4 Analysis

4.1 Temperature determination

We separate the cloud emission into two components, a bright filament and a surrounding envelope. The surrounding envelope is fitted using a second order polynomial (dashed lines in Fig. 2). The bright filament is obtained after subtraction of the envelope emission. The resulting profiles together with the IRAS beam profile at 100 micron are presented in Fig. 3. We see that the filament is resolved with a width of 8$^\prime$ (FWHM) at 260 $\mu$m. The width of the filament slightly decreases with increasing wavelength (Fig. 3). Moreover, the 100 and 200 $\mu$m profiles present a significant excess for angular offsets of 4$^\prime$-10$^\prime$ (4 $\sigma$ and 3 $\sigma$ respectively). The dust emission is fit by the following single modified black body:

$$I_{\lambda}^{\rm fit} = \epsilon_{\rm 250~\mu m} \times \left... ...m 250~\mu m}\right)^{-\beta} \times B_{\lambda}(T_{\rm dust})$$

where $\epsilon_{\rm 250~\mu m}$ is the dust emissivity at 250 $\mu$m, $\beta$ the emissivity spectral index, and $T_{\rm dust}$ the dust temperature. The parameters $\epsilon_{\rm 250~\mu m}$, $\beta$, and $T_{\rm dust}$ are obtained by minimising

$$\chi^{2} = \sum_{i} \left( \frac{I^{\rm fit}_{i}-I^{\rm obs}_{i}}{\sigma_{i}} \right)^{2}\cdot$$

All brightness values have been colour-corrected using the actual filter transmission and a grey body spectrum of the form $I_{\lambda} = \epsilon_{\lambda_{0}} (\lambda/\lambda_{0})^{-\beta} \times B_{\lambda}(T_{\rm dust})$ with $\beta$ and $T_{\rm dust}$ derived iteratively with the best fit (values in Table 3).

4.1.1 Filament

The spectrum of the brightest position of the filament is presented in Fig. 5 (Table 2). The 1 $\sigma$ error is the quadratic average of the calibration error (5$\%$ of the signal for PRONAOS/SPM and 10$\%$ for IRAS) and the rms dispersion of the scan average, essentially due to instrumental oscillations (Sect. 3.1). The results of the fitting procedure (see above, Sect. 2.6) are given in Table 3. The best fit is obtained for $T_{\rm dust}=12.1^{+0.2}_{-0.1}$ K and $\beta=1.9\pm 0.2$. An emissivity index of $\beta=2$ is within the error bars. In the following, we set the value of $\beta$ to 2, according to the value proposed by Boulanger et al. (1996) for the average submillimetre dust spectrum of the diffuse ISM.

 

 

Table 2: The spectral energy distribution of the filament at the brightest position measured by PRONAOS/SPM and IRAS.

$\lambda$ ($\mu$m)	60	100	200	260	360	580
signal (MJy/sr)	<0.15	5.8	65.9	79.9	55.2	20.4
1$\sigma$ error (MJy/sr)	-	1.0	4.7	4.4	3.2	1.3

Figure 5: Spectrum at the brightest position of the filament ( $\alpha _{2000}=4^{\rm h}18^{\rm m}50^{\rm s}, \delta _{2000}=25^{\circ }19^{\prime }15^{\prime \prime }$). The diamonds are data points. The error bars correspond to $\pm$1 $\sigma$ (Sect. 2.6.1). The solid line is our best fit ( $T_{\rm dust}=12.1$ K, $\beta =1.9$), and the dashed lines are the extremal fits ( $T_{\rm dust}=12.3$ K, $\beta =1.7$ and $T_{\rm dust}=12.0$ K, $\beta =2.1$) compatible with our 1 $\sigma$ error bars.

 

Table 3: The fitting parameters of the different cloud regions. For the envelope and the large-scale structure the spectral index $\beta$ is fixed to 2.

fitted	filament		envelope	large-
parameters				scale
$T_{\rm dust}$(K)	12.1 +0.2-0.1	12.0 +0.2-0.1	14.8 $\pm$ 0.6	16.8 $\pm$ 0.7
$\beta$	1.9 $\pm$ 0.2	2	2	2
$\epsilon_{\rm 250~\mu m} \times 10^{4}$	34 $\pm$ 5	37 $\pm$ 2	2.9 $\pm$ 0.3	2.7 $\pm$ 0.4

The brightness profiles (Fig. 3) indicate a temperature gradient across the filament from the centre toward the edges: from 12.0 ^+0.2_-0.1 K to $14.2 \pm 0.5$ K (Fig. 6a).

4.1.2 Envelope

The temperature variation over the whole cloud is presented in Fig. 6b. The decrease in $T_{\rm dust}$ toward the centre (offsets smaller than 8$^\prime$) is due to the increasing contribution of the cold dust located in the filament. Therefore, we can estimate the envelope temperature only for offsets greater than 8$^\prime$ (for negative offsets, the signal is near zero). We determine a temperature of $14.8 \pm 0.6$ K for the envelope at offsets greater than 8$^\prime$. For offsets smaller than -8' the signals are too weak for reliable temperature determination.

4.1.3 Large-scale structure

We now estimate the temperature of the large-scale structure surrounding the filament ( $\pm 1^{\circ}$ around the filament). We use DIRBE data at 140 and 240 $\mu$m with an angular resulution of about one degree to derive the dust temperature outside the PRONAOS/SPM map. We subtract from the DIRBE data the foreground and background cirrus emission estimated using a linear baseline. The large scale temperature outside the filament appears constant with a value of $16.8\pm 0.7$ K (Table 3). The quoted error is the root mean square of the spatial dispersion, and the calibration error of DIRBE ($5\%$). This temperature is close to that of the diffuse medium (17.5 K; Boulanger et al. 1996), indicating that the radiation field seems to be standard outside the filament.

We conclude that we have observed significant temperature variations from $16.8\pm 0.7$ K outside the cloud to 12.0 ^+0.2_-0.1 K inside the filament. The question is whether the attenuation of the radiation field due to extinction is the only mechanism that can explain the drop in temperature. In order to answer this we have computed the filament emission using a radiative transfer code and a range of models for the dust optical properties (Sect. 5).

Figure 6: Temperature profiles across the cloud (with the 1 $\sigma$ error bars), fitted with a $\beta$ value of 2. Upper panel  a) Filament alone (surrounding envelope subtracted.). Lower Lower panel  b) Whole cloud (filament + envelope). The dashed line in Fig. 5b represents T=14.8 K, which is the average temperature of the envelope surrounding the filament.

4.2 Density profile

We decompose the extinction profile into a constant large scale component, $A_{V}^{\rm large-scale}$, and a filament component which is a function of offset from the centre, $A_{V}^{\rm filament}$(r).
The total extinction can be written:

$$A_{V}({\it r}) = A_{V}^{\rm large-scale}+A_{V}^{\rm filament}({\it r})$$

$A_{V}^{\rm large-scale}$ is estimated from the observed extinction at offsets $\ge 30^{\prime}$. We model the density profile inside the filament n $_{H}^{\rm filament}$(r) assuming a cylindrical geometry and a power law density distribution (Fig. 8):

$$\begin{eqnarray*}\lefteqn{{\it n}_{\rm H}^{\rm filament}({\it r}) = {\it n}_{\rm... ...m\alpha} \hspace*{1cm}{\rm\ for\ } r_{\rm c} \leq r < r_{\max}} \end{eqnarray*}$$

where $r_{\rm c}$ is the inner radius below which the density is constant and $r_{\rm max}$ the edge radius of the cloud.

N_H(r) is converted into A_V(r) using $N_{H}/{A_{V}}=1.87 \times 10^{21} ~ \rm cm^{-2}~mag^{-1}$, from Savage $\&$ Mathis (1979). To reproduce the angular resolution of the observed A_V, we convolve with a Gaussian. We fit n₀, $r_{\rm c}$ and $r_{\max}$, to match the value of the A_V profile measured using a $\chi^{2}$ minimisation. The value of $\alpha$ has been set to -2, which is expected for a self-gravitating isothermal cloud. Variations in $\alpha$ do not improve the goodness of the fit, and have no significant influence on the computed emission. Since A_V is a lower limit for $r< 1.75^{\prime}$ (Sect. 3.1), we have fitted n₀, $r_{\rm c}$ and $r_{\max}$ for $r> 1.75^{\prime}$, independently for the positive and negative offset parts of the A_V profile. The best A_V fit is represented in Fig. 7, the corresponding n$_{\rm H}$ profile is given in Fig. 8, and the parameters in Table 4.

Figure 7: AV profile deduced from star counts method (Sect. 3.1) and fitted with our density model (dotted line), see Sect. 3.2. The error bars presented are 1 $\sigma$ error bars, and the lower limits given correspond to the central region. The vertical dotted lines delimit areas of 3.5$^\prime$ of diameter where we have only a lower limit for the extinction.

Figure 8: The normalised density profile of the filament ( $n_{H}^{\rm filament}$) is modelled by a power law: n $_{H}^{\rm filament}$( r) = n $_{\rm 0} \cdot (\frac{r}{r_{\rm c}})^{\rm -2}$. The r axis has been normalised to $r_{\max}$.

 

 

Table 4: Density profile parameters for the fitted A_V profile (Fig. 7).

angular	$A_{V}^{\rm large-scale}$	$\rm\alpha$	$n_{\rm0}$	$r_{\rm c}$	$r_{\max}$
offset	(mag)	-	(H cm-3)	(pc/$^\prime$)	(pc/$^\prime$)
positive	0.5	-2	5800	0.095/2.3	1.3/32
negative	0.4	-2	5200	0.11/2.7	0.78/19