Production of Lithium and Heavy Elements in AGB Stars Experiencing PIEs

Abstract

Asymptotic giant branch (AGB) stars can experience proton ingestion events (PIEs), leading to a rich nucleosynthesis. During a PIE, the intermediate neutron capture process (i-process) develops, leading to the production of trans-iron elements. It is also suggested that lithium is produced during these events. We investigate the production of lithium and trans-iron elements in AGB stars experiencing a PIE with $1<M_{\mathrm{ini}}/M_{\odot }<3$ and $-3<[\mathrm{Fe}/\mathrm{H}]<0$. We find that lithium is produced in all PIE models with surface abundances $3<$ A(Li) $<5$. The surface enrichment and overall AGB lithium yield increases with decreasing stellar mass. The lithium enrichment is accompanied by a production of ¹³C with $3{<}^{12}$C/¹³C $<9$ at the surface just after the PIE. AGB stars experiencing PIE may be related to J-type carbon stars whose main features are excesses of lithium and¹³C. In addition to Li and ¹³C, heavy elements (e.g., Sr, Ba, Eu, Pb) are significantly produced in low-metallicity stars up to [Fe/H] $\simeq -1$. The yields of our models are publicly available. Additionally, of interest to the Li nucleosynthesis, we provide an updated fitting formula for the ⁷Be($e^{-},{\nu }_e$)⁷Li electron capture rate.

1. Introduction

The asymptotic giant branch (AGB) phase corresponds to the life end of ∼1–8 $M_{\odot }$ stars (see, e.g., [1] for a review). This stage is characterized by recurrent convective thermal pulses (TPs) that develop in the H-He intershell region. When fully developed, the top of the convective pulse nearly reaches the bottom of the H-burning shell. In some cases, protons can be ingested in the TP, leading to a proton ingestion event (PIE, e.g., [2,3]). When a PIE arises, H atoms are transported downwards in the pulse and burnt on the flight via the ¹²C($p,\gamma$)¹³N reaction with ¹³N decaying to ¹³C in about 10 min. The ¹³C($\alpha ,n$) reaction also operating at the bottom of the TP, where $T\simeq 250$ MK, leads to neutron densities as high as a few ${10}^{15}$ cm⁻³, leading to the so-called intermediate neutron capture process (i-process, first coined by [4,5]) and to the production of trans-iron elements (e.g., [6,7]). In addition to AGB stars, PIEs (and thus i-process nucleosynthesis) can develop in accreting white dwarfs [8,9,10], low-metallicity massive stars [11,12,13,14], during the core helium flash of low-metallicity low-mass stars [15,16,17,18] and in post-AGB stars experiencing a late thermal pulse [19,20].

During PIEs, some ³He is also engulfed in the TP and burnt via ³He($\alpha ,\gamma$)⁷Be. The freshly produced ⁷Be is quickly transported by convection to colder regions where ⁷Li is produced by ⁷Be($e^{-},{\nu }_e$)⁷Li before being destroyed by ⁷Li($p,\alpha$)⁴He. This ⁷Li production channel is known as the Cameron–Fowler Beryllium transport mechanism [21] and has been shown to operate in low-mass low-metallicity AGB stars experiencing PIEs [3].

In this paper, we investigate the production of lithium and heavy elements (and ¹³C) in AGB stars experiencing PIEs over a wide range of masses and metallicities.

2. Computation of AGB Stellar Models

2.1. Initial Conditions and Nuclear Network

The AGB models considered in this work are those computed in Refs. [22,23]. Models have initial masses $1<M_{\mathrm{ini}}/M_{\odot }<3$ and metallicities1 $-3<$ [Fe/H] $<0$ using the solar mixture of [24]. We highlight below some relevant computational aspects and refer the reader to the aforementioned works for additional details. The models were computed with the stellar evolution code STAREVOL [25,26,27]. During a PIE, a network of 1160 nuclei is used, comprising 2123 nuclear reactions (n-, p-, $\alpha$-captures and $\alpha$-decays), weak (electron captures, $\beta$-decays), and electromagnetic interactions of relevance to follow neutron capture processes up to neutron densities of $\sim {10}^{17}$ cm⁻³. The nuclear network is coupled to the diffusion equation for the transport of chemical species since, during a PIE, the nuclear burning and convective transport timescales become similar. The nominal rate for the electron capture reaction ⁷Be($e^{-},{\nu }_e$)⁷Li is from [28] with a threshold value of ${\tau }_{1/2}=53$ days below $T<{10}^6$ K. The models presented here were computed with this rate. However, we tested the impact of adopting the theoretical rate of [29] (also tested in [30] to evaluate the impact on the solar neutrino fluxes) and found very little difference in the Li production during the PIE. We provide a new fitting formula to the temperature- and density-dependent rate of [29] in Appendix A.

2.2. Overshoot Mixing

PIEs have been shown to develop (even without extra mixing) during the early AGB phase of stars with $M_{\mathrm{ini}}<2.5M_{\odot }$ and [Fe/H] $<-2$ [3,6,7,22,23,31,32,33,34,35,36], considering overshooting above the convective TP facilitates PIEs [23]. Depending on the strength of overshoot (which is poorly constrained), PIEs can develop up to $M_{\mathrm{ini}}=4M_{\odot }$ and [Fe/H] $=0$ ([23,37]). In some of the models considered here, overshooting above the TP is included following the exponential law introduced in [27]. For these models, the depth of the mixing beyond the Schwarzschild boundary is controlled by the parameter $f_{\mathrm{top}}$ (cf. Sect. 2 in [23] ), the value of which is set to $f_{\mathrm{top}}=0.02$, $0.04$ or $0.10$. Setting $f_{\mathrm{top}}=0.10$ triggers a PIE in all our models except at solar metallicity ([Fe/H] $=0$). However, a 2$M_{\odot }$ model at [Fe/H] $=0$ with $f_{\mathrm{top}}=0.12$ can develop a PIE.

3. Results

3.1. Lithium Production in a 1 $M_{\odot }$ [Fe/H] $=-2.5$ AGB Model

Lithium is a fragile element that is destroyed by proton captures when the temperature exceeds $\sim 2.5$ MK. On the one hand, Li is burnt during the pre-main sequence phase, and its abundance further diluted during the first dredge-up event. In our 1$M_{\odot }$ [Fe/H] $=-2.5$ AGB model, the surface Li abundance2 drops to about 1 after the first dredge up (Figure 1, at $\log$($t_{\mathrm{fin}}-t$) $\simeq 8$). The A(Li) value further decreases to $0.5$ during the early AGB phase, when the convective envelope reaches deep layers (at $\log$($t_{\mathrm{fin}}-t$) $\simeq 6$). During the PIE (shown in Figure 2 top panel), the average3 stellar ⁷Be and ⁷Li mass fraction dramatically increase (Figure 2 bottom panel), reaching A(Li) values after the PIE up to 4.8 (Figure 1).

We describe below in detail the lithium production in this model. The abundance profiles just before the PIE are shown in Figure 3a. In the outer layers, the mass fraction of ³He is about ${10}^{-3}$. Some ⁷Be is present in the top of the H burning shell at $M_{\mathrm{r}}\sim 0.55M_{\odot }$ because of the operation of the ³He($\alpha ,\gamma$)⁷Be reaction. As the PIE develops, protons and ³He are engulfed in the convective pulse (Figure 3b) and ⁷Be is further produced. After about 2 yr, the mass fraction of ⁷Be in the pulse has increased to $\simeq {10}^{-6}$ (Figure 3c). Some ⁷Li (in red) starts to be synthesized by ⁷Be($e^{-},{\nu }_e$)⁷Li. As the convective pulse grows and engulfs more ³He, the average ⁷Be mass fraction in the star increases (bottom panel of Figure 2). Electron captures on ⁷Be progressively raise the overall abundance of ⁷Li in the star (red solid line in the bottom panel of Figure 2). From model $\sim$90,500, no more ⁷Be is synthesized despite the fact that the growing pulse is engulfing ³He (see the plateau in the bottom panel of Figure 2) because the temperature in the pulse is too low to activate ³He($\alpha ,\gamma$)⁷Be. After $8.5$ yr (Figure 3d), the pulse is about to merge with the envelope, and ⁷Li has been significantly synthesized. After the merging, ⁷Be and ⁷Li quickly reach the surface (Figure 3e) where the abundance of A(Li) raises from 0.46 to 4.8 (Figure 2, bottom panel). After a few decades, the ⁷Be in the envelope has been fully transformed into ⁷Li (Figure 3f).

3.2. PIE Lithium Production as a Function of Mass and Metallicity

All our PIE models experience a similar lithium evolution as described in Section 3.1 (with an exception for 3$M_{\odot }$ models as discussed later): dilution during the first and second dredge ups and then production during the PIE. At the beginning of the AGB phase, the surface A(Li) ranges from $-2.2$ to $0.9$ (Figure 4, symbols in the lower rectangle) and reaches values of $2.6<$ A(Li) $<5.3$ after the PIE (symbols in the upper rectangle). This Li production is sensitive to (1) the amount of ³He in the envelope right before the PIE, (2) the PIE characteristics (especially the thermodynamic conditions) and (3) the size of the convective pulse compared to the envelope. These three aspects are discussed below in more detail.

(1)

³He is massively synthesized in low mass stars during core H-burning and [38] showed a positive correlation between the main sequence duration, i.e., the initial stellar mass and the production of ³He. Following the first dredge up that brings ³He to the surface, the following evolutionary stages weakly affect its abundance, provided extra mixing mechanisms like thermohaline or rotation are not included (e.g., [39,40,41,42,43]). Given the higher ³He abundance in the lower mass stars at the time of the PIE (Figure 5), we would expect a higher production of Li in these lower mass models. As a numerical test, we increased and decreased the ³He mass fraction by a factor of 10 in the envelope of a 1$M_{\odot }$ at [Fe/H] $=-2.5$ right before the PIE. The resulting surface A(Li) after the PIE is accordingly impacted by a factor of ∼10 (black arrows in Figure 4).

(2)

As the PIE proceeds, the layers of the pulse expand and the temperature decreases. The production of ⁷Be (through ³He($\alpha ,\gamma$)⁷Be) thus depends on how long a sufficiently high temperature is maintained in the convective pulse. This is determined by the pulse characteristics which vary with initial mass, metallicity and, in a given model, from pulse to pulse. During a PIE, our high-mass AGB models maintain a large temperature longer at the bottom of the pulse before the merging of the pulse with the envelope. This tends to favor the production of ⁷Li in higher mass stars.

(3)

Finally, with increasing initial mass, the extent of the pulse decreases while the mass of the envelope increases. For example, in our 1, 2 and 3 $M_{\odot }$ models at [Fe/H] $=-2$, the ratio of the envelope to pulse mass is $\approx 4$, 40 and 200, respectively. The lithium is thus more diluted in the more massive envelope of higher mass stars, which results in smaller Li surface enrichments.

To summarize, (1) and (3) tend to favor higher Li enrichment in lower mass stars, while (2) leads to higher Li enrichment in higher mass stars. All together, these effects lead to higher Li enrichment in lower mass stars (Figure 4 and Figure 6). Right after the PIE, $3\lesssim$ A(Li) $\lesssim 5$ at the surface (Figure 4) with a rather clear dependence on the initial mass. After the PIE, 1$M_{\odot }$ models quickly lose their (Li-rich) envelope without experiencing any further thermal pulse. In contrast, the AGB phase resumes in more massive models. Lithium in the envelope is however left unchanged until the end of the AGB except in the 3$M_{\odot }$ models, where it is partly burnt due to the high temperature ($T>2.5$ MK) at the bottom of the convective envelope. As a consequence, the Li abundances A(Li), corresponding to our AGB model yields4 (Figure 6), are similar to the surface Li abundance after the PIE, except for the 3$M_{\odot }$ models where lithium is partially destroyed in the envelope, so that the ejected material becomes Li-poor. We note that the surface A(Li) values of the three PIE AGB models computed in [3] (small symbols in Figure 4) are in agreement with our models.

3.3. Production of ¹³C

During the first dredge up, the ashes of H burning and among them ¹³C are transported to the stellar surface. In standard models, this leads to a decrease in the surface ¹²C/¹³C ratio from 89 (solar value) to ∼15–30 (e.g., [44]). Without extra-mixing processes induced by, e.g., rotation, the ¹²C/¹³C ratio in low-mass stars is not expected to change significantly until the early AGB. Subsequently, recurrent third dredge-ups will inject ¹²C-rich pulse material into the envelope and the ratio will increase. In our standard solar metallicity 2$M_{\odot }$ model that does not experience a PIE, ¹²C/¹³C drops to 26 after the first dredge up and progressively rises during the AGB phase to reach a final value of 81. Including in this model strong overshooting above the pulse triggers a PIE, during which ¹³C is synthesized by ¹²C($p,\gamma$)¹³N(${\beta }^{+}$)¹³C. The ¹³C isotope is later dredged up to the surface when the pulse merges with the envelope, decreasing the ¹²C/¹³C ratio from 26 to 9. Considering all our models, the surface ¹²C/¹³C ratio decreases from 15–31 just before the PIE to 3–9 just after (Figure 7), i.e., close to the CNO equilibrium value of about 4. The models of [3] at [Fe/H] $=-2.7$ predict a similar low surface ¹²C/¹³C ratio right after the PIE (small symbols in Figure 7). We note that in AGB stars with $M_{\mathrm{ini}}\gtrsim 1.5M_{\odot }$, additional pulses and 3DUPs develop after the PIE [22,23], potentially increasing the ¹²C/¹³C ratio ([37]).

3.4. Heavy Element Production with the i-Process

The production of heavy elements by the i-process in PIE was extensively discussed in, e.g., [6,7,22,23,50,51]. We discuss here a few aspects related to the models presented in [22,23] and refer to these works for more details.

The maximal neutron density during the PIE shows no clear dependencies on initial mass and metallicity. It varies between $6.8\times {10}^{13}$ cm⁻³ and $2.2\times {10}^{15}$ cm⁻³. At [Fe/H] $\ge -0.5$, the production of heavy elements is very small (Figure 8): the amount of seed (mainly ⁵⁶Fe) increases with metallicity, leading to smaller neutron-to-seed ratios. This prevents a significant production of heavy elements at high metallicities. The production of Sr is maximal at $-2<$ [Fe/H] $<-1$ (Figure 8, top left panel). At [Fe/H] $<-2$, the neutron-to-seed ratio is high enough for (some) Sr to be processed in heavier elements (especially Pb). The production of Ba and Eu shows a clear drop between [Fe/H] $-1.5$ and $-1$. They are consistently produced below [Fe/H] $=-1.5$, especially by the 1 and 2$M_{\odot }$ models. The Pb yields increase with decreasing metallicity due to the higher neutron-to-seed ratio. Often, at a given metallicity, higher mass stars show smaller surface enrichments (Figure 8) as a consequence of larger dilution factors. Finally, as for lithium (cf. Section 3.2), overshooting can impact the yields. A strong overshooting can, for instance, trigger a PIE in an earlier TP, hence leading to different physical conditions and ultimately to a (generally slightly) different nucleosynthesis (e.g., the two black points at [Fe/H] $=-2.5$, Figure 8).

4. Conclusions

AGB stars can experience a proton ingestion event during the early AGB phase. This mechanism leads to the intermediate neutron capture process, which significantly produces heavy elements up to [Fe/H] $\simeq -1$. The production is particularly high in our $M_{\mathrm{ini}}\simeq$ 1–2 $M_{\odot }$ AGB models. PIEs also synthesize significant ⁷Li, coming from the chain ³He($\alpha ,\gamma$)⁷Be($e^{-},{\nu }_e$)⁷Li. In our models, spanning the mass range $1<M_{\mathrm{ini}}/M_{\odot }<3$ and metallicity range $-3<$ [Fe/H] $<0$, a surface enrichment of $3<$ A(Li) $<5$ is noticed just after the PIE. This lithium enrichment comes with an enrichment in ¹³C (also synthesized during the PIE), leading to surface ¹²C/¹³C ratios of $\sim 3$ to $\sim 9$ depending on the model. AGB models with $M_{\mathrm{ini}}\gtrsim 1.5M_{\odot }$ experience further thermal pulses and third dredge-up episodes after the PIE. This destroys some lithium in 3$M_{\odot }$ models and tends to increase (slightly) the surface ¹²C/¹³C ratio. Additional mixing mechanisms like thermohaline or rotation (not considered here) may change the picture. Interestingly, there exists a class of carbon stars called J-type, whose origin is still debated (e.g., [52]) and whose main characteristics are the presence of lithium and ¹³C. As recently shown in [37], most of the properties of J-type stars can be reproduced by AGB models experiencing a PIE, in particular their ¹²C/¹³C ratio (blue stars in Figure 7). Interestingly, some post-AGB sources also have very low ¹²C/¹³C ratios (blue shaded area in Figure 7 and [49,53]). They might be the descendants of C-rich stars that left the AGB phase shortly after a PIE. Further investigations are required to determine if this scenario is viable.