3 Results

3.1 CO distribution

In both galaxies, there is a strong concentration of molecular material in the central region. The central source, although not dominating the total CO emission from the galaxy, is nevertheless a major feature compared with the minor peaks occurring in the disk (see the NGC 6946 CO maps by Casoli et al. 1990; Sauty et al. 1998, as well as the M 83 interferometer map by Rand et al. 1999). A similar impression is provided by the SCUBA 850 $\mu$m continuum map of NGC 6946 (Bianchi et al. 2000), although the continuum image of the central source in particular is seriously contaminated by J=3-2 CO line emission.

In NGC 6946, the strong central CO emission is highly structured, as revealed in the J=1-0 interferometer map by Regan $\&$ Vogel (1995), and also partly in our lower-resolution maps in Fig. 2, in particular in the J=3-2 map, which shows close resemblance to their J=1-0 map. The central region of NGC 6946 has very similar CO and optical morphologies (Regan $\&$ Vogel 1995, see also Ables 1971). The maps show strong centralized emission superposed on more extended emission of lower surface brightness. The overall extent of the central CO source in NGC 6946 is about $50''\times25''$. Most of the extended emission occurs roughly along the minor axis of the galaxy and appears to be due to enhanced CO emission from spiral arm segments (cf. Regan $\&$ Vogel 1995) out to about R = 1 kpc in the plane of the galaxy. In addition to these minor axis extensions, there are also extensions along the major axis, particularly in the ENE direction. The bright central peak is especially prominent in the J=4-3 CO and [CI] maps, its increased contrast in these maps being caused mainly by higher resolution and higher excitation (see below). The source extent of about 10'' in these maps is consistent with the J = 1-0 CO scale length $r_{\rm e} = 160$ pc derived by Sakamoto et al. (1999). This compact source has also been detected and mapped interferometrically in J=1-0 HCN (Helfer $\&$ Blitz 1997). Evidence for further, unresolved structure is provided by the central emission profiles in Fig. 1 and the major axis position-velocity maps in Fig. 4. They show a clear double-peaked structure in all transitions with a minimum at about $V_{\rm LSR}$ = +45 $\,{\rm {km\,s^{-1}}}$ suggesting a deficit of material (a "hole'') at the very center of NGC 6946. The position-velocity maps show a steep central velocity gradient, undiscernible from rapid solid-body rotation, with steepness apparently increasing with increasing J number. The significantly lesser steepness in e.g. the J=2-1 CO map is caused by beamsmearing. This is readily seen from a comparison of the J=4-3 CO (Fig. 4) and the high-resolution J=1-0 CO (Fig. 4 in Sakamoto et al. 1999) velocity gradients which are practically identical with dV/d $\theta = 35 \,{\rm {km\,s^{-1}}}/''$ (in the plane of the galaxy corresponding to dV/d $R \approx 2 \,{\rm {km\,s^{-1}}}$/pc). From this gradient and the velocity separation of the central profile peaks in Fig. 1, we estimate the size of the "hole'' in the disk to be of the order of 2'' (R = 25 pc). The steep rotation curve turns over to a much flatter one at a radius of about R = 200 pc.

The structure of the central CO source in M 83 is, at least with the presently available data, much simpler. A central peak resolved only at resolutions $\leq$15'' is superposed on a more extended ridge along the major axis seen in the J=3-2, J=2-1 and J=1-0 CO maps (Fig. 3; see also Handa et al. 1990) with dimensions $55''\times25''$. The ridge thus extends outwards to a radius of about R = 1 kpc, so that the overall sizes of the central CO source in M 83 and NGC 6946 are very similar. The ridge shows some structure, perhaps including two symmetrical secondary maxima each at about R = 325 pc from the nucleus. In the J=4-3 CO and [CI] maps (Fig. 3), the central peak is just resolved along the major axis, extending to a radius R = 135 pc from the nucleus. Along the minor axis, it is unresolved. As is the case with NGC 6946, the contrast of the peak with its surroundings is higher than that in lower J transitions, at least in part because of higher resolution. Compact, barely resolved emission from the peak is also seen in the J=1-0 HCN transition interferometrically mapped by Helfer $\&$ Blitz (1997). The central emission profiles (Fig. 1 bottom) of M 83 do not resemble those of NGC 6946. They are clearly non-gaussian, but instead of a double-peaked shape, they are perhaps best described as a slightly asymmetric blend of a broad and a narrow component.

The position-velocity maps in Fig. 5 are quite interesting. A compact component in very rapid solid-body rotation is shown superposed on more extended emission in much more sedate rotation. The effect of beamsmearing is particularly noticeable in the apparently much greater extent of the rapidly rotating component in the lower J maps (for J=1-0 CO, see Handa et al. 1990). From the J=4-3 CO map in Fig. 5, we find that the rapidly rotating disk is contained with R = 95 pc from the nucleus, and that it has a velocity gradient dV/d$\theta$ = 18 $\,{\rm {km\,s^{-1}}}$/'', corresponding to dV/dR = 2.7 $\,{\rm {km\,s^{-1}}}$/pc in the plane of the galaxy. The more extended material has a velocity gradient dV/d$\theta$ = 0.6 $\,{\rm {km\,s^{-1}}}$/'', corresponding to only dV/d $R = 85 \,{\rm {km\,s^{-1}}}$/kpc in the plane of the galaxy. The J=4-3 CO and [CI] maps suggest that the rapidly rotating material is a relatively thin disk. Our results do not provide any evidence for the presence of the small central hole that may be surmised from the aperture synthesis observations by Handa et al. (1994). The JCMT J=3-2, J=4-3 and [CI] maps published by Petitpas $\&$Wilson (1997) show a clear double-peaked structure, the peaks being separated by some 16''. Our J=3-2 and J=4-3 CO maps do not reproduce the structure seen by Petitpas $\&$ Wilson (1997). In particular they do not show the secondary peak which should occur at $\Delta \alpha, \Delta \delta = +4''$, -9'' in our maps; that position is not fully covered by either [CI] map. Signal-to-noise ratio considerations, the poor baselines encountered by Petitpas $\&$ Wilson (1997) in the their J=3-2 observations and the limited extent (about one beamwidth) of the secondary peak lead us to question its prominence and perhaps even its existence.

3.2 Line ratios

From our observations, we have determined the intensity ratio of the observed transitions at various positions in both galaxies. For convenience, we have normalized all intensities to that of the J=2-1 $\,{\rm ^{12}CO}$ line. All ¹²CO ratios given for individual positions refer to a beam of 21''; where necessary we convolved higher-resolution observations to this beamsize to obtain an accurate ratio not susceptible to varying degrees of beam dilution. Isotopic ¹²CO/¹³CO ratios are given for the resolutions listed in the Table. The individual positions include, in addition to the nuclear positions of both galaxies, an offset position in NGC 6946 representing the off-nucleus CO cloud complex discussed in Sect. 4.3, and two offset positions in M 83 on the major and minor axis respectively. The J=1-0/J=2-1 ratios have relatively large uncertainties, because we have used J=1-0 intensities estimated for a 21'' beam from the references given in the table. These ratios are, in any case, close to unity.

In contrast, the columns in Table 4 marked Total Center refer to the intensities integrated over total source extent as shown in the maps. At the lower frequencies, source extents are larger than at the higher frequencies. This is mostly caused by limited and frequency-dependent resolution. When corrected for finite beamwidth, source dimensions at e.g. the J=2-1 and J=4-3 transitions are very similar for NGC 6946 and the bright peak of M 83. Nevertheless, the smaller area coverage at the higher frequencies may lead to an underestimate of the intensities of the emission at these frequencies and consequently the corresponding line ratios especially if extended emission of relatively low surface brightness is present. The entries in Table 4 suggest that this may indeed be the case for J=4-3 CO and [CI].

We have converted the [CII] intensities measured by Crawford et al. (1985) and Stacey et al. (1991) to velocity-integrated temperatures. The line ratios given in Table 4 were obtained after convolving our J=2-1 CO results to the same beam solid angle of 8.6 10^-8 sr (HPBW 55'') that was used to measure the [CII].

It is quite remarkable that NGC 6946 and M 83 are extremely similar in all ratios (and indeed intensities), except for the [CII] intensity. From the observed CO transitions only it is easily but mistakenly concluded that the two galaxies have identical ISM properties in their center. As it is, the intensity of the [CII] line suggests a much stronger PDR effect in M 83 than in NGC 6946, implying the presence of both high gas temperatures and densities in the medium as the critical values for this transition are $T_{\rm kin} \geq$ 91 K and $n \geq 3500 \,{\rm cm^{-3}}$. At the same time, such values must be reconciled with the much lower temperatures and (column) densities implied by the modest CO isotopic ratios.