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Astron. Astrophys. 342, 233-256 (1999)

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3. Observational results

3.1. SCUBA submillimetre continuum observations

Four field centres were mosaiced together at 850 and 450 µm, and one field centre which covered the three main fingers was observed at 750 and 350 µm. The final images are shown in Fig. 1.

[FIGURE] Fig. 1. a  Comparison of the SCUBA images at 850 and 450 [FORMULA]m, convolved to an effective resolution of [FORMULA], with the HST H[FORMULA] image from Hester et al. (1996) and the integrated CO J= 3-2 map (Sect. 3.2 of this paper), b  greyscale images of the raw images at the four scuba wavebands. This greyscale representation is shown to emphasise the strong cores relative to the weaker material in the fingers

The fluxes obtained with SCUBA at the main peaks, and their photometric errors (in units of Janskys) are listed in Table 2.


[TABLE]

Table 2. Photometry at the submm peaks (all fluxes in Janskys per beam, position offsets are in [FORMULA]


The errors quoted in the table are 1[FORMULA] photometric uncertainties, which are useful for assessing the signal to noise ratio. However, a more conservative estimate of the flux uncertainties based on observations of the planets and secondary calibrators, plus experience of making observations at these wavelengths is typically 2[FORMULA] [FORMULA] 5-7% at 850 µm, 10% at 750 µm, less than 5% at 1350 and 2000 µm, and 25% at 450 and 350 µm.

The 450 µm map, with an effective resolution of [FORMULA] FWHM, is shown in Fig. 2, overlaid onto the HST image of Hester et al. (1996), and the JCMT CO J = 3-2 (discussed in Sect. 3.2), ISOCAM and VLA (discussed in Sect. 3.5) images of the area which are reported in this paper. The stellar positions measured by Tucholke et al. (1986) and Hillenbrand et al. (1993) were used to solve for the HST and ISO astrometric reference frames.

[FIGURE] Fig. 2a-d. The SCUBA 450 [FORMULA]m map shown as contours, overlaid onto a  the HST H[FORMULA] image of Hester et al. (1996), b  the CO J = 3-2 integrated emission, c  the ISOCAM 6.7 [FORMULA]m image, and d  the 8.7 GHz image. The contour levels on the 450 [FORMULA]m map are 5, 10, 20, 30, 40, 50, 60, 70 and 80 mJy per beam. The lower part of the SCUBA map is omitted from panels a  and b , but included in the lower panels . M16 E31 is a bright IR source seen in the ISOCAM images of Pilbratt et al. (1998), and M16 HH1 is an Herbig-Haro object.

The H[FORMULA] and CO overlays in Fig. 2 show that the 450 µm peaks in several of the fingers are displaced back [FORMULA] from the ionised rims of the cloud (Fig. 2a), and that they lie between the molecular hot spots and the photoionised cloud edges (Fig. 2b). However, the ISOCAM overlay (Fig. 2c) shows a more complex situation, where the submm peak in [FORMULA] is co-incident with the brightest 6.7 µm emission, but in [FORMULA] the peak lies about [FORMULA] further into the finger, away from the bright rim. The VLA overlay (Fig. 2d) is also difficult to interpret: at the head of [FORMULA], the submm peak lies back into the finger relative to the radio free-free emission, whilst in [FORMULA], the submm peak coincides with a bright spot on an apparently limb-brightened finger. The VLA emission is more extended that the ionised gas traced in the H[FORMULA] image, probably because the radio emission is less affected by the extinction seen in the optical image. Thus the VLA data should trace the front and rear surfaces of the finger providing a complete census of the ionised gas.

In order to measure the mm and submillimetre spectral regions accessible to the JCMT, measurements were made using the photometric pixels of SCUBA, at the positions of the strongest submillimetre continuum peaks. The resultant spectra are shown in Fig. 3, along with greybody spectra fitted using the relationship:

[EQUATION]

where [FORMULA] is the dust temperature, [FORMULA] is dust opacity per unit mass column density, [FORMULA] is the Planck function, [FORMULA] is the volume mass density - assumed in this case to be constant, [FORMULA] is the radius of the emitting region, d is the distance to the Eagle Nebula (André & Montmerle 1994). Photometric measurements were also added from the ISOCAM data, and several points at 60 and 100 µm were estimated from the High Resolution IRAS Galaxy Atlas (IGA-IPAC 1997). These IRAS points should be treated with caution, since the region is confused at the [FORMULA] resolution of the image processed IGA maps; hence the IGA data are only useful to set upper limits to constrain the model fits.

[FIGURE] Fig. 3. Submillimetre wavelength spectra of five peaks in the Eagle Nebula from the 450 [FORMULA]m map shown in Fig. 2. The error bars represent the conservative 2[FORMULA] flux uncertainty. The fitted greybody curves were constrained by adopting the molecular masses (Sect. 3.2), and fitting the temperature and emissivity as free parameters, as described in the text. The IRAS points in the centre right frame are conservative estimates taken from the IRAS IGA survey. Since they involve assumptions about the sizes of the emitting region (which we assume to be the same those estimated from the SCUBA data), and are taken with a large beam ([FORMULA] FWHM) in a confused region, they are used only to constrain the fluxes.

To make these fits, the core masses were constrained to those estimated from the C18O observations (see Sect. 3.2), leaving the emissivity, [FORMULA], and temperature as free parameters. Initial attempts to fit both the absolute values of the fluxes and the spectral energy distribution were made by assuming that the value of [FORMULA] = 1.5. However, this was found to underestimate the flux from the cores in the fingertips at the longest wavelengths by factors of 2-3. It did not appear possible to account for this discrepancy by either calibration errors or beamwidth variations (the data were convolved to the same resolution). We have also considered the possibility that line contamination could influence the estimated dust emissivity. However, as will be seen in Table 3 later, the lines that are detected are all relatively weak, and their integrated emission is insignificant compared to that of the dust continuum. The possibility of multiple dust populations with different grain temperatures remains, although there is no a priori reason to assume this in the low temperature material. Finally, it is unlikely that free-free emission is responsible for the long-wavelength excess, as will be discussed in Sect. 3.5. Choosing [FORMULA] = 1.1-1.2 resulted in significantly better fits to the data than values of 1.5-2.0, which are often adopted for modelling the properties of clouds (White & Sandell 1995). The most likely conclusion is that to model the submm spectra from the finger tip cores, a relatively low value for the dust emissivity, [FORMULA] needs to be adopted. Such low values of [FORMULA] are possible for coagulated grains or for larger than average grains with thin icy mantles (Mathis & Whiffen 1989, Chandler et al. 1995). Low values of [FORMULA] have also been reported towards a few other protostellar cores (Ward-Thompson et al. 1995, Chandler et al. 1995, and Eiroa et al. 1998), and in circumstellar discs (Beckwith & Sargent 1991). The key result of this modelling is that the submillimetre peaks in the tips of the fingers are constrained to have relatively low dust temperatures [FORMULA] 10-20 K. The temperatures of the cores in the fingertips therefore appear to be cooler than both the surrounding warm gas layer ([FORMULA] 60 K) (discussed in Sects. 3 and 4), and the outer shell of hot (250-320 K) material reported from the ISOCAM observations (Pilbratt et al. 1998). These low core temperatures are consistent with our thermal and chemical modelling of a finger, which will be developed in Sect. 4 of this paper. It will be shown that coupled with the higher external temperatures and pressures at the edges of the fingers, the consequence will be that the cores in the tips of the fingers will shortly, or have just started to enter a phase of pressure-driven collapse.


[TABLE]

Table 3. Gaussian fit line parameters for [FORMULA]and [FORMULA]


The highest resolution SCUBA image at 350 µm was deconvolved from the beam (measured from observations of Mars and Uranus) using the standard Richardson-Lucy technique. The resultant image presented in Fig. 4 shows that several of the cores appear to be elongated along the fingers, with their major axes pointing towards the tops of the fingers. Elongated cores of this kind have previously been reported in the cores of cometary globules (White et al. 1997).

[FIGURE] Fig. 4. Richardson-Lucy deconvolution of the 350 [FORMULA]m map. The intensity scale is arbitrary, but linear. The beam profile was estimated by deconvolving maps of the beam which were obtained by scanning the planetary discs of Mars and Uranus, which had diameters of 4.1 and [FORMULA] respectively. The adopted beam profile was then used to deconvolve the Eagle Nebula map. The key feature is that these deconvolved images model the sizes of the cores at the tips of the fingers, and show that the two uppermost fingers are marginally elongated along the fingers. Simulations of data with a similar s/n ratio as the real data suggest that the effective resolution of the deconvolved beam for the cores is [FORMULA] to first order, although it is in fact dependent on the intensity at a given point in the raw data.

The cores of the submillimetre peak at the tips of [FORMULA] and [FORMULA] can be modelled as [FORMULA] FWHM gaussian shaped cores, whose major axes are elongated along the parent fingers. This is equivalent to a linear size of 4.2 [FORMULA] 6.0 1017 cm.

The submm data can also be used to estimate the column and volume densities of the material in the cores. Concentrating on [FORMULA], because it appears to be a simpler structure than [FORMULA], the gaussian core has a size [FORMULA] (determined from the maps, and confirmed by the Richardson-Lucy deconvolution). From the modelling above, the submm spectra of the cores are calculated by assuming a mass of 31 [FORMULA] (this is consistent with the mass derived from the molecular emission, as will be discussed in Sect. 3.2). Assuming that the density is constant in the core leads to a first order estimate for the volume density of [FORMULA] [FORMULA] 2.0 105 cm-3, based on the submm size. This is very close to the value that has been independently reported by Pound (1998).

As a check, the dust mass, and by assuming a dust to gas ratio, the total [FORMULA] mass, can be estimated using the standard relationship:

[EQUATION]

where D is the distance to the source, [FORMULA] is the dust temperature estimated from the previous fits, [FORMULA]([FORMULA]) is the dust opacity (mass absorption coefficient per gram of dust), and [FORMULA] is the gas-to-dust mass ratio. Assuming optically thin emission at 850 µm, we adopt [FORMULA]([FORMULA]) = 1.7 cm2 g -1 and [FORMULA] = 1.1 for coagulated dust grains with thin ice mantles for reasons discussed earlier. Assuming a standard dust-to-gas ratio of 150 (Launhardt et al. 1997), and the temperatures estimated from the greybody fits, the lower limits to the mass and particle density in the compact core of [FORMULA] are [FORMULA] 19 [FORMULA] and [FORMULA] [FORMULA] 1.5 105 cm-3 respectively. The agreement of these estimates points to a relatively cold, compact, massive core, whose parameters based on the submm continuum data agree to within a factor of 2 with values inferred from observations of the molecular emission (see Sect. 3.2).

3.2. CO mapping observations

The peak and integrated intensity maps in the CO J = 3-2 line are shown in Fig. 5.

[FIGURE] Fig. 5. a  CO J = 3-2 peak intensity map overlaid on the HST composite image of Hester et al. (1996). The lowest contour is at T mb = 6 K, and the contour intervals are at 6 K intervals, b  CO J = 3-2 integrated intensity map integrated from 18-30 km s-1. The lowest contour is at [FORMULA] = 17 K km s-1, and the contour intervals are at 23 K km s-1 intervals. The ionising stars that illuminate the fingers lie about 2 pc [FORMULA] to the NW.

Three narrow fingers of molecular emission extend diagonally across the map, and coincide with the dark regions seen in the HST images of Hester et al. (1996). The CO J = 3-2 lines are extremely bright in these fingers, reaching [FORMULA] values of [FORMULA] 60 K in [FORMULA] and [FORMULA]. Although this is a relatively hot CO line source, there is as yet no evidence, e.g. from near-infrared observations, that high-mass star-formation has currently started inside the fingers. There is one bright near-infrared source located [FORMULA] E of Walker 367 - the bright star visible on Fig. 5a between [FORMULA] and [FORMULA] - which lies near a minimum in the CO map (also labelled as M16E31 on Fig. 2c).

In each of the three main fingers, the integrated CO emission (Fig. 5b) appears clumpy and fragmented, although the gross structure is resolved by the JCMT beam. Although the integrated map has similarities to the peak temperature map (Fig. 5a), close inspection shows that the integrated CO peaks at the tips of [FORMULA] and [FORMULA] both lie closer to the optical rims than to the positions where the temperature peaks. The lines are all relatively narrow; no compelling evidence was seen anywhere in the mapped region for a discrete molecular outflow source (to the rms noise level of [FORMULA] [FORMULA] 0.5 K). Thus despite a plethora of evidence suggesting there are a number of regions which have recently undergone star-formation in the vicinity, there is no obvious sign of a prominent high-velocity molecular outflow source within the area covered by the CO map.

Spectra of the CO J = 3-2 line are shown in Fig. 6.

[FIGURE] Fig. 6. Overlay of CO J = 3-2 spectra on the HST H[FORMULA] image of Hester et al. (1996). The velocity range of the spectra extends from 20 to 35 km s-1, and the temperature units range in [FORMULA] units from -6 to 70 K.

The linewidths across the CO J = 3-2 map are typically in the range 3-5 km s-1, and are mostly single peaked. Towards the base of [FORMULA], the lineshapes are often asymmetrical; probably as a consequence of blending of the emission from [FORMULA]and [FORMULA]. The fingers appear to overlap each other on optical images, with [FORMULA] in the foreground (based on the apparently higher optical extinction to the nebular emission than shown by [FORMULA]). The velocity structure can be more clearly seen in the CO J = 3-2 channel maps integrated over 1 km s-1 intervals, which are displayed in Fig. 7.

[FIGURE] Fig. 7. CO J = 3-2 channel maps in 1 km s-1 intervals. The lowest contour is at [FORMULA] = 6 K km s-1, and the contour intervals are at 6 K km s-1 intervals.

Viewed in these channel maps, the fingers are made up of a series of clumps which overlap in velocity space. Emission from the gas associated with [FORMULA] extends over the velocity range 23-27 km s-1, whilst [FORMULA] and [FORMULA] are more prominent in the 20-24 km s-1 maps. The other molecular material seen towards the western edge of the map from [FORMULA]28-30 km s-1 is not clearly associated with the fingers, and may be physically unrelated gas lying along the line of sight. This range of velocities is similar to that shown in the CO, HI and H II observations reported by Mufson et al. (1981).

Each of the three main fingers was examined for evidence of any systematic velocity gradient, by making position-velocity maps along them, as shown in Fig. 8.

[FIGURE] Fig. 8. Position velocity maps in the CO J = 3-2 transition along the major axis of the three fingers. These plots were made by rotating the map 42.2 degrees in an anti-clockwise direction, then integrating along the major axis of the fingers, with a [FORMULA] slit centred on the axis of the finger. The tips of the fingers appear on the right hand side of these plots.

There is evidence for a systematic large-scale velocity gradient of [FORMULA] 1.7 km s-1pc- 1 along the whole length of [FORMULA], although such a trend is not clearly discernible along the other fingers. Similar velocity gradients have been reported from cometary globules, where the morphology is strongly influenced by the external radiation field (Schneps et al. 1980, White et al. 1997).

The optical appearance of [FORMULA] suggests that it is overlapped at its base by [FORMULA] This may lead to the complex velocity structure seen in the CO data, where the peak velocity varies from 21-25 km s-1 over a small distance. Consequently, any systematic trends in [FORMULA] over small distances may therefore be masked by the clumpy nature of this particular finger. The velocity shifts of up to [FORMULA]21 km s- 1 pc-1 claimed by Pound (1998) to trace material flowing along the front and back of the fingers are confirmed by our data. However, because of the difficulty of unambiguously showing that these velocity shifts are due to a coherent velocity field , that they trace such large gradients as have been claimed must remain a subject of speculation.

Observations were taken in the C18OJ = 2-1 and 3-2 lines which should allow column densities to be estimated, and hence the mass of molecular material to be inferred. The C18O J = 3-2 map is shown in Fig. 9.

[FIGURE] Fig. 9. C18O J = 3-2 integrated and peak intensity maps integrated over the velocity interval 20-28 km s-1. The lowest contour level shown on the integrated map is at 2.3 K km s-1, and the contour are spaced at 2.3 K km s-1 intervals. On the peak map the first contour has a value of 2.3 K, and the contours are spaced at 1.15 K intervals.

The C18O map is very clumpy and shows several condensed structures, particularly close to the tips of the fingers. This suggests that most of the column density (and mass) resides in small clumps or cores close to the fingertips. The peak C18O J = 3-2 main beam brightness temperatures reach [FORMULA] 12 K at the tip of [FORMULA], and range from [FORMULA] 2-8 K over the rest of the Finger structures. The linewidths are typically [FORMULA] 2 km s-1 over most of the map, i.e. about half that seen in CO. One striking difference between the CO and C18O distributions is the intense CO peak at offset (+5, +35). This is one of the most intense peaks in the CO map, yet is virtually absent in the C18O map, suggesting that the gas at this point is relativelyhot, but with a low column density.

Spectra in several CO lines and transitions taken at the tip of [FORMULA] are shown in Fig. 10, along with spectra of several other lines:

[FIGURE] Fig. 10. Spectra towards the core at the tip of [FORMULA]. For presentation purposes, the intensities of various lines have been scaled as indicated on the figure: thus CS J = 2-1 * 10 means that the line intensity is shown at 10 times its true value. The velocity component at 29 km s-1 may be unrelated line of sight material. It is clearly seen that the J = 1-0 CO and isotopomeric transitions appear weak relative to the other CO lines (note the factor of two difference in the scaling between the J = 1-0 lines and the other transitions).

The intensities (in main beam brightness temperature units - uncorrected for the source brightness distribution) and linewidths of several other lines detected towards the cores at the tips of [FORMULA] and [FORMULA] are listed in Table 3 (with the exception of the CO lines which are complex):

The CO and C18O J = 3-2 data were used to estimate the temperatures and column densities, and to infer the masses of the fingers following the techniques discussed in White & Sandell (1995). For this estimate, the abundance [C18O]/[H 2] was assumed to be 1.6 10-7. The total H 2 mass contained within the area covering the C 18O map is [FORMULA] 200 [FORMULA], of which 95, 56 and 14 [FORMULA] are contained in [FORMULA], [FORMULA] and [FORMULA] respectively. The remaining mass ([FORMULA] 35 [FORMULA]) is associated with the ridge in the southeast corner of the map. Most of the mass of [FORMULA], [FORMULA] and [FORMULA] is located in their tips, which contain [FORMULA] 60, 30 and 10 [FORMULA] respectively. Thus 63, 54 and 71% of the total masses of [FORMULA], [FORMULA] and [FORMULA] are concentrated into their tips. It is notable that the masses derived from the JCMT data are only about half of those estimated by Pound (1998). To examine this further, spectra and maps were taken in the CO, 13CO and C18O J = 1-0, 13CO and C18O J = 2-1 and the 13CO and C18 O J = 3-2 lines using the OSO 20 m, FCRAO 14 m and JCMT telescopes. An analysis of the data from these telescopes give very similar results for the J = 1-0 isotopomeric lines: i.e. that they are considerably weaker than might have been predicted, based on their more intense J = 2-1 and 3-2 counterparts. Despite attempts to model these ratios using an LVG code, the J = 1-0 lines are just consistently low by factors of 2-3. We believe that the J = 1-0 line and isotopes may suffer considerably from depletion onto the cold ([FORMULA] 20 K) dusty material in the cores. However, the higher excitation lines trace somewhat warmer gas, where the depletion is less effective. We therefore believe that the estimates of the cloud mass and the opacity using CO J = 1-0 line and isotope opacities may be affected by CO fractionation or by depletion onto the cold ([FORMULA] 20 K) grains in the core. These observational results and consequences are similar to the conclusions of Hogerheijde (1998), and coupled with isotopic fractionation, have major ramifications for the use of theJ = 1-0 transitions in estimating cloud masses. We note the problem, and defer further discussion until more quantitative modelling can be performed. We therefore will concentrate on using the J= 2-1 and 3-2 13CO and C18O lines as the more reliable estimator of column densities.

To summarise, the various maps obtained above are all consistent with the masses we have reported above, and appear to be factors of 2-3 times less than those estimated by Pound (1998). Further discussion of the molecular and dust masses of material in the Eagle Nebula fingers will be deferred to a subsequent paper (Deane et al. in prep) which will examine the excitation conditions in more detail than is relevant in this paper.

It is of interest to compare the masses in these tips with their virial masses. An estimate of the ratio of the clump masses to the virial masses is given by the relationship:

[EQUATION]

This ratio has values of 0.55, 0.97 and 0.6 respectively in the three tips of the fingers, so that each of the tip clumps appear to be close to gravitational stability, given the inherent uncertainties in this simple estimate. A more realistic estimate of the stability of the clumps, which considers surface pressure and the support of internal magnetic fields will be given in Sect. 6. It should be noted at this stage that there is no compelling evidence for the rapid gravitational collapse of the cores in the tips of the fingers. As will also be discussed later (Sect. 4.3), it is likely that the CO line emission comes predominantly from a hot sheath of gas close to the surfaces of the fingers. In this scenario the C18O lines trace cooler material inside the fingers: the consequences of this will be an increase of the gravitational potential energy of the cores.

Assuming that the clumps at the fingertips are symmetric, their volume densities, n (H 2), are [FORMULA] 2.3 105 and 2.0 105cm -3 respectively for [FORMULA] and [FORMULA], compared with nearby material in the fingers where n (H 2) [FORMULA] 3-5 104cm-3. It therefore appears that the clumps at the tips are already relatively centrally condensed, and should have free-fall times [FORMULA] 105 years.

3.3. HCO+ observations

As discussed earlier, the HST pictures show that material at the edges of the fingers is strongly photo-ionised. Consequently observations were made in the molecular ion HCO+ in the J = 4-3 line, shown in Fig. 11, to compare with the other molecular data.

[FIGURE] Fig. 11. HCO+ J = 4-3 integrated and peak and intensity maps over the range 20-28 km s-1. The lowest contour on the the integrated map is at 2 K km s-1, and the contour intervals are at 2 K km s-1 intervals, and on the peak map is [FORMULA] = 1.0 K, and the contour intervals are at 0.75 K intervals.

The HCO+ map has a very similar shape to that of the C18O map, suggesting that the two species are well mixed, and trace the material in the same regions. This contrasts with observations of HCO+ towards other sources by Gibb & Little (1998) and Hogerheijde (1998), who suggest that HCO+ may be a better tracer of a protostellar envelope than C18O - clearly conditions in the two sources are rather different - in the Eagle Nebula, both C18O and HCO+ track each other fairly closely, and there does not appear to be strong evidence for a relative spatial abundance variation, such as that which might be a result of strong C 18O depletion onto grains. The HCO+ line intensities are also relatively high, approaching [FORMULA] [FORMULA] 10 K at the tip of [FORMULA], and 7 K and 4 K at the tips of [FORMULA] and [FORMULA]. The column density of HCO+ was calculated from the relationship for theJ = 4-3 transition:

[EQUATION]

These column densities were then used with the CO and C18O data to estimate the various abundances (where the H 2 column density is estimated from the C18O data as described earlier) - the results are summarised, along with those estimated for CI in the next section, in Table 4:


[TABLE]

Table 4. Column densities and abundances at the finger tips


3.4. CI observations

A map made in the CI 3P 1-3P 0 line is shown in Fig. 12.

[FIGURE] Fig. 12. Top  13CO J=3 - 2 integrated emission over the range 20-28 km s-1. The lowest contour on the map is [FORMULA] = 10 K km s-1, and the contour intervals are at 10 K km s-1 intervals. C I 3P 1-3P 0 integrated intensity map over the range 20-28 km s-1. The lowest contour on the map is [FORMULA] = 3.3 K km s-1, and the contour intervals are at 3.3 K km s-1 intervals. Note that the tip of [FORMULA] lies just off the bottom right hand edge of this map.

The line temperatures, linewidths and integrated emission were measured at each point within the CO, C18O and CI data cubes, after convolving the CO and CI data to have the same spatial resolution as the C18O data. These data were then used to estimate the CI and CO column densities over the mapped region using standard methods for estimating column densities summarised in White & Padman (1991), White & Sandell (1995) and White et al. (1995). The variation of the CI and CO column abundances has been used in the past to probe the photodissociated outer edges of molecular clouds. The CI abundance relative to CO, [C I] / [CO], is shown in Fig. 13.

[FIGURE] Fig. 13. Plot showing the [CI]/[CO] abundance variations in the mapped area. Note that both axes are logarithmic.

There is a clear tendency for the [CI]/[CO] values to increase in regions where the column density is less - with the ratio increasing from [FORMULA] 0.02 in the highest column density material, to [FORMULA] 0.1 in the lowest. This is similar to the trend noted towards other molecular clouds (Keene 1987, White & Sandell 1995, White et al. 1995, Minchin et al. 1995) which has been interpreted as evidence for an increasing [C I/CO] abundance ratio at their UV exposed edges.

3.5. Radio continuum observations

During the analysis of the submillimetre continuum data, the relatively high fluxes at the longer wavelengths (compared to a single temperature greybody fit) led to speculation as to whether the longer mm wavelength excess (over blackbody emission) was due to free-free emission. To check this, data obtained with the VLA (Balser et al. 1995) were examined, to extend the spectral coverage into the radio spectrum. Although there is no information on the radio spectral index of the emission, it is highly likely that it traces the optically thin free-free emission from ionised gas at the surfaces of the fingers. The VLA map is shown as a contour map in Fig. 14 (see Fig. 2 for a grey-scale representation).

[FIGURE] Fig. 14. Contour map of the free-free emission measured at 8.69 GHz with the VLA in the D array configuration (see Fig. 2d) for a greyscale representation). The contours are at 1, 2, 4, 6 [FORMULA] 18 mJy / beam.

The VLA map shows [FORMULA] and [FORMULA] very clearly, as well as an indication of emission from [FORMULA]. The most intense radio emission comes from the tip of [FORMULA], where the distribution resembles the structure seen in the ISOCAM and optical data. The radio emission from [FORMULA] shows evidence for limb-brightening along both sides of the finger (seen as the two peaks close to the tip of [FORMULA] in Fig. 14, but more clearly seen on the greyscale representation in Fig. 2d)), but any such limb-brightening is less prominent towards [FORMULA]. In addition to emission from the fingers, radio emission can also be seen from the ridge several arc minutes SE of the fingers. This is visible in both the CO and SCUBA data, and contains the Herbig-Haro object HH 216. Integrating the free-free emission from the fingers we estimate the integrated and peak fluxes from [FORMULA], [FORMULA] and [FORMULA] as 123, 48 and 6 mJy, and 17, 7 and 5 mJy/beam respectively.

It is widely accepted that the UV radiation and winds from OB stars can affect the structure, dynamics and evolution of the edges of molecular clouds on which they impinge. The dominant processes include interaction with the expanding Strömgren spheres around the stars, photoevaporation, or disruption by shocks resulting from an overpressure of the hot ionised outer parts of clouds, on their lower pressure interiors - leading to a shock wave driving in towards the core. The structure of these regions is affected by the clumpy distribution of molecular cloud material, which can allow UV photons to penetrate deeply into the edges of clouds.

As UV radiation falls onto the outer layers of clouds, the low-density gas at the surfaces is photo-evaporated. The ionised material will flow outwards where the density gradient is largest. This often leads to the appearance of `rays' or striations emanating from the cloud surface. As this lower density material becomes photo-evaporated, dense clumps of gas deeper inside the cloud become exposed. Examples of this can be seen along the edges of the Eagle's fingers, many of which have EGG's close to their tips. Thus these are primordial clumps inside the cloud, whose presence is revealed as surrounding low-density material is removed. The surfaces of these primordial clumps themselves become photo-ionised, and may themselves be the sites of future star-formation.

As shown by Oort & Spitzer (1955), and subsequently developed by Bertoldi & McKee (1990), Lefloch & Lazareff (1994) and Megeath & Wilson (1997), an equilibrium is rapidly set up in which photo-ionised material streams off the surface of an UV irradiated clump. Some fraction of the hydrogen atoms recombine, self-shielding the neutral gas from the ionising radiation. A small fraction of the ionising photons do however manage to penetrate through to the neutral gas and to ionise material at the base of the flow. Megeath & Wilson (1997) show that the ratio of the total ionising flux to that which penetrates to a depth where it can ionise the neutral gas, q , is given by the relationship:

[EQUATION]

where S is the Lyman photon production rate of the illuminating stars, which are located at a distance R away from a spherical clump of radius r , where [FORMULA] is the recombination coefficient and [FORMULA] is the sound speed in the ionised gas. Using values appropriate to the Eagle Nebula, q [FORMULA] 50. Thus, assuming that the radio emission is produced within the photo-evaporating flow, the measured recombination rate should provide a good check on the rate of ionising photons incident on the surfaces of the fingers.

Following the work of Bertoldi (1989), Lefloch & Lazareff (1994) and Lefloch et al. (1997), the flux, [FORMULA], at 8.69 GHz is related to the total ionising flux [FORMULA] (cm-2 s-1) by the relationship:

[EQUATION]

where [FORMULA] is the electron temperature (which is adopted to be 6000 K (Balser et al. 1995)), and [FORMULA] is the solid angle of the emitting region. Similarly, the electron density n e cm-2, will be given by:

[EQUATION]

wheret is the thickness of the shell of ionised gas and electrons which surrounds the photo-ionised cloud (we adopt t [FORMULA] 6 1016 cm, based on the discussion by Lefloch et al. (1997)).

Using these relationships we estimate [FORMULA] [FORMULA] 5 1010, 2 10 10 and 9 109 cm-2 s-1 for [FORMULA], [FORMULA] and [FORMULA] respectively, and electron densities of [FORMULA] 500, 320 and 100 cm-3 respectively. The ionising flux estimated from the radio observations can be compared to the photon flux expected from the ionising stars. Hester et al. (1996) suggest that the ionising flux is dominated by a single O3.5 star and three O5.5 stars located 2 pc away, which together provide a total photon flux [FORMULA] 2 1050 s-1. This would correspond to an ionising flux at the surface of the pillars of [FORMULA] 1.5 1011 photons s-1 cm-2. The photon rate with energies from 6 and 13.6 eV (the spectral range where most of the ionisation occurs) is then estimated from stellar atmosphere models. Using a Kurucz model (Kurucz 1979), the fraction of UV photons with energies in the appropriate range (6-13.6 eV ) is [FORMULA] 35% of the total photon flux, which then leads to a value of G [FORMULA] 1700 G 0 [ G 0 is the `standard FUV interstellar radiation field' taken from Habing (1968)] . Thus the effective ionising flux at the surface of the fingers is [FORMULA] 1.75 1010 photons s-1 cm-2, which is close to that inferred above from the VLA data. Also, it is easy to show from the VLA data that the electron densities exceed the critical density of [FORMULA] 25 cm-3, above which an ionised shell should develop around a neutral cloud (see Lefloch & Lazareff 1994).

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Online publication: December 22, 1998
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