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Astron. Astrophys. 320, 575-579 (1997)

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3. Discussion

To obtain physical parameters of the envelope of CRL 2688, we have calculated the CS line intensities with the Large-Velocity-Gradient(LVG) approximation. In the modeling based on 13 CO interferometric observations (Yamamura et al. 1996), we calculated the gas density in the envelope of CRL 2688 under a given temperature distribution. The result was that the density distribution is roughly spherically symmetric in this source. In this model, the high-velocity component is present at the part of the core of radius of [FORMULA] cm. However, it is clear that the spherically symmetric model cannot reproduce the doubly peaked morphology in the observed CS maps.

For a new model to be consistent with the previous model based on the 13 CO observations, we introduce the model in which the CS abundance is enhanced at the narrow postshocked regions located at the inner core. Overall density and kinetic temperature distributions in the outer envelope are taken to be the same as used in the 13 CO modeling and the CS abundace is constant in the outer envelope. The postshocked regions are located near the center within a few arcsec. The shock is considered to propagate in narrow cones from the central star in the two opposite directions, reaching now at the radius [FORMULA] from the center. For simplicity, we assume that the postshocked regions are represented by two oppositely placed frustums of narrow cones (for geometry, see Fig. 13 of Yamamura et al. 1996) and that the CS abundance is uniform in the frustums. The axis of the narrow cone is taken to be rotated by 45 degree from the north (slightly misoriented from the bipolar axis). The top and bottom of the frustum of cone are taken to be located at radii, [FORMULA] and [FORMULA], from the central star. The CS abundance, an opening angle of the cone, and gas kinetic temperature in frustums of the cone are taken as free parameters and to be adjusted to fit the calculated to the observed intensity of the doubly peaked feature of CS emission. The gas density is given by the assumption of the constant mass loss rate of 3.0 [FORMULA] 10-4 [FORMULA] yr-1 for both inside and outside of the cone (Yamamura et al. 1996).

The rate equations are numerically solved under the LVG approximation. The level populations of CS up to [FORMULA] 12 are calculated and intensities at each position and at each frequency are multiplied by the beam factor and converted to the flux densities in velocity channel maps. They are compared with the observed channel maps. The calculated channel maps are shown on the three separated panels at the bottom right in Figs. 2 and 3. The best-fit parameters of the model are shown in Table 1. The model correctly reproduces the singly and the doubly peaked distributions in the the [FORMULA] 1-0 and [FORMULA] 2-1 channel maps and the peak fluxes of both [FORMULA] 1-0 and 2-1 lines in the model are consistent with the observational values (see also Fig. 4). The excitation temperature of the CS [FORMULA] 1-0 and 2-1 lines in the model is about 10 K at the outer envelope and at about 40 K in the cone.


Table 1. Model Parameters

The CS abundance in the postshocked region, [FORMULA] per H2, which is obtained in this paper is by about a factor of few smaller than the value obtained by the previous single-dish observations in the [FORMULA] 3-2, and 5-4 transitions (Bujarrabal et al. 1994). This is because the previous model assumed the mass loss rate by a factor of 3 smaller than used in this paper and the distribution of CS was uniform in the envelope. In addition, we use a higher kinetic temperature in the cone. The overall abundance of CS as [FORMULA] is consistent with the LTE atmospheric abundance in carbon stars (Lafont et al. 1982).

The increase of the CS abundance in the postshocked region can be explained by a shock chemistry. Based on time-dependent kinetic calculations, Mitchell (1984) demonstrated that the abundance of sulfur-containing molecules increases at postshock region. In this scheme, the CS molecule is created by the reaction, CH + S [FORMULA] CS + H . For the slow shock ([FORMULA] km s-1), the CS abundance is enhanced by about two orders of magnitude at postshocked region. The higher-velocity shock gives a lower CS abundance. This picture of shock chemistry seems to fit well to the present observations. The presence of emission of high J transitions for CO and CS (Jaminet et al. 1992, Bujarrabal et al. 1994) strengthens this idea. Moreover, the high abundance of complex radicals as C2 H and C4 H (Fukasaku et al. 1994) may indicate that the carbon chain molecules are dissociated in the shocked region.

The emission peaks of the [FORMULA] 2-1 line are not aligned in the direction of the optical bipolar axis (see the HST picture taken by Sahai et al. 1995), but rather in the direction close to the line connecting the center positions of the 13 CO high-velocity flow (Yamamura et al. 1995). It is possible that the positions of the shock are not on the bipolar axis but at slightly different locations . Mapping observations of near-infrared H2 lines revealed quadra-polar components which are oriented along and perpendicular to the optical bipolar axis. (Latter et al. 1993, Skinner et al. 1996).

In contrast to CS, the other high-density tracers as HCN (Bieging & Rieu 1996), H13 CN, HNC, HC3 N, and SiS (Nguyen-Q-Rieu and Bieging 1990) exhibit an feature elongated in the direction perpendicular to the optical bipolar axis in CRL 2688. The CS [FORMULA] -1 maps (Hajian et al. 1995) in CRL 618 does not exhibit any paticular sign of the shock enhancement of CS in the envelope but rather a clumpy structure which is similar to the structure found in CO (Shibata et al. 1993). It seems quite difficult to interpret all these observations consistently with a simple model. Models with clumpy or multiple-shell structures, may be necessary to explaine these observations. Higher spatial-resolution observations are definitely required to resolve complex morphological and kinematical structures of these sources.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998