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Astron. Astrophys. 327, 689-698 (1997)

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4. Mass, momentum and molecular abundances in OH 231.8+4.2

4.1. Calculation procedures and assumptions

We have calculated the mass and momentum of the clumps present in OH 231.8 and the abundances of the observed species. Some assumptions about the morphology and gas distribution in the source and the excitation conditions are needed. OH 231.8 does not show spherical symmetry but, as usually occurs for PPNe, a bipolar appearance. Moreover from our data we find that a clumpy structure is present in this nebula. For simplicity, we have defined six separated clumps, the central one that presents no axial velocity and presumably expands in a spherically symmetric way, and five kinematically independent regions of emitting gas flowing along the symmetry axis. The projected velocity ranges in km s-1 associated to the different clumps are the same used in Figs. 3 and 5 (see Sect. 3), I1 to I6. The source is found to be asymmetric about the system's equatorial plane. The I1 and I2 intervals are associated to the north lobe and the I4, I5 and I6 to the southern one. I3 is central spectral feature. We suppose that the clumps are homogeneous, i.e. molecular abundances do not vary inside the same clump. However, a change in the abundances from one emitting region to another is allowed.

We will assume that the 13 CO lines are optically thin. This is supported by the high difference between the observed 12 CO and 13 CO intensities, in spite of the expected similar excitation of both molecules. In fact both molecules are close to be thermalized for the density values, [FORMULA] 104 - 105 cm-3, that correspond to the mass we will derive below. If the excitation of the lines of both species is similar and the 12 CO lines are opaque, we can deduce the 13 CO line opacities. We so find from the 12 CO/13 CO intensity ratio (see Fig. 6) that the opacities of the 13 CO lines are [FORMULA] (2-1) [FORMULA] 0.4 and [FORMULA] (1-0) [FORMULA] 0.3, at the central velocities (and much smaller at other velocities). For these opacity values, the assumption of optically thin emission for the J =1-0 line, made below for the estimation of the nebular mass, would lead to an underestimation of the central clump mass of (only) 15%. Note from Fig. 6 that a strong opacity effect is expected in the 12 CO line core.

[FIGURE] Fig. 6. Ratio of the integrated intensity in representative velocity ranges, I1 to I5, for 12 CO and 13 CO transitions. The meaning of the different dashes is indicated in the top of the figure.

We will assume that the excitation temperature is the same in the CO low-J transitions, and equal to a rotational temperature, [FORMULA]. This assumption could be rough in some cases but is useful to derive physical parameters from the observations and the calculated values can be easily scaled if one wants to change the assumed excitation state. In the case of CO, that has a low permanent electric dipole moment, the probable thermalization by collisions would ensure the existence of a single rotational temperature. From our data we find that the rotational temperature does not practically vary along the axis. This can be seen in Fig. 6. In this figure we show that the 13 CO 2-1/1-0 main-beam temperature ratio in the different velocity ranges remains practically constant with a value [FORMULA] 2.8. Since the clumps at the different velocities are practically unresolved in this source we must take into account the beam size and the spatial extent of the source to obtain the brightness temperature ratio. Assuming an extent of the CO clumps of about [FORMULA] (see Sects. 1 and 3), we get that the 13 CO 2-1/1-0 brightness ratio is [FORMULA] 1.1 in agreement with the 13 CO opacities given above; see a similar discussion by Bujarrabal et al. (1997). A similar value is obtained if we take the 12 CO line ratio as estimator of the relative dilution factor at both frequencies (since 12 CO is probably optically thick). Following the general discussion and calculations by Bujarrabal et al., this ratio indicates that the rotational temperature has a low value, [FORMULA] 10 K. Note that the deduced value of the rotational temperature would be even lower if we assume a smaller extent for the emitting region. Those authors also find a low excitation temperature ([FORMULA] 15 K) in M1-92, an O-rich PPN in many respects comparable to OH 231.8, particularly in its CO emission. The calculated rotational temperature would be an underestimation if the lines are optically thick, but we note that for the typical opacities deduced in the above paragraph a weak effect is expected in the determination of the rotational temperature and values of [FORMULA] [FORMULA] 15 K are still calculated.

With the above assumptions and for a given 13 CO abundance, we can calculate the total mass of the clumps (Sect. 4.2). These values of the mass will be used to estimate the abundances of the other molecules. For such a purpose, we will further assume that their lines are optically thin and that the level excitation can be described by a single rotational temperature, that we take to be the same as for CO, [FORMULA] 10 K. The low opacity assumption could be wrong in some cases, particularly for the HCN emission, which would lead to an underestimation of the molecular abundance. However, the fact that the emission from other molecules than CO is never significantly stronger than that of 13 CO (for a given wavelength) suggests that their opacities are not much larger than those of 13 CO. The derived abundances can be easily scaled from our results if we assume a different rotational temperature. We so obtain a first estimation of abundances in the nebula, but we must keep in mind that a deeper analysis of the excitation of the different molecules could be useful to improve the determination of the abundances.

4.2. Clumps in OH 231.8: mass and momentum

We have computed the mass of the clumps in OH 231.8 from our 13 CO J =1-0 data taking into account the assumptions in Sect. 4.1 and a distance to the source of 1.5 kpc (a previous estimation of this mass from 12 CO data can be seen in Alcolea et al. 1996). For this molecule, we suppose a relative abundance X(13 CO) (= 13 CO/H2 abundance ratio) of 2 10-5 (see Bujarrabal et al. 1997). 13 CO data for the southern clump with the extreme positive velocity (I6 velocity range) was found to be too noisy to calculate its mass properly. Then we have made our calculations for this velocity range from the 12 CO 1-0 maps assuming a relative abundance X(12 CO) of 2 10-4. This value is consistent with the abundance that we would obtain in the I5 velocity range (also in the south lobe) applying to 12 CO the procedure described in Sect. 4.1, and also compatible with the CO abundances expected in this kind of objects (see e.g. Alcolea et al. 1996). All the results, presented in Table 1, have been calculated using [FORMULA] = 10 K. However we have also made calculations with values of [FORMULA] = 5 and [FORMULA] = 15 K (as we have mentioned, temperatures higher are improbable). The value of the mass contained in the nebula that we find in this two cases is higher than the obtained value using [FORMULA] = 10 K. Nevertheless, variations greater than 20% have not been found. As we see in Table 1, a total mass of [FORMULA] 0.5 [FORMULA] is calculated for the whole nebula. Approximately the 58% of the molecular mass is contained in the central component, and the 23% and 19% are distributed in the north and south lobes, respectively.


[TABLE]

Table 1. Mass, average (deprojected) velocity with respect to the systemic velocity, [FORMULA], and momentum associated to different spectral intervals.


There are however indications of that we are underestimating the actual mass. We have already discussed (see Sect. 4.1 and previous paragraph) that some underestimation in the mass calculation can be produced due to opacity effects and an erroneous assumed temperature, mainly for the central component. Moreover, the mass in dust grains deduced for this nebula (Kastner et al. 1995) is very large, [FORMULA] 0.01 [FORMULA] ; since the typical gas/dust mass ratio in these evolved objects is about 100, we expect a total mass somewhat larger than our estimation, [FORMULA] 1 [FORMULA]. Finally, we know that photodissociation begins to take place in the PPN phase destroying a large fraction of the molecules in the envelope, even 12 CO and 13 CO. Then the standard value of the 13 CO abundance that we have assumed could be an overestimation of the real one. This fact obviously gives place to a higher value of the calculated mass. However, we do not think that the molecular masses can exceed by more than a factor two those given here, since 1 [FORMULA] is similar to the mass value given from grain emission measurements and because it is already high for the mass ejected by an object of this kind (see discussion by Alcolea et al.).

The mass results presented in this paper are comparable to those given by Alcolea et al. (1996). However, our data indicate now a greater amount of molecular material in the lobes. The total mass flowing axially practically equals the mass in the central clump. We think that our new mass estimations from 13 CO data are better than the previous ones, from 12 CO observations, due to the uncertain correction for opacity in the 12 CO lines. Note also that the slightly lower rotational temperature assumed here has a more reliable empirical basis.

Once we have the mass of the clumps, we can calculate the momentum associated to these different regions of emitting gas. We have calculated the flow velocity taking into account the inclination of the polar axis with respect to the plane of the sky, 40 [FORMULA] (Sect. 1), and assuming a systemic velocity of 33 km s-1. The results are shown in Table 1. We find differences smaller than 10% between the momentum driven by the north and south lobes, since the larger velocity in the southern lobe is compensated by a smaller mass. These results are consistent with the actual ideas of post-AGB evolution, which suppose that the momentum of the post-AGB fast wind and the momentum transfer rate to the AGB shell is the same in both lobes (Sect. 5).

From the mass and velocity distribution given here we can also estimate the mass loss rate that originates, during the past AGB phase, the actual molecular envelope of OH 231.8 and the time spent in the post-AGB phase by this source, following the procedures described by Alcolea et al. (1996). Since the numerical values to be used are similar to those obtained by these authors, we just confirm their results, i.e. a past mass loss rate [FORMULA] 10-4 [FORMULA] yr-1 and a post-AGB time of about 1000 yr.

4.3. Molecular spatial distribution

Following the procedures explained in Sect. 4.1 and taking into account the total mass of the clumps obtained from the 13 CO data (see Sect. 4.2; note that, therefore, the calculated molecular abundances depend on the assumed relative abundance of CO) we have calculated the molecular abundances of the observed species (excepted 12 CO, the emission of which may be optically thick). We present these results in Table 2.


[TABLE]

Table 2. Calculated molecular abundances in the different clumps associated to the different velocity ranges (LSR).


We note from these results the approximately constant abundance along the whole nebula of HCN, HNC, and CS, that may be slightly more abundant in the central core (which could also be due to a weak opacity effect in the 13 CO emission and therefore to a slight underestimation of the mass of the central clump). It is also remarkable that the north lobe has a significantly larger SiO abundance than the south lobe; the opposite is found for SO2. Note that such an asymmetry in the SiO and SO2 abundances can be directly inferred from the intensity distributions (Figs. 1, 4) and that it cannot be due to excitation effects, since for both lines the levels are placed at a similar high energy from the ground.

The most interesting result from these calculations is the very strong decrease in the central clump of the [FORMULA] abundance, that is about three times lower than in the outer parts of the nebula. Also in this case, the behavior of the abundance is expected from the direct measurements. As discussed in Sects. 3 and 5 this effect cannot be explained invoking selfabsorption nor excitation effects. In general, the [FORMULA] intensity is found to be particularly high, as happens for other PPNe and PNe and contrarily to the case of the AGB envelopes, where [FORMULA] emission is very weak and its abundance is thought to be very low. This relatively high [FORMULA] abundance in PPNe could be due either to shock induced or to photon dominated chemistries (Cox et al. 1992). Our results suggest that the efficient formation of this molecule in OH 231.8 is due to shock chemistry, since the [FORMULA] emission appears particularly intense in the shock-accelerated lobes, and not in the clump close to the star where one expects the maximum photoionization rate. On the other hand, Cox et al. conclude that the high [FORMULA] abundance also deduced for another PPN, CRL618, is due to photochemistry, based on the relatively low wing/core intensity ratio observed in this source. We note that these diverging conclusions are difficult to avoid since they are directly based on the different properties of the observed [FORMULA] spectra in these sources, that are indeed quite different objects. The axial distortion in the molecular envelope of CRL618 is slight and the flow occupies a tiny region, moreover, CRL618 is carbon rich.

Our molecular abundances are somewhat lower than those derived by Morris et al. (1987) for the whole nebula. The discrepancy is mainly due to the different value of the total mass or, equivalently, of the 13 CO abundance. In Morris et al. the 13 CO relative abundance is quite high, 10-4, and subsequently the total mass is lower than ours. We also note the difference between the rotational temperature assumed in both works (Morris et al. assumed a rotational temperature equal to 25 K), which mainly affects the abundance determination for SO2, since we observed a relatively high-excitation line for this molecule. In both works, the rotational temperature has been obtained from observational data, but our observations (ten years after) are significantly more accurate and take into account the different parts of the nebula. We also note that Morris et al. only derive average values for the whole nebula, contrarily to our results that include information about the chemical variations across the nebular axis.

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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998
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