5 The disk model

The CO $J=6 \rightarrow 5$ linewidth of 3.6 km s^-1 is consistent with outflowing gas, but it can also be explained by gas infalling and/or orbiting towards a $\sim$$1~M_\odot$ central object. We already mentioned that the outflow/shock thesis has difficulty explaining why the water abundance is so low, less than $5 \times 10^{-7}$ in the specific case of El 29. In the following we explore as far as possible the hypothesis that the observed CO emission originates in the envelope+disk of EL 29. In an extensive study, BHC02 modeled the 2 to 1300 $\mu$m continuum spectrum (SED) of EL 29 and found that it can be reproduced by a relic envelope that surrounds a flaring disk whose mass is about 0.012 $M_\odot$. The same model predicts a contribution from the envelope to the ¹²CO  $J=6 \rightarrow 5$ emission equal to $T^*_{\rm R}=$ 18 K, i.e. a substantial fraction compared to the observed signal ( $T^*_{\rm R}=$ 20 K). However, the ¹³CO  $J=6 \rightarrow 5$ emission from the envelope would result in $T^*_{\rm R}=$ 1.5 K, compared to the observed 10 K. Similar results are obtained using the model of the envelope emission by Ceccarelli et al. (1996). Both models predict by far too low CO FIR line emission with respect to what is observed. We therefore conclude that the envelope does not contribute substantially to the observed CO FIR and ¹³CO  $J=6 \rightarrow 5$ emission (although the envelope dominates the ¹²CO  $J=6 \rightarrow 5$ emission), unless a key ingredient is missing in the two models mentioned. A possibility is the existence of a "super-heated'' envelope layer illuminated by the UV and/or X-ray emitted at the center, which neither the BHC02 or Ceccarelli et al. models include.

We hence explore the possibility that the disk is the main cause of the observed CO submm/FIR emission. In BHC02 we used the disk model by CG97 that predicts the existence of a disk "super-heated surface layer''. To reproduce the SED of EL 29 we used the CG97 temperature profile multiplied by a factor of 2.5 to account for the EL 29 luminosity (BHC02). This corresponds to a dust temperature of the super-heated layer at 250 AU of about 160 K, in remarkable agreement with the gas temperature that we find from the CO submm/FIR line LVG analysis. In addition, we found that the mass of the super-heated layer is $\sim$4-20  $\times 10^{-4}~M_\odot$, in remarkable agreement with that derived from the LVG analysis of the CO submm/FIR line data ($\sim$8-24  $\times 10^{-4}~M_\odot$). Even considering the various approximations in the analysis of both the continuum and line data, the substantial agreement of the derived disk parameters seems to be extremely encouraging and supportive of the thesis that the FIR CO emission originates in the super-heated layer of the EL 29 disk. We therefore computed the CO line emission from the flaring disk model which also fits the SED, hereinafter referred to as the BHC02 model. As expected, the CO column density predicted by the BHC02 model (about $5 \times 10^{18}$ cm^-2 in a 4'' region) agrees well with the required column density. In addition, we have computed the CO line emission and find that the predicted $J=6 \rightarrow 5$, ¹²CO and ¹³CO fluxes are comparable to the observed values.

On the contrary, the predicted FIR CO line fluxes are a factor 10 lower than the observed values. However, we think that this discrepancy is easily explained. Indeed, in the flaring disk used for the SED analysis we assumed the minimum density for the super-heated layer provided by CG97. As a consequence, the density in the BHC02 model is relatively low, being only 1/3 of the material in the super-heated layer with a density above 10⁶ cm^-3 and only 1/10⁴ above 10⁷ cm^-3. This explains why the FIR CO lines are not excited in this model. However, as CG97 themselves caution, the density in the super-heated layer can be some orders of magnitude larger that the minimum we used in the BHC02 model. The maximum density would be that of the disk midplane if the dust had fully settled, e.g. 10⁹ cm^-3 at 250 pc. Hence the density in the super-heated layer can be anything between 10⁶ cm^-3 and 10⁹ cm^-3. Since the SED analysis is not sensitive to the density but just to the column density of the dust, the BHC02 model could not constrain it. The present line observations may suggest a rather high density and therefore that the dust settling has already progressed in EL 29. Alternatively, the LVG modeling (Fig. 5) shows that lower densities are still possible but would require a somewhat larger temperature, $\sim$250 K, to account for the J=6 to J=20 observed emission together. From a theoretical point of view it would not be impossible that the gas and dust are thermally decoupled, with the gas warmer than the dust. From an observational point of view this seems rather the case (see next paragraph). Given all these uncertainties it is difficult to push further the BHC02 model/observations comparison.

Unfortunately, both the continuum and line data are not accurate enough to explore in more detail the scenario of whether the gas is decoupled from the dust and how much (a short discussion on this possibility is reported in the next section). Recently D'Alessio et al. (1999, 2001) modeled in a self-consistent way the vertical structure of flaring disks (Calvet et al. 1991; CG97) and found that their models predict too (geometrically) thick disks with respect to the observed T Tauri stars. They suggested that dust settling and/or dust coagulation could possible resolve this apparent contradiction between predictions and observations, even though the opacity is set by the small grains which settle with more difficulty. The present observations seem to support the thesis of dust settling in EL 29. However, it is clear is that the density, temperature and chemical structure of the disk are crucial parameters for a fully consistent modeling of line emission, but this is beyond the scope of this article, also because of the too large observational uncertainties. The main point we want to stress is that observationally the CO FIR emission indicates a reservoir of relatively dense and warm gas of mass about that of the dusty super-heated layer derived by the SED analysis. We therefore think that the hypothesis that the CO submm/FIR lines originate in the disk is very reasonable.