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Astron. Astrophys. 331, 669-696 (1998)

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4. Observational properties of the maps and line profiles

The structures observed in space and velocity are so intricately linked to one another that we discuss the maps and line profiles characteristics together. The three fields exhibit a broad variety of properties when they are studied in detail. However they share a common set of conspicuous properties which had never been observed so clearly before. In this paper, we focus on the analysis of these common properties.

4.1. Properties of the spatial and velocity distributions

The maps of integrated emission for the three fields and three isotopes (Fig. 2) reveal the marked differences in the structures traced by each isotope, in Polaris in particular. The differences are less pronounced in the L134A field. In Fig. 2 and all the others, the maps displayed are those of the [FORMULA] and [FORMULA] (J=2-1) lines smoothed to the resolution of the J=1-0 maps. The maps in the J=1-0 transitions of the same isotopes at this resolution are identical within the noise level.

[FIGURE] Fig. 2a-c. Maps of [FORMULA] (J=2-1), [FORMULA] (J=2-1) and [FORMULA] (J=1-0) integrated emission for a Polaris, b L1512 and c L134A. The transitions are indicated in the upper left corners. The linear scale, the resolution of the map and the velocity interval of the integration are shown. The intensity scales are different for each panel and are given in [FORMULA]. The offsets in arcsec are relative to the (0,0) positions, given in the caption of Fig. 1. The maps in Polaris are in galactic coordinates while the others in equatorial coordinates.

[FIGURE] Fig. 2. (continued) (c)

It is interesting to note that there is no visible unresolved structure in any of these maps of integrated emission. The smallest identified scales are, in Polaris, the thickness of the curved filament bright in [FORMULA] and [FORMULA] and in L1512, a few bright spots or filaments of comparable size. These structures are all resolved by the observations.

In the Polaris and L1512 fields, there are asymmetries in the gradients of line integrated intensities, although it is not clear at first sight how to relate them to the large scale environment of the fields. In L1512, the Galactic Plane lies [FORMULA] in the North-East of the field, and the associated anisotropy of the radiation field and radiation pressure is unlikely to be responsible for the extremely sharp Southern edge of the bright core, like in the case of cometary globules (Le Floch & Lazareff 1994, 1995). We have checked also that there is no nearby star brighter than G-type stars in the close environment of the core. In Polaris, the Flare is part of the North Celestial Pole loop which extends over several tens of degrees East of the field, but is not associated to any increase in the radiation field, as derived from the correlation between the far IR luminosity and HI column density at high galactic latitude (Boulanger & Pérault 1988).

The line profiles integrated over the whole fields (Fig. 3a) and those obtained at the (0,0) positions (Fig. 3b) show that, in the Polaris and L1512 fields, the velocity distributions of the [FORMULA] emission, on the one hand, and of the [FORMULA] and [FORMULA] emissions, on the other hand, are also markedly different. There are velocity intervals (relative to the width of the [FORMULA] lines) over which the rare isotopes emission is extremely weak or undetected although the [FORMULA] is strong. These velocity intervals are not symmetric relative to the line centroids and extend over [-2, -3 km s-1 ] in Polaris, [7.5, 8.2 km s-1 ] in L1512. L134A exhibits flat-topped and self-reversed profiles even in [FORMULA] and the [FORMULA] and [FORMULA] lines have comparable linewidths. The velocity interval over which [FORMULA] is not detected and [FORMULA] is still strong reduces to [1.5, 2 km s-1 ].

[FIGURE] Fig. 3a and b. a Line profiles integrated over the area of each field mapped in [FORMULA] and [FORMULA]. Top panels: the [FORMULA] (J=1-0) (thick), [FORMULA] (J=1-0) (thin) and [FORMULA] (J=1-0) (thinner) lines. Bottom panels: the [FORMULA] (J=2-1) (thick) and [FORMULA] (J=2-1) (thin) lines. The source names are indicated above each set of lines. b Line profiles obtained at the (0,0) position in each map. The display of the lines is the same as in a.

In the rest of the paper, we will distinguish the line-core emission from the line-wing emission: the former corresponds to velocity intervals where the [FORMULA] ([FORMULA])/ [FORMULA] ([FORMULA]) ratio, herafter R(12/13), is close to unity and the latter to velocity intervals where this ratio is larger than [FORMULA] 3 to 5, up to values [FORMULA] 20. Fig. 4 displays the spatial distribution of the line-core and line-wing [FORMULA] (J=1-0) emissions in the Polaris and L1512 fields, the two fields in which the line-wing component is clearly present. It illustrates the different morphologies of these two components: the gas which emits in the line-core and is bright in the rare isotopes has a rather smooth and extended spatial distribution while the gas which emits in the line-wing component and is barely visible in the rare isotopes has a more filamentary spatial distribution with more compact, almost unresolved, structures.

[FIGURE] Fig. 4. Spatial distribution of the [FORMULA] (J=1-0) line-core and line-wing emission in a Polaris and b L1512. The velocity intervals over which the emission is integrated are given in each case. Note that the intensity scales (in [FORMULA]) are different for the line-core and line-wing maps. The coordinates are the same as in Fig. 2.

These differences between the morphologies of the isotopic emissions are yet more visible in the velocity maps (Figs. 5 to 7). The texture of the [FORMULA] emission in the line-wing component is by far the most complex with disordered filamentary structures present over the whole fields of Polaris and L1512. Unlike in the maps of integrated emission, unresolved structures exist in the velocity maps, in the form of bright spots or filaments unresolved in one direction only. These velocity maps reveal an unexpected result: it is in the most opaque transitions, the [FORMULA] lines, and in the weaker component, the line-wing emission, that the largest amount of small scale structure has been found.

[FIGURE] Fig. 5a-c. Velocity maps of the Polaris field: a [FORMULA] (J=2-1), b [FORMULA] (J=2-1), c [FORMULA] (J=1-0). The velocity intervals are given at the top of each panel in km s-1. The linear size scale and the offsets in arcseconds appear only at the top left panel. The intensity scale, different for each map, is given in [FORMULA] at the right of each panel. The panels in extreme velocity intervals, where no line signal is detected, are therefore maps of the noise level in the given velocity intervals.

[FIGURE] Fig. 5. (continued) (b)

[FIGURE] Fig. 5. (continued) (c)

[FIGURE] Fig. 6a-c. Same as Fig5 for L1512.

[FIGURE] Fig. 6. (continued) (b)

[FIGURE] Fig. 6. (continued) (c)

[FIGURE] Fig. 7a-c. Same as Fig. 5 for L134A.

[FIGURE] Fig. 7. (continued) (b)

[FIGURE] Fig. 7. (continued) (c)

Velocity gradients and internal velocity dispersions are locally very large. The conspicuous [FORMULA] filaments observed in the Polaris field in the wing velocity intervals have diameters which do not exceed 0.03 pc (see Fig. 4a) but remain visible over 2 km s-1. In the L1512 [FORMULA] (J=1-0) velocity maps, a strong velocity gradient is visible across the filamentary structure in the North-East of the field. The transverse velocity shift of [FORMULA] 1 km s-1 over 0.06 pc corresponds to a gradient (or a rotational velocity) of 16 km s-1 pc-1. The arc visible in [FORMULA] in the Polaris field exhibits a longitudinal velocity gradient as large as [FORMULA] 10 km s-1 pc-1 at its Northern end. Whatever the origin of these gradients (rotation, infall or shear), they necessarily trace large accelerations of the gas at very small scales. Such large gradients and internal velocity dispersions have never been observed yet at small scale in non star-forming clouds.

4.2. Line profile properties: line smoothness and line ratios

The first property of relevance in the quantitative analysis to follow is the smoothness of the line profiles. The high signal-to-noise line profiles displayed in Figs. 3a and 3b exhibit a remarkable level of smoothness. Even when observed at high angular and spectral resolution, line profiles do not break up into many subprofiles, a point of importance already found by Langer et al. (1995) in their high angular and velocity resolution observations of molecular cloud cores in TMC1. This property is also illustrated in the maps of spectra obtained by integrating the emission over 1' [FORMULA] 1' fields (Figs. 8 to 10).

[FIGURE] Fig. 8. Map of [FORMULA] and [FORMULA] integrated spectra over 1' squares in Polaris. The temperature scale is [FORMULA] for the (J=1-0) lines (thick line) and is the same for the [FORMULA] and [FORMULA] isotopes. [FORMULA] (J=2-1) and [FORMULA] (J=2-1) profiles (thin lines) have been divided by the same factor R(2-1/1-0)=0.65. The coordinates of the individual 1' squares are given above each panel, in arc minutes.

[FIGURE] Fig. 9. Same as Fig. 8 for L1512

[FIGURE] Fig. 10. Same as Fig. 8 for L134A. Note that the arrangement of the 1' squares in the page is not that on the sky due to the elongation of the [FORMULA] map.

The second property, on which we rely below to infer characteristics of the spatial and velocity structure of the emitting gas, is the lack of systematic variations of the J=2-1 to J=1-0 line ratios, R(2-1/1-0), either across the line profiles or from one isotope to another or from one field to another. To illustrate this property, the [FORMULA] and [FORMULA] (J=2-1) line profiles in Figs. 8 to 10 have all been scaled up by the same factor 1/0.65. There are areas or velocity intervals where the J=1-0 and J=2-1 line profiles depart from one another, but on average the line ratio R(2-1/1-0) is remarkably uniform. 80% of the data points fall in the range R(2-1/1-0)=0.65 [FORMULA] 0.15 for [FORMULA] and [FORMULA], in the three fields, across the entire line profiles and for weak and strong lines, over a dynamical range in line intensity [FORMULA] 8. The scatter plots of Figs. 11 to 13 which display all the data at a common spatial resolution of 22" and a velocity resolution of 0.4 km s-1, illustrate this property.

[FIGURE] Fig. 11. Scatter plots of various pairs of temperatures in Polaris. Each point correspond to the [FORMULA] temperature within a resolution element of 0.4 km s-1. The scatter plots are performed on maps smoothed to the same angular resolution, 22". The noise level is provided by the size of the clouds of points around null temperatures.

[FIGURE] Fig. 12. Same as Fig. 11 for L1512.

[FIGURE] Fig. 13. Same as Fig. 11 for L134A.

The third set of properties is disclosed in the [FORMULA] vs. [FORMULA] and [FORMULA] vs. [FORMULA] scatter plots (Figs. 11 to 13). They have the same characteristics in the three fields, namely:
(i) the R(12/13) temperature ratios are small compared to the corresponding isotopic abundance ratios. They reach down to unity in all the fields and increase only up to 20, 10 and 14 for Polaris, L1512 and L134A respectively, well below the range of isotopic abundance ratio in the Solar Neighborhood, 40 [FORMULA] [ [FORMULA] ]/[ [FORMULA] ] [FORMULA] 70 (Langer et al. 1984). This is also true, but to a lesser extent, for most of the [FORMULA] and [FORMULA] lines for which the [FORMULA] ([FORMULA])/ [FORMULA] ([FORMULA]) ratios, hereafter R(13/18), are much smaller, for most data points, than the observed range of isotopic abundance ratios 5.5 [FORMULA] [ [FORMULA] ]/[ [FORMULA] ] [FORMULA] 7 (Frerking et al. 1982). R(13/18) reaches 2 in Polaris and L1512 and 1.5 in L134A. The largest observed values are [FORMULA] in the three fields (Figs. 11 to 13). Note that, despite the large apparent optical depths, suggested by the low isotopic line ratios, the line profiles of the brightest lines are neither flat-topped nor self-reversed, except for L134A (Figs. 9 to 11).
(ii) in the [FORMULA] versus [FORMULA] scatter plots of Polaris and L1512, the value R(12/13) [FORMULA] 3 to 5 adopted in the previous section to distinguish the line-core from the line-wing emissions also corresponds to a separation (see Figs. 12 and 13) between the gas for which R(2-1/1-0) [FORMULA] 0.6, and stays remarkably constant down to the lowest line intensities, and that for which R(2-1/1-0) is larger and increases with the line temperature up to R(2-1/1-0) [FORMULA] 0.8. In L134A, the rise of R(2-1/1-0) with [FORMULA] for the line core emission is replaced by a decrease of R(2-1/1-0) with [FORMULA], presumably because self-absorption in the J=2-1 lines is more pronounced than in the J=1-0 lines.

Some of the above line properties (i.e. the constancy of the R(2-1/1-0) ratio in quiescent regions and the line smoothness) have been known before, although never seen as clearly as in the present data sample. These spectral characteristics are shared by many (if not all) non star-forming clouds studied so far. The constancy of the [FORMULA] (2-1/1-0) line ratio, like that of [FORMULA] (3-2/2-1) (Falgarone et al. 1991), seems to be quite a general result in clouds of low average column density, i.e. less than a few 1021 [FORMULA] at the parsec scale, whether they are cloud edges or low mass complexes. This result has also been reported by Clemens & Barvainis (1988) for low mass dark clouds, by Falgarone et al. (1992) for [FORMULA] lines in non-star-forming clouds, and in high angular resolution observations of cloud edges (Falgarone & Phillips 1996). The apparently intrinsic smoothness of the line profiles has been noticed first by Tauber et al. (1991) on high signal-to-noise and high velocity resolution profiles and has been observed since then in many clouds. The other properties i.e. the sharp spectral differences between the line-core and line-wing emissions, and the conspicuous small scale structure seen in the [FORMULA] line-wing emission, are seen here for the first time, probably because of the size of the fields mapped, the set of lines used, the choice of the fields (non star-forming regions), the homogeneity of the data set, and the consistency of its internal calibration.

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© European Southern Observatory (ESO) 1998

Online publication: February 16, 1998