6 Interpretation

We have shown that, inside the densest part of the filament, (1) the transiently heated small particles are not present, (2) the ratio of the grain submillimetre emissivity to the dust extinction in band J is significantly enhanced, and (3) these two phenomena coincide spatially. We want to emphasis that our results are normalised to the value of the extinction observed in the J-band. In particular, an overestimate of the dust extinction in the J band produces an underestimate of the dust column density, and thus an apparent submillimetre emissivity increase. In our study, we have not shown an increase in the dust submillimetre emissivity, but an increase of the ratio between the dust submillimetre emissivity over the dust extinction in J band.

Several processes may affect the optical properties of dust in dense clouds: ice or molecular mantle formation on grains, coagulation of grains (e.g. Draine 1985). Preibisch et al. (1993) have shown that ice and carbon mantles on BGs do not increase significantly the ratio of submillimetre emissivity over extinction in J band. Therefore, grain mantle formation cannot be the main explanation for our observations.

6.1 Grain-grain coagulation

Dust coagulation is efficient at producing large aggregates (Weidenschilling $\&$ Ruzmaikina 1994; Ossenkopf 1993). These aggregates have irregular and fluffy shapes, which can be modelled by fractal grains (Meakin & Donn 1988; Wurm & Blum 2000). The optical properties of fluffy aggregates have been computed by several authors (Bazell $\&$ Dwek 1990; Ossenkopf $\&$ Henning 1994; Stognienko et al. 1995). The submillimetre emissivity increases with fluffiness. At 200 $\mu$m this increase is typically of a factor 1.5-3.5 for silicate and 3-20 for carbon aggregates (e.g. Stognienko et al. 1995). The UV, visible and near-IR absorptivity are not significantly modified if the fluffiness is increased (Bazell $\&$ Dwek 1990). As a result, the equilibrium temperature of fluffy aggregates is lower than that of compact particles. Fogel $\&$ Leung (1998) have found a temperature decrease of typically 10-20$\%$, for the grains of Bazell $\&$ Dwek (1990), heated by the local ISRF.

Coagulation simulations show that smallest grains (VSGs) coagulate faster than larger ones (Ossenkopf 1993). This can explain the strong decrease of the VSG abundance observed. We conclude that grain-grain coagulation into fluffy aggregates can produce both the strong variations of relative abundance and optical properties of dust observed in the Taurus filament.

6.2 Cloud lifetime and coagulation timescales

The cloud lifetime is at least equal to the free-fall timescale of the cloud (e.g. Walmsley 1991):

$$\tau_{\rm free-fall}=\left(\frac{3~\pi}{32~G~n_{H}}\right)^{-\frac{1}{2}} \cdot$$

The local density for $r> 1.75^{\prime}$ is around $4 \times 10^{3}$ cm^-3 (Sect. 3.2). For such densities the cloud lifetime is above 10⁶ years.

The coagulation timescale between two grains (grain type 1 on grain type 2) is estimated by the relation (e.g. Draine 1985):

$$\tau_{\rm coa}=\left[\sigma_{\rm 1/2} \times n_{\rm 1} \times v_{\rm 1/2}\right]^{-1}$$

where $\sigma_{\rm 1/2}$ is the coagulation cross-section, $n_{\rm 1}$ the density of grains type 1, and $v_{\rm 1/2}$ the relative velocity between the two grains. For an estimate, we consider the coagulation cross section equal to the geometric cross section: $\sigma_{\rm 1/2} = \pi \times (a_{\rm 1}+a_{\rm 2})^{2}$, where $a_{\rm 1}$ and $a_{\rm 2}$ are the radii of grains 1 and 2.

We compute the average grain radius $\langle a \rangle$ and corresponding density $n_{\langle a \rangle}$for the VSG and BG components in the standard dust model (Table 6). The resulting values of $\sigma_{\rm 1/2}$ and $n_{\rm 1}$ are given in Table 7.

 

Table 6: Average grain radii $\langle a \rangle$ and corresponding densities $n_{\langle a \rangle}$ computed from the standard dust model (see Table 2 of the Désert et al. 1990 paper).

dust component	$\langle a \rangle$	$n_{\langle a \rangle}/n_{H}$
VSG	3 nm	$5\times 10^{-9}$
BG	30 nm	$3\times 10^{-11}$

There is a critical velocity above which collisions do not lead to coagulation but destruction (Chokshi et al. 1993). This critical velocity depends on the size and the composition of porous grains (Dominik & Tielens 1997). Icy grains stick better than other particles, because their mantles can absorb a significant fraction of the collisional energy. Their critical velocity is higher than for naked grain aggregates, causing the coagulation timescale to become smaller than that of naked grain aggregates. By studying ice mantle formation in the Taurus molecular complex, Texeira & Emerson (1999) have found a linear relationship between the width of the ice mantles and A_V, and derived a threshold column density of A_v=2-3 for the detection of ice mantles. Towards the filament, the submillimeter excess is detectable in regions where $A_{V} \gtrsim 2$ suggesting that grains are coated with ice mantles.

We have calculated the critical velocity of ice grains according to Dominik & Tielens (1997), and found:

$$\rm {\it v}_{\rm critical}= 670 \times \left[ \left(\frac{1}{... ...}} \right) \times 10^{-5}~cm \right]^{\frac{5}{6}}~cm~s^{-1}.$$

Numerical results are given in Table 7. Brownian motions lead to very low relative velocities between grains of about 1 m/s (Draine 1985). These relative velocities are not efficient at producing grain coagulation. However, the presence of turbulent motions (Falgarone $\&$ Phillips 1990) can enhance the relative grain velocity. Volk et al. (1980) and Draine (1985) have analysed relative grain velocities in turbulent clouds with a Kolmogorov spectrum of turbulent eddies. Typically, relative grain velocities of about 1 km s^-1 are expected for 3-30 nm grains at a density of $4 \times 10^{3}$ cm^-3in molecular clouds (Tielens 1989). This value is roughly equal to the critical velocities of Table 7. Therefore, we assume that the relative grain-grain velocity ( ${\it v}_{\rm 1/2}$) inside the filament is equal to the critical velocity between grains ( ${\it v}_{\rm critical}$). The coagulation timescales for the possible interactions between VGSs and BGs are also presented in Table 7. The values of $\sigma_{\rm 1/2}$, n₁ and $v_{\rm critical}$ are reported in order to underline the relative importance of these factors. In Table 7, "VSGs on BGs'' means coagulation of VSGs onto BGs. The coagulation timescale of a VSG onto one BG is different from that of a BG onto a VSG. In the former case the BG is the choosen target grain, and the difference in timescales arises from the abundance of the incident grains.

 

Table 7: Dust parameters and their resulting coagulation timescales.

coagulation	$\sigma_{\rm 1/2}$	$n_{\rm 1}$	$v_{\rm critical}$	$\tau_{\rm coa}$
	(cm2)	(cm-3)	(km s-1)	(yr)
VSGs on VSGs	$1.1\times 10^{-12}$	$2\times 10^{-5}$	2.2	$7\times 10^{4}$
VSGs on BGs	$3.4\times 10^{-11}$	$2\times 10^{-5}$	1.3	$4 \times 10^{3}$
BGs on VSGs	$3.4\times 10^{-11}$	$1.2\times 10^{-7}$	1.3	$6\times 10^{5}$
BGs on BGs	$1.1\times 10^{-10}$	$1.2\times 10^{-7}$	0.3	$8\times 10^{5}$

The coagulation timescales computed above are simply the time that one type of grain meets another. However, the shortest timescale will dominate the coagulation process. The timescale for VSGs onto BGs is the smallest and results from a combination of (1) high velocities, (2) the large number of small grains, and (3) the large cross-section of the large grains. The total timescale to form one coagulated grain, to first order, has to be multiplied by the number of VSGs that have stuck to a BG. How many VSG particles are requiered to modify the optical properties of a BG particule? Bazell & Dweck (1990) have computed a submillimetre excess of 5 for fluffy aggregates of 136 grains of amorphous carbon of 10 nm. We say that it typically requires less than 100-200 VSGs to significantly alter the optical properties of BG particles. The coagulation timescale to form such aggregates is smaller than the cloud lifetime. We conclude from this simplified calculation that grain-grain coagulation is a likely process and that VSGs coagulation onto BGs could be the main mechanism to naturally explain the observations.

6.3 Other observations

Laureijs et al. (1991) measured, using IRAS data, strong emission deficits at 60 $\mu$m toward the translucent cloud L1780 ( $A_{B}\sim 4$, note that A_V/A_B=0.75 from Cardelli et al. 1989) and the dark clouds L183 and L134 ( $A_{B}\sim 10$). In these clouds, a significant deficit of the 60 $\mu$m emission flux appears for $A_{B} \gtrsim 2$ and $n_{H} \gtrsim 10^{3}~$cm^-3, which is in the range of our threshold values (Sect. 4.4).

Using PRONAOS/SPM data, Bernard et al. (1999) observed a low equilibrium temperature toward a high latitude cirrus cloud (MCLD 123.5+24.9), presenting a strong deficit of its 60 $\mu$m emission. The apparent equilibrium temperature with the radiation field is T=13.4 K (assuming $\beta=2$), while a radiative transfer model, using standard grains properties, predicts 15.6 K (with $\beta=2$). Bernard et al. (1999) proposed a change in the dust properties and the VSG coagulation to explain this unusual cold temperature in a cirrus. We find that an enhancement of the submillimetre emissivity by 2.8 in this cirrus produces an apparent temperature of 13.4 K.

On larger scales, Cambrésy et al. (2001) recently decomposed the far-infrared flux of the Polaris Flare into a cold component and a warm component, defined by the $I_{\rm 60 ~\mu m}/I_{\rm 100 ~\mu m}$ flux ratio following the method of Lagache et al. (1998). The comparison of the far-infrared cold component with extinction maps derived from star counts indicates an enhancement of the far-infrared emissivity by a factor of $\sim$3. In the Polaris Flare they measured the same observational effects that we have seen in the Taurus filament, but for a diffuse cloud (A_V<1). However, we want to emphasise that the Polaris Flare is a very particular region. It is a molecular region (Heithausen & Thaddeus 1990) and probably material reprocessed by a supernova shock (Meyerdierks et al. 1991).

Lagache et al. (1998) analysed the far-IR and submm emission of the Taurus molecular complex on large scales with DIRBE data (angular resolution $\sim$$1^{\circ}$). They have measured temperatures of 16-17 K in the diffuse parts of the Taurus complex. The molecular filaments in this complex shows an average temperature of 13.4 K. We suggest that the average temperature of 13.4 K in molecular regions is due to a mixture of 12 K in the dense regions with the diffuse medium at 16.5 K. Based on this assumption, we can reproduce the large scale DIRBE emission at 240 $\mu$m in this region. We suggest that the submillimetre emissivity could be enhanced in the central parts of all molecular regions by a factor of 3 (where typically n_H > 10³ cm^-3) in order to explain the observed temperatures.

These observations indicate that in our galaxy the 60 $\mu$m deficit seems to be associated with grain submillimetre emissivity enhancements by factors of 3, pointing towards dust evolution as a general process in the denser parts of molecular clouds.