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Astron. Astrophys. 325, 124-134 (1997)

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4. Cold dust in NGC 5907

4.1. Observational results

A contour map of the [FORMULA] 1.2 mm continuum emission, overlaid onto an optical image extracted from the Digitized Sky Survey, is shown in Fig. 4. This [FORMULA] 1.2 mm-map is already smoothed to a beamsize of [FORMULA] to improve the signal-to-noise ratio.

[FIGURE] Fig. 4. Contour map of the continuum emission of NGC 5907 at 245 GHz, overlaid onto an optical image extracted from the Digitized Sky Survey. The beam size of [FORMULA] is indicated by the filled white circle in the lower right corner. The rms noise depends on the location in the map; on the galaxy it is about 1.5 mJy/beam area, contour levels are 4, 8, ..., 24 mJy/beam area. The thin black lines indicate the [FORMULA] centre and the major axis of the galaxy as given in Table 1

The emission is concentrated along a narrow ridge which follows closely the dusty optical disk, but is less extended, perhaps because of the sensitivity limit of our data. Although the emission is enhanced near the centre, there is no evidence for a nuclear point source. Several local maxima are visible along the major axis, but with some difference between the northern and the southern half. Whereas in the north there are three separate peaks at projected radii of about [FORMULA], [FORMULA], and [FORMULA], they seem to be somehow smeared out in the southern half, except the one at [FORMULA].

In Fig. 5 we show the [FORMULA] 1.2 mm continuum map, smoothed to a resolution of [FORMULA] HPBW, together with an HI total intensity map as received from Sancisi (priv. comm.), and the positions observed in the CO lines. NGC 5907 is a really exemplary galaxy for the existence of galactic warps in neutral hydrogen (Sancisi 1976). It is, moreover, the first "normal" galaxy where a warp in the outer disk was observed. But in contrast to NGC 4565, another normal edge-on galaxy recently observed at [FORMULA] 1.2 mm (Neininger et al. 1996), no indication for a warp of the thermal dust emission can be seen (although the northernmost peak seems to be slightly shifted westwards with respect to the major axis). This may of course be due to the decreasing sensitivity at the outer edges of our dust map, which we reach at radii of [FORMULA], where the HI-warp is only marginally detected.

[FIGURE] Fig. 5. Contour maps of the [FORMULA] continuum emission (left) and the HI line emission (middle), as well as positions observed in the CO lines (right), all at the same scale and aligned in declination. The spatial resolution of the two maps is [FORMULA]. Contour levels are 3, 7, 12, 18, 25, 33 mJy/beam area for the [FORMULA] map and 8, 15, 25, 40, 55, 70 [FORMULA] for the HI map

4.2. ISM distributions along the major axis

Fig. 6 shows the distribution of the [FORMULA] 1.2 mm continuum emission along the major axis, together with the line intensities of the [FORMULA] and the HI emission. The spatial resolution of all three data sets is [FORMULA], as given by the [FORMULA] data.

[FIGURE] Fig. 6. The distribution of the [FORMULA] (thick dashed line, left scale) and the [FORMULA] 1.2 mm continuum (thick solid line, right scale) along the major axis of NGC 5907. The HI distribution (thin solid line, arbitrary units) is also shown. The spatial resolution in all three curves is [FORMULA]

The continuum emission shows (more clearly in this plot than in the maps) the existence of two bright maxima at the end of the emission ridge ([FORMULA]) and of two less pronounced ones at [FORMULA], even if the southeastern one seems to be smeared out. Besides these similarities between the northern and the southern half the distribution is slightly asymmetric on smaller scales. The emission is detected up to radii of [FORMULA] in the south and even further, up to [FORMULA], in the northern half (with a significance of [FORMULA]). Since there is [FORMULA] 1.2 mm continuum emission beyond the edge of the CO disk, dust associated with the atomic component makes a significant contribution to the 1.2 mm flux.

The distribution of the CO line-intensities (and therefore the column densities of the molecular gas) shows also a maximum in the central region and decreases with increasing distance from the centre. Two further maxima are apparent at [FORMULA]. These features may be due to molecular rings and/or spiral arms in the inner part of the disk.

The HI distribution shows a different behaviour. It has a minimum near the centre, increases at [FORMULA], stays then roughly constant with several local peaks up to [FORMULA], and drops again further outwards. Hence this component is much more extended than the molecular gas in this galaxy.

If we compare the dust emission with both gas phases, we find that it correlates with the molecular gas in the inner part of the disk. At large radii, on the other hand, where CO is no longer detected, it seems to follow the HI emission. This result confirms qualitatively that for NGC 4565 of Neininger et al. (1996). At smaller scales, we find the two outer peaks in the dust emission at [FORMULA] corresponding to local maxima in the HI distribution, although there is a small displacement, especially on the southeastern side. From both CO peaks at [FORMULA] only the northwestern one has a clear counterpart in the dust distribution, whereas in the southeastern half the dust emission shows just a small enhancement at this radius.

4.3. Disk thickness

García-Burillo et al. (1997) estimated from their Plateau de Bure observations of the central region of NGC 5907 an inclination of [FORMULA] and a thickness of the molecular disk of [FORMULA]. In order to check if this is in agreement with our observations, we fitted the observed z -distribution (the averaged spectra are shown in Fig. 7) with a Gaussian profile. Using the beamwidths given in Sect. 2.1 we determined a deconvolved thickness (FWHM) of the CO emission ridge of [FORMULA], somewhat thicker than in NGC 4565 (Neininger et al. 1996). Additional off-axis observations at [FORMULA] have shown that this apparent thickness is nearly constant along the major axis.

[FIGURE] Fig. 7. Averaged [FORMULA] and [FORMULA] spectra of the cuts through the centre. The portion of the spectra shown in each box ranges from [FORMULA] to [FORMULA] and from [FORMULA] to [FORMULA]

In order to estimate the extent of the atomic gas and the thermal dust emission perpendicular to the plane, we performed cuts along the minor axis of both maps. These lead to a mean beam deconvolved FWHM of the emission of [FORMULA] for the HI and [FORMULA] for the [FORMULA] emission.

Since the galaxy is not perfectly seen edge-on, but under an inclination of [FORMULA], a particular fraction of the off-axis emission is just projected from large radii to large z. We modelled this emission, using the radial CO profile obtained in Sect. 3.2 and a similar model, consisting of three rings, for the HI emission. The best agreement between model and data is found for a disk with a thickness (FWHM) of [FORMULA] (which corresponds to [FORMULA]) for the CO and of [FORMULA] ([FORMULA]) for the HI. Both values seem to be unexpectedly large for a non-interacting spiral with only moderate star forming activity.

We should note, however, that it is difficult to account for a warp in this simple modelling, and the results are very sensitive to the exact values of the inclination and the telescope beamwidth. Therefore, due to the large uncertainties, a thin molecular disk cannot be ruled out.

4.4. Dust properties

4.4.1. Non-dust contributions to the observed flux

Using a ring integration method, we have determined the total flux density at [FORMULA] and found [FORMULA]. This value, however, cannot be attributed to thermal dust radiation alone. The broad band emission measured with the bolometer at 245 GHz rather consists of several components: thermal dust emission, free-free radiation, synchrotron radiation, and the [FORMULA] and some weaker lines. Since we are mainly interested in the first, we have to determine the contributions due to the other processes and to subtract them.

The contribution of the [FORMULA] line to the surface brightness measured with the bolometer can be calculated through

[EQUATION]

(with [FORMULA] in Kkms-1) for a bolometer bandwidth of 70 GHz and a beamwidth of [FORMULA] for the continuum observations. With an assumed contribution of other isotopes and lines from other molecules of about 10 % of [FORMULA] we estimate a total flux density due to line contributions of [FORMULA] mJy.

The contribution of the continuum emission due to thermal and relativistic electrons is more difficult to determine since the radio continuum flux density at [FORMULA] originates partly in a double background source in the southern half of the galaxy (Hummel et al. 1984; Dumke et al. 1995). Furthermore the spectral behaviour of this background source is unknown, and the fraction of the galaxies' thermal emission is difficult to estimate. We used a total flux density of [FORMULA] mJy at a frequency of 10.55 GHz as derived by Dumke et al. (1995), a thermal fraction of 30 % at this frequency and a nonthermal spectral index of -0.85 which are typical for spiral galaxies (Niklas et al. 1997) to calculate a value of [FORMULA] mJy at 245 GHz, which is about 2 % of the total flux density.

Besides these integrated values, we had to estimate the non-dust contributions along the major axis. The fraction of the CO lines, i.e. the line-to-continuum ratio, was calculated for each position from the [FORMULA] line following Eq. 1 and subtracted. Again we assumed that a fraction of 10 % of the [FORMULA] -line stems from other lines in the bolometer band. For the free-free and synchrotron emission, we subtracted a fraction of 2 % at each position, in accordance with the value estimated above.

4.4.2. Dust temperatures

After subtracting the contributions of molecular lines and of synchrotron and free-free radiation, we determined a total flux density at 245 GHz due to thermal dust emission of

[EQUATION]

Including published IRAS flux densities (Young et al. 1989) our observations allow to estimate color temperatures for the dust. We fitted a two-component modified Planck function to the data, using the points from [FORMULA] to 1.2 mm and under the assumption of a dust spectral index of 2 (e.g. Chini et al. 1986).

The observed spectrum and the fitted curves (as well as their sum) are shown in Fig. 8. The estimated temperatures for the two components to which we refer as cold and warm dust are 18 K and 54 K respectively. This result shows that cold dust is necessary to explain the thermal continuum emission at [FORMULA] 1.2 mm. The warmer dust alone which can be detected in the far-infrared by IRAS is not sufficient to account for the strong mm-emission and to explain our data.

[FIGURE] Fig. 8. Total flux density spectrum of NGC 5907 fitted by a two-component model. The data points represent IRAS flux densities (Young et al. 1989) and our bolometer observations. The dotted lines show the fitted spectra for the individual temperature components, the solid line the sum of them

Although NGC 5907 is a relatively inactive galaxy which does not show any signs of remarkable star forming activity (e.g. Dumke et al. 1995), the dust emission is slightly enhanced at smaller galactocentric radii, and the dust may be somewhat warmer in this region. The FIR emission of NGC 5907 was mapped by Wainscoat et al. (1987), using the IRAS CPC instrument, at [FORMULA] 50 and 100 µm with a resolution of [FORMULA] and [FORMULA] respectively. These maps were used to obtain spectra at different positions along the major axis of NGC 5907. We found that the temperature of the cold dust is somewhat higher in the central region ([FORMULA]) than the value we got from the integrated flux densities, and drops to [FORMULA] at the outer disk. A similar decrease is also found for other normal disk galaxies like NGC 891 (Guélin et al. 1993), NGC 4565 (Neininger et al. 1996), or our Milky Way (Cox & Mezger 1989).

4.4.3. Dust absorption cross sections

Once we have removed the contributions to the [FORMULA] 1.2 mm continuum emission which are not due to cold dust, we can estimate the dust absorption cross section per hydrogen atom.

The flux density per beam emitted by a cloud (molecular or atomic) is given by

[EQUATION]

with [FORMULA], where [FORMULA] is the dust absorption cross section per hydrogen atom and [FORMULA] the beam-averaged hydrogen column density. Since [FORMULA] at [FORMULA] 1.2 mm, and under the assumption that the thermal dust emission comes only from matter in the neutral gas, we can express the cross section by (see Mezger et al. 1990)

[EQUATION]

with [FORMULA] and [FORMULA].

In a first step we use this equation to estimate the cross-sections at radii where no molecular line emission is detected and we have to consider only the contribution from the atomic gas. The values for [FORMULA] are taken from the HI map shown in Fig. 5. For this calculation we use a dust temperature of [FORMULA] since this value seems to be most appropriate for radii larger than [FORMULA]. The result is

[EQUATION]

Taking into account the grain composition of the dust and the metallicity, we can use a formulation following Mezger et al. (1990),

[EQUATION]

[FORMULA] is the dust absorption cross section at [FORMULA] 1 mm following from the theoretical curves of Draine & Lee (1984), [FORMULA] the wavelength in mm, Z the metallicity, and b an empirically determined factor which accounts for the differences between Draine & Lee's grain mixtures and real grains. This parameter is adjusted to reproduce absorption cross section estimates in the FIR and is usually assumed to vary between 1 and 3. [FORMULA] applies to dust in the diffuse interstellar HI gas, and may also serve as a lower limit for molecular clouds. Other authors used [FORMULA] for dust embedded in molecular gas of moderate density. Recent measurements of Goldsmith et al. (1995) in nearby molecular clouds yield [FORMULA], and Pajot et al. (1986) came to a similar value. Therefore we use [FORMULA] for all calculations throughout this paper. In any case, the chosen value for b does not change our results qualitatively.

Since one expects [FORMULA] for diffuse HI clouds at a galactocentric radius of [FORMULA] in a Sc-galaxy, our value of [FORMULA] is very close to that predicted by Draine & Lee (1984). It is also in excellent agreement with the values estimated for other nearby spiral galaxies (e.g.  Neininger et al. 1996).

In a second step we use the absorption cross section [FORMULA] estimated above and calculate the dust emission which is due to particles embedded in atomic hydrogen along the whole major axis. Therefore we take this value as an average over the radii at which hydrogen exists mainly in form of HI. The resulting amount is subtracted from the dust emission (as it was done for the non-dust contributions before). What is left must be due to dust grains embedded in clouds of molecular hydrogen, and this can be used as described in the following paragraph.

4.5. The conversion factor X and its radial variation

We continue with a third step where we make use of the radial distribution of the CO intensity and the expected radial variation of the metallicity - and therefore the absorption cross section - to estimate the column densities of the molecular hydrogen and the conversion factor X at different radii.

We take the deprojected CO intensity distribution obtained in Sect. 3.2 and calculate the corresponding radial [FORMULA] distribution, using a conversion ratio which varies along the radius as [FORMULA] with [FORMULA] and [FORMULA] as free parameters which have to be fitted. This exponential behaviour of X with radius was found by other authors for our galaxy (e.g. Arimoto et al. 1996). With [FORMULA], we calculate the radial distribution of the dust emission using Eq. 3. In this calculation we assume a decrease of the dust temperature with radius from [FORMULA] K in the centre to [FORMULA] K at [FORMULA], and the shallow radial metallicity distribution

[EQUATION]

which is an average for Sc galaxies and follows from the results of Vila-Costas & Edmunds (1992). This radial intensity distribution is then projected along the major axis and compared to the observed distribution (minus non-dust and HI contributions) by a least-squares-fit with [FORMULA] and [FORMULA] (see above) as free parameters.

This fit, which is restricted to [FORMULA] ([FORMULA]) to yield a higher significance, leads to the following radial variation of the X -factor:

[EQUATION]

where [FORMULA].

The result is plotted in Fig. 9: The conversion factor is clearly below the "standard" value of [FORMULA] (Strong et al. 1988) in the whole radial range considered here. We find [FORMULA] starting from [FORMULA] in the centre and increasing with galactocentric radius by a factor of more than 2 up to [FORMULA], and in all probability even more further out.

[FIGURE] Fig. 9. Radial variation of the CO-H2 -conversion factor X in NGC 5907 as obtained from the bolometer data. The thick line shows the best fit, the different greyscales the range of possible solutions considering the uncertainties in the different input parameters. See text for details

This increase of X with galactocentric radius is also found for our galaxy by Sodroski et al. (1995), using recent DIRBE results from the COBE satellite. Arimoto et al. (1996) came to the same result for the Milky Way and nearby spirals, using a method based on CO intensities and virial cloud masses.

The mentioned errors contain the statistical uncertainties in the bolometer and the HI distributions ([FORMULA]), the dust temperature ([FORMULA]), the metallicity ([FORMULA]), and the radial CO distribution ([FORMULA] -model). The numerical error values in Eq. 6 are estimated by varying the single input parameters, keeping the other parameters fixed. In fact the range of possible solutions is a confidence ellipsoid in a multi-dimensional parameter space.

The variation of the conversion factor with radius obviously has some effect on the estimated amount of molecular gas in galaxies. Since usually most of the CO emission is detected at smaller galactocentric radii where the conversion factor is rather small, one easily overestimates the gas mass using the "standard" value for X. On the other hand there may be large amounts of molecular hydrogen in the outer parts of galactic disks where we detect only weak CO emission.

4.6. The gas content of NGC 5907

Using the CO-H2 -conversion ratio of Strong et al. (1988), [FORMULA], we found a molecular mass for the major axis strip of NGC 5907 of [FORMULA]. Assuming that the extent of the CO emission in z -direction, as measured with our cuts through the center, is constant along the major axis, we estimate a total molecular mass of [FORMULA]. As we have seen, the "real" X -value seems to be well below this standard value in the inner part of the galaxy, where the major fraction of CO emission is detected. Once we have an idea about the radial variation of the X -factor, we make use of the radial CO intensity as modelled in Sect. 3.2 to calculate the corresponding distribution of the column densities [FORMULA]. With this method we get a molecular mass on the major axis strip of [FORMULA]. which leads to a total value (for the whole galaxy) of [FORMULA].

The amount of atomic hydrogen can be estimated from an HI line flux of [FORMULA] (Huchtmeier & Richter 1989, and references cited therein) to [FORMULA]. Using these values we calculate a total hydrogen mass of [FORMULA].

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© European Southern Observatory (ESO) 1997

Online publication: May 5, 1998

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