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Stellar yields and abundances: new directions from planetary nebulae

Planetary nebulae retain the signature of the nucleosynthesis and mixing events that occurred during the previous AGB phase. Observational signatures complement observations of AGB and post-AGB stars and their binary companions. The abundances of the elements heavier than iron such as Kr and Xe in planetary nebulae can be used to complement abundances of Sr/Y/Zr and Ba/La/Ce in AGB stars, respectively, to determine the operation of the slow neutron-capture process (the s process) in AGB stars. Additionally, observations of the Rb abundance in Type I planetary nebulae may allow us to infer the initial mass of the central star. Several noble gas components present in meteoritic stardust silicon carbide (SiC) grains are associated with implantation into the dust grains in the high-energy environment connected to the fast winds from the central stars during the planetary nebulae phase.


Introduction
The evolutionary track of the life of a star of 2 M after core H exhaustion proceeds to the red giant phase, until core He burning stars. After core He exhaustion, the star becomes a red giant again and climbs the asymptotic giant branch (AGB). During the AGB phase, the stars loses most of its envelope via strong stellar winds, until mainly the C-O degerate core is left, with a thin layer of H (∼ 10 −3 M ) still burning. At this point the star travels back in the H-R diagram towards hotter temperatures. If it becomes hot enough before all the material expelled in the previous AGB phase is dispersed, the UV photons from the central star illuminate the circumstellar material producing a planetary nebula. It follows that in planetary nebulae we observe the chemical abundances produced during the AGB phase.
During the AGB the structure of the star can be described by two components: the entended convective H-rich envelope and the compact core. The core is hot and dense, and nuclear reactions can occur there that produce and modify the chemical abundances. Two burning shells are present: the H and the He burning shells. These shells act alternately, 1 arXiv:1703.00280v1 [astro-ph.SR] 1 Mar 2017 1.1. The s process Because of their high number of protons (>26) the elements heavier than Fe have a large Coulomb barrier and can be produced only by capturing neutrons. The s process occurs typically in hydrostatic conditions at relatively low neutron densities (typical 10 8 n/cm 3 , but up to 10 13 n/cm 3 in the more massive AGB stars). The path of neutron captures proceeds mostly through stable nuclei, since unstable nuclei decay to their corresponding isobar before they can capture another neutron.
Along the path of stable nuclei, the flux of neutron captures encounters three bottlenecks corresponding to the magic number of neutrons N = 50, 82, 126 ( Fig. 1). Nuclei with such numbers of neutrons are relatively more stable against neutron captures than other nuclei, and tend to accumulate until the neutron flux reaches a large enough value to make the probability of neutron captures on these nuclei significant. The total, timeintegrated neutron flux is the crucial quantity that determines if the bottlenecks are bypassed and if the production flux can proceed to the next bottleneck. The bottleneck nuclei determine the final s-process distribution and correspond to the so-called first sprocess peak -or light s-process elements (ls) with N=50, Sr, Y, Zr; second s-process peak -or heavy s-process elements (hs) with N=82, Ba, La, Ce; and third s-process peak at N=126 (Pb), which can only accumulate since the s-process path ends there. N=126 where the s process accumulates Figure 1. Periodic table of the elements with the locations of the first, second and third s process peaks marked along with the corresponding neutron numbers. Also highlighted are the noble gases Kr and Xe and the element Rb, which can be observed in planetary nebulae.

The s-process in AGB stars
In the intershell of AGB stars free neutron are produced by two reactions. The 13 C(α,n) 16 O reaction is the main neutron surce in AGB stars of mass lower than roughly 4 M . A region rich in 13 C, the 13 C pocket, is assumed to form via mixing of protons from the envelope into the intershell at the deepest extent of the TDU (Gallino et al. 1998;Goriely & Mowlavi 2000;Lugaro et al. 2003b;Cristallo et al. 2009). The protons react with the abundant 12 C to produce 13 C via 12 C(p,γ) 13 N(β + ) 13 C. The 13 C pocket controls the total number of neutrons and thus the observed s-process distribution, i.e., the [hs/ls] ratio. The absolute s-process abundances [ls/Fe] and [hs/Fe] are controlled also by the TDU and other dilution effects. For example, binary transfer plays a crucial role in interpreting the data derived from an AGB star companion (a so-called extrinsic s-process enhanced star), rather than an AGB star itself (an intrinsic s-process enhanced star). Because both the formation of the 13 C pockets and the effects of stellar rotation and magnetic fields on the neutron flux are very uncertain, observations of [hs/ls] represent one of a few viable ways to understand the s process in low-mass AGB stars.
For AGB stars more massive than roughly 4 M , the main source of neutrons is instead the 22 Ne(α,n) 25 Mg reaction, which operates at higher temperatures (above 300 MK) inside the convective TPs. This neutron source produces a lower total number of neutrons but a higher neutron density than the 13 C source. As such, it controls the possible operation of branching points, introducing deviations from the main s-process path. For instance, the abundance ratio [Rb/Zr] is an indicator of the neutron density and of the activation of the 22 Ne source. The production of Rb is much increased when the neutron magic isotope 87 Rb (N=50) is reached by the s-process path via the activation of the branching points at the unstable 85 Kr and 86 Rb (Abia et al. 2001;van Raai et al. 2012). Large uncertainties are present in the operation of the 22 Ne neutron source including the rate of the neutron source reaction, the efficiency of the TDU, and the mass loss rate in massive AGB stars. The difficulty in constraining the operation of this neutron source using observations is that the [Rb/Zr] ratio in massive AGB stars is highly dependent on the model atmosphere used to analyse the spectra (Zamora et al. 2014). Independent constraints are crucial to settle the question of how much Rb is produced by massive AGB stars.

New directions
Observations of the elements heavier than Fe in planetary nebulae (see Sterling et al., these proceedings) provide us complementary indicators and independent constraints for the s-process in AGB stars. As it can be seen from Fig. 1 the noble gases Kr and Xe, which are observable in planetary nebulae, are located very close to the first and second sprocess peaks, respectively. Interestingly, only a small fraction of the cosmic abundances of these noble gases are produced by the s-process in AGB stars (Arlandini et al. 1999;Bisterzo et al. 2014): Xe is a typical element made by the rapid neutron captures in explosive environments (Thielemann et al. 2011). Krypton, on the other hand, is mostly produced in massive stars by a multitude of processes, including the weak s process and different explosive mechanisms (e.g., Roberts et al. 2010;Pignatari et al. 2016, and references therein).
Nevertheless, the s process in AGB stars contributes roughly 30% and 15% of the solar Kr and Xe, respectively (Bisterzo et al. 2014). This production, although much lower in absolute terms, follows the production of the s-process first and second peaks. This means that effectively the s-process models predict [Xe/Kr] values comparable to [hs/ls] values. The observed [Xe/Kr] ratios in planetary nebulae can be used to further constrain the total number of free neutrons and consequently the 13 C pocket (Sharpee et al. 2007;Pignatari et al. 2008). Furthemore, Rb can be directly seen in planetary nebulae, providing us with a constrain on the initial mass of the parent star and the opportunity to disentangle the effects of hot bottom burning in massive AGB stars (potentially Rb-rich) and of extra mixing in low-mass AGB stars (certainly Rb-poor) on the He and N excesses observed in Type I planetary nebulae.
collision strengths for [Cd IV] and [Ge VI]. The identification of [Rb IV]1.5973 μm is strengthened by the agreement between the Rb 3+ /H + abundance found from this line and an optical [Rb IV] feature at 5759.55Å. We derive elemental abundances for Rb, Cd, and Ge based on similarities between the IP ranges of the detected ions and O 2+ and Ne 4+ . The Rb and Cd abundances are factors of 2-4 greater than solar, comparable to Kr and Se. Ge is subsolar by about a factor of two in NGC7027, due to the uncertain ICF and/or depletion into dust. The abundances relative to H are approximately a factor of two larger than predicted by FRUITY models , but the relative enrichments are in reasonable agreement. The Cd abundances nominally fall below the theoretical curves, but are highly uncertain due to the current lack of atomic data. Kr and Xe appear to be slightly more enriched than predicted by this set of models, an effect that merits further investigation. These identifications provide new tools for studying s-process enrichments in PNe, and demonstrate the potential for using the growing number of ncapture elements detected in PNe to constrain and improve theoretical models of AGB evolution and nucleosynthesis.
N.C.S. and M.A.B. acknowledge support from the NSF (KASI) with the financial support of NSF grant AST-1229522, the University of Texas at Austin, and the Korean GMT Project of KASI. This work has made use of NASAʼs Astrophysics Data System, the Atomic Line List v2.05B18, and the FRUITY Database of nucleosynthetic yields from AGB stars.
The orbital wave functions were optimized by minimizing   From a preliminary analysis by Pignatari et al. (2008), the observations of the sprocess [Xe/Kr] in PNe seem to be consistent with the theoretical predictions of AGB models. However, Sterling et al. (2016) (see Fig. 2) show a mismatch between models and observations for Kr, with the observations being higher than the model predictions. This problem needs to be analyzed in more details, also in the light of the other independent s-process observations of noble gases available from meteoritic presolar silicon carbide (SiC) grains, which formed in the winds of C-rich AGB stars.   Lewis et al. 1994). In each case normalization is made arbitrary relative to one of the fractions, normally with concentration close to that for unseparated bulk SiC. The solid lines represent the results of calculations using the energies shown in Table 1, except for 82 Kr-G and -N, where each pair of data points is joined by a dashed line. The choice of normalization forces the theoretical line to go through that point (where concentration is equal to unity).    Lewis et al. 1994). In each case normalization is made arbitrary relative to one of the fractions, normally with concentration close to that for unseparated bulk SiC. The solid lines represent the results of calculations using the energies shown in Table 1, except for 82 Kr-G and -N, where each pair of data points is joined by a dashed line. The choice of normalization forces the theoretical line to go through that point (where concentration is equal to unity).    (2005) showing a comparision between the isotopic composition of Xe and Kr (normalised to 130 Xe and 82 Kr, respectively, and to the solar composition) measured in collections of millions of SiC grains (in bulk by Lewis et al. 1994) and predicted by AGB models for the typical parent stars of the grains (1.5-3 M and solar metallicity).

The record of planetary nebula processes in stardust SiC
Meteoritic stardust SiC grains contain noble gases that carry the signature of processes occurring in AGB stars and planetary nebulae. One of the first evidences that most of these grains originated from the envelopes of C-rich AGB star comes from the composition of the noble gas Xe (left panel of Fig. 3), which shows the indisputable signature of the s process in AGB stars. The Xe isotopic ratios produced by the s process are predominantly controlled by the neutron-capture cross sections of the different Xe isotopes, which strongly favour the production of 128 Xe and 130 Xe. These are the two Xe s-only isotopes that are shielded from r-process production by their isobars in Te and are predominantly produced by the s process. Very intriguing is the abundance trend of the different noble gases, He, Ne, Ar, Kr, and Xe with the size of the grains. Since noble gases are chemically inert, they are believed to have been incorporated in the SiC grains via an implantation process. Verchovsky et al. (2004) analysed the data from Lewis et al. (1994) in the light of an implantation model and discovered that the two different patterns (highlighted in green and blue in Fig. 4) can be reproduced by the models by varying the energy per nucleon, an input parameter of the model. A relatively low energy per nucleon, of the order of 0.5 keV, can reproduce the pattern observed in Xe. This energy can be associated with turbulence in the winds during the AGB phase, which have typical speeds of 10-30 km/s (the cold component, Table 1). As a consequence, Xe atoms must have been implanted carrying the signature of the matter in the winds of the AGB star. On the other hand, a much higher energy per nucleon ( 40 keV) is required to reproduce the pattern observed in He, Ne, Ar. This is because if the atom has too much energy, it cannot be stopped inside small grains. Post-AGB/planetary nebula fast winds ( 700 km/s) can imprint such an energy in the noble gases atoms (the hot component, Table 1). As a consequence, He, Ne, and Ar must have been implanted carrying the signature of matter in the post-AGB winds, the same winds invoked as one of the possible factors involved in the production of planetary nebulea. Finally, Kr is a mixute of the two components, some of it being implanted in the AGB phase, and some during the planetary nebula phase.  Lewis et al. 1994). In each case normalization is made arbitrary relative to one of the fractions, normally with concentration close to that for unseparated bulk SiC. The solid lines represent the results of calculations using the energies shown in Table 1, except for 82 Kr-G and -N, where each pair of data points is joined by a dashed line. The choice of normalization forces the theoretical line to go through that point (where concentration is equal to unity).
eventually forming a planetary nebula (Iben 1995). It seems entirely plausible that the high-energy components were implanted at this time. Supernova ejecta are also a possible source for the high-energy component. Moreover, presolar SiC grains from supernovae have been identified on the basis of their C, N, and Si isotopic compositions (Amari & Zinner 1997). However, the abundance of such grains is small (only $1% of all SiC grains), and the s-process patterns expected for supernova grains are different from those observed in the bulk of SiC grains. It is important to note that the high-energy (G1) component does not appear to include Xe, while in the low-energy (G2) component He, Ne, and Ar seem to be absent (Table 1). Since implantation is a chemically nonselective process, there must be another process responsible for the element fractionation. Indeed, based on the correlation between 86Kr/82Kr and 130Xe/82Kr ratios (Fig. 5), Lewis et al. (1994) have concluded that the noble gases represent a mixture of fractionated and nonfractionated components and suggested that fractionation has been caused by partial ionization at relatively low temperatures. Within the framework of our model the fractionated component was implanted at low energy (i.e., low stellar temperature), while the unfractionated component was incorporated by a high-energy process (planetary nebula event).
Note that AGB models predict very low 130Xe/82Kr ($0.1 for the high neutron density component) ratios in the s-process component (Gallino et al. 1990); thus, as inferred from the data in Figure 5, the fractionation factor between Xe and Kr during low-temperature ionization is at least a factor of 50, since at low neutron density the 130Xe/82Kr ratio is supposed to be even lower (Gallino et al. 1990). This is why we believe that only ionized atoms can be implanted; it is only during ionization that it is possible to produce the elemental fractionation that is ultimately observed. Extrapolating this fractionation factor to the lighter noble gases, with their higher ionization potentials than those for Kr and Xe, we can conclude that very little, if any, of these gases are expected to be implanted during the low-energy process (x 5). As far as the apparent absence of the unfractionated high-energy Xe component is concerned, it is not seen because the low-energy Xe dominates the mixture.
The isotopically normal Xe and Kr show the same lowenergy components as for the anomalous ones, indicating that these gases were well mixed before ionization and implantation. That is why no significant variations are observed in Fig. 4.-Illustration of the complex nature of the 82Kr-G component. After subtracting 82Kr-G1 with a pattern equal to that for 86Kr (Fig. 3) and 86Kr=82Kr ¼ 3:1 from the bulk 82Kr-G, the residual component 82Kr-G2 has a pattern very similar to that for 132Xe-G (see Fig. 3a). Fig. 5.-Correlation of 86Kr/82K isotopic ratios with 130Xe/82K elemental ratios indicating a mixture of two components: (1) generated at low neutron density, fractionated during ionization at low temperature, and implanted into SiC grains with low energies and (2) generated at high neutron density, completely ionized at high temperature, and implanted into SiC grains with high energy. Data are from Lewis et al. (1994).    Verchovsky et al. (2004) proposed that these signatures are due to the different ionisation energy of the noble gases, which decreases with the number of electrons: Xe has the lowest ( 12 eV) ionization energy, and He the highest ( 25 eV) ionisation energy. If we assume that the atoms must be ionized to be implanted in the grains, then their different ionization energies can fractionate their abundances.
From the observed isotopic ratios of the noble gases we can gather detailed information about the nucleosynthetic signature carried by the two components. The Xe isotopic ratios are matched by the composition predicted in the AGB winds (left panel of Fig. 3). This is the mixture of s-process-rich intershell material carried to the envelope by the TDU during the whole AGB phase and the initial composition of the stars, close to the solar system composition. On the other hand, to match the nucleosynthetic signatures presented by He and Ne, and in particular the so-called Ne-E(H) component extremely enriched in 22 Ne, almost pure intershell material is required, with no dilution by the original envelope material. Post-AGB winds can carry such almost pure signature only in the case some flavour of a late or very late TP occurred (Blöcker 2001), which affects ∼20% of the AGB population (e.g., Werner & Herwig 2006). It is possible that a nucleosynthetic signature such as that of the H-rich envelope is also present for He and Ne in the hot component, but, it is not seen because its abundance is much lower than that of the intershell in the late or very late TP scenario.
The 82 Kr abundance shows both the cold and the hot components (as Kr may be ionised in both cases), while 86 Kr shows only the fast wind/planetary nebula hot component. The most likely explanation is that the nucleosynthetic signature of the cold component carries a 82 Kr but not a 86 Kr excess, while the nucleosynthetic signature of the hot component carries both. The explanation for this difference lies in the fact that 82 Kr is located on the main s-process path, while 86 Kr is produced by the activation of the branching point at 85 Kr, for neutron densities exceeding few 10 8 n/cm 3 . The hot component recorded in large grains points to high 86 Kr/ 82 Kr ratios in the intershell (right panel of Fig. 3). The stellar origin of such signature remains debated. Potential proposed explanations are models of metallicity lower than solar and either a higher efficiency of the activation of 13 C pocket (Pignatari et al. 2006) or the ingestion of the 13 C pocket inside the TPs (Raut et al. 2013), which can occur if the initial mass is lower than 1.5 M . However, such models predict Sr and Ba isotopic ratios inconsistent with measurements of the same bulk and single SiC grains (Gallino et al. 1997;Lugaro et al. 2003a;Barzyk et al. 2007;Ávila et al. 2013;Liu et al. 2015). The impact of convective-boundary mixing processes at the bottom of the convective thermal pulse (e.g., Lugaro et al. 2003b;Battino et al. 2016) needs to be also evaluated for Kr and Xe. Another possibility would be that the production of extra 86 Kr occurs during the post-AGB phase in association with a late or a very late TP that is already required to carry to the stellar surface the almost pure intershell material seen in the hot component (e.g., as in the case of the intermediate neutron-capture process seen in Sakurai's object; Herwig et al. 2011).
Finally, it would be important to fully define the connection between the excess 86 Kr in the stardust data and the Kr excess seen in the planetary nebulae observations (Fig. 2). From a back-of-the-envelope calculation, if we increase by a factor of 4 the 86 Kr abundance in the 2.5 M model shown in Fig. 2, to simulate an extreme composition such as that shown by the high-density graphite grains (Fig. 3), the [Kr/Fe] ratio would increase from its current value of 0.43 to 0.66, which is a much better match with the data. As we mentioned ealier, the capability of theoretical AGB models to reproduce PN s-process observations of Kr and Xe is still matter of debate, and a consistent scenario should be derived that works for both PNe and measurements from presolar grains.

Summary and conclusions
Nucleosynthesis in AGB stars shapes the abundances observed in planetary nebulae via a complex interplay of nuclear reactions and mixing processes such as the third dredge-up and hot bottom burning. As such, planetary nebula abundances provide an independent, complementary testbed for all these processes, including the production of the elements heavier than rion via the s process. Conversely, the observed chemical abundance can be used to constraint the evolutionary path leading to the formation of planetary nebulae and the initial mass range. Specifically, we confirm that observations of [Xe/Kr] are a potential proxy for the traditional [hs/ls] s-process index and that the abundance of Rb can provide us crucial further constraints on the initial masses of planetary nebulae and the nucleosynthesis and mixing processes in massive AGB stars. Furthermore, noble gas abundances observed in meteoritic stardust grains are tracers of processes in planetary nebulae, from ionisation and implantation, to nucleosynthesis in the central star. The combination of all these different independent constraints will allow us to open new ways to understand planetary nebulae and the link to their parent AGB stars.