C-star lifetimes

C/O ratio with respect to the O- and C-rich regimes has already been shown (e.g. Marigo 2002, 2007, Cristallo et al. 2007). But the magnitude and the direction of this dependence with varying metallicity has not yet been investigated in detail. It is therefore important to study the sensitivity of these TDU-related fluctuations on Z. We saw that the total surface metallicity of an AGB star - which depends on M_ZAMS and ZZAMS - in connection to the C/O value, further influences the temperature-opacity interplay. As for most others factors regulating TP-AGB evolution in a complex and interconnected way, it is difficult to describe such dependencies by simple means.

Put aside the general opacity increase with increasing metallicity, a first step is noticing the aforementioned shift of the C-rich opacity curves to lower temperatures as Z increases. This is shown with more clarity in Figure 7.14 where a set of opacity profiles in the same temperature range (3.30 < log T< 3.65) for different C/O values is plotted at different metallicities. The transition, in terms of opacity changes from an O-rich to C-rich compo- sition, is less and less pronounced at decreasing metallicity. As suggested by the previous works of P. Marigo (Marigo 2002, Marigo & Girardi 2007), the effect of this transition can almost become negligible in AGB population of very low metallicity since the formation of molecules becomes less efficient at lower Z because of higher temperatures and lower abundances of involved isotopes. But for high values of the C/O ratio, we observe a note- worthy opacity decrease at the higher temperature end. As this dip also follows the general drift to lower temperatures, its influence can become important in metal-poor C-rich cases when the O-rich/C-rich transition does not play a role anymore.

In summary, we note that, while the sudden cooling, at the C/O=1 transition, of the TP- AGB tracks affecting the evolution is recovered with our new F06 opacities, we also put forward the opacity decrease and thus temperature increase that can occur in two different scenarios: a) metal-rich AGB stars that experience TDU as the C/O ratio goes from its initial low value to the critical transition one, b) metal-poor AGB stars that have already become C-rich because of very efficient TDU when the surface C/O ratio reaches higher values. Both of these cases can either result in an overall reduction of the expected strong cooling effect or in an actual increase of the surface temperature, thus moving the tracks towardsbluertemperatures and prolonging the TP-AGB evolution. The necessity to couple variable-C/O opacity tables and TP-AGB computations is therefore further asserted as these opacities can influence the evolution in two opposite directions.

7.3.4. C-star lifetimes

In section 7.3.1 we compared the TP-AGB lifetimes of our models with previous theoreti- cal tracks. Now we look at our results with respect to observational work from AGB stars in the Magellanic Clouds (LMC, SMC). We specifically compare theoretical values of our C-rich models to C-star lifetimes in the LMC and SMC.

The duration of the C-rich TP-AGB phase from our models is first plotted against initial mass in Figure 7.15. For the Z =0.04 case only results are unavailable because at these high metallicities no models attain a surface C/O value higher than unity.

(Z=0.02) because the TDU is less efficient in those stars. One should also expect to find longer lifetimes as metallicity decreases because the efficiency of the dredge-up episodes increases with decreasing Z. As in the total TP-AGB lifetime case (Figure 7.6) this is not what we find. The peak duration of the 2Mmodel is higher at Z=0.008 (solar) than at

Z=0.004. Furthermore all Z=0.0005 models have, put aside the solar metallicity case, the lowest lifetimes. This is once more related to the dependence on the core mass at the 1stTP. The Z=0.0005 models in Figure 6.7 show the smallest relative dip at the He-flash transition mass. As a result, the AGB maximum lifetime is not much higher at the peak then the other different mass models.

Figure 7.15.:Lifetimes of models during their C-rich TP-AGB phase.

Again, the metallicity dependence on the location of the peak is evident. The Z=0.0005 models lifetimes, reach their maximum at an initial mass of 1.8M, while the Z= 0.008

and 0.004 case do so at 2.0M. For the solar metallicity case there is no clear maximum

lifetime point. But a rather elongated bump, shifted towards higher masses, is seen. The O- and C-rich TP-AGB models, observationally correspond to M- and C-stars. Gi- rardi & Marigo (2007) by using M- and C-star counts in the Magellanic Cloud clusters, have derived limits to the lifetimes for the corresponding phases. For the M-stars, SMC lifetimes are poorly constrained by the data and LMC ones have maximum values of about 4 Myr but do not show any clear behavior.

The duration of the C-star phase has a clear peak reaching up to 2-3 Myr for stars with turn-offmasses between 1.5Mto 2.8M. Moreover they find a shift towards lower masses

of the lifetime peak as one moves from LMC to SMC metallicities. In their figure 3 (upper left panel of our Figure 7.16), they compare the observational results of LMC C-stars to C-rich TP-AGB models found in the literature that have already been used in population

7.3.4 C-star lifetimes

synthesis of galaxies. All model lifetimes - put aside the P. Marigo ones - are significantly shorter than the observed values. As discussed in Girardi & Marigo (2007), synthetic

Figure 7.16.:C-star phase lifetimes (Myr) as a function of turn-offmass. The black dots (with error bars) are results (Girardi & Marigo 2007, GM07) obtained from observational data of the Magellanic Cloud Clusters. Upper left panel- Figure 3 from GM07. Observational data corresponds to the LMC. Model details, indicated on the figure, are from, Renzini & Voli (1981), Groe- newegen & de Jong (1994), Mouhcine & Lançon (2002), Marigo (2001, 2002). Upper right panel- Observational results are from the LMC. Our TP-AGB models (dotted red line) correspond to a Z=0.008/solar-scaled metallicity. Lower panel- Observational results from the SMC. We plot our TP-AGB models (dotted red line) for a Z=0.004/solar-scaled metal- licity.

TP-AGB models prior to Groenewegen & de Jong (1993) fail to reproduce the C-star Luminosity Function (CSLF) observed in the Magellanic clouds. These produce C-star lifetimes that are too short with respect to the observations and display a bump that is shifted towards higher masses. The synthetic models of Groenewegen & de Jong (1993) were the first calibrated to the CSLF. All subsequent calibrated models are better behaved and centered around lower-mass values. They still however do not exhibit high enough lifetimes. Finally the P. Marigo synthetic models, which are also calibrated to the CSLF, give the best agreement between models and observations. They over- or underestimate the times depending on the inclusion of fixed- or variable-chemistry molecular opacities.

Our detailed TP-AGB models have not been calibrated to the CSLF. We plot in the upper left and lower panels of Figure 7.16 our C-star lifetimes for the two solar-scaled metallicities (Z = 0.008 / Z = 0.l04) that correspond to LMC and SMC compositions, and compare them to the results inferred from the observational cluster data by Girardi & Marigo (2007).

For the LMC, like it is also the case of the P. Marigo models, our results fit the data well in comparison to all the other sets of synthetic models. Actually, our lifetimes are very similar to the ones of M02 also with variable-C/O opacities. Our profile has its peak slightly displaced to lower metallicities and a little narrower than the observed and M02 ones. For the SMC C-star case as well, our Z=0.004 models reach the maximum observed lifetimes. The, broader and shifted to lower masses (≈1.2-1.8M) in comparison the LMC,

observational peak is less well recovered by out results.

This metallicity shift of the peak towards lower masses with decreasing Z is very similar to the core-mass dependence observed on AGB lifetimes in section 7.3.1. However, the observational shift is much more important than ours: for a metallicity decrease from LMC to SMC composition, the maximum C-star lifetime moves from 2.66Mto 1.62M.

Between our Z=0.008 and Z=0.004 sets of models, the peak remains at 2M. Even if

more mass resolution was available around the critical point, the difference would certainly not be as large as the observed one.

Notwithstanding these divergences, the important result of this section is that our models, without any specific calibration to observed C-stars, agree better with Magellanic Cloud cluster data than previous synthetic TP-AGB grids that have already been used in evolu- tionary population synthesis.