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):
.
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)
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
lines are optically thin
the observed line ratios yield only loose constraints:
the gas temperature is higher than
250 K and the density is higher
than
cm-3.
Allowing the lines to be optically thick, which in principle is possible,
does not improve the situation much.
Practically, modeling of the
observed emission
does not help to understand its origin.
We therefore try to model the CO
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
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
observations, i.e.
.
The fact that the 13CO
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
and
a CO column density between 3 and
cm-2.
The exact column density value depends on the gas temperature:
if N(CO)
cm-2 then the gas temperature is
90 K and the size is
;
the upper value N(CO)
cm-2 implies
200 K and
.
In the following we consider the median values:
N(CO)
cm-2,
170 K and
(=550 AU for a distance of 160 pc).
Using the parameters derived from the
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
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
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
109 cm-3 at
250 AU
(BHC02), the size derived by the CO
.
Figure 5 shows then
that most, if not all of the
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.
Parameter | Value |
Temperature | 170-250 K |
Density | ![]() |
Size | 4''=550 AU |
N(CO) |
![]() |
CO/H |
![]() |
Mass |
![]() |
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)/(
(H2)).
Taking into account the high extinction
toward EL 29 (
27 mag; Boogert et al. 2000, 2002)
and correcting for it assuming the
/Av ratio by Lutz et al.
(1996), gives CO/
.
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 (
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
1016 cm-2, giving a water abundance
(assuming
the largest possible CO abundance, i.e. CO/H
;
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
106 cm-3 and temperature
170 K (Table 2).
Copyright ESO 2002