Astron. Astrophys. 338, 262-272 (1998)

3. Results and analysis

3.1. The C⁺ line intensity and the C⁺ to FIR flux ratio

The distribution of the [CII] 158 µm emission is shown in Fig. 3 as a greyscale plot, overlaid on contours of a ¹²CO J=32 line integrated map, obtained with the KOSMA 3m telescope (Schneider et al. 1998). The two data sets match well in angular resolution, with 55" for the FIR and 70" for the CO data. The settings of the 55 pixel arrays of FIFI, together with a box labeling are also displayed. Due to considerable baseline problems, we decided to reject Arrays 6 and 13 for the data analysis.

Fig. 3. Top: A contour plot of the velocity integrated (4-24 km s-1) 12CO J=32 intensity (obtained with the KOSMA 3m telescope) is overlaid to a grey scale plot of the 158 µm [CII] emission. Each square marks one setting of the 55 pixel FIFI array. The region observed with IRAM (Monoceros Ridge) and displayed in Fig. 5 is indicated. Bottom:  The integrated 12CO J=32 intensity as a grey scale plot together with a numbering of the FIFI-arrays. The contour levels start at the 3-level (4.8 K km s-1) and end at 273 in steps of 3. The locations of IR sources are indicated by triangles. The direction of the UV flux of the central stellar cluster NGC 2244 is shown by arrows.

The peak C⁺ intensity is 510^-4 erg s^{- 1} cm^-2 sr^-1 which is about three times the noise level for one pixel. These intensities are found in the interface region between molecular cloud and HII region at the `Monoceros Ridge' (Array 11), in Array 5, and at the position of the IR source IR06314+0427 (Array 3). The C⁺ emission in the RMC is weak, compared to sources observed at similar angular resolution in which the C⁺ intensity is typically a factor 10 stronger (e.g. M17, Stutzki et al. 1988; Orion B, Jaffe et al. 1994; Orion A, Herrmann et al. 1997). The emission level in the RMC is thus comparable to that of the Galactic large-scale [CII] survey at approximately 4´ angular resolution, obtained with the Japanese Balloon-Borne Infrared Telescope (BIRT, Shibai et al. 1991), which is a few 10^-4 erg s^{- 1} cm^-2 sr^-1. During the same observing run with FIFI, the PDR region of the S140/L1204 complex reveals an equally weak C⁺ intensity of around 410^-4 erg s^{- 1} cm^-2 sr^-1 (Schneider et al. 1995). The total luminosity of the [CII] 158 µm line in the Galaxy is 5.410⁷ L (Wright et al. 1991) and 2.810⁷ L in the inner Galactic disk (Shibai et al. 1991), so that the few very bright PDR regions like e.g. M17, Orion A etc., which emit a few thousand L in this line, can not account for the overall Galatic C⁺ emission. Numerous lower density and UV intensity PDR regions contribute significantly to the observed C⁺ luminosity.

Though the C⁺ intensity in each pixel is weak, by positionally averaging the data of one array we confirm that the C⁺ line is significantly detected in every array except No. 17 at or above the 3-level (see Table 1). The absolute intensities range between 0.7 and 2.710^-4 erg s^{- 1} sr^-1 cm^-2 and the average value is 1.710^-4 erg s^{- 1} sr^-1 cm^-2. The total intensity by summing over all arrays is 2.610^-3 erg s^{- 1} sr^-1 cm^-2, which is equivalent to a total flux of 3.6510^-8 erg s^{- 1} cm^-2 or 2900 L, considering a distance of 1.6 kpc. From the IRAS 60 µm and 100 µm maps, analyzed by Cox et al. (1990), we adapt a lower limit for the FIR luminosity of 2.710⁵ L, averaged across the observed region. We then obtain a higher limit for the flux ratio / of approximately 1% which is in accordance, but on the high end, with values of 0.1% to 1% for other active star forming regions in the Galaxy and extragalactic nuclei (Howe et al. 1991, Stacey et al. 1991). The average value for the Galaxy is 0.3% (Stacey et al. 1985, Shibai et al. 1991, Wright et al. 1991). The comparatively high value of 1% for the Rosette cloud indicates a large efficiency of grain photoelectrical heating which might be due to the low incident UV field. Bakes & Tielens (1994) theoretically modeled the photoelectrical heating mechanism for a wide range of parameters by considering small grains (100 Å) and give an analytical expression for the heating efficiency for gas temperatures T [K] lower than 10⁴ K:

with the far-UV field in units of the Habing field and the electron density [cm^-3]. A low incident UV field, as it is found in Rosette (see Sect. 3.2), will lead to a low ionization rate so that the fraction of neutral particles increase and therefore the heating efficiency. This is not valid for larger grains (100 Å) which absorb half of the UV photons and contribute not significantly to the heating. Comparison with other Galactic PDRs shows that a source with an equally high ratio / of 1% is NGC 1977 (Howe et al. 1991) which has an UV flux of only a few Hundret at the edge of the molecular cloud to the HII region.

3.2. The large scale C⁺ emission distribution and its correlation with UV flux

It is now generally accepted that the [CII] 158 µm fine structure line originates in Photon Dominated Regions (PDRs), created by FUV radiation, on the surfaces of molecular clumps. The prominent PDRs studied so far are found in bright and massive molecular cloud complexes like Orion A (Stacey et al. 1991) or M17 (Stutzki et al. 1988, Meixner et al. 1992). A careful examination of Fig. 3 reveals that the C⁺ emitting gas in the Rosette cloud is intimately mixed with the clumpy molecular material, traced by the ¹²CO J=32 line. Good examples of a close morphological correspondence between the structures visible in the different maps are the regions with the highest signal-to-noise ratio (Array 3, 11 and 12). Some of the remaining areas seem to lack a direct morphological correlation which may be due to the low S/N-ratio. We emphasize, however, that the 2-dimensional projection of the complex 3-dimensional cloud structure, together with the expected stratification of the C⁺/CO transition layer on the clump surfaces, leads to a merging of foreground and background structures viewed at many different inclinations.

In order to model the FUV flux from the central OB cluster NGC 2244 into the molecular cloud, we assume that the UV radiation gets blocked by the clumps. We then estimate an attenuated average flux F within the molecular cloud by following the arguments of Stutzki et al. (1988). The flux decreases with 1/ where R equals the distance to the OB cluster. In addition, proceeding into the molecular cloud, the UV flux gets blocked by the dense clumps and is redistributed in angle due to dust scattering. With representing the radius of the HII region (15 pc), the clump volume filling factor and the diameter of the clumps, we thus get:

The Lyman continuum luminosity L is taken from Cox et al. (1990) with a value of L=12.310⁵ L. The clump volume filling factor is estimated by the ratio of hydrogen density to critical density (/). From CO J=10 data obtained by Blitz & Thaddeus (1980) we adapted an average diameter =1.3 pc for the molecular clumps, and an average hydrogen density of =580 cm^-3. With =2.910³ cm^-3 we thus obtain =0.15. Together, this implies a flux variation from about at the molecular cloud/HII region interface at 15 pc (30´) distance from the central OB cluster, down to a few to in the remote part of the cloud, approximatley 30 pc (60´) away.

An independent confirmation of these values is to use the color temperature derived from the IRAS 60 µm to 100 µm intensity ratio I(60µm)/I(100µm) and apply it to the model of Hollenbach et al. (1991) in which becomes a function of . From Cox et al. (1990), we get a ratio I(60µm)/I(100µm) of around 0.3 at the molecular cloud/HII region interface down to 0.23 in the remote part of the cloud (at the same distances given above). This implies dust color temperatures of 30 K and 26 K for an assumed dust emissivity law of . By using Fig. 19 in Hollenbach et al. (1991) in which I(60µm)/I(100µm) is given as a function of , we obtain a UV flux of at the interface and in the remote part of the cloud. The flux at the interface agrees very well with our result whereas the value for the flux in the remote cloud is higher. However, the authors point out that the observational agreement for regions with low flux () is poor which might be due to the restriction of the standard low-density PDR model used, with a one-dimensional slab illuminated from one side.

Fig. 4 shows the calculated flux (using our model with blocking by clumps) on a logarithmic scale together with ¹²CO and ¹³CO J=21 and C⁺ line intensities along two cuts at constant Galactic latitude. Both cuts reflect the positional variation of the line integrated intensities, starting in the HII region and crossing the interface region into the molecular cloud core.

Fig. 4. Middle: Within a map of the integrated KOSMA 12CO J=21 intensity, the FIFI arrays of C+ emission are indicated along two cuts at constant galactic latitude ( and ). The triangles mark the positions of IR sources. Top and bottom: The line integrated 12CO and 13CO J=21 and C+ intensities are displayed along the two cuts. The C+ intensities are determined by averaging five data points at constant longitude. The error bars at for boff=0´ and for b are representative for all C+ data. The grey line roughly indicates the HII region/molecular cloud border, the continuous line shows the logarithmic decrease of the UV flux and the dashed line the best fit to the decrease of the C+ intensities, leaving out the local peak at IR06314+0427.

The lower cut at b covers the interface region between molecular cloud and HII region at the Monoceros Ridge. The bend in the line, describing the UV flux, coincides with the location of the ionization front. Towards the molecular cloud, there is a sharp increase of CO and C⁺ intensity within a region of about 2 pc linear extent. The IRAM ¹³CO J=21 observations confirm the general run of the KOSMA CO and the C⁺ intensity. However, small scale variations of the IRAM data which does not match the C⁺ emission are due to the different angular resolutions (12" for the IRAM and 55" for the C⁺ observations) and the low S/N-ratio of the C⁺ data. Further into the cloud, the C⁺ emission rapidly decreases. The last datapoint at l has a C⁺ intensity of about 10^-4 erg s^-1 cm^{- 2} sr^-1.

In the upper cut at b_off=0´, the C⁺ and CO emission peak at the location of the IR source IR06314+0427. Apart from this local peak which is due to the UV illumination of a small star cluster (see Sect. 3.3), the C⁺ emission gradually drops from the interface region into the molecular cloud (as long as the local peak at IR06314+0427 is ignored). The dashed line approximates this smooth decrease of (1.10.1)10^-5 erg s^{- 1} cm^-2 sr^-1 / pc. The line runs nearly parallel to the line describing the attenuation of the UV flux. This behaviour is in accordance with the models of Hollenbach et al. (1991) as discussed in Wolfire et al. (1989) in which the C⁺ intensity scales logarithmicially with the UV flux F, provided that F is lower than and that the condition holds. In this parameter space, self-shielding of H₂ and CO becomes important and moves the transition zone closer to the clump surface and therewith lowers the C⁺ column density. As a consequence, the C⁺ intensity () decreases and the C⁺/CO line ratio drops. This is what we observe in the Rosette Cloud: close to the HII region at the Monoceros Ridge, is 600-700 whereas further into the cloud (in a distance of approx. 10 pc from the Ridge) the ratio is 200-300. This finding contrasts to higher density and UV flux regions in which the relation is valid: A constant C⁺ to ¹²CO J=10 ratio of 4400 was found by Crawford et al. (1985) in Galactic and extragalactic sources. Jaffe et al. (1994) derived a ratio of 1300 from their observations of NGC 2024. In these regions, the C⁺ intensity scales roughly with (Howe et al. 1991) and is rather insensitive to the UV flux.

3.3. The small scale C⁺ emission distribution

As presented in Sect. 3.1 and 3.2, we find direct evidence for the penetration of UV radiation from the NGC 2244 OB cluster deep into the adjacent molecular cloud. Though the 158 µm [CII] line emission is generally rather weak, the regions with stronger C⁺ emission are correlated with molecular clumps, traced in the ¹²CO J=32 line. We will now discuss these two regions, the `Monoceros Ridge' and the central part of the cloud, and the detection of C⁺ emission deep in the molecular cloud.

C⁺ emission at the Monoceros Ridge

The Monoceros Ridge region is composed of clumpy molecular gas (Schneider et al. 1998) and marks the border between the HII region and molecular cloud and extends diagonally between Array 6 and 16. This region gives a good example for the strong morphological correlation between C⁺ emission, arising from the PDR's on the molecular clump surface, and CO emission from the interior of the clump. The peak intensity of the [CII] line in this interface region is of the order of 4.510^-4 erg s^{- 1} cm^-2 sr^-1 and is found in a clump containing the IR source IR06306+0437, directly facing the HII region. A recent IR-survey of Phelps & Lada (1997) indicates that IR06306+0437 most likely consists of several sources. The IR luminosity is 1222 L, determined by adding the IRAS flux densities in the 4 wavelengths bands of 12, 25, 60 and 100 µm. This value does not even account for a single star of spectral type B3 or B4 and in any case, the photon emission rate is too low to contribute to the observed strong C⁺ emission. Unfortunately, no data at wavelengths longer than 100 µm are available which might show a strong FIR-/submm-emission spectrum. Therefore, by considering the low IRAS flux value of the cluster, the emission must be ascribed to the PDR layers of the molecular clumps in this interface region, illuminated by NGC 2244. The UV flux at this distance to the OB cluster (17 pc in linear projection) is estimated to be around (see 3.2).

As an example for the C⁺ and CO correspondence at higher angular resolution, we show in Fig. 5 an overlay of the C⁺ emission as a grey scale and channel maps of the IRAM ¹³CO J=21 observations (Schneider et al. 1998) at 12" angular resolution as contours in the region containing Arrays 11 and 12. Because in these arrays the S/N-ratio of the data is rather high, the good small scale correlation of the [CII]- and CO-emission in the velocity range between 11 and 17 km s^-1 is significant. The C⁺ emitting regions are located on the edges of the molecular clumps, outlined by the CO emission, indicating the presence of UV illuminated PDRs on the surface of dense molecular clump. The main CO peak at around 15 km s^-1 is close to the position of the IRAS source (IR06306+0437) and marks a region of intense C⁺ emission. The morphologial correlation does not continue for higher velocities (19 km s^-1), in particular the clump at offsets , does not show up in C⁺. However, due to its high velocity it is presumably located in the background of the complex.

Fig. 5. A grey scale plot of the integrated [CII] 158 µm intensity is overlaid on a contour plot of the IRAM line integrated 13CO J=21 intensity (Levels 0.8 (3) to 14.6 by 2.3 K km s-1) with 12" angular resolution. The location of the IR source IR6306+437 is indicated by a triangle. The offsets are relative to the position , .

C⁺ emission at the cloud center

Another high intensity C⁺ emission region is the cloud center, coinciding with the location of the IR source IR06314+0427 (Array 3) and an extended CO clump. The strong C⁺ emission there can not be explained by the UV illumination of the central OB cluster NGC 2244 alone, the logarithmic decrease of the UV flux (see the cut at offset b=0´ in Fig. 4) leads to a linear decrease in C⁺ intensity. But the observed intensities are locally a factor of at least 1.5 higher. This suggests that the intense C⁺ emission in Array 3 is due to the interaction between a molecular clump core with the dissociating radiation from a single young star or a cluster of stars. This source was initially thought to be a single O7 star (Block 1990) but recent near-IR observations of Phelps & Lada (1997) revealed a small embedded cluster of stars though their spectral types are not known. Because no radio continuum data are available, we roughly estimate the extent of the PDR region created by the star cluster by assuming a photon emission rate S of about 7.210⁴⁸ s^-1 (Spitzer 1978) of an O7 star. We derived a Stromgren radius R of 0.29 pc (35") for a compact HII region around the star by using the relation R [pc] = 66.9 (/) from McKee, vanBuren & Lazareff (1984) with the photon rate in units of 10⁴⁹ s^-1 and the average hydrogen density n [cm^-3] with a value of 310³ cm^-3, derived from IRAM ¹³CO J=21 observations (Schneider et al. 1998).

Even if this source is a cluster of B stars and the photon emission rate decreased by a factor of 10, it would still be sufficient to support a compact HII region and create PDRs on the surface of the surrounding molecular clumps outside this region. This is confirmed by the KOSMA CO observations: The integrated ¹²CO J=32 line intensity (contour lines in Fig. 6) peaks at the position of maximum C⁺ emission (greyscale), both close to the location of the IR source. The IR position was taken from the point source catalog with an positional uncertainty of 25" in RA and 6" in DEC and a position angle of .

Fig. 6. A grey scale plot of the integrated [CII] 158 µm intensity is overlaid on a contour plot of the KOSMA line integrated 12CO J=32 intensity (Levels 45 to 110 by 5 K km s-1). The location of the IR source IR06314+0427 is indicated by a triangle. This is an enlargement of the region around array 3.

C⁺ emission in the remote molecular cloud

The arrays 1 and 2 are located deep in the molecular cloud where the UV flux already decreased to about (Array 2) down to a few (Array 1). Accordingly, the observed C⁺ intensities are low, with an average value of 1.3 and 1.110^-4 erg s^{- 1} cm^-2 sr^-1 for Array 1 and 2, which is just above the noise level (S/N-ratios are 3 and 4). The weak C⁺ emission in Array 1 indicates that the proximity of the strong IR source AFGL 961 nearby does not influence the excitation of the C⁺ line. The near-IR survey of Phelps & Lada (1997) revealed that AFGL 961 consists of a number of embedded bright sources though it seems not contain a luminous O and/or B star, providing enough UV flux for creating a PDR region with a C⁺ emitting layer.

Therefore, the observed C⁺ emission is consistent with the picture that only the UV radiation from the central cluster of the Rosette nebula, NGC 2244, is responsible for the UV illumination of the molecular cloud. Due to the clumpiness, the radiation can leak deep into the cloud and create PDRs on the surfaces of individual clumps, giving rise to the observed C⁺ emission. In a homogeneous molecular cloud, the UV flux is too rapidly attenuated in order to account for the observed C⁺ emission deep in the cloud interior. From CO observations (Schneider 1995), we obtain an H₂-column density of 1.410²² cm^-2 from the ionization front to the remote cloud in a distance of 30 pc. This corresponds to a visual extinction of A_v=14^m for a homogeneous cloud which contrasts to the typical thickness of 3^m for the C⁺-emitting layer in a PDR in the models of Hollenbach et al. (1991).

From PDR models (see Sect. 4) we derive a density of n=10⁴ to 10⁵ cm^-3 in the clumps whereas the average density is 300 cm³ (obtained by ¹³CO J=21 maps at 2´ angular resolution from Schneider et al. 1998), resulting in a density contrast of 30-300. A similar value is evaluated by using CO J=10 data obtained by Blitz & Thaddeus (1980). They derived an average H₂-density of 50 cm^-3 and because Blitz (1991) argued that 10-50% of the column density arises from the interclump gas this gives an average density of 5-25 cm^-3 for the interclump medium. Taking the critical density of the CO 10 transition as the local clump density (10³ cm^-3) gives again a high density contrast of 40-200 between dense molecular clumps and low density interclump gas. A more detailed analysis of the nature of the interclump gas and the high density clumps is found in Schneider et al. (1996).

© European Southern Observatory (ESO) 1998

Online publication: September 8, 1998
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