Astron. Astrophys. 317, 962-967 (1997)

3. Modelling of the chemical scheme in IRC+10216 envelope

In order to take into account the stellar envelope expansion, the chemical scheme described previously must be solved by means of the coupled continuity equations:

where are the species concentrations, v is the mean flow velocity and are respectively the product and loss rates of the i compound in the chemical reactions. Considering a steady spherically symetric flow, the equation set can be expressed as:

where are the reaction rates. This system has been solved using Runge-Kutta method (4th order). The abundance of acetylene in the internal part of the envelope has been deduced from the measurement of its absorption band at 3.04 µm (Keady et al. 1993). It corresponds to (within a factor 2 of accuracy). We have used this value as the initial abundance in the internal envelope. In fact, the acetylene molecule is involved in a large number of ion-molecule or radical-molecule reactions. However, the modelling of Cherchneff et al. (1993) shows that a very small fraction of its initial abundance is effectively converted to subproducts in the internal and intermediate envelope (about ). It is only in the external part () that gets completely photodissociated into . The metal (M) initial abundance has been taken equal to that of free iron, supposed to be the most abundant transition metal in the envelope, as in the Interstellar Medium. We have adopted its cosmic abundance with a depletion factor () to take into account the fraction already included into the grains formed in the internal envelope. This depletion factor will be kept as a free parameter in the model. As it was noticed in Sect. 2, when considering M as a metallic cluster of n atoms, one must multiply the value by in order to compensate for the change both of the cross section and of the abundance (varying respectively as and ). In addition, we have considered that the competitive accretion process was continuing all along the envelope expansion ( is considered as inactive for the cyclotrimerization).

The physical parameters of the envelope (temperature, gas density and dust properties) and the central star characteristics have been deduced from the modellings of Cherchneff et al. (1993) and Rouleau & Martin (1991). In particular, we have considered small grains of amorphous carbon with an average size of . The photon density has been determined as the resulting flux coming from the central star (, stellar photosphere radius: ), and the interstellar radiation field, taking into account the dust extinction inside the envelope. In a first approximation, we have considered a radial scattering direction through the envelope. The dust density distribution is assumed to be a power law with a sharp cut-off at , according to the IR continuum on modelling of Martin & Rodgers (1987) using the dust characteristics supported by Cherchneff et al.(1993). A first estimation of the efficiency of the organometallic process in the envelope can be assessed by comparing the average colliding times between a free M atom and an acetylene molecule or a destructive photon (i.e. with ). The characteristic times are displayed on Fig. 3, as a function of the radial distance in the envelope. The results depend strongly on the bonding energy value. If , the photodestruction frequency is much higher than the coordination one, everywhere invelope. On the contrary, if , the catalytic process can develop within the radius range: . For a higher value, this favourable range increases. We have plotted on Fig. 4 the abundances given by the modelling if the mean value is adopted. The formation of aromatic molecules turns out to be very efficient and the steady-state values for and abundances are rapidly reached (within ). With a mean expansion velocity of 14km/s (Cherchneff et al. 1993), this corresponds to a very short time scale of about 30 yrs. The various abundances are given in Table 2 as a function of the bounding energy.

Fig. 3. Comparison of the mean colliding times between an iron atom and i) (solid curve), ii) a destructive photon (), with , originating from the central star (dash-dot curve) or the ISRF (dashed curve).

Fig. 4. Relative abundances given by the modelling if , and .

Table 2. Steady-state abundances of and for different values of the metal depletion factor ) and the bonding energy .

© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
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