Astron. Astrophys. 326, 59-68 (1997)

4. Discussion

4.1. Physical conditions

4.1.1.

Formaldehyde is a slightly asymmetric top molecule that exists in ortho- ( ...) and para- ( ...) forms that are not connected by allowed transitions. Thus, they can be considered independent molecular species. The asymmetry splits each rotational level in the -ladders into a so-called K -doublet (see, e. g. , Henkel (1980) for a level diagram and more details).

Since relative populations of different ladders are determined by collisions, line intensity ratios of transitions from different ladders of a given species are excellent tracers of the gas kinetic temperature (Mangum & Wootten 1993). The level populations within a ladder are determined by an equilibrium between collisional excitation and spontaneous and collisional deexcitation, making the relative level populations within a ladder sensitive to the H₂ density and, to a lesser degree, to kinetic temperatures.

We have carried out large velocity gradient (LVG) statistical equilibrium computations of the population of the ladder of ortho formaldehyde (o- ), for which we have the most complete data. The model is described in detail in Henkel et al. (1980). We included 16 levels of that rotational ladder fixing the kinetic temperatures to a value of 80 K. Setting to 50 K changes the line intensity ratios only by a few percent. As a result of these calculations, line ratios for the 140, 150 and 211 GHz transitions of o- are related to the H₂ density and the column density per unit linewidth (see Fig. 4).

It is evident from Fig. 4 that the 1.3 mm and 2 mm lines have similar intensities if densities exceed (this also holds for para formaldehyde). In order to derive column densities of o-H₂ CO from the integrated intensities of one or several lines, an assumption must be made about the H₂ density and, to a lesser degree, the kinetic temperature, both of which determine the rotational temperature, or more generally, the partition function. An integrated intensity of 1 K kms^-1 of the 140 GHz line corresponds e.g. to if one assumes a low H₂ density of 10⁴ cm^-3 ; if, however, is assumed, then the o-H₂ CO column densities for the same line intensity are an order of magnitude lower. In Table 4, we estimate from the intensities of the 140 GHz lines, and the densities from the measured line intensity ratios. The most reliable densities from mm-wave line intensity ratios are estimated for regions where n (H₂) cm^-3. For lower densities, mm-wave lines of become optically thick if cm . In this case, the line intensity ratios not only depend on n (H₂), but also strongly on . Upper limits on n (H₂) estimated in Table 4 are based on the optically thin limit.

Table 4. Beam averaged and column densities and relative abundances.

Fig. 4. Predicted line intensity ratios of ortho-formaldehyde lines as a function of (in cm-3) and N (ortho-H2 CO)/ (in cm-2 /(km s-1). Solid contours: , thin contours: . The assumed is 80 K.

In order to determine relative abundances, the H₂ column density has to be known. In Table 4, we use values deduced from CO measurements, and the standard conversion formula of Strong et al. (1988), i.e. ()^-1. However, there is growing evidence that this conventional conversion factor cannot be applied to Galactic bulge regions (see Dahmen et al. 1996a,b for our Galactic center, Mauersberger et al. 1996a, b for NGC 253 and NGC 4945, Shier et al. 1994 for IR-luminous galaxies). The correction factor might be as large as 10, and is likely to be different for different galaxies. It will, however, always decrease H₂ column densities and increase the relative abundance of the molecule.

NGC 253. Toward this galaxy, we have the largest data base. In order to compare line intensities which have been obtained at different wavelengths one has to take into account the different beam sizes and the spatial structure of the source. Since we did not map the distribution of H₂ CO toward any of our sources, we assume that the distribution of this molecule toward NGC 253 is similar to that of the line of ¹² CO, which has been mapped with 12 resolution and convolved to different resolutions by Mauersberger et al. (1996a). From an interpolation of the data toward the central position of NGC 253 in their Table 1, intensities in a 16 beam are a factor 0.85 weaker than data at 12 resolution. In the following analysis we assume the same correction factor for the 2 mm data of M 82 and IC 342 where the size of the molecular emission is similar to that of NGC 253.

We can use the intensity ratios of lines within the ladder of ortho formaldehyde to estimate the H₂ density of the H₂ CO emitting gas. In practice, a difficulty in assessing the line ratios arises if the line shapes and/or the velocity coverage differs. One might then incorrectly compare different gas components. The (211 GHz) and the (140 GHz) lines were observed toward slightly different positions, adding to the uncertainty. If only the clear overlap region in the spectra is considered, a line intensity ratio of 0.42( 0.07) results. From Fig. 4 such a low ratio is compatible with , and even lower densities if H₂ CO lines are saturated. We conclude that for the bulk of the H₂ CO emitting gas. From our limit to the line and the detection of the line of para H₂ CO, the corresponding ratio is which is compatible with .

The ratio of the (ortho, 150 GHz) and the (para, 146 GHz) transitions depends on the ortho/para (o/p) ratio. For the high temperature limit of the o/p ratio of 3, one would expect a line intensity ratio of (for ) and . The value we actually observe is 0.6, or even lower, if one argues that not the entire velocity range for the wide line should be considered for the ratio. We therefore suggest that the o/p ratio of H₂ CO actually has a value close to 1, which is lower than the value derived by Aalto et al. (1997) for the 1 mm transitions. Since the o/p ratio bears important information on the formation of molecular gas, and our result, involving a blended line, is uncertain, further observations are very desirable.

M 82. We have measured ortho-H₂ CO lines toward two positions in M 82, namely toward the nucleus and toward the so called SW molecular hotspot at an offset of (Mauersberger & Henkel 1991). The ratio (for the same beam size) of the (211 GHz) and the (140 GHz) lines is toward the nucleus, regarding the tentatively detected as contributing an upper limit only. Toward the SW hotspot, however, it is as high as 1.2(), or even , if we restrict the intensity from the line to the width of the slightly narrower transition. Thus, toward the nucleus, ; while densities are as high as toward the SW hotspot. This estimate is relatively robust to whether or not the H₂ CO lines are saturated.

Such density variations were already predicted from an analysis of centimeter wave transitions of ortho formaldehyde observed with lower angular resolution by Baan et al. (1990). While the 6 cm line shows a broad absorption (Graham et al. 1978) over the entire velocity range, the 2 cm line is seen in emission over a velocity range that hints toward an origin which is confined toward the southwestern part of the nuclear region. The 2 cm H₂ CO line is usually observed in absorption, even against the 2.7 K cosmic background. 2 cm emission requires H₂ densities exceeding 10 . This is in very good agreement with our results from millimetric lines toward the SW hotspot. Also the central concentration of , a molecular ion that is destroyed in a high density medium, indicates that the gas toward the central region has a much lower density than toward the SW hotspot (Mauersberger & Henkel 1991).

From the observed line intensity ratio of the and lines of , the o/p ratio toward the SW hotspot is (assuming ) , i.e. close to the high temperature limit. Note, however, that, as for NGC 253, this result may be affected by the uncertainty of the fit to the blended transition.

IC 342. This nearby ( Mpc; McCall 1989, Karachentsev & Tikhonov 1993) and nearly face-on spiral galaxy is very similar to the Milky Way galaxy with respect to the IR luminosity and the gas mass in its central region.

We have observed formaldehyde toward the nucleus (), where the velocity coverage and the line shapes of all transition are in excellent agreement, and toward one offset position, ), where the (tentative) transition seems to appear at a different velocity. The beam toward the () position also contains the molecular clump B (Downes et al. 1992), which is associated with free-free emission equivalent to 300 O5 stars or 30 times more than the emission from the Galactic center star forming region Sgr B2.

/ (211 GHz/150 GHz) line ratios indicate high densities of toward the position. The limit to the / (140 GHz/150 GHz) line ratio toward the nucleus of is also suggesting high densities, while the limit toward the () offset (, considering the tentative detection to be an upper limit, and regarding a common velocity interval for both lines), indicates a far lower density of . As in M 82, our two beams pick up contributions from two molecular phases, namely from a moderately dense interclump gas and from the clumps themselves. The presence of several molecular gas components has also been inferred by Downes et al. (1992) from the comparison of single dish and interferometric observations in CO.

Maffei 2. The ratios of the 150 and 140 GHz line, which agree very well in velocity coverage and line shape, indicate typical densities of the order of .

4.1.2.

Methanol is an asymmetric top molecule capable of hindered internal rotation. Transitions from A-type (internal rotation) to E-type (no internal rotation) levels are strictly forbidden; the two types behave as separate molecular species in the ISM. In addition, a and b -type transitions have to be distinguished according the component of the dipole moment that is is parallel to the axis of rotation. All transitions contributing to the and lines are a -type ( Debye), while the transition is b -type ( Debye) (Lees et al. 1973, Sastry et al. 1981; for a detailed discussion of the molecule, see e. g. Menten 1987).

An analysis of the group of transitions is difficult since the lines are blended. We have, however, carried out LVG calculations analogous to those for , using a program provided by C.M. Walmsley (see, e.g. Walmsley et al. 1988, Bachiller et al. 1995). We have modelled the intensity ratios of the sum of all transitions contributing to the group to the sum of the transitions and the ratio of the group to the line as a function of H₂ density and column density per unit linewidth (Fig. 5), for a kinetic temperature of 80 K. Clearly, for N () cm^-2 /km s^-1, the line ratios are independent of column density. Thus, the lines are very likely to be optically thin in all our sources. We have used the H₂ densities determined from Fig. 5 and the integrated intensities of the group of transitions to determine the column densities given in Table 4.

Fig. 5. Predicted intensity ratios of methanol lines for a raster of values for (in cm-3) and (in cm-2 /(km s-1). Solid contours: , dashed contours: . The assumed is 80 K.

NGC 253. The map we obtained in the transition toward NGC 253 (Fig. 3) shows the same general shape as maps in other high density tracing molecules like HNC (Hüttemeister et al. 1995) and CS (Mauersberger & Henkel 1989). The emission extends from the north-east to the south-west, with a (not deconvolved) full source size of , which is similar to the extent of intense ¹² CO(2-1) emission (Mauersberger et al. 1996a).

Therefore, it seems reasonable to correct the / and the / line ratios for the different beamsizes in the same way as for (Sect. 4.1.1), based on the Mauersberger et al. (1996a) data. The line intensities of the 3 mm lines then have to be multiplied by to make them directly comparable to the 2 mm lines. The linewidths of the two groups of transitions agree well. The resulting / ratio (0.8 0.15) implies a H₂ density of . The line is much narrower than the group. Since we are comparing a group of transitions spaced by to an unblended line, this is to be expected. However, it might not account for the entire difference. The ratio of the integrated intensities (6.8 2.4) thus is an upper limit, yielding a lower limit to the density of . If we consider only the velocity interval for the group where emission is present, this lower limit to the intensity ratio of 3.1 0.7 corresponds to a an upper limit to the H₂ density of (see Fig. 5). In any case, the values from the / and the / line ratios embrace the H₂ density estimated from . The critical density of the transition is smaller than the mean of the group by a factor of , while the difference is much less pronounced between the and the groups. This might explain the difference in the density estimates resulting from the two line intensity ratios.

At an H₂ density close to , both the and the groups of lines are subthermally excited ( ), with excitation tem- peratures for the individual transitions ranging from 10 K to 20 K. We thus obtain a value for N () which is lower by a factor of than what is determined under the assumption that the density is sufficiently high to thermalize the emission (Henkel et al. 1987).

M 82. The clear non-detection of any methanol line in M 82 is one of our most striking results. Henkel et al. (1987) searched for the transition in this galaxy and established an upper limit of 30 mK rms for this line. We obtained upper limits of 10-15 mK rms for the transition toward the central position and the north-eastern and south-western peak positions of the molecular ring.

Since no line ratios could be determined, we have used the LTE approximation for optically thin lines to estimate the total column density:

(: Energy of lower level, : line frequency in GHz, : dipole moment in Debye, S: linestrength; Menten et al. 1988).

Using Eq. 1, we have fitted all components of the group to the limit to the integrated intensity. For subthermally excited lines ( = 10 K), we find column densities ranging from smaller than 1 (SW hotspot) to less than 2 (center and NE hotspot), corresponding to an abundance of [ ]/ [ ] (see Table 4). If we assume that the H₂ densities are the same as the ones found for and apply our LVG model, the only change is a slight increase in the limit for N () to 2 in the dense SW hotspot (see Table 4).

IC 342. Within the blend, two groups of lines are separated by @ The group of 5 lines at higher frequency has generally higher energies than the lower frequency group. Because the lines in IC 342 are narrow, these two groups are resolved, and the higher energy transitions are below the detection limit. Thus, LTE fits to the group already greatly constrain the possible excitation conditions: has to be 10 K or lower. Since the kinetic temperature of the gas in IC 342 is likely to be at least 50 K (Ho et al. 1990), has to be very subthermally excited, with lower than for NGC 253.

The LVG calculations confirm this: For a (beam size corrected) / intensity ratio of 0.6( 0.1), observed toward the (0 5 ) position, we find an H₂ density of only ( = 80 K) to ( = 50 K) and excitation temperatures of K. This implies that is sensitive to interclump gas of only low to moderate density.

The beam-averaged column density we derive is 1.1 for a position slightly north of the center of IC 342, and half that for offsets to the south and further to the north (assuming the same low density), corresponding to an abundance of [ ]/ [ ] (Table 4). We note that the column densities given in Henkel et al. (1988), based on = 50 K and derived from the line, are far too high. A recalculation using = 8 K and Eq. 1(with and K) yields a total column density that agrees to within 10% with our result for the line, showing that the LTE and LVG approximations converge in this case. The limit given by the non-detection of the transition is also compatible with a total column density of .

Maffei 2 and NGC 6946. The / line ratios, corrected for beam size, imply H₂ densities of . It thus seems likely that the excitation of in both galaxies is similar to what is found in NGC 253.

4.2. Chemical variations

Molecular abundances. For most of the galaxies observed, the column densities of o-H₂ CO and CH₃ OH are comparable. This might also be the case for the M 82 SW hotspot, where we have only a limit for the CH₃ OH column density. The notable exception is the nucleus of M 82 where the column density of CH₃ OH is at least an order of magnitude lower than that of H₂ CO. It is quite clear that this is not just mimicked by excitation effects. Such a discrepancy between M 82 and other starburst galaxies, especially NGC 253, has already been noticed before (e.g. Mauersberger & Henkel 1993).

Evaporation from grain surfaces is in many cases a crucial process to maintain a high gas phase abundance of complex molecular species. Models predict that these molecules, such as CH₃ OH and also , are chemically converted into simpler species on a timescale of order 10⁵ years (Helmich 1996). Methanol evaporates at a temperature around 70 K (Turner 1989, Nakagawa 1990) and is known to be a tracer of hot, dense gas (Menten et al. 1988), since its abundance is observed to increase dramatically in the vicinity of young massive stars.

Formaldehyde, on the other hand, empirically shows far smaller abundance variations in Galactic interstellar clouds (Mangum and Wootten 1993) although it is 3-25 times more abundant in the Orion hot core than in other molecular clouds (Mangum et al. 1990). Contrary to CH₃ OH, H₂ CO is also abundant in cirrus clouds (Turner 1993) and cool, dense Galactic disk sources. It seems certain that processing on dust grains must play a role in the chemistry of , but the replenishment process is unclear (Federman & Allen 1991, Turner 1993, Liszt & Lucas 1995).

Takano et al. (1995) notice that all molecules that are known to be depleted in M 82 (besides CH₃ OH also SiO, HNCO, CH₃ CN and SO) form preferentially under high temperature conditions. In the presence of a steep gravitational potential and a central bar, we expect shocks and turbulence to play a significant role in the heating of molecular clouds distant from the actual sites of star formation (e.g. Hüttemeister et al. 1993, Das & Jog 1995). This can explain the high temperatures toward the central molecular condensation of NGC 253, which is much more compact than that of M 82, a smaller, irregular galaxy. Tidal heating should therefore operate less efficiently in M 82 than in larger spirals like NGC 253, NGC 6946 or IC 342. Thus, one would expect the bulk of the gas in the center of NGC 253 to be warmer than that toward the center of M 82 (with the exception of those clouds which are heated directly by newly formed stars).

The abundance of in NGC 253 does not seem to be exceptionally high when compared to NGC 6946 or non-starburst nuclei like Maffei 2 and IC 342. But we tentatively find that the gas traced by in NGC 253 is at a similar density as the gas traced by , while the gas traced by close to the nucleus of IC 342 is at a lower density. If temperature is indeed the key to the distribution of , we may conclude that the warm gas in IC 342 is less dense than in NGC 253. Since IC 342 is not a starburst galaxy, this agrees with the fact that warm gas in the center of our Galaxy is, in the absence of massive star formation, at lower densities than cooler gas (Hüttemeister et al. 1993), while the opposite is expected for active star forming regions. NGC 253 might be lacking the high temperature, low density interclump gas component picked up by in IC342; the bulk of the molecular material in NGC 253 is warm, at least moderately dense gas. In this scheme, M 82 has a cooler interclump component, seen in and N₂ H (Mauersberger & Henkel 1991), but not in .

Extended methanol emission in NGC 253. While the general shape of the central molecular condensation seen in and other molecules is similar, in a detailed comparison differences are apparent. The maps of total integrated intensity in ¹² CO(2-1), CS and HNC all show only one central peak. Only when the red- and blueshifted emission is displayed separately, two distinct peaks, separated by , become visible, with the redshifted emission centered toward the south-west. The map (Fig. 3) shows these two peaks even for the total velocity range. The positions of the peaks agree to within better than with the 'red' and 'blue' peaks seen in the other molecules. From the channel maps, the blueshifted emission is strongest at 200 and the red-shifted emission peaks at 300 @ In addition, there is a third peak, visible in the intensity and channel maps, at an offset of (-25 ,-10 ), at an even higher velocity of 350 - 450 @

Only the interferometric ¹² CO(1-0) map obtained by Canzian et al. (1988) with a beam also shows two resolved peaks (at the same positions as the peaks) when the total velocity range is considered. Thus, the single dish data match the interferometric data not only more closely than the single dish ¹² CO data, but also better than single dish maps of other high density tracers, namely CS and HNC. Since the interferometer misses extended emission, we can conclude that traces a more confined gas component than CS or HNC. Since the critical densities of @ ), CS(2-1) and HNC(1-0) are roughly similar at , the dif- ferences in spatial distribution seem to be caused by chemical fractionation rather than gas density. Since production of is favored in high temperatures, the differences in distribution may reflect differences in gas temperatures within the generally at least moderately dense gas in the bulge of NGC 253, with preferentially tracing the sites of ongoing massive star formation.

© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998
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