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Astron. Astrophys. 336, L53-L56 (1998)

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3. Origin of the [C ii] Line

The results of the [C ii] 158 µm observations are presented in Fig. 2. The uncertainty in the observations is dominated by the present flux calibration uncertainty of about 30% for the LWS (Swinyard et al. 1996). Statistical uncertainties, computed from the noise level near the line, are generally smaller than this.

[FIGURE] Fig. 2. [C ii] 158 µm line fluxes for the positions along cut 1 and 2 (see Fig. 1). The zero positions are given in Sect. 2. The error bars are computed from the noise level on the continuum. The dotted line indicates the [C ii] cooling of the CNM deduced from present data, whilst the other two lines (dashed and dash-dot) are from Matsuhara et al. (1997) and Dwek et al. (1997), respectively. The lower plot represents the CO(1-0) line fluxes along cut 1 and 2.

The [C ii] 158 µm emission along the two cuts varies by a factor of [FORMULA]2 and peaks on or close to the densest CO(1-0) clump (see Figs. 1 and 2). The appropriate peak values are [FORMULA] erg s- 1cm-2sr-1 for cut 2 and cut 1, respectively, whilst the minimum value is [FORMULA] erg s-1cm- 2sr-1 at the eastermost ends of the cuts. At these positions the CO(1-0) emission has dropped to almost zero which implies the absence of molecular material. Since the [C ii] 158 µm line flux is not zero, the emission originates from non-molecular gas. We argue it is due to the cooling of the diffuse atomic neutral hydrogen gas in the line of sight toward L1457.

3.1. C+-cooling of the Cold Neutral Medium

Emission from the [C ii] 158 µm line is thought to be the dominant cooling process for the cold neutral medium (CNM). The C+-cooling of the diffuse ISM has been inferred from two observations. Dwek et al. (1997) and Matsuhara et al. (1997) deduced cooling rates of [FORMULA](H I ) of [FORMULA] and [FORMULA] erg s-1 H-atom- 1 at high galactic latitude using COBE and rocket-borne observations, respectively. The latter authors detected also excess [C ii] emission that originates from molecular MBM clouds.

H i observations indicate the L1457 complex is associated with about 50 [FORMULA] of atomic hydrogen (Moriarty-Schieven et al. 1997). The column densities derived for the positions on the two cuts are N(H i)[FORMULA][FORMULA] cm-2 (Moriarty-Schieven, priv. comm. 1998), where the variation ([FORMULA]5%) along the two cuts was found to be negligible. Their beam size ([FORMULA]) is roughly comparable with ISO's beam (see also Fig. 1). If we assume the [C ii] emission from the easternmost parts of the cuts ([FORMULA] erg s-1cm- 2sr-1) originates exclusively from non-molecular gas, we deduce a cooling efficiency of [FORMULA] erg s- 1 H-atom-1 (dotted line in Fig. 2) for the CNM. Its uncertainty is [FORMULA]40%. The cooling rates of Matsuhara et al. (1997) and Dwek et al. (1997) are smaller than ours by a factor of 2.

Utilizing the present value for the [C ii] emission from the CNM, we can derive the atomic hydrogen density and temperature of the CNM (Table 1). We assumed a [C+]/[H] ratio of [FORMULA] (Dwek et al. 1997) and a fractional ionization [FORMULA] (Kulkarni & Heiles 1987). The collision rates for C+-H and C+-e were adopted from Launay & Roueff (1977) and Hayes & Nussbaumer (1984), respectively, and the Einstein coefficient is from Nussbaumer & Storey (1981). Moriarty-Schieven et al. (1997) derive a density [FORMULA] cm-3 for the atomic hydrogen in the line of sight toward L1457 from the H i column density and the extent of the H i 21 cm emission. This infers a kinetic temperature [FORMULA] K for the atomic hydrogen (Table 1) which is lower than that commonly adopted ([FORMULA] K) (Moriarty-Schieven et al. 1997).


[TABLE]

Table 1. Physical parameters of the CNM


No [O i] 63 µm emission was detected at any position and we infer an upper limit of [FORMULA] erg s-1cm- 2sr-1 ([FORMULA]). The third column of Table 1 is the calculated O i column density deduced from this limit. The atomic data for [O i], Einstein coefficients and collision rates, were employed from Baluja & Zeippen (1988) and Launay & Roueff (1977), respectively. We emphasize that N(O i) [FORMULA] cm-2 if we assume [O]/[H] [FORMULA]. Hence, our [O i] observation puts a limit to [FORMULA] cm-3. This observational limit is not good enough to constrain the density/temperature any further, since [FORMULA] cm-3 (Moriarty-Schieven et al. 1997).

3.2. Excess C+-emission from molecular gas

In addition to [C ii] emission from the CNM we detected excess emission that shows a maximum on or close to the brightest CO(1-0) peak (see Figs. 1 and 2). In order to deduce the [C ii] line flux that originates from the molecular gas the value for the [C ii] cooling of the CNM (see Sect. 3.1) was subtracted from the observed emission. Hence, [C ii] emission peaks at [FORMULA] erg s-1cm- 2sr-1 for cut 2 and cut 1, respectively. We argue that this emission emanates from dense molecular clumps that are irradiated by the mean interstellar FUV-field.

In order to determine the physical parameters of the dense clumps we employed PDR models for spherical symmetric clumps (Störzer et al. 1996) with different densities, clump masses, and FUV-radiation fields and compared the computed line fluxes with those observed at [C ii] 158 µm, [C i] 492 GHz, CO(1-0) , 13CO(1-0) and (2-1) . The cosmic ray flux was set to [FORMULA] s-1. Table 2 summerizes the results for the best fit models. We ran models with [FORMULA], 1.0 and [FORMULA] to evalutate the sensitivity of the [C ii] emission on the FUV-radiation and found the [C ii] line flux to vary strongly upon [FORMULA]. For [FORMULA] the line flux turned out to be lower by more than a factor of 10 compared to that at [FORMULA] and fails to explain the observations. The area filling factor of clumps in the beam [FORMULA] needed to match the [C ii] observations is so large that the total mass required exceeds that deduced from 13CO(1-0) observations. The PDR models also rule out clumps with average densities [FORMULA][FORMULA][FORMULA] in excess of [FORMULA] cm-3 because the 13CO line fluxes are much higher than those observed, whilst the calculated [C ii] emission is lower than observed. For [FORMULA] [C ii] emission exceeds that observed by far.


[TABLE]

Table 2. Line fluxes predicted for a single clump using a PDR model of spherical symmetry.
Notes:
[FORMULA] Zimmermann & Ungerechts (1990);
[FORMULA] Pound et al. (1990);
[FORMULA] Ingalls et al. (1994);
[FORMULA] Zimmermann (1993)


As seen in Table 2 one layer of clumps is not sufficient to explain the observations. We need [FORMULA] 4 and 1.5 for the best fit models M=[FORMULA] [FORMULA] ([FORMULA]=[FORMULA]) and M=[FORMULA] [FORMULA] ([FORMULA]=[FORMULA]) at [FORMULA][FORMULA][FORMULA]=[FORMULA] cm-3, which implies a total mass of [FORMULA] and 0.48 [FORMULA], respectively, within a diameter of 0.17 pc (9[FORMULA]0). This is a factor of [FORMULA]3 lower than that deduced from 13CO(1-0) observations (Pounds et al. 1990). We note that models with clump densities [FORMULA][FORMULA][FORMULA]=[FORMULA] cm-3 generally find a better match to the CO observations, whilst models with [FORMULA][FORMULA][FORMULA]=[FORMULA] cm-3 require usually smaller filling factors and seem to be more consistent with the [C i] 492 GHz observations. However, larger clump masses are required in order to match the CO observations.

We caution against multiplying the computed line fluxes by filling factors [FORMULA] for cases in which the optical depth of a line for an individual clump is [FORMULA], e.g. for 12CO. We should mention, however, that the observed line 13CO(2-1) width for the clump CO03 is v(FWHM) [FORMULA] km s-1 (Ingalls et al. 1994), whilst our computations assumed 1.2 km s-1 for indivudual clumps. The observed line width may therefore be caused by a superposition of individual clumps lying at slightly different velocities and the line fluxes from a single clump may be simply multiplied by [FORMULA].

The calculated [O i] 63 µm emission turned out [FORMULA] erg s-1cm- 2sr-1 for all models owing to the low temperature of the molecular gas. This is about 2 orders of magnitude lower than our upper limit. [O i] 63 µm emission would have been detected in our spectra if the FUV-radiation field [FORMULA] for clumps with M=[FORMULA] [FORMULA] and [FORMULA][FORMULA][FORMULA]=[FORMULA] cm-3, according to our PDR models.

3.3. Dust temperature and FIR Intensity

The dust temperatures deduced from 60 and 100 µm IRAS observations of L1457 were found to be [FORMULA] K and 30-35 K for the cloud core and the outer regions, respectively (Clemens & Leach 1989). The 100 µm maps (Corneliussen 1991) show the dust emssion is well correlated with that of CO(1-0) . The 100 µm intensity is [FORMULA]31 MJy/sr on the CO(1-0) peak and [FORMULA]5 MJy/sr at the easternmost edges of the cuts. Combining the results we infer an energy density of the far-IR radiation field [FORMULA] for the cloud core and [FORMULA] for the edges if we assume the black body temperature [FORMULA] and a [FORMULA] emissivity law for the dust. This is on the same order of the computed FUV-radiation field.

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© European Southern Observatory (ESO) 1998

Online publication: July 27, 1998
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