +[$NII]EW.

7.4 The star formation efficiency

The efficiency in transforming gas into stars can be estimated using the star formation rate (SFR) according to Boselli et al. (2001), i.e. using H$\alpha$+[NII] fluxes corrected for the contribution of the [NII] line, for extinction, and transformed into SFR (in solar masses per year) assuming a IMF of slope $\alpha={-}2.5$ in the mass range $M_{\rm up}=80~M_{\odot}$ and $M_{\rm low}=0.1~M_{\odot}$.

Figure 9: The relationship between the present star formation efficiency SFE and a) the H luminosity and b) the morphological type. Filled symbols are for the unperturbed sample ( ${\rm HI}-{\rm deficiency}$ $\leq$ 0.3). Triangles indicate lower limits to the SFE.

Figure 9 shows the relationship between the present SFE, defined as:

$${SFE = SFR/M({\rm H}_2)~({\rm yr^{-1}})}$$ (10)

and the H luminosity or the morphological type for the sample galaxies. If we were to consider the SFE on cosmological timescales, the whole gas reservoir (HI + H₂) would have to be taken into account, as done in Boselli et al. (2001). Figure 9 shows that the present SFE is similar for galaxies of different morphological type or luminosity. This result does not change if the SFE is determined using the total gas mass (Boselli et al. 2001; Boissier et al. 2001), as expected being the HI to H₂ratio constant (Fig. 6). Furthermore we do not see significant systematic differences in the SFE, as determined using H₂ gas masses (Eq. (10)), for the HI-deficient objects.