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Astron. Astrophys. 363, 93-107 (2000)

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4. Discussion

4.1. Gas masses based on CO isotopomers

The total flux in our map would correspond to an H2 mass of [FORMULA] [FORMULA] if the `standard' CO to N(H2) conversion factor (SCF = [FORMULA] cm-2 (K km s-1)-1, Strong et al. 1988) were applicable, which is, however, not the case (see discussion below). Instead of giving more masses based on the standard conversion factor, which are unlikely to be very meaningful, we compare the `standard' mass derived from 12CO to masses from 13CO obtained with the simple LTE assumptions of optically thin emission and a kinetic gas temperature of 20 K. Globally , i.e. avaraged over the entire map, the 13CO-derived mass is a factor of 16-27 (for 12CO/13CO abundance ratios between 30 and 50) lower than the SCF mass. If the upper limit for the 13CO total flux (see below) is taken, the discrepancy decreases to 8-13, still remaining very substantial. A mass discrepancy of [FORMULA] is also derived for the central condensation. In 12CO peaks along the bar, the disagreement between the SCF and the 13CO LTE mass reaches values exceeding 30, while in the 13CO maximum in the southern bar, it comes down to [FORMULA]. Of course, these varying mass discrepancies simply reflect the changing line intensity ratios discussed above.

The SCF mass still exceeds the 13CO LTE mass by a factor 2-10 if the kinetic gas temperature is raised from 20 K to 100 K for the 13CO - based estimate. Only in the 13CO peak in the bar south of the central condensation the SCF mass drops to about half the 13CO LTE mass under these conditions, which are, of course, not realistic for a 13CO condensation, presumably consisting of dense gas. However, it seems that the SCF might be correct in this (and only in this) location, which has almost exactly the 12CO/13CO line ratio found in Galactic GMCs. This can be considered as a way to confirm the SCF for a normal spiral environment.

Of course, assuming LTE conditions when deriving N(H2) from 13CO could underestimate the true N(H2) when non-LTE conditions apply. Padoan et al. (2000) find a discrepancy of a factor 1.3-7 between `LTE masses' and `true' masses in their cloud models. This discrepancy is smaller than the difference between the 13CO LTE masses and the SCF masses we find both for the gas in the center and, even more pronounced, for the gas in 12CO peaks along the bar away from center. Still, the 13CO masses derived for LTE should be considered as a lower limit to the real mass, while the SCF masses are upper limits.

Simple non-LTE radiative transfer calculations (using the Large Velocity Gradient (LVG) assumption) reproduce the results of Padoan et al. to within roughly a factor of two and can thus serve as a guide to possible scenarios. These calculations show that the 12CO-to-H2 conversion factor can be brought down significantly (by a factor of [FORMULA]) in low density gas ([FORMULA] cm-3). Then, high 12CO/13CO 1 [FORMULA] 0 line intensity ratios of [FORMULA] are predicted. Thus, this scenario points to the presence of `diffuse' gas, discussed in detail in the next section.

When the density is reduced even further, in the LVG models the 12CO-to-H2 conversion factor rises again. The SCF can be recovered for a H2 density of [FORMULA] cm-3, while [FORMULA] remains high. We consider these extremely low densities required for the bulk of the gas unlikely for the following reasons: To reach a column density that is sufficient to ensure shielding of the molecules against UV radiation and to be consistent with the observed brightness of the lines, even for an extreme and very unlikely beam filling factor of unity, the models require an unrealistically low velocity dispersion for a given pathlength ([FORMULA] km s-1 pc-1). This is in contradiction to the expectation that diffuse gas should be characterized by a large velocity dispersion (see below). Another argument against extremely low density gas is the expected very low 12CO (2[FORMULA]1)/(1[FORMULA]0) line intensity ratio ([FORMULA]), in contradiction to single-dish (Sempere et al. 1995) and recent interferometric observations of 12CO (2[FORMULA]1) (Baker 2000).

4.2. Physical conditions - diffuse molecular gas

In this section, we present simple scenarios that might explain the variations in [FORMULA]. The key component of these scenarios is the presence of a diffuse or `intercloud' molecular medium (ICM) . This medium consists of low density ([FORMULA] cm-3), gravitationally unbound, molecular gas. For a given column density, N, the 13CO 1 [FORMULA] 0 line emission from gravitationally unbound gas will be weaker than that from self-gravitating clouds, because the velocity dispersion, [FORMULA], is higher for unbound material and thus [FORMULA] is lower for the unbound gas. A low [FORMULA] results in a low optical depth and, in low-density gas, also results in a low excitation temperature of the transition because of reduced radiative trapping. Hence, the ICM will be difficult to detect in the 13CO [FORMULA] line. One may see the ICM as somewhat analogous to high latitude molecular clouds detected in the disk of our Galaxy. These are also low density structures which, unlike most of the disk molecular clouds, are not in virial equilibrium.

While, under these conditions, 13CO is optically thin and subthermal, 12CO reaches a moderate optical depth close to unity. Thus, 12CO still radiates efficiently (and is self-shielding) while the 13CO intensity falls off. This moderate optical depth of the 12CO [FORMULA] line is the main reason why the `standard' [FORMULA] conversion factor cannot be applied to regions where a significant amount of diffuse gas is found : the gas is neither optically thick nor virialized and the `standard' [FORMULA] overestimates the molecular gas mass by up to an order of magnitude. This situation is encountered, e.g., in our Galactic center (Dahmen et al. 1998).

4.2.1. The bar - outside the central 10" diameter

The large variations in [FORMULA] along the bar, with values ranging from 5 to [FORMULA] (and even 73 in one extreme case) is best explained by the presence of a large amount of diffuse (thin, warm, unbound) ICM gas which dominates the 12CO 1[FORMULA]0 emission and is very distinctly different from the dense molecular clouds preferentially detected by 13CO. In the southern part of the bar, where 13CO is detected, the difference in linewidth is most dramatic close to the 12CO maxima. Here, the 12CO lines have a width of [FORMULA] km s-1, compared to [FORMULA] km s-1 for 13CO. This explains the significant difference in [FORMULA] depending on whether integrated or peak intensities are used (Table 3). The large linewidths of the 12CO spectra suggest large velocity dispersions at the 12CO maxima along the bar. This provides a strong argument in favour of a diffuse medium contrary to [12CO]/[13CO] abundance variations. While in a `standard' 12CO emitting ISM, i.e. a medium where low J 12CO lines are optically thick, the [12CO ]/[13CO ] abundance ratio is not traced by changes in [FORMULA], a change in the 13CO abundance itself could contribute to changes in [FORMULA]. However, if such a variation reflects changes in [12C]/[13C] with galactocentric radius, it should not exceed a factor of two (Wilson & Matteucci 1992, Langer & Penzias 1990). Even a gradient this small and insufficient to explain the observed changes in [FORMULA] is almost impossible to maintain in the bar due to efficient mixing (see e.g. Friedli et al. 1994for model calculations, Martin & Roy 1994and Zaritsky et al. 1994for empirical studies). Thus, we consider diffuse gas to provide the only viable explanation for the large variations in [FORMULA] we find along the bar of NGC 7479.

Of course, 13CO may be selectively photodissociated in the diffuse medium and thus really be underabundant, since it is not self-shielding. However, the efficiency of this mechanism also relies on the diffuse nature of the gas.

According to the single dish map of Sempere et al. (1995), the 12CO (2[FORMULA]1)/(1[FORMULA]0) ratio along the bar is [FORMULA]. This is, of course, a global value which is likely to vary at higher resolution. It is compatible with cold gas at moderate density ([FORMULA] cm-3) or warm, thin gas (density a few 100 cm-3). Given the evidence discussed aboved, we obviously favour the latter explanation for this line ratio.

The fact that the 13CO intensity maximum is clearly offset along the bar minor axis from the 12CO maximum in the southern bar indicates that 13CO traces a largely different component. The relation of the two tracers to dust, shocks and star formation will be discussed further in Sect. 4.3.

4.2.2. The inner region - inside the central 10"

At first glance, the situation in the center of NGC 7479 might be taken to argue against the ICM scenario outlined above, since the HCN is coincident with the 12CO maximum and offset from 13CO. A situation like this was sometimes seen as suggesting abundance changes for the CO isotopomers (e.g. Casoli et al. 1992), since HCN requires high gas densities of at least [FORMULA] cm-3 to be significantly excited and may be identified with the region where most of the mass resides. In a turbulent environment like the nuclear region of NGC 7479, we consider the alternative explanation of a kinetic temperature gradient between the 13CO and HCN peaks to be more likely. For the high gas densities we expect in the central region (i.e. n(H[FORMULA] cm-3), the higher kinetic temperature would occur at the HCN peak rather than the 13CO peak because the brightness of the 13CO 1[FORMULA]0 line is a decreasing function of kinetic temperature (for temperatures above 8 K in the LTE, optically thin limit).

The HCN molecule has a high dipole moment and is thus much more sensitive to density variations than 12CO and 13CO. Thus the HCN peak is not expected to coincide with the 13CO peak if the latter is at lower densities than the HCN 1[FORMULA]0 critical density. This is true even if the HCN 1[FORMULA]0 transition is optically thin, due to the spreading of the molecules over many rotational levels that occurs at high densities (i.e. [FORMULA] cm-3 for HCN) because of the high collision rates at these densities.

We can give an order-of-magnitude estimate of the gas density that is likely to occur at the HCN peak: Having the bulk of the gas in the central beam at densities of [FORMULA] cm-3 requires a very low volume filling factor of [FORMULA], which seems unlikely in the center of a galaxy undergoing a mild starburst. Also, very high densities suggest a velocity dispersion per pathlength that is too high to be realistic (several 100 km s-1 pc-1). If, on the other hand, the density was low enough for HCN to be subthermally excited, the HCN 1[FORMULA]0 line would be optically thick, because the molecules would pile up in the [FORMULA] level. However, in this case (at peak densities of [FORMULA] cm-3) we would expect the emission to be more widespread. Low densities close to [FORMULA] cm-3 lead to very subthermal conditions and very weak HCN 1[FORMULA]0 emission. Thus, we consider [FORMULA] cm-3 to be a reasonable density at the HCN peak.

In summary, since the HCN distribution is confined closely to the 12CO peak, we expect this region to also be a peak in density (but not necessarily in column density), in addition to being a peak in [FORMULA]. In contrast, the 13CO 1[FORMULA]0 emission will preferentially trace cool and/or lower density gas.

A kinetic temperature gradient was also used to explain the different spatial extents of the 13CO (3[FORMULA]2) and HCN emission in NGC 253 (Wall et al. 1991). The kinetic temperature gradient in NGC 7479 leads to the prediction that the 13CO (2[FORMULA]1)/(1[FORMULA]0) ratio should be higher in the HCN peak than in the 13CO peak, as is seen in the nucleus of IC 694 in the Arp 299 merger (Aalto et al. 1997b). It also means that the nuclear 12CO (2[FORMULA]1)/12CO (1[FORMULA]0) ratio is expected to be high, at least close to unity; this seems to be the case (Baker 2000). 13CO 2[FORMULA]1 observations will be crucial to further investigate the gas properties in the central 1.5 kpc of NGC 7479 and make comparisons to luminous mergers, where Casoli et al. (1992) and Taniguchi et al. (1999), based on data by Aalto et al. 1995and Casoli et al., have argued that 13CO 2[FORMULA]1 is also relatively faint and thus 13CO may be depressed, at least in some cases.

We note, however, 13CO 1[FORMULA]0 is not as faint at the 12CO maximum as under the extreme conditions of mergers: Fig. 5 shows the line to be as strong as HCN - it just peaks in a different position. The central 12CO/HCN line ratio of [FORMULA] is on the high side if compared to the range found in the central region of a number of galaxies, where 10 is more typical; however the scatter is very large even among barred starburst spirals (Contini et al. 1997). Still, a value of 20 may be an indication that the amount of warm dense gas in the nuclear region of NGC 7479 is only moderate and confined to a small region.

Diffuse gas is likely to be also important even in the central condensation of NGC 7479. This is indicated by the high values [FORMULA] reaches away from the curved `13CO- ridge' in the central condensation. In these areas, the 13CO lines are much narrower than the 12CO transitions (150 km s-1 - 300 km s-1 for 12CO versus 50 km s-1 - 80 km s-1 for 13CO). These differences in line shape are also obvious from the global single dish spectra (Fig. 8).

Diffuse molecular gas has been detected in the centers of a large number of barred and starburst galaxies such as IC 342 (Downes et al. 1992) or NGC 1808 (Aalto et al. 1994) and, of course, in the bar region of the Milky Way (Dahmen et al. 1998). It has also been detected in the center of the elliptical galaxy NGC 759 (Wiklind et al. 1997) where a low line ratio of 0.4 is indicative of a two component medium made up of dense, cold clumps embedded in a warm, diffuse molecular medium. A scenario where 12CO and 13CO emission arises from separate components was suggested for IC 342 as early as 1990 by Wall & Jaffe. The idea that diffuse gas characterized by 12CO emission of moderate optical depth is important even in regions of extreme star formation, usually associated with large amounts of dense molecular gas, has recently gained credibility even for ultraluminous infrared galaxies (Aalto et al. 1995, Downes & Solomon 1998).

It is interesting to note that the 13CO ridge in the central condensation is precisely aligned with the steepest velocity gradient (derived from 12CO, Fig. 10).

[FIGURE] Fig. 10. a The integrated 12CO intensity (white contours) superposed on the velocity field derived from12CO (grayscale and thin gray contours). The velocity contours range from 2280 km s-1 to 2440 km s-1 and increase by 10 km s-1. b  The integrated 13CO intensity (white contours) superposed on the velocity field from panel a . The velocity contours are the same as in panel a and thus facilitate a direct comparison of the two panels. c  12CO channel map for the velocity range 2280 km s-1 - 2340 km s-1 (white contours) overlaid on the 12CO velocity field in the central part of the bar (grayscale and gray contours). The intensity contours are multiples of [FORMULA] (5.9 K km s-1 (1.24  Jy beam-1 km s- 1 or 2[FORMULA]). The velocity contours are the same as in panel a . In grayscale, dark corresponds to higher velocities. d  The central velocity field for 13CO. The velocity contour levels are the same as in panel a .

4.3. Production of an ICM by tidal disruption and cloud collisions

Cloud disruption due to the tidal field along a bar is one mechanism that could produce a diffuse ICM, especially close to the central condensation. Another possible source of the ICM are off-center cloud collisions.

(i) Cloud evaporation due to the tidal field : As a bound cloud moves in a bar potential or elliptical orbit, the tidal field across it will vary in time. This produces both internal heating of the cloud and clump evaporation from the outer regions of the cloud (Das & Jog 1995). The evaporated cloud mass will become part of the low density, molecular ICM, raising [FORMULA].

To get a lower estimate of how the tidal field changes over the bar, we first determined the potential of the galaxy from the deprojected K image data (Combes, private communication). The potential was azimuthally averaged to determine [FORMULA], which was fitted with a polynomial function that was used to derive a rotation curve for the galaxy. The mass to luminosity ratio [FORMULA] was chosen so as to obtain the best fit of the derived rotation curve to that observed. We then used this azimuthally averaged potential to calculate the tidal field over the galaxy. Though this does not give the exact variation of the tidal field across a cloud in the bar potential, it will give a first appoximation as to how the tidal field varies. In Fig. 11 we have plotted the tidal field per unit mass, across unit length, [FORMULA] = [FORMULA] against radial distance r in kpc.

[FIGURE] Fig. 11. Tidal field per unit mass and across unit length (see text for explanation) along the bar. The dotted lines indicate the tidal field at radii 1 kpc and 5.5 kpc, which are the semiminor and semimajor axes of the bar. This illustrates the change in tidal force that a cloud on an elongated bar orbit can experience.

With a projected bar length of approximately 10.4 kpc and width 1.6 kpc (Fig. 1), an inclination angle of 41o and a position angle 25o for the bar (Sempere at al. 1995), the deprojected bar length is about 11 kpc and its width is about 2 kpc (Arnaboldi et al. 1995). So at the semimajor axis distance of r=5.5 kpc, [FORMULA] and at the semiminor axis distance of [FORMULA] kpc, [FORMULA]. Thus, the tidal field changes from being disruptive at the bar ends to compressive close to the bar center. This considerable change in tidal field, which is steepest in the central region, may produce significant cloud evaporation, thus leading to large amounts of diffuse gas.

(ii) Cloud Collisions : Hydrodynamic simulations have shown that off-center cloud collisions lead to gas being sheared off the colliding clouds, forming trailing extensions in the interstellar medium; the gas then dissipates into the ISM (Hausman 1981). This gas may form part of the diffuse ICM. In bars, the crowding of closed [FORMULA] orbits at the bar ends enhances the cloud collision frequency signigicantly and also produces shocked gas. Collisions also cause the clouds to lose angular momentum and sink inwards leading to the central buildup of gas. This increased concentration of gas in the centers of starburst galaxies and barred galaxies means the rate of formation of diffuse gas in these galaxies will also be high. NGC 7479 has a strong bar and may have undergone a recent minor merger (Laine & Heller 1999). Thus, the cloud collision rate should be high and there should be a considerable amount of diffuse gas in the central [FORMULA] kpc.

Distinguishing between the two mechanisms observationally is not easy. The diffuse gas produced by cloud collisions may often be accompanied by shocked, dense gas. Tidally evaporated gas will not have this association. However, diffuse gas is expected to spread over the bar more quickly than dense gas, which will make it difficult to determine its origin. Still, in the future sensitive, high resolution observations of a shock tracer like SiO may be useful to decide this question.

4.4. The relation between tracers of shocks and star formation

The S-shaped, complex velocity field of the gas in the bar of NGC 7479 (see Fig. 10) has been convincingly explained by e.g. Laine et al. (1999) as the result of gas streaming motions in a strong bar potential. They further argue that H[FORMULA], dust lanes, a large velocity gradient and strong 12CO emission more or less coincide. These are all taken to trace, in some sense, shocks, gas compression and star formation.

Including 13CO and the varying line ratios, indicative of at least two different components of molecular gas, (and seeing all the 12CO) leads to a more complex picture. In Fig. 12, we overlay the 12CO (right) and 13CO (left) intensity distributions on an HST red image retrieved from the archive. In the north, where no 13CO is detected outside the central region, 12CO follows the strong dust lane almost perfectly. In the south, the visual dust lane is weaker or more diffuse and the correlation with the 12CO distribution is much less evident. However, the southern 13CO peak coincides with a (faint) peak in a dust lane. South of the center, [FORMULA] grows when we move upstream (west) across the bar (assuming that the spiral arms are trailing). In other words, the 13CO concentration is located downstream from the 12CO maximum, and possibly also downstream from the peak of the shock, if we identify the 12CO maximum with the shockfront. This may be justified by the close coincidence of the 12CO maximum with the optical dust lane in the north and also by the excellent agreement Laine et al. (1999) find between 12CO peaks (both in the north and in the south) and the maxima in a [FORMULA] NIR color map that is an even better indicator of dust than an optical image.

[FIGURE] Fig. 12. Superposition of the 12CO distribution (right) and the 13CO distribution on an archival HST (Planetary Camera) red image that shows the shape of the dust lanes.

In the central concentration, the course of the dust lanes is not clear. However, here it is the 13CO that very clearly follows the steepest velocity gradient (Fig. 10b), while 12CO is distributed fairly independently of the velocity gradient. 12CO-emitting gas at a velocity between 2280 km s-1 and 2340 km s-1 traces the velocity gradient somewhat more closely than gas at other velocities (Fig. 10c), but even in this restricted velocity range the 12CO emission does not follow the velocity field as clearly as the 13CO emission does. A number of spectra from the central 15" have their emission peak close to 2300 km s-1, and a narrow emission component may be associated with this peak (faintly visible in Fig. 4).

The velocity field based on 13CO is displayed in Fig. 10d. It is even more dramatically S-shaped than the 12CO velocity field. We further note that the 12CO velocity field determined by Laine et al. closely resembles our 13CO velocity field, and that their 12CO distribution in the central 15" appears more bent than ours.

This evidence leads us to the following scenario: The 13CO emission and a part of the 12CO emission, especially at mid-velocities, traces dense or at least high column density gas that follows the velocity field and is compressed in the region with the steepest velocity gradient. We suspect that this region coincides with the central dust lane, which is, however, not clearly visible in the HST image. In terms of 12CO emissivity, this gas component is not dominant enough to clearly reduce [FORMULA]. Also, the dust lane may be fairly narrow and unresolved in our data. Thus, this component is seen most clearly in the 13CO data, but Laine et al. also trace it in 12CO since they are not sensitive to much of the extended emsission. The 12CO and 13CO distributions in our maps deviate because the 12CO emission, especially but not exclusively at non-central velocities, is due to diffuse gas that is far less confined to the shock region in the central [FORMULA] ([FORMULA]. The dramatic S-shape in the 13CO velocity field (Fig. 10d) indicates that the strong inner bar of NGC 7479 is the feature dominating the kinematics of the denser gas in this central region. As discussed earlier (Fig. 2), a rotating disk or gas on [FORMULA]-orbits, perpendicular to the main bar axis, is interacting with the bar on the scale of a few hundred pc at the very center.

It is conceivable that the diffuse gas rises to higher altitudes above the plane of the galaxy than the dense gas, which may be less turbulent and more strongly dominated by the bar potential, which is defined by the stellar potential, since most of the dynamical mass is almost certain to be in the form of stars.

Outside the central 2 kpc, the relation between the various tracers changes: both the detached northern and the southern 13CO peaks are found close to, but not coincident with, regions of steep velocity gradients (Fig. 10). The dust lane (and presumably the region of the strongest shock) is now traced well by the 12CO emission. Possibly, the larger overall amount of gas in the central 2 kpc allows a diffuse component to spread throughout this region, while in the outer bar the gas associated with the shock remains diffuse.

It seems possible that the 13CO peaks in the outer bar indicate conditions that are more quiescent and favourable to the formation of bound clouds and ultimately star formation activity. The low value of [FORMULA] in these complexes suggests that their properties are similar to GMCs in the spiral arms of normal galaxies. The cuts presented by Sempere et al. (1995) indicate that the H[FORMULA] emission peaks along with the 13CO in the southern condensation, i.e. is offset from the 12CO and main dust lane in this area. If the H[FORMULA] traces star formation, this shift away from a region that seems to be totally dominated by diffuse gas may reflect that star formation occurs wherever the gas density is high enough, while the proximity to the shock front may play a secondary role. The fact that the 13CO condensations are close to (offset [FORMULA]) strong (12CO) velocity gradients need not be a contradiction to quiescent conditions. The peaks of the condensations are downstream of the strongest gradient by several hundred pc. In addition, the interiors of the condensations could be quiescent while the condensations themselves are following a strong overall large-scale flow. This question, however, requires further study on smaller spatial scales.

Offsets between molecular gas concentrations and dust lanes have recently been reported by Rand et al. (1999) for a part of a spiral arm in M 83. They used 12CO as a tracer, but see only 2% - 5% of the single dish flux in their interferometer map. Thus, they probably filter out the diffuse component, so their 12CO data might trace a dense, clumpy component similar to what we see in 13CO.

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Online publication: December 5, 2000