8. Post-AGB Evolution
8.3. The Models
8.3.2. Transition Times
On the contrary, for the more massive stars, the mass-loss rate remains high for a larger fraction of the interpulse: the phase numbers at which stars will leave the TP-AGB will therefore correspond to a much wider range and relatively less tracks will be He-burners.
Regardless of the initial mass of the models, in both low- and high-mass cases, the strong mass-loss rates always come into play during the more advanced cycle phases. In that sense, considering the entire [1M, 6M] mass-range, our mass-loss prescription favors
post-AGB models with high cycle phases and therefore H-burning tracks which are more subject to experience a LTP or a VLTP. In order to get more models to depart form the TP- AGB close to shell-flash, mass-loss rate would need to be extremely well adjusted with cycle phase, something which is very unlikely.
8.3.2. Transition Times
The transition times,ttr, have already been defined earlier in this chapter. Between models from different studies, the ttr values will greatly depend on the moment the high mass- loss is switched off and an end to the TP-AGB is assigned. B95 keep high rates until the pulsation period has fallen below 50 days, whereas VW94 switch it offmuch earlier (when the model has moved offthe TP-AGB by ∆log10Teff = 0.3). As a consequence the starting post-AGB temperatures are much higher for the B95 models. Specifically the VW94 tracks begin withTeff values between 3500 K and 5000 K, while the B95 starting temperature range is [6000 K, 7900 K].
Our post-AGB models get going earlier than the B95 ones because we do not wait until the period drop to 50 days. Instead we already stop the TP-AGB mass-loss at a period of 100 days; however we do not start as early as VW94. Accordingly our kickofftemperatures range from 3.58 to 3.73 (in logarithmic units), or≈3800 K - 5400 K.
The models starting point will not be the only influencing factor on the transition times; the used mass-loss prescriptions also play an important role. Although both B95 and VW94 use the PN results compiled by Pauldrach et al. (1988) for radiation-driven winds in order to adopt an appropriate prescription, they derive distinct formulas and apply them differently. For example, contrarily to VW94, B95 does not include an effective tempera- ture dependence. On the other hand, VW94 implement the radiation-driven wind relation for the PN regime as soon as the star has effectively left the AGB, whereas B95 uses a stronger Reimers rate until effective temperatures reach values that correspond more to the PN phase - around 20 000 K. Our approach is very similar to the B95 one (see Chapter 3), but we keep a higher Reimers mass-loss for the low-mass stars (η=1.0 instead of B95’s 0.5 value) until the radiation-driven wind values exceed it (this happens also around 20 000 K depending a stellar mass).
As a result, the transition times will behave differently in the various cases. The VW94 prescription leads to, an abrupt and steeper decrease of the mass-loss, lower average rates, and finally longer transition times. The B95 times (solar composition) strongly decrease with mass by almost two orders of magnitude (see figure 3 in Schonberner 1997). On the contrary the higher VW94 values stay constant and even slightly increase with core mass. In Figure 8.4 we plot our results for the ttr values as well as those of VW94. We only
show our transition times that correspond to models that really do start at P= 100 days (those for which no asterisk is printed beside thettrvalues in the 8.1 and 8.2 Tables). Our core-mass range overlaps with the one from VW94 only over a few values below 0.6M.
No particular dependence on metallicity or metal-scaling is discernible. We see that our transition times mainly decrease with increasing mass (except for the Z= 0.004 case) as did those of B95 for higher core masses between 0.524Mand 0.836M(see figure 3 in
Schonberner 1997). Most of our transition times gather around the 1000/2000 year marks, and only a few reach values above. In comparison, for a 0.524Mmodel, B95 gets≈4000
days while his lowest transition times are obtained for 0.835Mwith less than 10 days.
Figure 8.4.:Post-AGB transition times as defined in the text. Our results as well as those of (Vassiliadis & Wood 1994) [VW94] are given. Allttrvalues correspond to H-burning post-AGB tracks, except for the large triangle and square sym- bols which are our 4 He-burning tracks.
Finally, it is to be noted that He-burning models have on average higher transition times than H-burning ones. This is of course expected because of the lower He-burning rates and thus the slower consumption of the envelope.
According to Schonberner & Blocker (1993) and Schonberner (1997) observations show that the coolest post-AGB stars have effective temperature around 5000K. The VW94 tem- peratures are therefore much too low. Instead the B95 ones seem to be better-suited. Our results cover a temperature range in between both and close to the 5000 K value. Further- more, the constraints set by dynamical ages of the youngest PNe favor fast evolutionary