We have used the 3D radiative transfer code developed by Bernard et al. (1992, 1993) and improved by Le Peintre et al. (2002). Assuming a radiation field, a cloud geometry, dust properties, and a density distribution, we can compute the grain temperature distribution and the dust continuum emission of an interstellar cloud.

We assume that the incident radiation field is isotropic. We adopt the average interstellar radiation field (ISRF) of Mathis et al. (1983) attenuated by the visual extinction $A_{V}^{\rm large-scale}$ determined in Sect. 3.2. The filamentary shape of the cloud is modelled assuming a cylindrical geometry. The cloud radial density distribution $n_{H}^{\rm filament}(r)$ was determined in Sect. 3.2. For each position inside the cloud, we compute the cloud emission in three steps. First, we calculate the attenuation of the incident radiation field. Second, we determine the temperature distribution of the dust and its emission spectrum. The dust emission is computed using the method of Désert et al. (1990). Third, we integrate the dust emission along the line of sight, taking the dust self absorption into account. The model is self-consistent for dust extinction and emission, and includes emission from transiently-heated small grains. The results of the model are independent of the gas-to-dust ratio. The star counts provide the column density of dust and the radiative transfer model directly uses the inferred dust density distribution.

5.2 Modelling using standard dust composition

We assume the same dust properties throughout the cloud. We use the standard dust composition adopted by Désert et al. (1990). This is an empirical model consisting of three grain components in which the abundance and size distributions reproduce both the extinction curve and the emission spectrum measured by IRAS in the Solar neighbourhood. The three dust components are: Polycyclic Aromatic Hydrocarbons (PAHs), Very Small Grains (VSGs), and Big Grains (BGs). Both PAHs and VSGs are transiently heated by single photon absorption. While BGs are in thermal equilibrium with the radiation field.

We have integrated the emission computed by the model over the instrument filter bands, degraded the angular resolution to that of the appropriate filter band, simulated the beam modulation on the sky and deconvolved the signal as was done with the actual data (Sect. 2.4). In addition, to compare the model spectra with the observations, we have degraded all the computed profiles to the IRAS 100 $\mu$ m resolution.

$\begin{figure} \par\includegraphics[width=16.1cm,clip]{fig9_a_stepnik.ps}\\ [5mm... ...ace*{0.7cm}\includegraphics[width=13.2cm,clip]{fig9_b_stepnik.ps} } \end{figure}$

Figure 9: We compare the data in solid lines with the models (other lines). Dashed lines are for the standard model, dash-dotted for the model using a additional central A_V value of 35 in the central part of the filament (3.5 $^\prime$ ), and dotted lines for the model using non-standard dust properties inside the filament. Upper panel: observed and modelled brightness profiles of the filament at the angular resolution of Table 1. Lower panel: spectra of the brightest position of the filament for the different cases. Diamonds are the data points and the error bars correspond to 1 $\sigma$ . The dashed curve represents a $T_{\rm dust}=14.2$ K spectrum and the others $T_{\rm dust} \sim 12$ K. We have also reported the filament level emission modelled at 60 $\mu$ m and the 1 $\sigma$ upper limit measured.

5.3 The need for non-standard grains

In order to better reproduce the dust temperature observed toward the centre of the filament (12 K), we can in principle modify the incident radiation field, the column density, or the optical properties of the dust particles. The influence of these various parameters is investigated in the following subsections.

5.3.1 Influence of the incident radiation field

The Taurus molecular complex is a relatively quiescent region, so we have assumed a radiation field equal to the local ISRF. Can we change the incident radiation field intensity in order to reproduce our observations? A decrease in the incident radiation field has to be compatible with the apparent dust temperature measured by DIRBE outside the cloud (offsets $\sim$ $1^{\circ}$ ): $16.8\pm 0.7$ K (Sect. 2.6.3). For the standard dust model of Désert et al. (1990) an apparent temperature of $16.8\pm 0.7$ K is reached for an ISRF multiplied by a factor 0.77 ^+0.23_-0.14. The resulting emission profile (Fig. 9) is almost identical to the one obtained from the standard model of Sect. 4.2, and unable to reproduce our observations. The apparent dust temperature at the central position of the filament is 14.0 K. In order to reach an apparent dust temperature of 12 K we have to multiply the ISRF by a factor of $\sim$ 0.33. This is not compatible with the DIRBE measurements outside the cloud. The predicted envelope (10 $^{\prime} \lesssim {\rm offset} \lesssim 30^{\prime}$ ) temperature is too low and the amplitude of the synthetic spectrum, at the central position ( ${\rm offset} = 0^{\circ}$ ), drops with a factor of two at all wavelengths.

Another solution is an attenuation of the incident radiation field by an additional A_V value ( $A_{V} \sim 1$ typically). The UV part of the radiation field is more attenuated than the visible and near-IR parts, so the spectrum changes. The results of such an attenuation are (1) to decrease the temperature of the whole cloud (envelope + filament), and (2) to decrease the amplitude of the synthetic profiles at each wavelength. We conclude that we cannot reproduce the observations by changing the hardness of the radiation field.

5.3.2 Influence of the column density profile

The discrepancy between our model and the observations may be due to an underestimate of the column density in the centre where we measured only an upper limit for the extinction. We have increased A_V for $r< 1.75^{\prime}$ and maintained the profile found in Sect. 3.1 for larger r. Using the radiative transfer model, we have fitted this A_V(0) value in order to reproduce a temperature of 12 K toward the centre of the filament (Fig. 9). The temperature and the amplitude of the dust spectrum are well reproduced at the peak emission, but the widths of the computed emission profiles are too narrow.

To match the data we have to increase A_V over an area larger than 3.5 $^\prime$ . Typically, a value of A_V=15 within a region of a size-scale of 7 $^\prime$ reproduces the observations. Such a profile is not compatible with the 2MASS observations, where a significant amount of stars were counted in the annulus $3.5^{\prime}<r<7^{\prime}$ (Fig. 6). The presence of these stars indicates a value of A_V less than 15 (typically A_V=4, as seen in Fig. 7). We conclude that a change of the A_V profile alone, within the error bars (Fig. 7), is not compatible with the observed emission profiles.

5.3.3 Fitting the data with standard grains?

One solution may be to change both the incident radiation field and the A_V profile. A combination of an incident field multiplied by a factor larger than 0.63 (=0.77-0.14, the lower limit for the incident radiation field intensity, see Sect. 4.3.1) and an A_V profile with high values in the central area of 3.5 $^\prime$ produces emission profiles which are too narrow. Therefore the only remaining option is to assume that the optical properties and the relative abundance of the grains change inside the filament.

5.4 Modelling the filament emission with non-standard grains

We have seen that the standard model only reproduces the observations in the envelope. For the filament, the abundance of the VSGs has to be decreased and the submillimetre emissivity must be enhanced. Two mechanisms are possible: (1) to transform the VSGs into particles emitting in the submillimetre range, and (2) to increase the BG submillimetre emissivity.

The two solutions proposed are linked, and their effects not independent. VSG coagulation onto BGs leads to a decrease of VSG abundance and at the same time changes the emission of the BGs. VSG mutual coagulation onto larger grains leads also to a decrease of VSG abundance, and may form aggregates partaking in the BG size distribution.

We introduce four new parametres in the model: $r_{\rm VSG}$ , $f_{\rm VSG}$ , $r_{\rm BG}$ and $f_{\rm BG}$ . The VSG abundance is multiplied by a factor $f_{\rm VSG}$ (<1), for offsets lower than $r_{\rm VSG}$ . The BG emissivity, for wavelengths greater than 20 $\mu$ m, is multiplied by a factor $f_{\rm BG}$ (>1) for offsets smaller than $r_{\rm BG}$ . We use a factor $f_{\rm BG}$ independent of the wavelength in order to keep the spectral index equal to 2, as we have measured in Sect. 2.6.1. The choice of the threshold wavelength (20 $\mu$ m) is not critical, since BGs absorb radiation at wavelengths shorter than 10 $\mu$ m, and emit at wavelengths greater than 50 $\mu$ m, since they are colder than 20 K. Variations of this wavelength threshold between 10 and 50 $\mu$ m changes the final BG equilibrium temperature by less than 1 $\%$ . We determine the values of these four parameters by fitting the computed emission profile with the data. The error bars correspond to the different parameter values compatible with the 1 $\sigma$ error bars of the emission profiles. First, we use the standard incident radiation field and the A_V profile of Sect. 4.2.2. The 60 $\mu$ m deficit is reproduced with $r_{\rm VSG}=4^{\prime} \pm 1$ and $f_{\rm VSG}=0.1 \pm 0.1$ , and the submillimetre enhancement is fitted with $r_{\rm BG}=4^{\prime} \pm 0.5^{\prime}$ and $f_{\rm BG}=3.4_{-0.3}^{+0.2}$ . With these values, we are able to reproduce correctly the cloud emission: dust temperature, spectrum amplitude and profile widths at all wavelengths and at all positions (Fig. 9).

Then, we investigate the effects of different incident radiation fields and A_V profiles. We have seen (Sect. 4.3.1) that the incident radiation field is compatible with the local ISRF multiplied by a factor down to 0.63. The use of this lower incident radiation field slightly modifies the $f_{\rm BG}$ determination. In this case we find $f_{\rm BG}=3.0 \pm 0.2$ . A change in the A_V profile within the error bars (Sect. 3.1 and Fig. 7) also increases the uncertainty on $f_{\rm BG}$ by $\pm$ 0.1. The determination of $r_{\rm VSG}$ and $f_{\rm VSG}$ are not significantly modified by these changes.

Finally, the values and the error bars of the four parameters are reported in Table 5.

Table 5: The four new parameters of our model (see the text).
particle modified

component property

VSGs $r_{\rm VSG}=4^{\prime} \pm 1^{\prime}$ $f_{\rm VSG}=0.1 \pm 0.1$ abundance

BGs $r_{\rm BG}=4^{\prime} \pm 0.5^{\prime}$ $f_{\rm BG}=3.4_{-0.7}^{+0.3}$ submm emissivity

**Table 5:** The four new parameters of our model (see the text).
particle			modified
component			property
VSGs	$r_{\rm VSG}=4^{\prime} \pm 1^{\prime}$	$f_{\rm VSG}=0.1 \pm 0.1$	abundance
BGs	$r_{\rm BG}=4^{\prime} \pm 0.5^{\prime}$	$f_{\rm BG}=3.4_{-0.7}^{+0.3}$	submm emissivity

This simple cloud model in two dust phases separated by an abrupt transition reproduces our data very well (Fig. 9). The size of the region where the dust properties are modified is the same for the BGs (4 $^{\prime} \pm 0.5^{\prime}$ ) and the VSGs (4 $^{\prime} \pm 1^{\prime}$ ) within the error bars. Therefore BG properties and VSG abundance seem to be physically connected and it is likely that a common physical process affects these two components. With our data, we cannot resolve the dust property variations inside each phase. Thus, the interface between the two phases is smaller than the beam size of our observations (3.5 $^\prime$ or 0.14 pc). Such an abrupt change in the dust properties is the signature of an efficient and fast process which appears for a threshold of $A_{V}=2.1 \pm 0.5$ (measured on the line of sight or $A_{V}^{\perp}=0.9 \pm 0.2$ when computed along the filament radial direction) and $n_{H} = 3\pm 2 \times 10^{3}~\rm cm^{-3}$ .