© ESO, 2011

1. Introduction

A major and longlasting debate in astronomy involves the relative roles of “nature” and “nurture” in galaxy formation and evolution (e.g. Sulentic 1976; Larson & Tinsley 1978; Joseph & Wright 1985; Bushouse 1987). Although it is broadly accepted that galaxy evolution strongly depends on the environment, the quantitative effect of “nurture” on certain galactic properties is still a matter of debate.

The molecular gas content is an important quantity of a galaxy because it is directly related to its capacity for star formation SF. We still need to determine, however, how the environment affects the amount of the molecular gas. Galaxies in clusters (Kenney & Young 1989; Boselli et al. 1997; Scott et al., in prep.) and groups (Verdes-Montenegro et al. 1998; Leon et al. 1998) seem to have a normal molecular gas content, even though they can be highly deficient in atomic gas. On the other hand, some authors (Braine & Combes 1993; Combes et al. 1994; Casasola et al. 2004) find an enhanced molecular gas content in interacting galaxies, in contrast to the results of Perea et al. (1997), who concluded that the molecular gas content is not affected by interaction in strongly interacting pairs or Virgo cluster galaxies.

To clarify the role played by the environment, a well-defined sample of isolated galaxies is needed to serve as a zero level for studies dealing with the effect of interactions. Most previous studies investigating the properties of molecular gas in isolated and interacting galaxies (Solomon & Sage 1988; Sage 1993; Boselli et al. 1997; Nishiyama & Nakai 2001; Helfer et al. 2003; Leroy et al. 2009) have generally not defined any very clear criterion for isolation. Perea et al. (1997) carried out a CO study comparing isolated and interacting galaxies. Their sample of isolated galaxies is composed of 68 galaxies from various sources, selected in a much less rigorous way than the present study and biased towards infrared-luminous objects. The only survey explicitly focusing on isolated galaxies, and in particular on galaxies from the Catalogue of Isolated Galaxies, is the one by Sauty et al. (2003). They present the CO data of 99 optically-selected spiral galaxies with recession velocities up to 14 000 km s^-1 and briefly compare the properties of the molecular gas mass to the blue luminosity and atomic gas mass. A detailed analysis of the properties of that sample is, however, not presented there. The largest previous CO survey was the FCRAO Extragalactic CO survey (Young et al. 1995) observing  ~300 nearby galaxies. The major difference with respect to the present study is that it did not consider the isolation of the galaxies as a criterion. Furthermore, it only contained bright galaxies (either m_B,corr < 13 mag, or F_60   μm > 5 Jy or F_100   μm > 100 Jy) whereas our samples also includes fainter objects.

The project AMIGA (“Analysis of the interstellar Medium of Isolated GAlaxies”, Verdes-Montenegro et al. 2005) was started to provide such a reference sample by characterizing the properties of the interstellar medium (ISM) and SF in isolated galaxies in the local Universe. It is based on the Catalogue of Isolated Galaxies (CIG Karachentseva 1973) which is composed of 1050 galaxies located in the Northern hemisphere. The AMIGA project is presented in Verdes-Montenegro et al. (2005). A considerable amount of work has been done since then in order to refine the sample. This work includes the revision of all CIG positions (Leon & Verdes-Montenegro 2003), the determination of POSS2-based morphologies and the identification of galaxies showing signs of possible interaction (Sulentic et al. 2006) and the reevaluation and quantification of the degree of isolation (Verley et al. 2007a,b). The results of this project consistently find that the AMIGA galaxies have the lowest SF activity as well as the lowest presence of active galactic nuclei (AGN) in the local Universe. This is obtained both from the far-infrared (FIR) luminosity derived from IRAS data (Lisenfeld et al. 2007), and the radio continumm emission (Leon et al. 2008), which are both SF tracers. The rate of AGN candidates, derived from IRAS colors and radio continuum emission of the AMIGA galaxies is lowest compared to similar studies from the literature (Sabater et al. 2008). Optical photometric analysis of Sb-Sc galaxies in the AMIGA sample showed that most galaxies have pseudo-bulges instead of classical bulges, and a comparison with samples of spiral galaxies selected without isolation criteria revealed that the isolated galaxies tend to host larger bars, are more symmetric, less concentrated and less clumpy (Durbala et al. 2008). These findings strongly support that the AMIGA sample represents the most isolated galaxies in the local Universe where secular evolution is dominant. Espada et al. (in prep.) study the HI content and (Espada et al. 2011) found the smallest fraction of asymmetric HI profiles in the AMIGA sample when compared with any sample yet studied.

The revised AMIGA sample is reasonably complete (~80−95%) down to m_{B,   corr} ≤ 15.0 mag (Verdes-Montenegro et al. 2005) and it is currently one of the largest sample of nearby isolated galaxies in the Northern hemisphere. It consists of galaxies whose structure and evolution have been driven largely or entirely by internal rather than by external forces at least during the last 3 Gyr (Verdes-Montenegro et al. 2005). The data are being released and periodically updated at http:// amiga.iaa.es where a Virtual Observatory interface with different query modes has been implemented.

In the present paper we present and analyze CO observations of a redshift-limited subsample of this catalogue. The goal is to characterize the properties of the molecular gas, traced by CO, of isolated galaxies and to provide a reference sample for studies investigating the role of the environment.

2. The sample

For a study of the molecular gas content we had to restrict the number of galaxies, since observation of the entire optically complete sample (n ~ 700) required too much telescope time. We chose to build a redshift-limited subsample by selecting galaxies with recession velocities in the range of 1500–5000 km s^-1. The completeness limit of the AMIGA sample of 15 mag corresponds to blue luminosities of log 10(L_B/L_⊙) = 8.55 and log 10(L_B/L_⊙) = 9.60 at the distances derived for these velocities with a Hubble constant of 75 km s^-1 Mpc^-1. The range was chosen in order to avoid (i) very nearby galaxies for which the condition of isolation is not reliable (Verley et al. 2007a) and (ii) distant galaxies which are difficult to detect in CO. The restriction in velocity provides us with a sample probing a defined volume in space.

There are 278 galaxies in this velocity range in the CIG. We have CO data for 201 of these objects, mostly from our own observations (180 galaxies) with the 30 m telescope of the Instituto de Radioastronomía Milimétrica (IRAM) at the Pico Veleta and with the 14 m Five College Radio Astronomical Observatory (FCRAO), and the rest from the literature. We then excluded those galaxies that were identified by us in a visual inspection of optical images as having signs of a possible present or past interaction (see description of Table 1 for more details on the criteria). This leaves us with 173 isolated galaxies with CO data in the velocity range between 1500 and 5000 km s^-1. We refer to this sample as the redshift-limited CO sample and we will use it for the statistical analysis throughout this paper.

Additionally, we have CO data for 72 galaxies outside this velocity range. Six galaxies are from our own observations (with velocities between 5000 and 5500 km s^-1) and the rest is from the literature. Thus, in total, we have ¹²CO(1–0) data for 273 CIG galaxies. We refer to this sample as the total CO sample, and list the corresponding data in Tables 1 and 5, but we do not use it for any statistical analysis.

Recently, an update of the basic properties of the galaxies in the AMIGA sample was carried out for the blue magnitude, optical isophotal diameter D₂₅, velocity, and morphology and interaction degree based on higher resolution images (from SDSS or our own images). The details are described in Espada et al. (in prep.). In order to provide a self-contained data set for the present paper, we list in Table 1 the basic data relevant for the total CO sample. The columns are:

• 1.

  CIG: entry number in the Catalogue of Isolated Galaxies (CIG);

• 2.

  Dist: distance in Mpc, based on H₀ = 75 km s^-1 Mpc^-1;

• 3.

  Vel: recession velocity in  km s^-1;

• 4.

  D₂₅: isophotal optical major diameter at the isophotal level 25 mag arcsec^-1 in the B-band, D₂₅, in arcmin from the Lyon Extragalactic Database (LEDA);

• 5.

  i: inclination from LEDA;

• 6.

  T(RC3): morphological type T(RC3) as determined by our morphological revision, given in the RC3 numerical scale (de Vaucouleurs et al. 1991);

• 7.

  Inter: code for morphological signs of a possible interaction. 0: No signs of large distortions which cannot be clearly explained by e.g. dust. 1: At least one of the following signs of possible interaction: asymmetric, lopsided, distorted, confirmed pair in the Nasa Extragalactic Database (NED) or in Verley et al. (2007b), integral sign shape, warp, tidal features (tail, bridge, shell). 2: Merger-like morphology or superposition of two galaxies;

• 8.

  log(L_B): decimal logarithm of the blue luminosity, L_B, in units of solar bolometric luminosities. We calculated L_B, from the flux, f_B, as L_B = νf_B, where ν is the central frequency of the blue band;

• 9.

  log(L_FIR): decimal logarithm of the far-infrared luminosity in units of solar bolometric luminosities, taken from Lisenfeld et al. (2007) and adapted to the revised distances used in the present paper. L_FIR is computed from the IRAS fluxes at 60 and 100 μm, F₆₀ and F₁₀₀), as log (L_FIR/L_⊙) = log (FIR) + 2log (D) + 19.495, where D is distance in Mpc and FIR = 1.26 × 10^-14(2.58F₆₀ + F₁₀₀) W m^-2 (Helou et al. 1988);

• 10.

  log(L_K): decimal logarithm of the luminosity in the K-band, in units of the solar luminosity in the K_S-band (L_K, ⊙  = 5.0735 × 10³² erg s^-1), calculated from the extrapolated magnitude in the K_S (2.17 μm) band from the 2MASS Extended Source Catalogue (Jarrett et al. 2000). The magnitudes were available for 250 galaxies of our sample. We calculated the K_S luminosity, L_K, from the total (extrapolated) K_S flux, f_K, as L_K = νf_K(ν), where ν is the central frequency of the K_S-band. L_K is a good measure of the total stellar mass.

In Fig. 1 we present some of the basic characteristics of the CO samples and compare them to those of the optically complete sample (Verdes-Montenegro et al. 2005). The latter (n = 712) is composed of CIG galaxies with m_B in the range of 11–15 mag and is 80–95% complete. The main difference between the CO and the optically complete sample is the larger spread in velocity of the latter (Fig. 1a). The CO samples are at a lower velocity, especially the redshift-restricted sample. This leads to a slightly lower optical luminosity (Fig. 1b) of the CO samples since the number of luminous objects is higher at larger distances due to the Malmquist bias.

The distribution of the morphological types (Fig. 1c) is very similar in all the three samples. All samples are dominated by spiral galaxies. The relative number of early type galaxies (T = (−5) − 0) is 8% for the optically complete sample and 13% for the CO redshift-restricted sample. The distribution is peaked around galaxies with types T = 3−5 (63% for the optically complete sample and 51% for the CO redshift-restricted sample).

3. CO observations and analysis

We carried out CO(1–0) observations with the FCRAO and with the IRAM 30 m telescope. We observed galaxies with isophotal diameters D₂₅  < 100″ at the 30 m telescope and galaxies with D₂₅  ≥ 100″ at the 14 m FCRAO telescope. In this way we tried to optimize the agreement between beam size and optical diameters and minimize the fraction of missing flux in the observations done with a single pointing. We observed 100 galaxies at the FCRAO radio-telescope and 101 at the IRAM 30 m telescope. In order to check the consistency of the results we observed 15 galaxies at both telescopes.

3.1. Observations

3.1.1. IRAM 30 m telescope

We observed the ¹²CO(1–0) line at 115 GHz with the IRAM 30-m telescope on Pico Veleta using the dual polarization receivers A100 and B100, together with the 512  ×  1 MHz filterbanks. The observations were done in wobbler switching mode with a wobbler throw of 120′′ in azimuthal direction. Pointing was monitored on nearby quasars every 60–90 min. The integration time on source was typically 0.5 to 1.5 h. The mean system temperatures was 320 K on the scale. All CO spectra and intensities are presented on the main beam temperature scale (T_mb) which is defined as . The IRAM forward efficiency, F_eff, was 0.95 and the beam efficiency, B_eff, 0.75. The peak intensities of our sources ranged between about 10 and 80 mK (T_mb).

Most galaxies were observed at the central position with a single pointing. The galaxies with the strongest emission at the center (19 galaxies) were mapped along the major axis with a spacing of 15″, until a root mean square (rms) noise of about 3 mK was reached for a velocity resolution of 10.6  km s^-1.

3.1.2. FCRAO 14 m telescope

The observations at the FCRAO were done with the receiver SEQUOIA, a 4 × 4 pixel array operating from 85 to 115 GHz. We used the so called “beam switching” mode, in which the telescope switches position between the source and a reference position 89.2″ apart in azimuth. Two of the pixels in the array alternated between the ON- and the OFF-position, doubling in this way the effective integration time.

The typical observing time per object was about 2 h. The pointing was checked between the observations of different sources using a nearby quasar. The mean system temperatures was 380 K (on the scale). All CO spectra and luminosities are presented on the main beam temperature scale (T_mb) which is defined as . The main beam efficiency is B_eff = 0.45. We observed each galaxy with one pointing at their central position. The peak intensities of our sources ranged between about 10 and 80 mK (T_mb).

3.1.3. Literature data

We furthermore searched the literature and found CO(1–0) data for 131 objects, 87 of them had not been observed by us. We list the references for these data in Table 2. Some galaxies were observed at several telescopes. Table 3 provides information about the telescopes used in the different surveys: the antenna size (Col. 3), the half power beam width (HPBW) (Col. 4) and the conversion factor Jy/K (on the T_mb scale) at 115 GHz (Col. 5).

3.2. Data reduction

The data from both telescopes were reduced in the standard way using the CLASS software in the GILDAS package¹. The data reduction consisted in dismissing poor scans, flagging bad channels, subtracting a baseline and averaging the spectra for the same object and position. In most cases a constant baseline was subtracted and only in a few cases the subtraction of a linear baseline was required.

3.3. Spectra and integrated intensities

The CO(1–0) profiles of the detections and tentative detections observed by us at the IRAM 30 m and FCRAO 14 m are shown in Appendix A (Figs. A.1 and A.2, respectively). The spectral shapes observed are very diverse. Both single and double peaked lines are present and the line widths span a wide range.

The velocity integrated intensity, (in K km s^-1), was calculated from the spectra with a velocity resolution of 10.6  km s^-1 for the IRAM spectra, respectively 13.1  km s^-1 for the FCRAO spectra by summing up all channels with significant emission. Its error was calculated as: where σ is the rms noise of the spectrum, W_CO is the CO line width, and δV_CO is the spectral resolution. For undetected galaxies, we calculate a 3σ upper limit, assuming a line width of 300  km s^-1, as:

In Table 4 we list the following items:

• 1.

  entry number in the Catalogue of Isolated Galaxies (CIG). An asterisk added to the number means that the detection is marginal. In our statistical analysis we treat marginal detections as upper limits;

• 2.

  off. α: RA offset from the center in arcsec;

• 3.

  off. δ: Declination offset from the center in arcsec;

• 4.

  rms: root mean square noise in mK for a velocity resolution of 10.6  km s^-1 (IRAM), respectively 13.1  km s^-1 (FCRAO);

• 5.

  I_CO: velocity integrated CO line temperature ^∫T_mb   dv, in K km s^-1, and its error;

• 6.

  V_CO: mean velocity of the CO line, in km s^-1;

• 7.

  W_CO: zero line-width of the CO spectrum, in km s^-1;

• 8.

  Tel: radio-telescope code, as listed in Table 3.

3.4. Comparison between IRAM and FCRAO data

In order to check the relative calibration between the IRAM 30 m and the FCRAO 14 m telescope and to guarantee that these two data sets are comparable, we observed 15 galaxies with both telescopes. We expect a ratio of the velocity integrated intensities of I_CO−IRAM/I_CO−FCRAO = 1 for emission homogeneously filling the beams, and I_CO−IRAM/I_CO−FCRAO = (Θ_FCRAO/Θ_IRAM)² = 4.5, where Θ_FCRAO and Θ_IRAM are the FWHM of the respective beams, for a point-like emission.

Four galaxies (CIG 66, 181, 281 and 330) were detected at both telescopes. The ratios of I_CO−IRAM/I_CO−FCRAO range between 1.1 and 2.3, consistent with the value expected for slightly concentrated emission. Six galaxies were detected at IRAM, but only tentatively detected (CIG 176, CIG 355) or undetected (CIG 217, CIG 561, CIG 609, CIG 622) at the FCRAO. The lower limit for I_CO−IRAM/I_CO−FCRAO in five cases was between 0.94 and 3.6, consistent with the expected range of values. For CIG 217 this value is higher (I_CO−IRAM/I_CO−FCRAO = 6.1) than the theoretical upper limit. Since the detection at IRAM has a high signal-to-noise ratio, the most likely reason is an underestimate of the upper limit of the FCRAO data. There is one object with a detection at the FCRAO and only a tentative detection at IRAM (CIG 433), and one with a nondetection at IRAM (CIG 268). The ratio of the intensities in both cases is I_CO−IRAM/I_CO−FCRAO = 0.3, indicating an underestimate in the IRAM data. In the remaining three cases, both observations were either no detection or tentative detections.

We conclude that there is very good agreement between the detected values at both telescopes, and in most cases (with the exception of three galaxies) also for objects only detected at one telescope. This gives us confidence that the calibration of the two data sets is consistent.

3.5. Calculation of the molecular gas mass

The molecular gas mass (M_H2) is calculated using a Galactic conversion factor of N(H₂)/I_CO = 2.0 × 10²⁰ cm^-2(K km s^-1)^-1 (e.g. Dickman et al. 1986) yielding: (1)where I_CO is the velocity integrated CO line intensity in K  km s^-1, D is the distance in Mpc and Ω is the area covered by the observations in arcsec² (i.e. for a single pointing with a Gaussian beam of FWHM Θ_B). We do not include the mass of heavy metal (mostly helium) in the molecular gas mass.

Most of our objects were observed at the central position in a single pointing since the mapping of the entire galaxy would have been too time-consuming. We therefore might have missed part of the CO emission for galaxies where the emission is more extended than the beam. This fraction depends on the galaxy size, inclination and on the telescope beams. It is thus necessary to correct for this loss, and we do this by extrapolating M_H2 observed in the central beam to the total mass in the galaxy. In the next subsection we explain how we carried out this correction.

3.5.1. Aperture correction

In order to apply an aperture correction, we need to predict the distribution of the CO emission. CO maps of nearby spiral galaxies (Nishiyama et al. 2001; Regan et al. 2001; Leroy et al. 2008) have shown that the radial distribution of I_CO(r) in galaxies can be well described by an exponential function with a scale length r_e: (2)The CO scale length, r_e, is well correlated and similar to the optical exponential scale length (Regan et al. 2001; Leroy et al. 2008). It also correlates, although less tightly, with the optical radius at the 25mag isophote, r₂₅. Leroy et al. (2008) derived for spiral galaxies from the THINGS survey a mean value of α = r_e/r₂₅ = 0.2. We derived the same mean value for α from the data of Regan et al. (2001) for 15 spiral galaxies observed in the BIMA Survey of Nearby Galaxies (BIMA-SONG) and from the data of Nishiyama & Nakai (2001) for 25 spiral galaxies observed with the Nobeyama 45 m telescope. We also used the data of Young et al. (1995), who studied the molecular gas content and distribution in a sample of 300 nearby galaxies, to derive the r_e. They found a mean ratio between the effective CO diameter, D_CO, the diameter within which 70% of the CO emission is situated, and the optical diameter of D_CO/D₂₅ = 0.5. For an exponential distribution one can derive that D_CO × 0.5 = 2.5r_e. Thus, their data also yield .

Finally, we use the data of the 19 galaxies (all of them with morphological type T ≥ 2) mapped along the major axis with the IRAM 30 m telescope as a further test. Although our data is not sufficiently detailed to fit the radial distribution (we have only 3–5 detected spectra along the major axis), we can use it to test whether (i) an exponential distribution is a reasonable description of the CO distribution, (ii) the scale length derived by other studies is in agreement with our data, and (iii) the predictions for the extrapolated M_H2 are in agreement with our mapped values.

For the first two tests, we fitted an exponential distribution independently to each side of the CO distribution along the major axis. From the 38 resulting fits, there were only six cases where no exponential fit could be applied within the error bars. In five cases we derived α ≥ 0.4, in seven cases 0.4 < α < 0.25, in three cases α < 0.15 and in 17 cases, the majority, 0.15 ≤ α ≤ 0.25. Thus, our data are in general consistent with the value of α found by other studies.

In summary, we conclude that an exponential distribution of the molecular gas distribution with α = r_e/r₂₅ = 0.2 is a good approximation based on the CO maps for nearby spiral galaxies available up to date and also consistent with our data. We adopt the same value for both spiral galaxies and early type galaxies. In early-type galaxies, the molecular gas extent is much less known. However, for our study, this uncertainty is not important because the number of objects with T ≤ 0 is low (n = 23, with eight detections) and we focus on our results and conclusions on spiral galaxies, in particular of types T = 3–5, which dominate the sample.

We now use these results to calculate the aperture correction which we define as the ratio between the total (extrapolated) molecular gas mass M_H2, and the molecular gas mass in the central pointing, M_{H2,   center}, (3)The total molecular gas mass is calculated by spatially integrating I_CO(r) from Eq. (2) and using Eq. (1). This yields: (4)Similarly, we calculate M_{H2,   center} by convolving the exponential CO intensity distribution with a Gaussian beam. This yields: (5)where i is the inclination of the disk. The integration of Eq. (5) is carried out numerically.

Thus, the correction factor, f_ap =  M_H2/M_{H2,   center}, depends on the ratio of the scale length and the beam size, r_e/Θ_B, as well as the galaxy inclination i. Figure 2 shows the distribution of f_ap for the galaxies in our sample. The correction factors are generally low: 81% of the galaxies have f_ap < 2, and 92% f_ap < 3. Only nine galaxies have a correction factor above 5. All of them are nearby (v < 1000 km s^-1) galaxies with a large angular size (between 4′ and 20′) that are not included in our redshift-limited sample.

In order to carry out test (iii) we compared for the 19 galaxies, that were mapped along their major axis with the IRAM 30 m telescope, the extrapolated M_H2 to the mapped molecular gas mass which we extrapolated to the mass in the entire disk by assuming azimuthal symmetry (M_{H2,   map,   extra}). Figure 3 presents the ratio of these two masses as a function of D₂₅ and i. For most objects, both masses agree reasonably well, with ratios ranging between 0.5 and 1.3. There are only two outliers, with ratios around 2. These galaxies (CIG 84 and CIG 28) have a very flat CO distribution along the major axis so that our extrapolation, assuming an exponentially decreasing distribution, underestimates the true amount of molecular gas. No trend with neither D₂₅ nor the inclination is seen, showing that no apparent bias is introduced by the aperture correction. The mean mass ratio is 1.0, with a standard deviation of 0.3.

4. Results

4.1. Molecular gas content

In Table  5 we list M_H2 for the individual galaxies. If observations from different references were available for a single galaxy, we inspected the spectra and discarded those of poorer quality. In case of similarly good data we gave preference to mapped observations or to observations from the telescope with a larger beam in order to avoid flux loss. For the 44 objects that had data from the literature and were also observed by us, our data was in general of better quality, with the exception of three objects (CIG 512, CIG 604, CIG 626). The columns in Table  5 are:

• 1.

  CIG: entry number in the Catalogue of Isolated Galaxies (CIG);

• 2.

  log(M_H2) center: decimal logarithm of M_H2 towards the central pointing in solar masses, derived from Eq. (1). An asterix denotes tentative detections that are treated as upper limits in the statistical analysis;

• 3.

  log(M_H2) mapped: decimal logarithm of the mapped M_H2  in solar masses, calculated in the following way: for the data from the literature, the angular separation between the individual pointings was always larger than the beam size so that the total M_H2 could be calculated as the sum of the individual pointings. For our own observations with the IRAM 30 m telescope, the spacing between the individual pointing was 15′′, which is smaller than the FWHM of the beam (21″) so that in this case we had to take the overlap of the individual pointings into account. We calculated the mapped M_H2 from Eq. (1) where I_CO is taken as the mean value of the different pointings, and Ω is the total area covered by the mapping, approximated as 21″    ×    36″, 21″    ×    51″, 21″    ×    66″, 21″    ×    81″ for 2, 3, 4, and 5 pointings, respectively;

• 4.

  log(M_H2) extrapol.: total (extrapolated) M_H2 in solar masses, calculated as described in Sect. 3.5.1. An asterisk denotes tentative detections that are treated as upper limits in the statistical analysis;

• 5.

  Tel.: radio-telescope code, as in Table 3;

• 6.

  Ref.: bibliographic code, as in Table 2.

Figure 4 shows the distribution of log(M_H2)², for detections in the total and redshift-limited CO samples and for nondetections in the latter. The distributions in the total and in the redshift-limited samples are very similar. The mean M_H2 of the redshift-limited sample is log(M_H2) = 8.30  ±  0.08 (see Table 6), calculated with the package ASURV that takes into account the upper limits. Here and throughout the paper we use the ASURV³ package which applies survival analysis in the presence of upper or lower limits and calculates the mean value based on the Kaplan-Meier estimator.

Figure 5 shows the distribution of the molecular gas mass as a function of the morphological type. The mean and median values are listed in Table 6. Our sample is dominated by spiral galaxies of type T = 3–5 (Sb-Sc). Not only is the total number of objects greatest in this range, but also the detection rate. Therefore, we can derive the most reliable results for these types. Both for earlier and for later types, the detection rates are very low, making a detailed analysis difficult. The molecular gas mass is largest for spiral galaxies of T = 3–5, and decreases both for earlier and later types. There are eight early-type galaxies, of type S0 and S0a, with detections in M_H2, and five of them have unusually high molecular gas masses in the range of those for spiral galaxies (CIG 332, CIG 481, CIG 498, CIG 733 and CIG 1015).

4.2. Relation of M_H2 to other parameters

In the following we investigate the relations between M_H2 and L_B, D₂₅, L_FIR, L_K and M_HI. The first two quantities (L_B, D₂₅) were chosen because they are in general available for any galaxy and are therefore useful to predict the expected M_H2. L_FIR is very closely related to M_H2 because of their common relation to SF.L_K is dominated by the emission of low-mass stars which are the result of the long-term SF history of an object and determine the gravitational potential which influences the SF activity. Finally, we compare M_H2 to M_HI in order to derive the molecular-to-atomic gas mass ratio as a function of morphological type.

The results of the regression analysis as well as the Spearman rho correlation coefficient derived in this section are listed in Table 7, and the mean and median values of the ratios for different subsamples are in Table 6. We use the package ASURV to calculate the bisector regression line applying the Schmitt’s binning method (Schmitt 1985) as the only method offered by ASURV able to deal with censored data in both the dependent and the independent variable⁴.

4.2.1. Optical luminosity

Figure 6 shows the relation between M_H2 and L_B, for the the entire redshift-limited sample and for subsamples of different morphological types, together with the the best-fit bisector regression lines. The high number of upper limits for galaxies of type T = (−5) − 2 and T = 6–10 impedes the calculation of a reliable regression line for these individual subgroups. However, we note that there is no apparent deviation from the mean best-fit regression for all morphological types for these two groups. A slope considerably larger than 1 is found for the correlation between M_H2 and L_B, in agreement with Perea et al. (1997). This means that the ratio M_H2/L_B tends to increase with L_B. Even though the scatter around the best-fit is large, so that no strong correlation exists between M_H2/L_B and L_B, we confirm the variation of M_H2/L_B by finding that the mean values is indeed higher for high L_B than for low L_B: for galaxies (all morphological types) with L_B  < 10¹⁰ L_⊙ (n = 123 galaxies,  upper limits) we obtain M_H2/L_B =  − 1.36 ± 0.05 and for galaxies with L_B  ≥ 10¹⁰ L_⊙ (/11) M_H2/L_B =  −1.10 ± 0.06. The corresponding numbers for the T = 3–5 subsample are  − 1.16 ± 0.06 (L_B  < 10¹⁰ L_⊙, /16) and  − 1.04 ± 0.05 (L_B  ≥ 10¹⁰ L_⊙, n/n = 40/5). This trend has to be taken into account when using this ratio as an indicator of an enhancement of M_H2.

The ratio between M_H2 and L_B is shown in Fig. 7 as a function of morphological type. The values are listed in Table 6. The ratio is highest for galaxies of type T = 3–5. It is however remarkable that galaxies of type S0 and S0a with detections in CO have much higher values of M_H2/L_B, in the range of spiral galaxies of type T = 3–5, than early-type galaxies with nondetection in CO.

In order to check whether the extrapolation of the molecular gas mass to the entire disk has introduced any biases, we show in Fig. 8 the relation between M_H2 and L_B only for galaxies with f_ap < 1.5. No significant difference compared to the entire redshift-limited CO sample can be seen, and the best-fit regression coefficients are the same within the errors (Table 7). We found this good agreement between entire redshift-limited CO sample and the subsample of galaxies with f_ap < 1.5 for all correlations studied. Therefore, in the following subsections we do not show the f_ap < 1.5 correlation separately, but we list in Tables 6 and 7 the mean values and the regression coefficients for this subsample.

4.2.2. Optical isophotal diameter

Figure 9 shows the relation between M_H2 and , for the entire redshift-limited sample and for subsamples of different morphological types, together with the best-fit bisector regression lines. For early-type galaxies (T ≤ 0) only a very poor correlation is visible, whereas galaxies of type T = 6–10 seem to follow the same correlation as those of type T = 3–5.

The correlation between M_H2 and , has the lowest correlation coefficient (r ~ 0.5) among those considered in this paper (Table 7). Although the bisector slope is formally larger than 1, we do not find a variation of M_H2/ with increasing optical diameter. This shows that for this poor correlation the regression slope has to be taken with caution.

Figure 10 shows the ratio M_H2/ as a function of morphological type. The values are listed in Table 6. The ratio is highest for spiral galaxies of type T = 3–5. Similarly to M_H2/L_B, S0 and S0a galaxies with detections in CO have high values of M_H2/, similar to those of spiral galaxies of type T = 3–5, whereas M_H2/ of the nondetections is much lower.

4.2.3. Luminosity in the K-band

Figure 11 shows the relation between M_H2 and L_K, for the entire redshift-limited sample and for subsamples of different morphological types, together with the the best-fit bisector regression lines. The relation is close to linear. The correlation is very good (r = 0.73) for spiral galaxies of type T = 3–5. The distribution of the emission from spiral galaxies of later types (T = 6–10) is consistent with this correlation. However, early-type galaxies (T ≤ 0) show a very poor correlation. Only the objects with CO detections follow the same correlation as spiral galaxies whereas most galaxies with CO nondetections have upper limits for M_H2 that lie considerably below it.

The ratio M_H2/L_K is shown in Fig. 12. It is lowest for early-type galaxies (up to T = 2), and increases for later types by a factor 3 − 5. From T = 3 on, the ratio is approximately constant and does not show the decrease it shows for M_H2/L_B and M_H2/. Early-type (E+S0s) galaxies have a lower mean molecular gas mass per L_K than spiral galaxies. This is caused by galaxies not detected in CO, whereas, as seen before, S0 and S0a detected in CO have higher values of M_H2/L_K, in the same range as spiral galaxies.

4.2.4. FIR luminosity, SF rate and efficiency

A good correlation is known to exist between M_H2 and L_FIR (e.g. Young & Scoville 1991) because both quantities are directly related to SF: the molecular gas as the fuel for SF and L_FIR as a tracer for SF based on the heating of the dust by newly born stars. Figure 13 shows the relation between M_H2 and L_FIR, for the entire redshift-limited sample and for subsamples of different morphological types, together with the best-fit bisector regression lines. We find a good correlations with a roughly linear slope (Table 7). For early (T ≤ 0) and late (T = 6–10) type galaxies, the distribution of M_H2 vs. L_FIR is consistent with the correlation found for galaxies of type T = 3–5.

Figure 14 shows the ratio L_FIR/M_H2 as a function of morphological type. Early-type galaxies have a higher value, possibly due to a large fraction of their FIR emission not being heated by young stars but by the general interstellar radiation field. For late-type spirals (T ≥ 6) the mean ratio increases again, but the low number of values and detections make any firm conclusion difficult.

These values and trends for L_FIR/M_H2 are consistent with earlier results of Young et al. (1996) who studied them in a sample of 120 galaxies included in the FCRAO survey. They used a higher value of N(H₂)/I_CO = 2.8 × 10²⁰ cm^-2 (K km s^-1)^-1, but also define the FIR luminosity in the range between 1−500   μm which is, according to their prescription, between  ~0.1−0.2 dex higher. Since both differences roughly compensate, their values of L_IR/M_H2 are comparable to our values L_FIR/M_H2. They find very similar values of L_FIR/M_H2 for different morphological types as we do. They obtain value between 0.55 ± 0.08 and 0.61 ± 0.06 for morphological types T = 3–5 (n = 45), higher values (between 0.70 ± 0.13 and 1.53 ± 0.24) for later type galaxies (T = 6−10,n = 19), and, for earlier spiral types (T = 1−2,n = 14), mean values (0.65 ± 0.20 and 0.53 ± 0.09) that are similar to galaxies of type T = 3–5. Their sample only includes three galaxies of type S0-S0a and no elliptical galaxies, so that we cannot compare earlier types.

L_FIR is a good tracer for the star formation rate (SFR) due to two reasons: (i) young stars are formed in dense regions where dust opacities are high and (ii) the dust extinction curve peaks in the ultraviolet so that the radiation from young, massive stars is preferentially absorbed. Therefore, L_FIR as a good SFR tracer especially for actively SF galaxies. It has to be used with some caution in galaxies with a low SFR where dust heated from old stars can contribute to L_FIR, or in galaxies with a low metallicity and thus a low dust opacity (e.g. Bell 2003).

Keeping these limitations in mind, we use the formula of Kennicutt (1998) to calculate the SFR: (6)where L_IR is the total FIR luminosity in the range 8–1000 μm. This formula assumes a Salpeter Initial Mass Function. We convert this to a value based on the Kroupa (2001) IMF by deviding by a factor 1.59 (Leroy et al. 2008). In our analysis we use L_FIR, calculated following the formula given by Helou et al. (1988), which estimates the FIR emission in the wavelength range of 42–122.5 μm. We estimate L_IR from L_FIR using the result of Bell (2003) that on average L_IR ~ 2 ×  L_FIR for a heterogenous sample of normal and starbursting galaxies. Adopting this factor and the conversion to the Kroupa IMF we calculate the SFR from the L_FIR as: (7)We derive an average SFR for galaxies of type T = 3–5 of  ~ 0.7 M_⊙ yr^-1. The ratio L_FIR/M_H2 is proportional to the star formation efficiency (SFE), defined here as the ratio between SFR and M_H2. The mean value of the SFE for galaxies of type T = 3–5 is 10^-9 yr^-1 (Table 6).

4.2.5. Atomic gas mass

Figure 15 shows the relation between M_H2 and M_HI for different groups of morphological types. The correlation with M_HI is much poorer than the other correlations considered here, with a Spearman correlation coefficients of r = 0.44,0.44,0.29,0.57 for the entire redshift-limited sample, T = (−5) − 2, T = 3–5 and T = 6–10, respectively. In most galaxies M_HI is higher than M_H2. Some differences can be seen for the different morphological types: Early type galaxies (T =  −5–2) have a high number of upper limits in both M_H2 and M_HI. The upper limits mainly populate the low M_HI and M_H2 part of the diagram, whereas the detections have values of M_H2 and M_HI comparable to those of spiral galaxies. Late-type galaxies (T = 6–10) are shifted towards higher M_HI (≳10⁹ M_⊙) but lower ( ≲ 10⁹ M_⊙) M_H2 with a large number of upper limits in the latter. Galaxies of morphological types T = 3–5 have both high atomic gas and molecular gas masses ( ≳ 10⁹ M_⊙) with a low number of upper limits in M_H2 and almost none in M_HI.

Figure 16 displays the ratio M_H2/M_HI as a function of morphological type, showing a strong variation with T. The highest values are found for early-type galaxies, up to T = 0 (albeit with a high uncertainty due to the high number of upper limits). For later types, M_H2/M_HI is decreasing strongly. The mean ratio M_H2/M_HI is significantly lower than 1 for all morphological types.

4.3. Expected molecular gas content in a galaxy

We showed in Sect. 4.2 that good correlations exist between M_H2 and other parameters of a galaxy (L_B, L_K and L_FIR) and a somewhat poorer correlation with . In Table 7 we list, apart from the linear regression parameters, also the Spearman’s rho correlation coefficient and in Table 6 the different ratios depending on the morphological types. All these relations can be used to study differences in the molecular gas content of other sample, like e.g. interacting galaxies, with respect to isolated galaxies.

The best correlation exists between M_H2 and L_FIR (r ≥ 0.8). L_FIR is thus a very reliable way for predicting the expected molecular gas content in a galaxy. However, L_FIR might not be a good parameter when searching for variations of M_H2 in interacting galaxies because L_FIR itself, tracing the SFR, is easily affected in such an environment. A very good, and roughly linear, correlation also exists between M_H2 and L_K for galaxies of type T = 3–5 (r = 0.73). The luminosity in the K-band as a measure of the total stellar mass is less affected by recent events than L_FIR or L_B and thus a good normalization parameter when searching for changes in M_H2. This correlation is, however, poor for early type galaxies (T ≤ 2), where the undetected objects have ratios M_H2/L_K well below the values for spiral galaxies with T ≥ 3 (see Fig. 11 and Table 6) so that for those types L_K is not recommened as a measure of the expected M_H2. There is also a good correlation between M_H2 and L_B (r ~ 0.65). The ratio M_H2/L_B is however not constant, but increases with L_B which has to taken into account in any comparison. Finally, the poorest correlation (r ~ 0.5) exists with the isophotal diameter which is not a very reliable parameter for predicting M_H2.

Apart from using the ratio of M_H2 to another parameter,we can use the correlations, defined by the linear regression parameters listed in Table 7, for predicting the expected M_H2 and determine whether a deficiency or an excess of M_H2 exists in an object in comparison to isolated galaxies.

We define the deficiency in M_H2 in an analogous way to the definition in M_HI of Haynes & Giovanelli (e.g. 1984): (8)Note that in this definition, a positive value of Def(M_H2) means a deficiency and a negative value means an excess. We can derive the predicted M_H2, M_H2,predicted, from any of the parameters, X, (L_B, , L_K or L_FIR) as: (9)where intercept and slope are the parameters of the best fit listed in Table 7. These definitions allow us to directly take the effect of a nonlinearity of a correlation into account.

In Table 7 we have given the values for two types of regressions: the bisector fit and the fit obtained by taking M_H2 as the dependent variable, O(Y | X), and minimizing the distance of the M_H2 measurements from the best-fit regression line. The regression parameters are different for both methods because of the scatter in the data and the difference is larger for poorer correlations. The O(Y | X) fit is the appropiate regression for predicting M_H2 from L_B, whereas the bisector regression is the best estimate for the underlying correlation between two parameters (Isobe et al. 1990). For a sample covering the same luminosity range, O(Y | X) is the best way for predicting the expected M_H2. For samples with a different luminosity range, however, the bisector fit is better since it provides a more reliable extrapolation.

4.4. The Kennicutt-Schmidt law

We used our data to calculate the Kennicutt-Schmidt law, i.e. the relation between the disk-averaged gas column density and the disk-averaged SFR per area, Σ_SFR. Figure 17a shows the relation with the molecular gas column density, Σ_H2, and Fig. 17b with the total (molecular+atomic) gas column density, Σ_H2 + HI. The surface densities were calculated by dividing the SFR, respectively the (extrapolated) molecular or total gas mass, by the galaxy surface π /4. A clear correlation exists with the molecular gas, but none with the total gas, showing a lack of correlation with the atomic gas column density. Our findings are in agreement with previous results based on spatially resolved analysis (Wong & Blitz 2002; Bigiel et al. 2008; Verley et al. 2010), showing that the SFR is strongly related to molecular gas only. The best-fit regression yields (Table 7). This slope, close to unity, is again consistent with the results of Wong & Blitz (2002) and Bigiel et al. (2008) for a spatially resolved analysis.

5. Discussion

We compare our data to that of other samples of “normal” galaxies and also search for differences in samples of interacting galaxies. The samples of normal galaxies that we consider are made of not obviously interacting galaxies, which are however selected without a clear isolation criteria, and some of these samples contain, e.g. several cluster galaxies. In all these comparisons we have adjusted the molecular gas masses to our definition, i.e. same conversion factor and no consideration of the helium fraction.

5.1. Comparison to studies of normal galaxies

5.1.1. Relation between molecular gas, FIR and blue luminosity

The nonlinear relation between M_H2 and L_B has been found by other groups as well (see Perea et al. 1997, and references therein), with similar slopes as found by us. Their study was based on a smaller number (n = 68) of galaxies selected with a less rigorous criterion with respect to the environment. They discussed the cause of the nonlinearity and conclude that the most likely reason is extinction affecting L_B and increasing with galaxy luminosity. They predicted that the relation between M_H2 and luminosities at longer wavelengths should be more linear. This prediction is confirmed by the nearly linear relation found between M_H2 and L_K in our analysis.

We compared our mean value of M_H2/L_B for galaxies of type T = 3–5 to results for a large sample of normal galaxies, studied by Bettoni et al. (2003). They searched the literature for galaxies with data for their ISM properties, excluding galaxies with a known pecularity (interacting, disturbed, galaxies with polar rings or counterrotation) and with active galactic nuclei. Their sample includes 177 galaxies of type T = 3–5 with CO(1–0) data (160 detections and 17 upper limits) with values of log(L_B) between 9 and 11. They derive a mean value (adapted to our convention for the calculation of the M_H2 and L_B) of M_H2/L_B =  −0.92 ± 0.04 for these galaxies. When restricting the range of L_B to log(L_B) = 10–10.6, the mean value is  − 0.82 ± 0.05, about 0.2 dex higher than the corresponding value for the AMIGA sample (see Table 8) showing that AMIGA galaxies have a lower molecular gas content. When comparing their values for M_H2/ a similar difference is found.

The relation between M_H2 and L_FIR in nonstarburst galaxies has been found to be close to linear in other studies (e.g. Perea et al. 1997; Gao & Solomon 2004), in agreement with our results.

5.1.2. Gas depletion time

We derived in Sect. 4.2.4 the SFE (defined as the SFR/M_H2). The SFE is directly related to the molecular gas depletion time, τ_dep, by τ_dep= SFE^-1. The gas depletion time for our sample has a mean value of log(τ_dep) = 8.9 yr for the entire redshift-limited sample and log(τ_dep) = 9 yr for galaxies of type T = 3–5 (see Table 6), with a spread of values roughly ranging between log(τ_dep) = 8.5 yr and log(τ_dep) = 9.5 yr (see Fig. 14).

This value can be compared to those found in recent surveys. Bigiel et al. (2011) derived a mean gas depletion time of 2.35 Gyr from spatially resolved observations of 30 nearby galaxies in the HERACLES survey. This values includes a helium fraction of a factor 1.36, thus giving τ_dep = 1.7 Gyr without helium. They furthermore showed that this value is consistent with a wide range of molecular gas depletion times from the literature, albeit with a large standard deviation of 0.23 dex. This value is only slightly higher than our value for isolated galaxies. The small difference could be due to the fact that our value is global, and thus might encompass some FIR emission not directly associated to SF from the outskirts of the galaxies, whereas the value from Bigiel et al. (2011) is from a spatially resolved study.

Saintonge et al. (2011) studied the molecular gas depletion time, τ_dep, for a volume limited sample of 222 galaxies with 0.025 < z < 0.05 observed in the COLD GASS survey. They found values for the gas depletion time in the range of roughly log(τ_dep) = 8.6 yr and 9.5 yr, with a mean value of τ_dep = 1 Gyr (for a Chabrier (2003) IMF which gives a mass comparable to within  ~ 10% to the Kroupa IMF). Both the range and the mean agree very well with our values.

They furthermore found a good correlation of τ_dep with M_∗ and with the specific SFR, sSFR = SFR/M_∗. We tested both correlations with our data. We did not find a similarly good correlation with L_K(which is in a good approximation proportional to the stellar mass M_∗) although our sample covered a similar range of stellar masses, up to several 10¹¹ M_⊙. Taking into account all morphological types, we found evidence for a weak trend (correlation coefficient r = 0.25) which completely disappeared when restricting the sample to T = 3–5 (r = 0.08).

We could confirm with our data the existence of a correlation between τ_dep and sSFR. This correlation is however expected because both τ_dep and the sSFR depend on the SFR, and L_K and M_H2 show a good correlation. Thus, the respective ratios are expected to correlate.

5.1.3. The molecular-to-atomic gas ratio

The value of M_H2/M_HI in galaxies as a function of morphological type has been controversial. In a large survey of spiral galaxies, Young et al. (1995) mapped a sample of about 300 galaxies with the FCRAO telescope. Young & Knezek (1989) studied the dependence of M_H2 on M_HI for that sample. They derived a continous decrease of M_H2/M_HI from early to late-type galaxies with mean values above 1 for early types. Casoli et al. (1998) studied the molecular gas properties of a large (n = 528), heterogenous sample of galaxies, composed of data from the literature and their own observations. Their data consisted both of mapped galaxies and of objects where only the central position had been observed. In agreement with Young et al. (1995), they found a decrease in M_H2/M_HI from early to late-type galaxies, but obtained much lower values for M_H2/M_HI, especially for early-type spirals. In Fig. 18 we compare our results to these two studies and furthermore to the THINGS sample (Leroy et al. 2008) and the Nobeyama survey (Nishiyama & Nakai 2001). Bettoni et al. (2003) (not included in Fig. 18 ) provide values for a sample of 427 normal galaxies in agreement with Casoli et al. (1998) for T > 0 and higher values (by 0.5–1 dex) for T ≤ 0.

The data from all studies show a decrease of the M_H2/M_HI gas mass ratio towards late morphological types. A pronounced step in the ratio takes place at T ~ 6. The low values found for late-type galaxies could be due to two effects: (i) late-type galaxies are richer in HI (Haynes & Giovanelli 1984) or (ii) they have a lower molecular gas content. A comparison of M_HI and M_H2 to the blue luminosity or the optical diameter shows that both effects take place: the ratio M_HI/L_B (respectively M_HI/) increases for types T ≥ 6 by  ~ 0.2–0.3 dex whereas M_H2/L_B (respectively M_H2/) decreases by  ~ 0.3–0.5 dex (Young & Knezek 1989; Casoli et al. 1998; Bettoni et al. 2003). Our data show the same behaviour. The strong decrease of M_H2/L_B and M_H2/ could be due to a real decrease in the molecular gas mass or due to the fact that late-type galaxies tend to have lower metallicities so that we probably underestimate the true M_H2 by using the Galactic conversion factor.

Although the general trends in the data sets are the same, with a pronounced and continous decrease of M_H2/M_HI from early to late-type galaxies, there are considerable differences between the different samples (see Fig. 18). The differences are up to an order of magnitude for elliptical, lenticular and early-type spiral galaxies (up to T ~ 3), and less (up to 0.4 dex) for later type spirals. There is in general a good agreement between the values found by Casoli et al. and ours, the match being very good for early-type galaxies (up to T = 0) whereas for later-type galaxies our values lie somewhat below. The results from the THINGS survey (Leroy et al. 2008) are also in agreement with the data of Casoli et al., and only slightly higher than our values. The results by Young & Knezek (1989) and Nishiyama & Nakai (2001) give much higher values than the other surveys. This could be due to the sample selection. In the sample of Young & Knezek (1989) FIR or optically bright galaxies were selected, so that a high CO emission can be expected. Furthermore, the Young & Knezek (1989) survey contains objects from the Virgo Cluster, and cluster galaxies are known to be HI deficient on average. Cluster galaxies were excluded in Casoli et al., and are not present in our sample either. A selection effect can also account for the difference between the samples of Nishiyama & Nakai, Leroy et al. and our data. The samples differ in the mean L_FIR/L_B with the Nishiyama & Nakai sample being the FIR brightest with a mean log(L_FIR/L_B) = 0.10 ± 0.07 whereas the Leroy et al. and our sample show lower values (log(L_FIR/L_B)  =  −0.51 ± 0.06, respectively log(L_FIR/L_B)  =  −0.49 ± 0.03). Since galaxies with a higher log(L_FIR/L_B) tend to have a higher M_H2/M_HI, the observed trend is understandable.

A noticeable point is that the mean M_H2/M_HI of the AMIGA sample represents for all morphological types the lower limit of all samples. For late-types, the AMIGA galaxies have the lowest M_H2/M_HI, even though the M_H2 is extrapolated unlike other studies that are usually based on a central pointing only. This is in line with the low molecular gas content that we found in comparison to the sample of Bettoni et al. (2003).

5.2. Comparison to studies of interacting galaxies

5.2.1. Is the molecular gas content enhanced in interacting galaxies?

Several studies in the past have concluded that M_H2 in interacting galaxies is enhanced (Braine & Combes 1993; Casasola et al. 2004; Combes et al. 1994), based on a higher value of M_H2/L_B or M_H2/ compared to noninteracting galaxies. However, we found that the ratio M_H2/L_B increases with L_B and this trend has to be taken into account when comparing isolated and interacting samples. Indeed, Perea et al. (1997) found no difference in the correlation between M_H2 and L_B for samples of isolated, strongly and weakly perturbed galaxies.

We use the sample of Casasola et al. (2004) of interacting galaxies to search for a possible excess in M_H2 with respect to AMIGA galaxies. Their sample includes 153 galaxies with molecular gas data from different sources. Casasola et al. found that the mean ratio of M_H2/L_B for spiral galaxies was, depending on the morphological type, between about 0.2 and 1.0 dex higher than for a sample of 427 noninteracting galaxies from Bettoni et al. (2003) and concluded that M_H2 was enhanced in interacting galaxies. However, since their sample of interacting galaxies is on average 0.5 mag brighter, a higher M_H2/L_B is already expected due to the higher luminosity. We furthermore include the samples of strongly and weakly perturbed galaxies from Perea et al. (1997) in this test. The weakly perturbed sample has 43 galaxies and includes classes 1, 2, and 3 of Solomon & Sage (1988) and class 2 objects from the luminous IRAS sample of Sanders et al. (1991). The strongly perturbed sample has 35 galaxies and includes interaction class 4 of Solomon & Sage (1988), interaction classes 3 and 4 of Sanders et al. (1991) and closely interacting pairs from Combes et al. (1994).

We searched for a possible enhancement of M_H2 in comparison to L_B and to L_K in these samples, both by applying the deficiency parameter and by comparing the ratios. The mean values are listed in Table 8. We note that the interacting samples are more luminous (by about 0.5 dex) in both L_B and L_K than the AMIGA sample so that we have to extrapolate the relations found for the AMIGA galaxies to higher luminosities. For the calculation of the deficiency parameter we therefore use the bisector fit as the best fitting method for extrapolations. We use the fits for the AMIGA T = 3–5 subsample to compare to the weakly and strongly perturbed samples WPER and SPER, since spiral galaxies are the better comparison for these actively star-forming objects. For the Casasola et al. sample information about the morphological types are available and we are able to do the analysis both for the entire sample and for T = 3–5, using the values for the corresponding morphological types in AMIGA. When comparing the ratio M_H2/L_B we restrict the galaxies that we consider to the same range of L_B in order to avoid effects caused by the nonlinearity in the correlation. For the roughly linear M_H2/L_K ratio this is not necessary (we checked that no difference in M_H2/L_K was present for low and high L_K in the AMIGA sample).

Figure 19 shows M_H2 vs. L_B for the three samples compared to the bisector fit of the AMIGA T = 3–5 sample. An excess of M_H2 is visible for both the Casasola T = 3–5 and SPER sample. This is confirmed by the mean value of the deficiency (Table 8), both for the Casasola et al.T = 3–5 and the SPER sample a clear excess (i.e. a negative value of the deficiency) of M_H2 is found. This excess in the SPER sample was not found in Perea et al. (1997) due to the different regression line they used. For the WPER sample, on the other hand, no deficiency nor excess is found. When comparing the ratio M_H2/L_B we confirm the higher values for both the Casasola and the SPER sample, with mean values of about 0.3 dex higher than for the AMIGA T = 3–5 sample. The value of M_H2/L_B for the WPER sample is compatible with AMIGA within the errors. The entire (i.e. all morphological types) Casasola et al. sample has a value of M_H2/L_B compatible with AMIGA, showing the importance of taking the morphological type into account.

When doing a similar analysis based on L_K (see Fig. 20), we find again no indications for an enhancement in M_H2 for the WPER sample nor for the total Casasola sample, neither from the deficiency nor from the ratio. There is a clear excess in M_H2 for galaxies of type T = 3–5 from the Casasola sample, quantified both in the ratio, which is about 0.3 dex higher for T = 3–5 AMIGA galaxies, and in the deficiency parameter. Also the SPER sample shows a higher M_H2/L_K ratio than the AMIGA sample, however, no indication of an M_H2 excess from the deficiency parameter. The discrepancy between the two indicators (mean and deficiency) is probably due to the small sample size and the small amount of the molecular gas excess. We suggest to rely in this case on M_H2/L_K as the more robust indicator.

In summary, by comparing the molecular gas mass to L_K and L_B and using both the deficiency and the ratios M_H2/L_K and M_H2/L_B we found the clearest evidence for an enhancement of M_H2 in the Casasola sample of interacting galaxies of type T = 3–5, which is the largest comparison sample in our study. Evidence for an enhancement was also found for the Perea sample of strongly perturbed interacting galaxies (SPER). No evidence for any enhancement was found for the Perea sample of weakly perturbed interacting sample (WPER). Based on the present data, it is not entirely clear where the differences between these samples come from. A possible reason could be a lower degree of interaction in the WPER sample. We would like to point out the importance of matching the luminosity range when comparing parameters with a nonlinear correlation, as M_H2/L_B, and the importance of comparing the same morphological types, since there are generally large difference between early type and spiral galaxies, in particular for M_H2/L_K.

What influence has the fact that the molecular gas masses in these samples are not aperture corrected as in the AMIGA sample? We do not expect this effect to be very important in interacting galaxies where the SF and thus the molecular gas usually tend to be more concentrated to the central regions. However, we can make an estimate of the importance of this effect for the Casasola et al. sample. The median angular diameter of the galaxies of type T = 3–5 in this sample is 90″. If we assume that the galaxies were observed only at the central position with a beam size of 50″ (the typical beam size of the radio telescopes used in surveys) the predicted aperture correction according to our prescription is between a factor of 1.2 and 1.4 (for edge-on and face-on galaxies, respectively). Thus, in this case the total molecular gas content would be 0.08–0.15 dex higher. Thus, if the molecular gas in the interacting galaxies of the Casasola sample are distributed in a similar way as in isolated galaxies, this difference would strengthen the finding that M_H2 is enhanced in this sample of interacting galaxies. It also shows the importance of mapping the molecular gas in galaxies in order to be able to compare different samples in a relyable way.

5.2.2. Is L_fir and the SFE enhanced in interacting galaxies?

We use the same samples as in the previous subsection to look for a possible enhancement of L_FIR in interacting galaxies. In Fig. 21L_FIR is compared to the blue luminosity. We include the best-fit regression line found for the AMIGA T = 3–5 sample presented in Lisenfeld et al. (2007) (Table 6, log(L_FIR) = 1.35  ×  log(L_B)  −  3.98). We see a clear excess of L_FIR with respect to this regression line for the three samples, the strongest for the sample of strongly perturbed galaxies (SPER). The excess can be quantified by calculating the L_FIR deficiency, defined in an anologous way as the M_H2 deficiency. The values are listed in Table 8 and confirm the visual impressions of an excess in L_FIR of about an order of magintude for the SPER sample.

The large excess in L_FIR together with a smaller (or no) excess in M_H2 results in a higher value of SFE  ∝  L_FIR/M_H2 compared to the AMIGA sample for the strongly and weakly perturbed samples. Comparing these values to the results for the AMIGA sample we find an increase of about a factor 5 for the strongly perturbed sample and of about 2 for the weakly perturbed sample. The SFE in the Casasola sample is similar to the AMIGA sample.

For higher infrared luminosities, the value of L_FIR/M_H2 is known to increase strongly. Sanders et al. (1991) studied the molecular gas content in luminous infrared galaxies, ranging from L_IR = 10¹⁰L_⊙ to several 10¹² L_⊙, and showed that the ratio L_IR/M_H2 increases strongly with IR luminosity and with the degree of interaction. Whereas for isolated, low-luminosity (L_IR  < 10¹¹L_⊙) galaxies they found values of L_IR/M_H2 similar to ours, L_IR/M_H2 increases by a factor of about 10 for galaxies with L_IR  ~ 10¹²L_⊙ which are mostly advanced mergers. Similarly high values of L_FIR/M_H2  ~ 50 have been found by Solomon et al. (1997) for ULIRGs.

6. Conclusions and summary

We presented molecular gas masses, based on CO observations, for a sample of 273 isolated galaxies and we performed a statistical analysis for a redshift-limited sample of 173 isolated galaxies with recession velocities between 1500 and 5000  km s^-1. The observations covered in most cases only the central position of the galaxies. In order to correct for the missing molecular gas mass outside the observed area, we derived and applied an aperture correction assuming an exponentially decreasing CO disk. We obtained the following results:

• 1.

  We compared the molecular gas mass to different parameters (L_B, L_K, and L_FIR) in order to characterize the relations followed by isolated galaxies and establish a baseline that can be used to find possible deviations for interacting galaxies. We concentrated our analysis on the morphological types T = 3–5 (Sb-Sc) which represents the bulk of our sample (51% of the galaxies are of these types) where also the detection rate of CO (74%) was highest.

• 2.

  We found good correlations with these parameters, roughly linear in the case of L_K and L_FIR and nonlinear for L_B and . The tightest correlations are with L_FIR and, for spiral galaxies with T = 3–5, with L_K, whereas the correlation with is the poorest. Due to the nonlinearity of the correlation, the ratio M_H2/ L_B changes with L_B which has to be taken into account when comparing it to other samples. We describe a deficiency parameter, defined in analogy to the deficiency parameter for the atomic gas as the difference between the logarithm of the expected molecular gas mass and the logarithm of the observed molecular gas mass. The expected molecular gas mass can be calculated from any of the parameters studied by us (L_B, D₂₅, L_K, L_FIR) using the correlation coefficients listed in Table 7.

• 3.

  We applied these relations and the resulting expressions to three samples from the literature (Perea et al. 1997; Casasola et al. 2004). For the sample of Casasola et al. and the sample of strongly interacting galaxies of Perea et al., we found clear evidence for an enhancement of M_H2 in comparison to L_B and L_K, while for a sample of weakly interacting galaxies from Perea et al. no difference with respect to the AMIGA sample was found. A possible reason for this difference could be a higher degree of interaction in the first two samples.

• 4.

  We derived a mean molecular gas depletion time, τ_dep (defined as M_H2/SFR), of log(τ_dep) = 9.0 yr for spiral galaxies (T = 3–5) and a slightly lower value of log(τ_dep) = 8.9 yr for all morphological types (both values for a Kroupa IMF), in reasonable agreement with other studies of nearby galaxies (Bigiel et al. 2011; Saintonge et al. 2011).

• 5.

  No good correlation was found between M_H2 and M_HI. The ratio between the molecular and the atomic gas mass decreases significantly from early to late-type galaxies, with a difference of up to a factor of 10. The ratio M_H2/M_HI of the AMIGA galaxies is well below 1 for all morphological types, with a mean value of log(M_H2/M_HI) =  − 0.72 for galaxies of type T = 3–5. We compared our values to those of other noninteracting samples and found that the AMIGA galaxies had the lowest values for all spiral galaxies.

• 6.

  We used our data to compare the disk averaged surface densities of the molecular, Σ_H2, and molecular+atomic gas, Σ_H2 + HI, to those of the SFR, Σ_SFR. We found a good correlation between the logarithms of Σ_H2 and Σ_SFR, with a slope close to 1. No correlation with of Σ_SFR with Σ_H2 + HI was found.

---

Acknowledgments

We would like to thank the referee for useful comments and suggestions. This work has been supported by the research projects AYA2008-06181-C02 and AYA2007-67625-C02-02 from the Spanish Ministerio de Ciencia y Educación and the Junta de Andalucía (Spain) grants P08-FQM-4205, FQM-0108 and TIC-114. D.E. was supported by a Marie Curie International Fellowship within the 6th European Community Framework Programme (MOIF-CT-2006-40298). U.L. warmly thanks IPAC (Caltech), where this work was finished during a sabbatical stay, for their hospitality. We also thank K. C. Xu for helpful discussion. This work is based on observations with the Instituto de Radioastronomia Milimétrica IRAM 30 m and the Five College Radio Astronomy (FCRAO) 14 m. IRAM is supported by INSU/CNRS (France), MPG (Germany, and IGN (Spain). The FCRAO is supported by NSF grant AST 0838222. We made use of the Nasa Extragalactic Database (NED) and of the Lyon Extragalactic Database (LEDA).

References

Online material

Appendix A: CO Spectra

Figure A.1 shows the CO(1–0) profiles of the detections and tentative detections observed by us at the IRAM 30 m telescope and Fig. A.2 those observed at the FCRAO 14 m telescope.

All Tables

All Figures