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Astron. Astrophys. 353, 583-597 (2000)

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5. Possible scenarios for the shell formation

5.1. The case for a He-shell flash

Whatever the underlying cause of the shell is, it seems impossible to escape the conclusion that TT Cyg has gone through a period of considerable variations in its mass loss properties although the exact time scale is uncertain. Certainly, the expansion velocity of the gas must have been considerably higher in the past, and this normally means also a substantially higher mass loss rate. The ratio of the mechanical momentum rate of the shell gas and the radiation momentum rate is high, [[FORMULA][FORMULA]/[FORMULA]] / [L/c] [FORMULA] 4 (this could be even higher if the shell width, [FORMULA], is mainly due to broadening during the expansion, or considerably less if the gas is mainly swept-up during a longer time scale). Taken at face value it suggests a mass loss driven by radiation pressure on dust at the maximum possible rate, perhaps at a higher luminosity than the present one, or the presence of another mechanism. The corresponding ratio for the present mass loss epoch is 0.003.

TT Cyg is one out of five C stars with clearly detected detached CO shells: R Scl (radius [FORMULA]10", a shell expansion velocity of 16[FORMULA] results in a shell age of [FORMULA]1300 yr at a distance of 420 pc; Olofsson et al. 1996), U Cam (8", 23[FORMULA], [FORMULA]800 yr at 500 pc; Lindqvist et al. 1999), U Ant (41", 20[FORMULA], [FORMULA]2300 yr at 260 pc; Olofsson et al. 1996), S Sct (67", 17[FORMULA], [FORMULA]8100 yr at 400 pc; Olofsson et al. 1996), and TT Cyg (35", 13[FORMULA], [FORMULA]6800 yr at 510 pc). The shell velocities are high when compared with the expansion velocities of normal envelopes of bright carbon stars (Olofsson et al. 1993). Within the considerable uncertainties the shell masses are all about 0.01[FORMULA] (Olofsson et al. 1996), except for the young shell around U Cam for which the shell mass is estimated to be [FORMULA]0.001[FORMULA] (Lindqvist et al. 1999). The three stars with the older CO shells have very low present mass loss rates, a few[FORMULA]10[FORMULA], and low present wind velocities, [FORMULA]5[FORMULA]. For U Cam a present mass loss rate of [FORMULA]2[FORMULA]10[FORMULA] and a present wind velocity of [FORMULA]12[FORMULA] have been estimated (Lindqvist et al. 1999); for R Scl these quantities have not been possible to estimate due to the limited spatial resolution of the observations. The stars with detached CO shells belong to the sample of 68 visually bright C stars detected in circumstellar CO radio line emission by Olofsson et al. (1993), and they are all irregular or semiregular variables. The full sample of Olofsson et al. consists of [FORMULA]120 C stars, and it is expected to be reasonably complete in C stars out to a distance of [FORMULA]1 kpc. According to the calculation in Sect. 4.5 (see also Bergman et al. 1993) detached shells of this type are detectable in CO radio line emission for [FORMULA]104 yr if the medium is clumped. The fraction of stars with detached CO shells suggests that the process responsible for the shell formation occurs on a time scale of [FORMULA]105 yr. This is in fact the time scale between He-shell flashes for lower-mass C stars (Wagenhuber & Groenewegen 1998). Therefore, in our opinion the `He-shell flash'-induced ejection of matter, suggested by Olofsson et al. (1990) and further elaborated by Vassiliadis & Wood (1993), Schröder et al. (1998, 1999), and Steffen & Schönberner (1999), remains the most reasonable explanation for the detached CO shells, and consequently also for the TT Cyg shell. We note here that Izumiura et al. (1997) used this scenario and the possible presence of two detached dust shells around U Ant to derive its present (high) core mass and its main sequence mass. Steffen et al. (1998) present an alternative origin for the detached shells. According to them, a narrow shell develops when the star is recovering to its normal luminosity, a few thousand years after the He-shell flash, and the wind goes from being shock-driven (low [FORMULA]) to being dust-driven (high [FORMULA]). However, the very low present mass loss rates of our stars suggest that they are not presently increasing their mass loss rates above the dust-driven wind limit. Although this mechanism may work we find this an unlikely explanation for the existence of the CO shells.

It is somewhat puzzling that the only C stars with detected CO shells are all members of the Olofsson et al. (1993) sample. Afterall, it represents only about 10% of all AGB-stars detected in circumstellar CO. This sample is clearly dominated by low mass loss rate objects (mainly irregulars and semiregulars), as opposed to most other surveys that have concentrated on higher mass loss rate objects (e.g., selected based on the IR-colours). It is conceivable that also the high mass loss rate objects have detached CO shells, but their contrast (in the CO radio line emission) against the normal envelope emission is much lower, and their on average larger distances make the spectral features of the shell emission (markedly double-peaked if spatially resolved) less conspicuous. Schröder et al. (1998, 1999) suggest that the shells are extra prominent in low mass objects, since these can drive (by radiation pressure on dust) substantial mass loss only during a He-shell flash. This result is, however, dependent on a prescription for how the mass loss rate depends on e.g. the stellar luminosity and, in particular, the effective temperature.

In principle, one would expect to see detached CO shells also around similar M stars. However, this is not the case as shown in a recent survey of irregularly and semi-regularly variable M stars by Kerschbaum & Olofsson (1999), where 66 low mass loss rate objects were detected in circumstellar CO. According to Little et al. (1987) these stars very rarely, if ever, show any evidence of technetium in their atmospheres, and it is therefore not clear whether they have gone through a He-shell flash. So far, only a tentative detection of a detached dust shell around the M-Mira R Hya exists (Hashimoto et al. 1998). We note that Wood & Zarro (1981) argue, for other reasons, that this star is going through a He-shell flash. In view of the results by Schröder et al. (1998, 1999) one may speculate that the absence of CO shells around M stars is related to lower luminosities and/or the different composition(s) of their dust grains. Finally, we note that Knapp et al. (1998) suggest that the presence of multi-component CO radio line profiles towards a number of C and M stars may be related to episodic mass loss.

Even if a He-shell flash induced mass ejection has caused the formation of the shell around TT Cyg, it is not clear how the present day properties of the shell relate to the variations of the stellar properties during the mass ejection. We can imagine two (extreme) scenarios in connection with this: i) all the material in the shell was ejected at a very high rate during a short period and it has subsequently evolved during the expansion, or ii) the ejected material has interacted with a previous slow stellar wind leading to a narrow shell of mainly swept-up gas. Below we discuss the pros and cons of these two scenarios. In Sect. 6 we present various ways to reach a better understanding of the shell formation process.

5.2. A brief high mass loss rate period

This is an attractive scenario since it relates the present density distribution in the shell more directly to the mass ejection, but it is not without difficulties. The mass loss rate must have been of the order 0.007[FORMULA]/500 yr [FORMULA] 10[FORMULA], which is no problem in itself. However, the ejection must have been very isotropic in mass - within a factor of two the same amount of material appears to have been ejected in all directions (averaged over about 0.2 steradians) -, and also in velocity - the ejection velocity must have been isotropic to within [FORMULA]3%, i.e., [FORMULA] varies by less than [FORMULA]0.3[FORMULA]. In particular, the latter is surprising considering the (presumed) complexities of the mass loss process and the inhomogeneous density structure of the shell gas. This points in the direction of a coordination of the ejection, i.e., something that can be provided by a He-shell flash. Furthermore, one would expect the shell to broaden during expansion due to thermal/turbulent motion. We can put a limit to the present random motion using the line shapes and the overlaps of the brightness distributions in nearby velocity intervals. This suggests a random motion less than [FORMULA]1[FORMULA]. If this applies also to earlier times we expect a broadening of the shell by [FORMULA]3", i.e., comparable to the shell width. Consequently, the ejection time scale may have been very short, perhaps substantially shorter than the time scale corresponding to the present shell width, [FORMULA]500 yr. During such a short period the mass loss rate must have been very high, perhaps even higher than what can be driven by radiation pressure on dust. Finally, it is most likely that the star was losing mass at some rate and probably at a lower velocity before the mass ejection, and some interaction with the previous wind could therefore be expected. We also note here the considerable variations in shell width, and in particular the broadening towards the northern pole, that may indicate the presence of an interaction at some level.

5.3. Interacting winds and swept-up gas

This scenario is reasonable, but it makes it far more difficult to relate the present properties of the shell to the mass ejection mechanism. There are obvious problems also with this scenario. The surrounding medium must be extremely homogeneous, since an interaction tends to enhance any asymmetries there are. Most likely such a medium consists of a previous slow stellar wind, rather than an interstellar medium (since the tangential proper motion of the star and the shell by [FORMULA]40" since ejection has not led to any appreciable effects, see Sect. 4.4). In this scenario the mass estimate could be a severe underestimate unless substantial amounts of CO were still present in the slow wind and survived the shock (which may be possible considering the expected low shock velocity) or were produced in the swept-up post-shock gas. A lower limit to the slow wind average mass loss rate is roughly given by 0.007[FORMULA] / 7000 yr [FORMULA] 10[FORMULA], a not impossible value for this type of C star although it is almost an order of magnitude higher than the median mass loss rate found by Olofsson et al. (1993) for their sample of bright carbon stars. The CO photodissociation radius of a 10[FORMULA] wind is [FORMULA]1017 cm or [FORMULA]10" (Mamon et al. 1988), i.e, very little CO would remain in the swept-up gas if it is relatively homogeneous. However, if the shell mass is severely underestimated, a considerably higher mass loss rate will result and this will impose a problem, since there is no evidence for any material outside the shell, the CO brightness contrast is at least a factor of ten.

The conditions in the circumstellar environment of an AGB-star are such that an interaction between two stellar winds is not an unreasonable event. A 10[FORMULA] wind will have an H2 density of [FORMULA]150[FORMULA][FORMULA] cm-3 if the expansion velocity is 10[FORMULA] ([FORMULA] is the radius measured in units of 1017 cm). The mean time between collisions when such a wind interacts with a higher-velocity wind is [FORMULA]1[FORMULA][FORMULA]/[FORMULA] yr ([FORMULA] is the relative wind velocity in units of 10[FORMULA]). Thus, for [FORMULA]=1 we get a collision time of [FORMULA]10 yr at the present location of the shell, i.e. considerably shorter than the expansion time scale. We can make some quantitative estimates using the formulae derived by Kwok et al. (1978) for a fully momentum coupled wind interaction with a strongly radiative shock. In steady state the shell velocity is given by


the shell mass by


and the relative shell width by


where the subscripts 1 and 2 refer to the slow and the fast wind, respectively, and [FORMULA] is the kinetic temperature of the shell gas. As an example we choose [FORMULA]=[FORMULA]=10-6[FORMULA], [FORMULA]=10[FORMULA], [FORMULA]=20[FORMULA], [FORMULA]=100 K (see Sect. 4.5), and t=7000 yr, and obtain [FORMULA][FORMULA]14[FORMULA], [FORMULA][FORMULA]0.005[FORMULA], and [FORMULA][FORMULA]0.01, i.e., results comparable to those estimated for the TT Cyg shell except for the shell width, which is a factor of 4-10 smaller than the width of the CO emission. The density compression by a factor of 10-15 requires effective cooling of the post-shock gas. However, a simple calculation for the relevant conditions in the shell suggests that this cannot be provided by the gas. Dust cooling could be more effective if the temperature is high enough. We estimate that in the present shell the dust cooling time scale would be of the order 103 yr, which is marginally sufficient. The time scale for formation of CO in the swept-up gas is determined by the time scale for C to collide with O (or compounds thereof) and this is lower, by at least a factor of 103, than the collisional time scale. Considering the estimated density and temperature in the shell, this puts some severe doubts on the efficiency of CO production in the post-shock gas. Thus, the case for an interacting wind scenario is not fully convincing, but the time scales will decrease if the medium is highly clumped.

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Online publication: December 17, 1999