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Astron. Astrophys. 362, 1008-1019 (2000)

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5. Late He-shell flash scenario

Theoretical evolutionary PNN models predict that in some cases an initially H-burning PNN after having extinguished its H-burning shell and while being on the cooling phase can enter in a He-shell flash (Schönberner 1979, Iben et al. 1983). Convection which develops above the He-burning shell cuts into the remaining H-rich envelope. Hydrogen while being brought down to the base of the convective envelope is burnt. Helium and carbon are brought up to the surface. The star quickly brightens, expands and sets up close to the AGB. Then it repeats the PNN evolution, now as a He-burner having, most probably, a H-deficient atmosphere. Iben (1984) estimates that 5-9% of the PNN population is expected to pass through this evolutionary path.

The very late He-shell flash scenario is very appealing when trying to explain the origin of the H-deficient PNNi (Schönberner & Blöcker 1992; Iben & MacDonald 1995). First of all it explains easily the observed surface abundances (roughly 50% of He and 50% of C, by mass). Statistics also seems to agree. Tylenda (1996) estimates that about 6.5% of the PN population have [WC] type nuclei. This should be considered as a lower limit for the H-deficient PNN population, thus in agreement with the Iben's estimate.

However, this scenario inevitably implies that H-deficient PNNi should be observed preferentially in old, extended nebulae. This is of course the case of the PG 1159 type objects but not of the [WC] PNNi. As has been discussed in Sect. 3 the late-[WC] PNNi usually are observed to have dense, high surface brightness nebulae (cf. Fig. 1, Fig. 2, and Fig. 3). As concluded in Sect. 4 the histograms in Fig. 4, Fig. 5, and Fig. 6 show that the youngest nebulae (i.e. having the highest values of [FORMULA], [FORMULA] and [FORMULA]) with H-deficient nuclei are of similar evolutionary age as those with other (mostly H-rich) PNNi. One may argue that the [WC] PNNi are more massive than the others (e.g. Heap 1982). Their evolution before the late He-shell flash would then be fast and the second passage across the PNN region would occur in relatively compact nebulae. However, a detailed study of nebular abundances and morphologies in Górny & Stasinska (1995) and Górny (2000) shows that the [WC] phenomenon does not preferentially occur in massive stars. The same conclusion can also be drawn from the observed distribution of the PNe in the Galaxy (Acker et al. 1996).

5.1. Models versus observations

We have attempted to make a quantitative comparison between the late He-shell flash scenario and the observations of the H-deficient PNNi and their nebulae. In this point of the present study we follow the general approach elaborated in our previous works devoted to comparison of theoretical evolutionary models with the PN observations (e.g. Górny et al. 1994, Stasinska & Tylenda 1994, Górny et al. 1997a, Stasinska et al. 1997). The main point of our approach is that instead of trying to determine absolute values (e.g. PNN luminosity, effective temperature or PN radius) we use parameters which are easy to derive from observations and which are distance independent. Then from theoretical modelling of a given scenario we obtain values of the same parameters for direct comparison with the observations. In the present study the comparison is done in the [FORMULA] - [FORMULA] plane.

As the base of our simulations of the late He-shell flash scenario we have adopted the [FORMULA] PNN model from Iben at al. (1983) (in fact it is the only late He-shell flash model available in literature for our purpose). We also adopt that the PN is formed when the star for the first time leaves the AGB and starts evolving fast towards the PNN domain. This takes place at [FORMULA] yrs in the notation of Fig. 1 of Iben et al. (1983) when [FORMULA]. Thus we take this moment as the zero age of the PN. The PNN initially evolves as a H-burner and at the PN age of 28 600 yrs it experiences a late He-shell flash. The star quickly returns almost to the AGB and repeats its evolution through the PNN domain now as a He-burner. During this phase the star is expected to be H-deficient.

The PNN model of Iben et al. (1983) comes from calculations done for the abundances relevant to the Magellanic Clouds (Z = 0.001). This is probably the main reason why during the initial H-burning phase it evolves much slower than [FORMULA] H-burning models done by other authors for the Population I abundances (see Schönberner 1989). Indeed our preliminary calculations show that the PNN evolution in the H-burning phase of Iben at al. is not compatible with the observed distribution of the others in Fig. 7. Therefore in order to have a PNN model more relevant to the Galactic objects we have accelerated the evolutionary speed of the PNN model of Iben et al. by factor 3. In this way we have obtained a PNN model which in the H-burning phase evolves more or less like the [FORMULA] model of Schönberner (1981) and the [FORMULA] model of Blöcker (1995). Thus in our modified PNN model the late He-shell flash begins about 9500 yrs after the PN formation.

In order to be able to place the model evolution on the [FORMULA] - [FORMULA] diagram we have to adopt a model nebula. We take a simple, standard PN being a spherically symmetric shell of [FORMULA]. The PN mass is kept constant during its evolution. The PN expands during the H-burning phase at a constant velocity of 20 km s-1. At the begining of the He-burning phase we have increased the expansion velocity up to 30 km s-1. These values correspond to the mean expansion velocities for the others (presumably mostly H-burning) and for the [WC] type PNe, respectively (Tylenda & Górny 1993; Górny & Stasinska 1995). The filling factor of nebular shell [FORMULA] is adopted to be 0.5 and is kept constant with time. The model PN is ionized by the PNN assumed to radiate as a black body. Certainly the black body is a crude approximation of the PNN spectrum. However, what we need to calculate is the extension of the H+ region in the nebula which depends on the total number of ionizing photons rather than on their exact spectral distribution. In this respect the black body is expected to be a reasonable approximation as can be inferred from Leuenhagen et al. (1996). These authors have obtained a good agreement between the Zanstra (black body) temperature, TZ(HI), and their values of [FORMULA] (referring to the radius when the observed PNN radiation is mostly formed). Having derived the hydrogen ionization structure of the model nebula we can calculate the model values of [FORMULA] and [FORMULA].

The results of the above described model (later on referred to as the standard model) are displayed and compared to the observations in Fig. 8. The dashed curve shows the model evolution for the H-burning phase. The dotted curve represents the fast evolution during the thermal pulse. The full curve corresponds to the He-burning phase after the born again AGB. Large symbols represent H-deficient PNNi, small ones - the others.

[FIGURE] Fig. 8. Comparison of the modelled evolution in the very late He-flash scenario with the observations. Large symbols - H-deficient PNNi, small symbols - the others. Dashed, dotted and full lines show H-burning, thermal pulse and born-again He-burning phases, respectively.

As can be seen from Fig. 8 the dashed curve, representing the H-burning phase, can be considered as a typical model for the whole population of PNe. It fits quite well the observed positions of the others. Obviously it does not reach the lower-right part of the observed distribution in Fig. 8 as its evolution towards faint objects has been interrupted by the He-shell flash. After the flash, when the model returns to the PN region as a He-burner, it should represent the evolution of H-deficient PNNi. However, as can be seen from Fig. 8, it is not the case for the majority of the observed H-deficient objects. The full curve matches the lower-right part of the observed distribution occupied mainly be the PG 1159 objects. However, in the case of the [WC] objects the full curve cannot be considered as reproducing the observed positions. The model predicts that there should be no H-deficient PNNi for nebulae with log [FORMULA] whereas the [WC] objects in the bulk do have log [FORMULA].

In order to get a better agreement between the model and the observations one can consider larger masses of the model nebula and/or higher masses of the central star. An increase in the PN mass would obviously increase [FORMULA] and the full curve in Fig. 8 would be shifted towards the region occupied by the late-[WC] PNNi. A higher PNN mass would result in a faster evolution of the central star and the He-burning phase would begin when the nebula is smaller and denser, i.e. while having higher [FORMULA].

Fig. 9 shows the results of the calculations done with the same model parameters as in our standard model except the PN mass which is here [FORMULA] and [FORMULA]. The He-burning tracks in Fig. 9 are in better agreement with the observed positions of the H-deficient PNNi. However, in order to get a reasonable agreement of the model with the late-[WC], high surface brightness objects the model nebula as massive as [FORMULA] has to be adopted. This is unacceptably large for a PN. Moreover, as can be seen from Fig. 9, such a massive nebula evolves above the positions of the early-[WC] and PG 1159 objects.

[FIGURE] Fig. 9. The very late He-flash scenario calculated adopting PN mass of [FORMULA] (A) and 10.0 [FORMULA] (B). Other parameters as in the standard model. The same notation as in Fig. 8. Symbols - observed H-deficient PNNi.

We cannot explicitly increase the mass of the central star in our model calculations as the [FORMULA] model of Iben et al. (1983) is the only available PNN model with a late He-shell flash. However, we can, to some extend, simulate the evolution of a more massive central star by increasing the evolutionary speed of the model PNN. Although a higher PNN mass generally implies a higher PNN luminosity and the evolution to higher effective temperatures it is the evolutionary speed which has the strongest dependence on the PNN mass (e.g. Iben & Renzini 1983). We have carried out calculations in which the central star evolves 5 and 10 times faster than the original model of Iben et al., i.e. 1.7 and 3.3 faster than in our standard model. Judging from the H-burning PNN models (Schönberner 1981, Blöcker 1995, see also Iben & Renzini 1983) an increase by factor 1.7 and 3.3 in the evolutionary speed would correspond to an increase in the PNN mass by 5% and 13%, respectively. Obviously this is to be considered as a crude estimate. In the case of [WC] PNNi we deal with He-burning and very intense mass loss and the dependence of the evolutionary time scale on the PNN mass may be different.

The results of the calculations in which the PNN evolves faster than in the standard one (other model parameters remain the same) are displayed in Fig. 10. As can be seen from Fig. 9 and Fig. 10 an acceleration of the evolution of the central star has a very similar effect as an increase in the nebular mass. The full curves in Fig. 10 fit the positions of the [WC] objects better than in Fig. 8. A reasonable representation of the observed positions of the late-[WC] objects is provided by the PNN evolving 3.3 times faster than in our standard model. According to our crude estimates this would correspond to the PNN mass of [FORMULA]. From the point of view of the expected parameters in the PN population this solution is certainly more acceptable than the [FORMULA] PN displayed in Fig. 9.

[FIGURE] Fig. 10. The very late He-flash scenario modified by adopting the central star evolution to be 1.7 times (A) and 3.3 times (B) faster than in our standard model. Other parameters as in the standard model. The same notation as in Fig. 8.

The main conclusion which can be drawn from our modelling presented in Fig. 8, Fig. 9, and Fig. 10, is that if the observed H-deficient PNNi are to be interpreted as resulting from the late He-shell flash than this phenomenon should preferentially occur in objects with high PNN mass and/or large PN mass. Low mass and typical PNe should rather avoid it.

The question that now arises is: in the observed PN population, do we have enough "potential progenitors" of the H-deficient PNNi if they are supposed to be preferentially massive objects? As it is evident from Fig. 8, Fig. 9, and Fig. 10 these progenitors should be observed among the H-rich PNNi brighter in [FORMULA] than the brightest H-deficient objects. This seems to be in conflict with the finding of Sect. 4 that the H-deficient and the H-rich populations are not distinguishable in the [FORMULA] histogram, including the brightest portions of the distributions. Especially that, as can be seen from Fig. 9 and Fig. 10, for the models fitting reasonably well the [WC] objects the dashed curves (representing the H-burning) pass at upper bounds of the PN population, where only a few objects are observed (see positions of the others in Fig. 7 or Fig. 8).

In order to investigate this point we have produced expected distributions in [FORMULA] of the H-deficient PNNi and their H-burning progenitors from our models. Assuming that the number of objects in a particular [FORMULA] bin is proportional to the time spent by the model within this bin we have obtained histograms presented in Fig. 11 and Fig. 12. For each model the histograms have been normalized to 100 objects in the H-burning sample.

[FIGURE] Fig. 11. Expected distributions in [FORMULA] of the H-deficient PNNi and their H-burning progenitors from the model with the PN mass of [FORMULA]. Other parameters as in our standard model. Histograms have been normalized to 100 objects in the H-burning sample.

[FIGURE] Fig. 12. Expected distributions in [FORMULA] of the H-deficient PNNi and their H-burning progenitors from model with the central star evolving 3.3 times faster than in our standard model. Other parameters the same as in the standard model. Histograms have been normalized to 100 objects in the H-burning sample.

Fig. 11 and Fig. 12 present the results from two models only, i.e. the [FORMULA] PN model displayed in Fig. 9 and the 3.3 times faster (than the standard one) evolving model from Fig. 10. Obviously the derived histograms look somewhat different and are shifted to higher or lower surface brightnesses, depending on the model used. However in all cases they show the same feature: the H-burning progenitors of the H-deficient PNNi are expected to be 2-3 orders of magnitude brighter in [FORMULA] than the brightest H-deficient PNNi. From all our models it results that the number of the H-deficient PNNi in the first two (three) brightest bins in log [FORMULA] should be comparable to (twice larger than) the number of the H-burning progenitors. The progenitors should be at least as bright in [FORMULA] as the brightest H-deficient stars.

In our sample of the H-deficient stars we have 11 (27) objects which have log [FORMULA] greater than -1.0 (-2.0) (see Table 1 and Fig. 5). Thus in the PN population we can expect to have about 10-13 H-burning progenitors having log [FORMULA]. However the number of the so bright PNe in the observed population should be much larger. The point is that only a small part of the H-burning PNNi has a chance to undergo a He-shell flash during its life time. According to Iben (1984) only 9% of the PNNi are expected to experience a very late He-shell flash. Thus we should observe at least 100 PNe with log [FORMULA] and many of them should be as bright as log [FORMULA]. In the observed sample of 781 PNe (for which we have been able to determine [FORMULA]) there are only 14 objects with [FORMULA] and none for log [FORMULA]. Therefore our final conclusion is that the H-deficient PNNi, at least of the [WC] type, in their majority do not result from the very late He-shell flash (or born again AGB).

5.2. Observed cases of the late He-shell flash in PNNi

The above conclusion may seem to be contradicted by the fact that there are a few PNe for which we have strong observational arguments that their central stars have indeed experienced a late He-shell flash. As we show below this is not the case and in fact the analysis of the observational data for these objects reinforces the conclusion drawn in the previous subsection.

Fig. 13 shows the [FORMULA] - [FORMULA] diagram in which the observed positions of the objects discussed in this subsection are compared with other H-deficient PNNi and the predictions from our standard model of the late He-shell flash.

[FIGURE] Fig. 13. Comparison of observed positions of FG Sge, V4334 Sgr, A 30 and A 78 with predictions from our standard model of the late He-shell flash. The same notation of the model as in Fig. 8.

As discussed in Iben et al. (1983) the central stars of A 30 and A 78 have very probably suffered from a late He-shell flash. These two large, low surface brightness PNe display in their central parts H-deficient material (Hazard et al. 1980; Jacoby & Ford 1983) which have apparently been ejected from the central star well after the main nebula had been formed (Reay et al. 1983). A low expansion velocity of the H-deficient nebular knots (22-25 km s-1 - Reay et al. 1983) compared to the wind velocity from the central star (4000 km s-1 - Leuenhagen et al. 1993) strongly suggests that the knots have been ejected while the central star had giant dimensions. As can be seen from Fig. 13 the positions of A 30 and A 78 in the [FORMULA] - [FORMULA] diagram are consistent with the expected evolution after a late He-shell flash in a typical PNN.

A 58 is an object similar to the two discussed above. It is an extended, faint PN. Its central star, V605 Aql, had a nova-like outburst in 1919 which can be interpreted as a thermal pulse due to a He-shell flash (e.g. Bond et al. 1993). At present the central parts of A 58 show nebular emission from H-deficient material while the central star seems to display [WC] characteristics (Seitter 1989). The lack of reliable measurements of the [FORMULA] flux from A 58 and of the brightness of its central star has prevented us from placing this object in Fig. 13. However, it is clear that A 58 has a very low surface brightness (Abell 1966, Ford 1971).

FG Sge is probably the best documented case of a PNN which has recently experienced a He-shell flash. From an analysis of the observed evolution of its visual brightness Blöcker & Schönberner (1997) have concluded that FG Sge has a mass of [FORMULA]. FG Sge is at present too cool to be able to ionize the surrounding PN, He 1-5. However the observed spectrum of He 1-5 can easily be accounted for by a recombining nebula (Tylenda 1980). The present position of the object in the [FORMULA] - [FORMULA] diagram is shown in Fig. 13. The observational data for the nebula and the central star have been taken from Hawley & Miller (1978) and Yudin & Tatarnikov (1999), respectively. As can be seen from Fig. 13 this position fits nicely with the predictions of our standard model during the thermal pulse.

V4334 Sgr, also known as the Sakurai's object, is presumably another example of a PNN undergoing a late He-shell flash (e.g. Kerber et al. 1999). The star is surrounded by an extended faint PN investigated recently by Kerber et al. (1999) and Pollacco (1999). Using the results from these studies and the V brightness of V4334 Sgr from Yudin & Tatarnikov (1999) we have derived the present position of the object in Fig. 13 which is quite close to that of FG Sge.

The general conlcusion from Fig. 13 is that the observational data for A 30, A 78, FG Sge and V4334 Sgr are indeed consistent with the idea that these object have suffered (or are suffering) from a late He-shell flash. A better agreement between the model and the observational data in Fig. 13 would be obtained if the He-shell flash occured a bit later than in our standard model. The position of A 58 in Fig. 13 cannot be determined but judging from the low surface brightness of the nebula it should also agree with the model predictions.

From the observational data for the above objects it can be clearly shown that none of them has a real chance to evolve towards typical PNe with [WC] PNNi. The two objects which have recently experienced a late He-shell flash, i.e. FG Sge and V4334 Sgr, have nebulae with log [FORMULA]. In course of time their surface brightnesses will decrease. [FORMULA] will also decrease due to the expansion of the nebulae and the expected decrease of the V magnitude of the central stars when recovering from the thermal pulse. Thus, as can be seen from Fig. 13, these objects will evolve directly to the region occupied by the PG 1159 objects. They have no chance to pass through the region of the typical [WC] PNNi. Obviously A 30 and A 78 are already well within the PG 1159 region.

Another observation indicating that the nature of the discussed objects is probably different from that of the [WC] PNNi can be made from observational appearances of the nebulae. The three objects which have already evolved to the PNN region after the late He-shell flash, i.e. A 30, A 58 and A 78, display H-defficient nebular regions inside the main nebula. As discussed above these regions have probably been formed during the flash when the central star was a born again AGB star. No such H-deficient regions have been detected inside any PN with the [WC] nucleus.

Thus the final conclusion of the discussion in this subsection is that the [WC] PNNi do not follow the evolutionary path of the PNNi for which we have direct observational evidences that they have experienced (or are experiencing) a late He-shell flash. Obviously the statistics is low and it would be premature to conclude that the late He-shell flash never gives origin to a [WC] PNN. Nevertheless the observational facts for the above five objects, at least, do not contradict this hypothesis.

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Online publication: October 30, 2000