Asymptotic-Giant-Branch Models at Very Low Metallicity

Keywords: nuclear reactions, nucleosynthesis, abundances — stars: AGB and post-AGB

The interpretation of the already available and still growing amount of data concerning very metal-poor stars (see Beers & Christlieb (2005) for the classification of these objects) require reliable stellar models. A significant fraction (~25%) of stars with [Fe/H] < –2.5 show carbon-enriched atmospheres (Carbon-Enhanced, Metal-Poor, CEMP, stars). Moreover, many CEMP stars (~75%) are characterized by s-process enhanced patterns (CEMP-s): in this paper we will only address this sub-class of low-metallicity stars. CEMP-s stars belong to the Galactic Halo and, therefore, are old (~14 Gyr) low-mass (M < 0.9 M_⊙) objects; notwithstanding they show the concomitant enhancements of C, N and s-process elements, which are commonly ascribed to the complex interplay of nucleosynthesis, mixing and mass loss taking place along the Asymptotic Giant Branch. When these low mass stars reach the AGB, their envelope is so small that third dredge up (TDU) may not take place, so they are probably dwarfs or giants belonging to binary systems. Therefore, C enhancement and the products of neutron-capture nucleosynthesis could result from an ancient accretion process (via stellar wind or, less likely, via Roche-Lobe overflow) from the (now extinct) AGB companion (see, e.g., Roederer et al. 2008; Thompson et al. 2008). Note that a recent determination of radial velocities for a sample of CEMP-s stars suggests that all of these objects are members of binary systems (Lucatello et al. 2005). Some of these stars present exotic chemical distributions and, for this reason, represent the current frontier of AGB modeling.

At very low metallicities, there is a minimum mass (which increases with decreasing the metallicity) under which models suffer proton ingestion from the envelope down to the underlying convective He intershell. This occurs during the first fully developed thermal pulse (TP). We refer to this episode as the Proton Ingestion Episode (PIE). Larger mass models follow a standard TP-AGB evolution. This feature has already been found by many authors (Hollowell, Iben & Fujimoto 1990; Fujimoto, Ikeda & Iben 2000; Iwamoto et al. 2004; Straniero et al. 2004; Suda et al. 2004; Cristallo et al. 2007; Campbell & Lattanzio 2008; Lau, Stancliffe & Tout 2009): the occurrence of PIE is therefore a robust prediction, in spite of the different physics adopted in the various works. Moreover, recent 3D hydrodynamical simulations (Woodward et al. 2008) confirm this peculiarity, which characterizes very metal-poor models. A full understanding of the involved physics is therefore mandatory.

In the following sections, we present and discuss the evolution of an AGB model with initial mass M = 1.5 M_⊙ and Z = 5 × 10^–5, with emphasis on the effects on the stellar structure caused by the PIE. The model has been computed with the FRANEC stellar evolutionary code (Chieffi, Limongi & Straniero 1998); details of the mixing scheme (see next Section) and latest improvements to the code are described in Cristallo et al. (2009). We assume a solar-scaled initial distribution (Lodders 2003), although at low metallicities a clear oxygen enhancement has been observed by many authors (see, e.g., Abia & Rebolo 1989).

As outlined in the previous section, at the beginning of the thermally pulsing phase of low mass metal-poor models, the convective shell powered by 3α reactions may extend up to the base of the H-rich envelope. This only occurs at low metallicities and is due to the flattening of the entropy peak characterizing the H-burning shell. At low Z, in order to compensate the reduction of CNO catalysts, the temperature of the H-shell increases and, consequently, the entropy within the H-shell decreases (entropy variation is defined as dS = dQ/T, where dQ is the exchanged heat and T is the temperature). Therefore, while at larger metallicities mixing is prevented by the entropy peak of the H shell (Iben 1977), at low metallicities protons can be mixed within the convective shell and captured by the abundant ¹²C. The temperature profile within the convective shell runs from about T = 5.0 × 10⁷ K at the outer border to T = 2.3 × 10⁸ K at the bottom (see Panel c of Figure 1). At such high temperatures H burning is very efficient and, therefore, protons are captured on-flight by CNO isotopes before reaching the bottom of the convective shell. In these conditions, we can distinguish three different regions within the flash-driven convective shell:

• the external zone, where the CNO-burning time scale (τ_CNO) is largely greater than the mixing time scale

• the inner zone, where temperature is so high that the mixing efficiency is largely smaller than the burning one

• an intermediate zone, where the nuclear and mixing time scales are comparable.

Figure 1.  Evolution of the temperature within the He-intershell during the PIE. We plot the profiles at the beginning of proton ingestion (Panel a, Δ t = 0 yr), soon before the convective shell splitting (Panel b, Δ t = 1.6457 yr), soon after the convective shell splitting (Panel c, Δ t = 1.6468 yr) and during the relaxing phase (Panel d, Δ t = 2.1843 yr). Note how the convective shell (shaded region) in the top left panel is not yet fully developed. Different shading directions (Panels c and d) indicate separate convective regions. See text for details.

The best approach to this situation is the simultaneous solution of the differential equations describing the physical structure of a star, the nuclear burning and the mixing. However, it has to be noticed that this computational scheme can be used only with small nuclear network, while it can not be applied when using very large network, including several hundreds of isotopes and nuclear processes. For this reason, in our simulations we adopt a different approach. We fully couple the structure equations with those describing the nuclear burning, so that we directly take into account the energetic feedback of nuclear reactions on the physical properties of the model (mainly the temperature profile). Moreover, this allows us to determine accurately the temperature gradient and, thus, the location and the mass extension of the zones unstable for convection. Hence, convection-induced mixing is computed by adopting the time dependent formalism described in Chieffi et al. (2001), where the mixing efficiency depends linearly on the temporal time step Δ t of the model.

In our simulation, during the PIE, we limit Δ t to 50% of the mixing turnover time scale for the whole convective shell (τ_mix), in order to avoid the unrealistic fully homogenization of that region. All the chemical species are mixed within the whole unstable zone, with the exception of protons, which are mixed from the outer border of the convective shell down to the mass coordinate M _P, where τ_CNO = fΔ t, f > 1 being a free parameter. According to our choice on Δ t, at M _P τ_CNO results definitively smaller than τ_mix (at least by a factor of 2/f): this implies that protons consumption via nuclear burning is much more rapid than the supply via the convection-driven mixing. As a consequence, in nature below this point it is hardly unlikely for protons to survive. In the computation of PIE, we fix f = 1/3 (this implies that at M _P the temperature roughly corresponds to T ~ 1.3 × 10⁸). Such a choice is based on a a series of evolutionary sequences computed with different values of f. Our results show that for f > 1/3 protons are accumulated in cool zones where H burning is inefficient, while for f > 1/3 protons are mixed down to zones inconsistent with the on-flight burning.

In Panel a of Figure 2 we report the abundances of H, ¹²C, ¹³C and ¹⁴N at the beginning of proton ingestion. Note the large ¹²C abundance, due to the partial He burning inside the convective shell via 3 α reactions, and the relatively low abundances of ¹³C and ¹⁴N, which result from the dilution, within the convective shell, of the ashes left by the H-burning shell during the previous interpulse phase. Similarly, in Panel a of Figure 3 we plot the contributions to energetics generated by proton captures (blue long-dashed curve) and by α captures (dark solid curve). Two peaks clearly emerge from the figure: the most internal one is due to 3α reactions (which power convection within the He-intershell) while the second peak (more external and shallow) comes from the CNO cycle in the H-burning shell. We plot apart the contribution of the ¹³C(α,n)¹⁶O reactions, in which we also consider the energy release by the related neutron captures (short-dashed red curve).

Figure 2.  Evolution of selected key isotopes within the He intershell during the PIE.

Figure 3.  Evolution of different contributions to energetics within the He intershell during the PIE.

Upper-right panels (Panels b) of Figures 1, 2 and 3 depict the situation 1.6457 yr after the beginning of protons ingestion. Protons are captured by the abundant ¹²C, leading to the nucleosynthesis of ¹³C and ¹⁴N. Due to the concomitant actions of mixing and burning, the resulting abundances strongly differ with respect to the ones of the radiative H-burning shell, in which a full CNO equilibrium is attained and the most abundant synthesized isotope is ¹⁴N. During the PIE, the H burning is instead always out of equilibrium and this translates in a large production of ¹³C and, at a lower level, of ¹⁴N, while ¹⁶O remains practically untouched. Technically, this is due to the fact that isotopes cannot pile up locally (and then reach the equilibrium value) due to the presence of convective motions. Note that ¹³C and ¹⁴N are correctly mixed down to the base of the convective shell, because their burning timescales are always lower than the model temporal step. The hydrogen profile extends down to M ~ 0.548 M_⊙. The very small H abundance under this limit basically derives from ¹⁴N(n,p)¹⁴C reactions: neutrons mainly come from the ¹³C(α,n)¹⁶O reaction, which is very efficiently activated at the bottom of the convective shell. This is clearly shown in Panel b of Figure 3, in which emerges that¹³C(α,n)¹⁶O reactions (and related neutron captures) represent the major energy source at the bottom of the convective shell. At the same time, the contribution of CNO burning boosts a second energy peak, whose mass coordinate is determined by the maximum penetration of protons within the convective shell. When the maximum CNO energy peak slightly exceeds the value of the He-burning peak, an inversion in the temperature profile occurs (see Panel c of Figure 1) and the convective shell splits into two sub-shells: the lower one boosted by the ¹³C(α,n)¹⁶O reactions and the upper one by the CNO cycle. After the splitting event, the two convective shells follow separate evolutions.

In the lower shell, the ¹³C(α,n)¹⁶O reaction consumes the available ¹³C and produces a very large neutron flux. At the bottom of the shell, a neutron density as large as n _n ~ 10¹⁵ cm^–3 is attained, allowing the synthesis of isotopes by-passed by a standard s process. Since so high a neutron density moves the nucleosynthetic path away from the β stability valley, we extended the nuclear network with respect to that one used in previous works: the number of isotopes is increased from 500 to about 700 and the number of nuclear reactions grows from 700 to about 1200.

In the the upper shell, the ¹³C and the ¹⁴N continue to increase thanks to the burning of freshly ingested protons from the external layers. In this phase, the CNO cycle is the major energy source in the star (see Panel c of Figure 3). Then, the structure starts expanding, causing the temperature of the whole region to rapidly decrease (see Panel d of Figure 1). During this phase, both the energy sources boosting the two shells quench off (see Panel d of Figure 3); in the meantime, the upper shell extends in mass.

Later on, the envelope completely engulfs the upper shell, dredging up to the surface a large amount of ¹³C and ¹⁴N (hereafter, we refer to this deep TDU as d-TDU). The lower shell, thanks to the steep pressure and density gradients formed in the splitting region, remains part of the He-intershell region and the isotopes synthesized in this region are later diluted in the following TP. Owing to the increase of the CN abundance in the envelope, the further evolution of this models resembles that of a standard AGB, preventing the occurrence of further PIEs. In the upper panel of Figure 4 we report the temporal evolution of the mass coordinates of (top to bottom): the inner border of the convective envelope, the maximum energy production of the H-burning shell and the maximum energy production within the H-depleted core. In the lower panel we plot the H-burning and He-burning contributions to luminosity. Note the burst of H burning (L_H > 10⁹ L_⊙) caused by the PIE. This model undergoes 25 additional TDU episodes, each one followed by the formation of a ¹³C pocket (Straniero, Gallino & Cristallo 2006; Cristallo et al. 2009), which radiatively burns during the interpulse period. The final surface composition is therefore a combination of two different nucleosynthetic channels: the first being a consequence of the PIE and the second coming from the s process in the radiative ¹³C pockets.

Figure 4.  Upper panel: temporal evolution of the mass coordinates of (top to bottom) the inner border of the convective envelope, the maximum energy production of the H-burning shell and the maximum energy production within the H-depleted core. Note the occurrence of a deep TDU (hereafter d-TDU) at the beginning of the TP-AGB phase, as a consequence of proton ingestion. Lower panel: temporal evolution of the H-burning and He-burning contributions to luminosity.

In Figure 5 we report the evolution of selected heavy isotopes during the PIE: ⁸⁹Y (representative of light, ls, s-process elements), ¹³⁹La (representative of heavy, hs, s-process elements) and ²⁰⁸Pb (which is strongly produced by the s process in metal-poor stars). Tracing s-process elements have been selected basing on Busso et al. (2001). During the first phases of proton ingestion (see Panel a of Figure 5), the ¹³C abundance (about 10^–9 in mass fraction) does not allow an appreciable s-process production: heavy elements abundances are therefore the initial ones (in the previous phases of the stellar evolution no neutron sources have been in fact efficiently activated). During the following phase, up to the splitting event, we obtain a non negligible production of heavy elements, with particular efficiency in the production of hs elements (see Panel b of Figure 5). Once the splitting has occurred, the nucleosynthesis in the two shells follow completely different behaviors. In the lower shell, where ¹³C is destroyed at high temperatures (T _max = 2.5 × 10⁸ K), lead and hs elements are produced. In the upper shell, instead, ¹³C burns at lower temperatures (T _max ≤ 10⁸ K, see Panels c and d in Figure 1) and it is continuously added by the active proton burning. The final effect is a net production of ls elements only (see Panel d in Figure 5). When the envelope dredges up the isotopes synthesized in the upper shell, the surface distribution of the model is therefore enriched in ls elements, showing hs and lead abundances close to the initial ones (blue dotted curve in Figure 6). The mass dredged up during the d-TDU is Δ M _TDU ~1.7 × 10^–2 M_⊙; the corresponding efficiency (defined by means of the λ Factor ¹ ) is 2.7. After the d-TDU episode, the model follows a standard evolution. The isotopes synthesized in the lower shell are diluted in the convective shell generated by the following TP and their signature appears at the surface after the second TDU episode (red short-dashed curve in Figure 6). The surface s-process distribution after the second TDU mimics the expected distribution of models at low metallicity (Bisterzo et al. 2008), characterized by a growing sequence ls–hs–lead. Such a trend is even more strong as the number of TPs grows, displaying a final distribution characterized by [ls/Fe] = 2.02, [hs/Fe] = 2.55 and [Pb/Fe] = 3.50 (dark solid curve in Figure 6). In the plotted final distribution we took into account the decays of radioactive isotopes (as, for example, the β decay of long-lived ⁹³Zr to ⁹³Nb) and, therefore, this distribution can be compared with observational data of extrinsic AGBs.

Figure 5.  Temporal evolution of selected heavy isotopes during the PIE.

Figure 6.  Surface abundances (in spectroscopic notation) of a model with initial mass M = 1.5 M_⊙ model and Z = 5 × 10^–5 after selected TDU episodes. Gaps at Z = 43 and Z = 61 correspond to unstable elements, Tc and Pm, respectively.

In this contribution we present the evolution of a low mass model (M = 1.5 M_⊙) of very low metallicity (Z = 5 × 10^–5). We discussed in details the effect that proton ingestion has on the physical stellar structure and on the following nucleosynthesis. As a by-product of the PIE, we found a large production of ¹³C, ¹⁴N and ⁷Li. Moreover, we discussed the surface s-process distributions after the deep TDU following the PIE and after the standard TDU episodes. We are now exploring the effects of the Proton Ingestion Episode on models with different masses (0.85 ≤ M/M _⊙ ≤ 2.0) and Z = 5 × 10^–5 (Cristallo et al., in preparation). Proton ingestion occurs in all these models. While in the 1.5- and 2.0-M_⊙ mass models the effects of proton ingestion on the final surface compositions are integrated by the occurrence of standard TDU episodes (as shown in this contribution), lower masses (0.85 and 1.0 M_⊙) show peculiar final surface compositions, determined by the PIE only. Note that PIE remarkably lowers the minimum mass for the occurrence of TDU.