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4 LVG modeling of the CO emission

As discussed in Sect. 3, the CO  $J=6 \rightarrow 5$ emission is due to two components: the dense envelope+disk system, probed by the 13CO emission, whose linewidth is $\sim$3.6 km s-1 (Fig. 2) and the outflow, probed by the 12CO wing emission, whose linewidth is $\sim$10 km s-1 (Fig. 3). Both components are in principle within the 80'' LWS beam and therefore the observed CO J=15 to J=20 emission may be due to either or both of them, or, finally, none of them. Unfortunately, the spectral resolution of the ISO observations is not enough to disentangle the two contributions so that the origin of the CO J=15 to J=20 emission is unclear based only on the observational facts. We will therefore try to use theoretical arguments to shed light on the origin of the $J \geq 15$ emission.

To interpret the observed CO spectrum we used an LVG model, applied to a slab geometry, where the escape probability depends on the line opacity through the relation (Scoville & Solomon 1974): $ \beta = \frac{1-{\rm exp}[-3 \tau]}{3 \tau} $. Our model considers the first 50 rotational levels, with the collisional excitation rates taken from McKee et al. (1982). More details on the code used and formalism can be found in Ceccarelli et al. (2002). In the present computations we neglect the dust radiation pumping of the CO levels. The computed CO line emission depends on five parameters: the density and the temperature of the gas, the linewidth, the angular extent of the emitting region and the CO column density. We ran several models spanning a large parameter space: density between 105 and 108 cm-3, temperature between 50 K and 800 K, N(CO) between 1016 and 1019 cm-2.

When the lines are optically thin (i.e. N(CO)  $\leq 10^{18}$ cm-3) the line ratios do not depend on the CO column density and can be used to constrain approximatively the gas temperature and density, whereas when the lines are moderately optically thick, the line ratios also depend on the CO column density. Even assuming that the $J \geq 15$ lines are optically thin the observed line ratios yield only loose constraints: the gas temperature is higher than $\sim$250 K and the density is higher than $\sim$ $ 3 \times 10^5$ cm-3. Allowing the lines to be optically thick, which in principle is possible, does not improve the situation much. Practically, modeling of the $J \geq 15$ observed emission does not help to understand its origin. We therefore try to model the CO $J=6 \rightarrow 5$ emission and to see whether it can help to understand the origin of the J=15 to J=20 emission too. As discussed in Sect. 3, the CO  $J=6 \rightarrow 5$ emission observed in the central position originates mainly in the envelope+disk. These observations, and in particular the 13CO ones, turn out to be the key to understand where the FIR CO lines originate. To interpret the observed J=6 to J=20 lines, we use the LVG model described above. Although a LVG model is by definition a rough description of the emission associated with the envelope+disk, whose temperature and density is far from constant, we think it is worth having a first approximation of the average density and temperature of the gas responsible for the CO emission. We assume then that the emission is generated by a gas whose linewidth is 3.6 km s-1 (Fig. 2) and whose extent is smaller than the beam of the CO  $J=6 \rightarrow 5$ observations, i.e. $12'' \times 12''$.

The fact that the 13CO  $J=6 \rightarrow 5$ line intensity is half the 12CO intensity puts a stringent constraint on the line opacity and consequently on the CO column density, the emitting sizes and gas temperature. Taking the isotope abundance 12CO/13CO = 80 (Boogert et al. 2000), the observed line ratio implies $\tau \sim 15$ and a CO column density between 3 and  $7\times 10^{18}$ cm-2. The exact column density value depends on the gas temperature: if N(CO)  $=3 \times 10^{18}$ cm-2 then the gas temperature is $T_{\rm gas}=$ 90 K and the size is $\Delta \theta=5''$; the upper value N(CO)  $=7 \times 10^{18}$ cm-2 implies $T_{\rm gas}=$ 200 K and  $\Delta \theta=3''$. In the following we consider the median values: N(CO)  $=5 \times 10^{18}$ cm-2, $T_{\rm gas}=$ 170 K and $\Delta \theta=4''$ (=550 AU for a distance of 160 pc). Using the parameters derived from the  $J=6 \rightarrow 5$ observations, we computed the J=15 to J=20 CO spectrum for a gas density from 106 to 108 cm-3 (Fig. 5). Although the CO  $J=6 \rightarrow 5$ data do not allow us to constrain the density, we can reasonably assume that it is higher than at least 106 cm-3, as the (more extended) ridge in which EL 29 is embedded has itself a density of $\sim$ $5 \times 10^5$ cm-3 (BHC02). Actually, the model by Chiang & Goldreich (1997; hereinafter CG97) which fits the EL 29 continuum spectrum predicts a midplane disk density of $\sim$109 cm-3 at $\sim$250 AU (BHC02), the size derived by the CO  $J=6 \rightarrow 5$. Figure 5 shows then that most, if not all of the $J \geq 15$ emission is also due to this envelope+disk component. Gradients in the density and/or temperature would certainly account for the minor differences between the observed and predicted FIR fluxes.

   
Table 2: Warm gas: parameters derived from the LVG analysis of the CO submm and FIR line emission towards EL 29.
Parameter Value
Temperature 170-250 K
Density $\geq$106 cm-3
Size 4''=550 AU
N(CO) $5 \times 10^{18}$ cm-2
CO/H $1-3 \times 10^{-4}$
Mass $8-24 \times 10^{-4}~M_\odot$

The upper limits on the H2 line fluxes put some stringent limit on the CO abundance. Assuming LTE and optically thin lines, as is likely for the H2 rotational lines under consideration, the upper limits on the observed fluxes translate into an upper limit to the H2 column density, and hence a lower limit to the CO abundance x(CO) =N(CO)/( $2 \times N$(H2)). Taking into account the high extinction toward EL 29 ($\sim$27 mag; Boogert et al. 2000, 2002) and correcting for it assuming the $A_\lambda$/Av ratio by Lutz et al. (1996), gives CO/ $H\geq 1 \times 10^{-4}$. In practice, as expected based on the temperature, CO is not depleted in the warm region. It is worth noting that CO is not photo-dissociated either, probably because of the shielding from the remaining envelope. Finally, the computed 13CO FIR line fluxes ($\leq$ $5\times 10^{-14}$ erg s-1 cm-2) are below the LWS detection limit and therefore consistent with their non-detection, despite the fact that 12CO lines are moderately optically thick. The non-detection of water lines implies a H2O column density lower than $\sim$1016 cm-2, giving a water abundance $\leq$ $5 \times 10^{-7}$ (assuming the largest possible CO abundance, i.e. CO/H  $= 3 \times 10^{-4}$; Lacy et al. 1994) in the gas emitting the warm CO.

In summary, the CO J=6, J=15 to J=20 observed emission may originate in a component located at about 250 AU from the center and whose mean density is $\geq$106 cm-3 and temperature $\sim$170 K (Table 2).

  \begin{figure}
\par\includegraphics[width=6.6cm,clip]{ms2628f5.ps}\end{figure} Figure 5: Observed and modeled CO spectrum towards EL 29. Fluxes are in erg s-1 cm-2. Solid lines represent a model with N(CO)  $=5 \times 10^{18}$ cm-2, emitting sizes equal to 4'', the gas temperature equal to 170 K, and density from 106 to 108 cm-3, as marked in the plot. The dashed line shows a case with density equal to 106 cm-3 and a temperature equal to 250 K. Note that the error bars do not include the 20% absolute calibration uncertainty in the $J \geq 15$ lines with respect to the J=6 line.

The mass of this warm gas amounts to $\sim$ $8 \times 10^{-4}~M_\odot$ (assuming CO/H  $=1 \times 10^{-4}$; a larger CO abundance would give a linearly lower warm gas mass). It is worth emphasizing that this result stems mostly from the interpretation of the CO  $J=6 \rightarrow 5$ observations (12C and 13C observations), without further adjustments other than the density to explain the J=15 to J=19 observed emission too.


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