THE REDSHIFT SEARCH RECEIVER 3 mm WAVELENGTH SPECTRA OF 10 GALAXIES

The spectra shown in Figure 1 display a number of strong lines that are in common to almost all of the galaxies observed. In addition to the strong lines of ¹³CO, HCN, HCO⁺, HNC, and CS, many additional much weaker lines are also detected. The spectral scans of Orion KL and Sgr B2 (Turner 1989) were used as a guide to compile a list of spectral lines and line blends that are likely to be detectable in these galaxies and from this compilation we have identified all of the spectral features in the 10 galaxies. Lines from CO, CS, HCN, HCO⁺, HNC, N₂H⁺, C₂H, HNCO, CH₃OH, HC₃N, C₃H₃, SO, and CH₃C₂H are detected in one or more of these galaxies. In addition, at least one of the hydrogen recombination lines was detected in M82, NGC 1068, and NGC 4258.

One of the most important advantages of obtaining each 3 mm wavelength spectrum simultaneously with the RSR is the perfect pointing registration in all spectral lines. These galaxies all have complex small-scale structure, so even small pointing errors can seriously affect line ratios. In addition, because the lines were obtained simultaneously with a single instrument, the relative calibration of the spectral line intensities is very good.

The intensities of the spectral features were determined by fitting each spectrum with a template of spectral lines assuming a common line width and redshift. The list of lines was developed from the strong lines seen in the spectral scans of Orion and Sgr B2 (Turner 1989), and include all plausible lines, even if the chemistry is different than these Galactic sources. The benefit of such a simultaneous fit is that the line width and redshift can be well constrained by the stronger spectral lines, permitting more accurate determination of the intensities of the weaker lines. Of course, this assumes that the emission from the various molecular species is distributed similarly so they share a common line width and line velocity. Examination of the residuals to the template fits finds them consistent with the baseline noise, thus, we believe that these assumptions are satisfied. The 33 spectral features that were fitted are listed in Table 2, which include the isotopic lines of H¹³CN, H¹³CO⁺, HN¹³C, and C³⁴S. Although these isotopic lines were not detected in any of the galaxies, they were included in the simultaneous fits to provide upper limits on the isotopic emission. Since hydrogen recombination lines were possibly detected in three of these galaxies, the entire series of hydrogen recombination lines were included in the fits. In several cases, a single spectral feature was fitted to a blend of lines (marked blend in Table 2) when the line separation in frequency was much smaller than the 31 MHz spectral resolution of the RSR. In most cases, these were blends of lines from the same molecular species.

Fits to the 33 spectra features are shown superimposed on the spectra in Figure 1. All features with any significance are well fit by this line template. Features detected at a significance of 3σ or greater are labeled in Figure 1. The results of our template fitting procedure for all of the galaxies are summarized in Table 3. For features detected at a significance of 3σ or greater, the table provides the peak intensity and the 1σ uncertainty on these intensities (in parentheses). For features not detected at the 3σ significance level, the table provides the 3σ upper limit to the intensity of the spectral transition or blend. Only one of the six hydrogen recombination lines was detected in M82, however, two other recombination lines were just slightly below the detection threshold and remaining two recombination lines were present at the 2σ level. Thus, the presence of hydrogen recombination lines is probably secure. In NGC 1068 and NGC 4258 only the H41α recombination line was detected and in NGC 4258 this was only one of the three lines detected. In both of these galaxies there is no evidence for any of the other recombination lines at comparable strengths as the H41α line as would be expected, therefore, the identification of this feature at 92.035 GHz as a hydrogen recombination line is suspect. The only other plausible identification for this feature is a blend of CH₃CN lines from the J = 5–4 transition, however if correct, CH₃CN would be surprisingly strong in these two galaxies.

The only spectral line detected in all 10 galaxies is HCO⁺. ¹³CO was detected in nine galaxies, HCN, HNC, and CS were detected in seven galaxies, and C¹⁸O was detected in six galaxies. Because our sample of galaxies varies in distance from 2.9 to 101 Mpc, the absolute detection threshold is not the same for these galaxies, however, in all subsequent analysis we utilize line ratios. The richest spectrum is that for NGC 253, where 16 of the 33 spectral features listed in Table 2 were detected. We note that there have been many spectroscopic observations of these same galaxies, and a number of the spectral lines in Table 2, not detected in our survey, were detected in more sensitive measurements focused on single spectral lines. In only six galaxies, Arp 220, NGC 1068, NGC 253, M82, IC 342, and Maffei 2, five or more spectral features are detected. In NGC 6240, the only line detectable is HCO⁺, and in two other galaxies, NGC 3690 and NGC 4258, we detect HCO⁺ but not HCN. In the following section, the template fits are used to examine several line intensity ratios and investigate variations in these ratios from galaxy to galaxy.

3.2.1. Isotopic Ratios

3.2.2. HCN/¹³CO Ratio

3.2.3. HCO⁺/HCN Ratio

Early models of the chemistry of X-ray irradiated gas suggested that HCO⁺ would be underabundant in gas near a hard X-ray source (Lepp & Dalgarno 1996; Maloney et al. 1996). These results led to the suggestion that the HCO⁺/HCN ratio may distinguish between PDR and XDR dominated gas and thus between central regions of galaxies dominated by either starbursts or AGNs. Subsequent observations (Kohno et al. 2001; Graciá-Carpio et al. 2006; Imanishi et al. 2007; Baan et al. 2008) seemed to confirm this prediction. These observations also showed an anti-correlation between the observed HCN/CO ratio and the HCO⁺/HCN ratio. However, the more recent theoretical work of Meijerink & Spaans (2005) and Meijerink et al. (2007) places this interpretation in question. Meijerink et al. (2007) showed that in the high density gas, the HCO⁺/HCN ratio is larger in XDR regions than in PDR regions, just the opposite of that suggested by Lepp & Dalgarno (1996). They also noted a strong density dependence for this ratio in both PDR and XDR gas.

In Figure 2, we plot the HCO⁺/HCN ratio versus the HCN/¹³CO ratio. We find a similar trend to that found in previous observational papers, that is, the HCO⁺/HCN ratio is inversely correlated with the HCN/¹³CO ratio. The agreement of our result with past papers is not surprising, since there is considerable overlap between our galaxy sample and those in the previous studies. We will address the role density plays in these ratio trends later, however, NGC 3690, NGC 4258, and NGC 6240 are quite anomalous in having unusually large ratios of HCO⁺/HCN, and variations in chemistry are almost certainly needed to explain these ratios. NGC 6240 is not plotted in Figure 2 because we did not detect either HCN or ¹³CO, but the ratio of HCO⁺/HCN is greater than 2.3 (3σ limit). NGC 3690 and NGC 6240 were both part of the Juneau et al. (2009) study of ULIRGS, and these galaxies were among those with the largest HCO⁺/HCN ratio.

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3.2.4. HNC/HCN Ratio

The two galaxies with the strongest emission lines are M82 and NGC 253 which enable a comparison of emission from other molecular species, such as C₂H, N₂H⁺, HNCO, CH₃OH, HC₃N, C₃H₂, SO, and CH₃C₂H, that had only a limited number of detections in our galaxy sample as a whole. In both of these galaxies the emissions observed are likely dominated by molecular clouds associated with their nuclear starbursts. However there are differences, Aladro et al. (2010) suggested that the starburst in M82 is more evolved and the chemistry is dominated by PDR regions, while the chemistry in the younger starburst, NGC 253, is dominated by shocks.

Notable differences between these two galaxies are the detection of HNCO, CH₃OH, N₂H⁺, and HC₃N in NGC 253 but not in M82, although these lines would have been readily detected if they had the same line strength relative to HCN as they have in NGC 253. Both HNCO and CH₃OH are thought to have a shock origin, as these molecules are believed to form on grain surfaces (Tideswell et al. 2009) and then ejected from the grains by low velocity shocks (Martín et al. 2008). Thus, the presence of these lines in NGC 253 agrees with the idea that shocks are an important component to the chemistry in the nuclear regions of this galaxy. Omont (2007) also noted that SiO and CH₃CN, both thought to have a shock origin, are more abundant in NGC 253 than M82. We note that HNCO and CH₃OH are even stronger relative to HCN in IC 342 and Maffei 2, both whose chemistry may also be dominated by shocks (Aladro et al. 2010). A similar conclusion concerning IC 342 was reached by Meier & Turner (2005). The largest CH₃OH/HCN ratio was measured in NGC 3079, and thus the chemistry in NGC 253, IC 342, Maffei 2, and NGC 3079 may all be strongly influenced by shocks. HC₃N was also detected in NGC 253 and not in M82. The only other galaxy where HC₃N was detected was Arp 220, where the ratio of HC₃N/HCN was about three times larger than in NGC 253. Based on the strong emission in Arp 220 (Aalto et al. 2002), Aalto et al. (2007) speculated that strong HC₃N emission might be indicative of young starbursts and this perhaps may explain the stronger emission in NGC 253 relative to the older starburst M82.

The other notable difference is the detection of CH₃C₂H in M82 but not in NGC 253, and the CH₃C₂H/HCN ratio measured in M82 is three times larger than the 3σ upper limit established in NGC 253. In fact, other hydrocarbon molecules, such as C₂H, C₃H₂, and CH₃C₂H, have strengths relative to HCN much larger in M82 than in NGC 253. The enhancement of these hydrocarbon molecules in M82 is discussed in Fuente et al. (2005) and they suggested that photon-dominated chemistry was important for the production of hydrocarbons in the central region of M82. Thus, the pattern of lines seen in M82 and NGC 253 supports the suggestion of Aladro et al. (2010) that the chemistry in NGC 253 is influenced by shocks, while the chemistry in M82 is more PDR dominated.

From our sample of galaxies, we can also examine the differences between the starburst and AGN galaxies. We have already noted that NGC 3690, NGC 4258, and NGC 6240, all with AGNs, have anomalously large HCO⁺/HCN ratios. We have formed composite spectra of a sample of starburst galaxies (NGC 253, Maffei 2, IC 342, M82, and Arp 220) and galaxies with AGNs (NGC 1068, NGC 3690, NGC 4258, and NGC 6240). The emission in each spectra was first normalized to the strength of the HCO⁺ line (the only line seen in all the galaxies), then the frequency axis was adjusted by a factor of 1 + z, and finally the spectra were averaged using equal weights. Equal weighting was used so that no galaxy dominated the composite spectrum, although this meant that the weaker line galaxies added more noise than the strong line galaxies to the composite spectra. The composite spectra were fitted using the same procedure described earlier for the individual galaxies and, as before, a 3σ cutoff was used to define line detections. Unfortunately, the AGN composite consisted primarily of weak-line galaxies, so fewer lines were detected in the composite spectrum relative to the starburst composite. The most interesting ratio is the HCO⁺/HCN ratio and in the starburst galaxies this ratio has a value of 0.71 ± 0.06, while in the AGN galaxies, the ratio was 1.9 ± 0.3, significantly larger. We can also compare the HCN/¹³CO ratio, which for the starbursts was 1.11 ± 0.07 and for the AGNs was 0.64 ± 0.09. Ratios of HNC/HCN and CS/HCN were similar in the two samples.

In the AGN galaxies, NGC 1068 has the strongest lines. Earlier we noted that none of the observed line ratios distinguishes NGC 1068 from the sample of starburst galaxies. The emission observed in NGC 1068 may be dominated by the starburst ring and not gas closely associated with the Seyfert nucleus. Removing NGC 1068, we can form a new AGN composite spectrum from the remaining three AGN galaxies. Although HCN was not detected in any of the individual galaxies, it is readily detected in their composite spectrum. In this new composite AGN spectrum, we find ratios of HCO⁺/HCN = 3.4 ± 0.9 and HCN/¹³CO = 0.45 ± 0.12. Not surprising, these ratios are even more extreme relative to the starburst sample than the AGN composite including NGC 1068.

The line ratios discussed in the previous section depend on both the physical (density, column density, and temperature) and chemical (molecular abundance) properties of the gas. The information available in our spectra is inadequate to constrain all the needed gas properties. We have consequently modeled the line ratios with a very simplistic approach in which we assume that the emission arises from a collection of identical molecular cloud cores which are characterized by a single temperature and density, with equal abundances of the various molecular species. Molecular abundances were taken from the well-studied Galactic GMC cores M17 and Ceph A summarized by Bergin et al. (1997). We further assume abundance ratios of CO/H₂ = 1 × 10⁻⁴ and ¹³CO/CO = 2 × 10⁻²; the resulting molecular abundances relative to H₂ are given in Table 4. An E/A ratio of 1 for CH₃OH and an ortho/para ratio of 3 for C₃H₂ were also assumed. The assumed molecular abundances are very similar to those derived by Martín et al. (2006) for NGC 253 based on their 2 mm wavelength spectral survey (see comparison in Table 4).

The emission from an ensemble of GMC cores was modeled with the RADEX code (Van der Tak et al. 2007) using the Einstein A-coefficients and collision rate coefficients from the Leiden Atomic and Molecular Database (Schöier et al. 2005). To compute the line intensities, besides the molecular abundances, the gas density, n, gas temperature, T, and the H₂ column density per unit line width, N(H₂)/Δv, need to be specified. Our standard GMC core model assumes T = 35 K, n = 1 × 10⁵ cm⁻³, and N(H₂)/Δv = 1 × 10²² cm⁻² (km s⁻¹)⁻¹. Line widths for GMCs in the Galactic disk are around 3 km s⁻¹ (Snell et al. 1984), leading to a H₂ column density of 3 × 10²² cm⁻². Molecular clouds near the center of our Galaxy, such as Sgr B2, have line widths around 20 km s⁻¹ (Cummins et al. 1986), and for this line width the modeled H₂ column density is 2 × 10²³ cm⁻².

The line ratios computed from our standard model are compared with the observations of NGC 253, the galaxy with the richest spectrum, in Figure 3. Since HCN usually has the strongest emission of any of the "high dipole moment" molecules, all intensity ratios are computed relative to HCN. Multiple lines were observed for several molecular species and for the line ratio analysis the 87.9252 GHz line for HNCO, the 96.7414 GHz line for CH₃OH, and the 99.2999 GHz line for SO were used in forming the intensity ratios. For HC₃N, the two lines at 81.8815 and 100.0764 GHz, which were in the least line confused regions of the spectrum, were summed together. The line ratios for our standard core model agree well with those observed for NGC 253. The largest discrepancies between the observed and modeled line ratios is less than a factor of two. The observed ratios in this galaxy are well fit using this simple model.

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Our model can also be used to address the sensitivity of the various line ratios to density and temperature. The line ratios were computed from the standard model for densities of 1 × 10⁴ and 1 × 10⁶ cm⁻³ and the resulting line ratios shown in Figure 3. For our assumed abundances, a density of 1 × 10⁵ cm⁻³ is the better fit to the observed line ratios in NGC 253. Figure 3 illustrates that several of the line ratios, due to differences in the critical density of the lines forming the ratio, are highly sensitive to density. As expected, one of the values most affected is the HCN/¹³CO ratio; however, in addition, the line ratios CH₃OH/HCN and HNCO/HCN are also density sensitive. The temperature sensitivity of these ratios can also be explored, and in Figure 4 the observed line ratios in NGC 253 are compared to those derived from our standard model with density 1 × 10⁵ cm⁻³ and with varying temperatures. Temperature has a much smaller effect on the line ratios than does density, largely because the molecular transitions we observed all arise from similar energy levels above the ground rotational state.

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NGC 253 has been widely studied and there are a number of estimates of the density of the molecular gas. Based on fitting multiple lines of CS, HCN, and HCO⁺ led Martín et al. (2005) and Knudsen et al. (2007) to estimate a density of approximately 2 × 10⁵ cm⁻³, higher than an earlier estimate based on H₂CO emission (Hüttemeister et al. 1997). Recently, Bayet et al. (2009) fitted the CS emission from NGC 253 with a two-component model consisting of a cool, lower density component and a warm, higher density component. For the two velocity features in NGC 253, they found densities for the cooler component of order 2 × 10⁴ and for the warmer component of order 2 × 10⁶ cm⁻³. The density in our standard model agrees well with the single density fits of Martín et al. (2005) and Knudsen et al. (2007) and is consistent with the average of the components fit by Bayet et al. (2009). Based on this density, the abundances we assumed in our standard model, including those molecules (HNCO and CH₃OH) that may be produced in shocks, are consistent with the observations in NGC 253. A better determination of the physical properties of the molecular gas is needed to refine the abundance estimates.

Our model can be used to examine the anti-correlation between the HCO⁺/HCN and ¹³CO/HCN ratios shown in Figure 2. Overlaid on the data in Figure 2 is a line connecting the results for five models in which only the density is varied, from 1 × 10⁴ to 1 × 10⁶ cm⁻³. The comparison between data and models suggests that much of the variation observed in the ¹³CO/HCN ratio can be explained if the average density of the molecular gas varies among these galaxies. For densities below 1 × 10⁴ cm⁻³, it is difficult to produce detectable HCN or ¹³CO emission without having unrealistically large column densities of these molecular species. Although the HCO⁺/HCN ratio is not strongly affected by density, some of the anti-correlation found between this ratio and the ¹³CO/HCN ratio can be explained by variations in the average density. Juneau et al. (2009) came to a similar conclusion and the sensitivity of these line ratios to density is also apparent in the modeling presented by Meijerink et al. (2007). Based on the line ratios, and ignoring any chemical differences, the data suggest that the molecular gas in Arp 220 is the densest and the molecular gas in NGC 3079 the least dense. However, density alone cannot explain the large HCO⁺/HCN line ratios measured in NGC 3690, NGC 4258, and NGC 6240, all with AGNs. In the models of Meijerink et al. (2007), only the XDR models predict HCO⁺/HCN ratios greater than 1, thus, if these XDR models are correct, it is possible that the AGN has an influence on the chemistry and is responsible for the enhanced HCO⁺ abundance in the central regions of these three galaxies. However, the large sample of ULIRGs presented by Juneau et al. (2009) show no correlation between the HCO⁺/HCN ratio and whether these galaxies are believed to be AGN or star formation dominated, putting some doubt in this AGN hypothesis for the enhanced HCO⁺ emission.

The comparison between models and observations can be extended to the line ratios measured for IC342, M82, Arp 220, Maffei 2, NGC 1068, and NGC 3079. These comparisons are shown in Figure 4. Since density has the greatest influence on the line ratios, only models with varying density at a fixed temperature of 35 K are included in this figure. Based on model comparisons shown in Figures 2 and 4, IC 342, Maffei 2, and NGC 3079 would be expected to have the lowest average gas density of ∼10⁴ cm⁻³. This low average density is borne out by the other density sensitive ratios. With this density, we find the abundances from our standard core model reproduce well the measured line ratios in these three galaxies. Similarly, the average density for M82 is expected to be somewhat larger (∼3 × 10⁴ cm⁻³) and assuming this density we confirm that the abundances of HC₃N, CH₃OH, N₂H⁺, and HNCO relative to HCN are smaller than in our standard model and for those found in NGC 253. Again based on the result shown in Figures 2 and 4, NGC 1068 is expected to have a somewhat larger average density (∼10⁵ cm⁻³), while Arp 220 is expected to have the highest average density (∼10⁶ cm⁻³). As suggested earlier, we find an overabundance of HC₃N relative to HCN in Arp 220 for any of the modeled densities. Thus, if we allow for the average molecular gas density to vary from galaxy to galaxy, our standard model with fixed abundances provides a reasonably good fit to the measured ratios in these galaxies.

There have been a number of estimates of the average molecular gas density for galaxies in our sample. Most of these estimates utilize multiple transitions of a single molecular species, thus they are independent of derived abundances. However, despite this, estimates for a single galaxy can still differ by an order of magnitude. Density estimates for IC 342 (Hüttemeister et al. 1997; Meijerink & Spaans 2005), Maffei 2 (Hüttemeister et al. 1997), M82 (Naylor et al. 2010), and Arp 220 (Greve et al. 2009) are in reasonable agreement with our estimates. The HCN line SEDS shown in Knudsen et al. (2007) are also consistent with the trend in density variations for the galaxies M82, NGC 253, and Arp 220. Fitting the gas in the central regions of these galaxies with a single density is an oversimplification and Bayet et al. (2009) and Aladro et al. (2010) have fitted multiple-density components for NGC 253, M82, IC 342, Maffei 2, and NGC 1068. With the exception of M82, their column density weighted average density is consistent with our findings. For M82, both find a column density weighted density about an order of magnitude higher than that of Naylor et al. (2010).

The simple model we presented in the previous section, in which the molecular emission observed arises from an ensemble of identical cloud cores, can be used to estimate the beam filling factor and mass of molecular gas, independent of the X_CO-factor. Since the distances of the galaxies in our sample vary enormously, the region probed ranges from just the central starburst core to nearly the entire galaxy. The linear diameter of the FCRAO beam at the frequency of the ¹³CO line for the distance of these galaxies (D_B) is given in Table 5.

The beam surface area filling factor (f_area) is related to the observed antenna temperature of the line corrected for the main beam efficiency (T_MB), the line intensity from our model (T_model), the assumed core line width in the model (Δv_model), and the observed line width of the galaxy (Δv_obs), which is dominated by galactic rotation, by the following equation:

$$\begin{equation} f_{\rm area} = \frac{T_{\rm MB}}{T_{\rm model}} \frac{\Delta v_{\rm obs}}{\Delta v_{\rm model}}. \end{equation} \tag{ 1 }$$

The observed ¹³CO emission is used to estimate the beam filling factor from the above relation. The modeled intensity ratios, discussed previously, did not depend on the line width, however, the total integrated intensity, and hence the beam surface filling factor, does. We have no information on the line widths of cloud cores in these galaxies, so we assume a line width of 10 km s⁻¹ for our model cores, which corresponds to an H₂ column density of 1 × 10²³ cm⁻². Although a density of 1 × 10⁵ cm⁻³ was assumed, the emission from ¹³CO has very little density dependence as long as n ⩾ 1 × 10⁴ cm⁻³. Based on the observed line intensities and line widths presented in Table 3, the computed beam area filling factor is summarized in Table 5. Not surprisingly, the beam filling factor is strongly dependent on galaxy distance. For the nearer galaxies, the beam area filling factor can be as large as 0.26, implying that one-fourth of the FCRAO ∼ 50'' beam is covered with gas with a total gas column density of 1 × 10²³ cm⁻², corresponding to an A_v of approximately 100 mag. Similar beam area filling factors would have been found if we had used other molecular species, such as HCN or HCO⁺. However, the results would have been more sensitive to the assumed density of the cloud cores.

The molecular gas mass can also be estimated from our model. The mass is given by

$$\begin{equation} M = m_{\rm H_2}\: N_{\rm model}\: f_{\rm area}\: d^2\: \Omega _B, \end{equation} \tag{ 2 }$$

where m$_{\rm H_2}$ is the mass of a molecular hydrogen molecule, N_model is the gas column density in the core model, d is the distance to the galaxy, and Ω_B is the main beam solid angle. As long as the ¹³CO emission is optically thin, the mass determination is independent of many of the assumed core model parameters. However, two important parameters in deriving masses are (1) the assumed core gas temperature, as this affects the partition function, and (2) the assumed ¹³CO/H₂ ratio of 2 × 10⁻⁶. The mass of molecular hydrogen derived from the above equation is summarized in Table 5. Because of the varying distance of these galaxies, the mass of the nearby galaxies (NGC 253, Maffei 2, IC 342, and M82) includes only the gas in the central 1 kpc regions, whereas for the most distant galaxies (NGC 3690 and Arp 220) it includes the entire molecular mass of the galaxy.

These mass estimates can be compared with those derived from CO using an assumed X_CO-factor. To make certain that we are comparing the mass from comparable regions of these galaxies, we have used CO observations also obtained with the FCRAO 14 m telescope as part of the FCRAO Extragalactic CO Survey (Young et al. 1995). Observations of all of the galaxies except Maffei 2 are covered in this survey, and these observations were obtained with nearly an identical beam size as our observations of ¹³CO. The CO fluxes from the survey are summarized in Table 5, where the integrated intensity to flux conversion factor provided in Young et al. (1995) was used.

To estimate the mass from the CO fluxes, an X_CO-factor of 1.8 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹ was used which is representative of Galactic molecular clouds (Omont 2007). The molecular hydrogen gas mass can then be written (Kenney & Young 1989) as

$$\begin{equation} M(\rm H_2) = 7.1\times 10^3 d^2 S_{\rm CO}, \end{equation} \tag{ 3 }$$

where d is the distance in Mpc and S_CO is CO flux in units of Jy km s⁻¹. The masses derived from this expression are presented in Table 5. Mass estimates from CO are 1.2–4.3 times larger than that derived from ¹³CO. It is possible to reconcile these masses if we either lower the ¹³CO abundance, increase the gas temperature assumed in our core model, or decrease the X_CO-factor used. We cannot rule out any of these possibilities; however, a more likely scenario is that some of the CO emission is arising from lower density and lower column density gas that does not produce significant ¹³CO emission. No matter what the reason for the mass difference, we can conclude that the mass of dense gas must represent a significant fraction of the total molecular gas in these galaxy centers.

We find that between about 25% and 85% of the total molecular mass in these galaxies must have high density and column density. These properties are likely associated with the molecular clouds in the central ∼1 kpc regions of these galaxies. Bally et al. (1987) estimated the mean density of the molecular gas in the inner 500 pc radius region of the Milky Way to be 2 × 10⁴ cm⁻³, similar to the average density estimated for several of the galaxies in our survey. However, the properties of the molecular clouds in the disk of the Milky Way are quite different. Lee et al. (1990) mapped a 3 deg² region around ℓ = 24° in both ¹³CO and CS. Although, no estimate was made of the mean density of the gas, the quoted emission ratio of CS/¹³CO of 0.008 is substantially lower than the range of ratios, 0.12–1.0, we measured for our galaxy sample. The largest CS/¹³CO ratio was observed in Arp 220, which is also modeled to have the highest mean molecular gas density. Since this ratio is sensitive to the mean gas density, this comparison suggests that a large fraction of the molecular gas in the central regions of the galaxies in our sample, and the Milky Way, must be dense, while molecular clouds in the Milky Way disk have a much smaller fraction of dense gas. Studies of individual molecular clouds in the disk of the Milky Way (Carpenter et al. 1995) confirm this and show that high density and high column density cores represent only a small fraction of the area and mass of the molecular cloud.