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.
The [C ii] 158 µm emission along the two cuts varies by a factor of 2 and peaks on or close to the densest CO(1-0) clump (see Figs. 1 and 2). The appropriate peak values are erg s- 1cm-2sr-1 for cut 2 and cut 1, respectively, whilst the minimum value is 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 (H I ) of and 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 of atomic hydrogen (Moriarty-Schieven et al. 1997). The column densities derived for the positions on the two cuts are N(H i) cm-2 (Moriarty-Schieven, priv. comm. 1998), where the variation (5%) along the two cuts was found to be negligible. Their beam size () 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 ( erg s-1cm- 2sr-1) originates exclusively from non-molecular gas, we deduce a cooling efficiency of erg s- 1 H-atom-1 (dotted line in Fig. 2) for the CNM. Its uncertainty is 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 (Dwek et al. 1997) and a fractional ionization (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 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 K for the atomic hydrogen (Table 1) which is lower than that commonly adopted ( K) (Moriarty-Schieven et al. 1997).
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 erg s-1cm- 2sr-1 (). 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) cm-2 if we assume [O]/[H] . Hence, our [O i] observation puts a limit to cm-3. This observational limit is not good enough to constrain the density/temperature any further, since 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 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 s-1. Table 2 summerizes the results for the best fit models. We ran models with , 1.0 and to evalutate the sensitivity of the [C ii] emission on the FUV-radiation and found the [C ii] line flux to vary strongly upon . For the line flux turned out to be lower by more than a factor of 10 compared to that at and fails to explain the observations. The area filling factor of clumps in the beam 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 in excess of cm-3 because the 13CO line fluxes are much higher than those observed, whilst the calculated [C ii] emission is lower than observed. For [C ii] emission exceeds that observed by far.
As seen in Table 2 one layer of clumps is not sufficient to explain the observations. We need 4 and 1.5 for the best fit models M= (=) and M= (=) at = cm-3, which implies a total mass of and 0.48 , respectively, within a diameter of 0.17 pc (90). This is a factor of 3 lower than that deduced from 13CO(1-0) observations (Pounds et al. 1990). We note that models with clump densities = cm-3 generally find a better match to the CO observations, whilst models with = 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 for cases in which the optical depth of a line for an individual clump is , e.g. for 12CO. We should mention, however, that the observed line 13CO(2-1) width for the clump CO03 is v(FWHM) 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 .
The calculated [O i] 63 µm emission turned out 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 for clumps with M= and = 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 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 31 MJy/sr on the CO(1-0) peak and 5 MJy/sr at the easternmost edges of the cuts. Combining the results we infer an energy density of the far-IR radiation field for the cloud core and for the edges if we assume the black body temperature and a emissivity law for the dust. This is on the same order of the computed FUV-radiation field.
© European Southern Observatory (ESO) 1998
Online publication: July 27, 1998