Nucleosynthetic yields of Z=1e-5 intermediate-mass stars

Astronomy &Astrophysics manuscript no. aa_yields1e-5_ref ©ESO 2020 October 19, 2020 Nucleosynthetic yields of Z=10−5intermediate-mass stars P. Gil-Pons1,2, C.L. Doherty3,4, J. Gutiérrez1,2, S. W. Campbell4, L. Siess5, and J. C. Lattanzio4 1EETAC, Universitat Politècnica de Catalunya, Campus Baix Llobregat, C3, 08840 Castelldefels, Spain. e-mail: [email protected] 2Institut d’Estudis Espacials de Catalunya, Ed- Nexus Campus Nord, Barcelona, Spain. 3Konkoly Observatory, Hungarian Academy of Sciences, 1121 Budapest. 4School of Physics and Astronomy, Monash University, Australia. 5Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles, ULB, Belgium Received Month Day, Year; accepted Month Day, Year ABSTRACT Context. Observed abundances of extremely metal-poor stars in the Galactic Halo hold clues for the understanding of the ancient universe. Interpreting these clues requires theoretical stellar models in a wide range of masses at the low-metallicity regime. The existing literature is relatively rich with extremely metal-poor massive and low-mass stellar models. However, the evolution of intermediatemass stars of Z .10−5remains poorly known, and the impact of the uncertain input physics on the evolution and nucleosynthesis has not been systematically analysed. Aims. We aim to provide the nucleosynthetic yields of intermediate-mass Z =10−5stars between 3 and 7.5 M, and quantify the effects of the uncertain wind rates. We expect these yields can be eventually used to assess the contribution to the chemical inventory of the early universe, and to help interpret abundances of selected C-enhanced extremely metal-poor stars (CEMP) stars. Methods. We compute and analyse the evolution of surface abundances and nucleosynthetic yields of Z =10−5intermediate-mass stars, from their main sequence till the late stages of their thermally-pulsing (Super) AGB phase, with different prescriptions for stellar winds. We use the postprocessing code MONSOON to compute the nucleosynthesis based on the evolution structure obtained with the Monash-Mount Stromlo stellar evolution code MONSTAR. By comparing our models and other existing in the literature, we explore evolutionary and nucleosynthetic trends with wind prescriptions and with initial metallicity (in the very low-Z regime). We also compare our nucleosynthetic yields to observations of CEMP-s stars belonging to the Galactic Halo. Results. The yields of intermediate-mass extremely metal-poor stars reflect the effects of very deep or corrosive second dredge-up (for the most massive models), superimposed with the combined signatures of hot-bottom burning and third dredge-up. Specifically, we confirm the reported trend that models with initial metallicity Zini .10−3give positive yields of 12C, 15N, 16O, and 26Mg. The 20Ne, 21Ne, and 24Mg yields, which were reported to be negative at Zini &10−4, become positive for Z =10−5. The results using two different prescriptions for mass-loss rates differ widely in terms of the duration of the thermally-pulsing (Super) AGB phase, overall efficiency of the third dredge-up episode, and nucleosynthetic yields. We find that the most efficient of the standard wind rates frequently used in the literature seems to favour agreement between our yield results and observational data. Regardless of the wind prescription, all our models become N-enhanced EMP stars. Key words. nuclear reactions, nucleosynthesis, abundances–stars: evolution – stars: Population II – stars: AGB and post-AGB – ISM: abundances. 1. Introduction Stellar evolution models and nucleosynthetic yields of extremely metal-poor stars (hereafter EMPs) are important pieces of the big puzzle of the chemical evolution history of the universe. EMPs are those with Z .10−5or [Fe/H].−3 (Beers & Christlieb 2005)1. A number of interesting works have been presented in this field during the last decades (e.g. Fujimoto et al. 1984, Cassisi & Castellani 1993,Fujimoto et al. 2000,Marigo et al. 2001,Chieffiet al. 2001,Siess et al. 2002,Denissenkov & Herwig 2003,Herwig et al. 2014,Gil-Pons et al. 2008,Lau et al. 2009,Campbell & Lattanzio 2008,Suda & Fujimoto 2010 and Gil-Pons et al. 2013, to mention a few). However, the evolution, nucleosynthesis, and even the fates of intermediate-mass stars between ∼3 and ∼7-9 Mis still poorly constrained, and the- 1Metallicity may be expressed as referred to the solar value according to the standard expression [Fe/H]=log (NFe/NH)?−log (NFe/NH). Abundances of an elementor isotope X can also expressed as referred to solar as [X/Fe]=log (Nx/NFe)?−log (NX/NFe) oretical results from different authors frequently differ widely (Gil-Pons et al. 2018). The above mentioned works not withstanding, the amount of results reported in this metallicity regime is much smaller than those dedicated to intermediate-mass stars of higher metallicity (see the review by Karakas & Lattanzio 2014, and references therein). The main reasons are, probably, the historical difficulty in the detection of stars at the lowest metallicities; the very substantial uncertainties which hamper our knowledge of these stars (mainly related to the treatment of convection, mixing and massloss rates, which can hardly be calibrated by observations); the fact that evolutionary calculations of these objects tend to involve the computation of huge numbers of thermal pulses (Lau et al. 2008); and finally the limitations of 1-dimensional hydrostatic codes for computing certain phases of the evolution of low-metallicity stars (Woodward et al. 2015), such as dual-shell flashes (Campbell & Lattanzio 2008;Mocák et al. 2010). These limitations in our knowledge of the evolution and fates of intermediate mass EMPs (IM EMPs) necessarily imply an even Article number, page 1 of 18 arXiv:2010.08449v1 [astro-ph.SR] 16 Oct 2020 A&A proofs: manuscript no. aa_yields1e-5_ref poorer understanding of the associated nucleosynthesis, and thus our knowledge of their yields is restricted to a limited number of isotopes (see, e.g. Abia et al. 2001,Iwamoto 2009, and Gil-Pons et al. 2013). The lack of nucleosynthetic yields of intermediate-mass stars at the lowest Z-regime (Z.10−5) is also reflected in the inputs of chemical evolution models (see, for instance, Chiappini et al. 1997,Kobayashi et al. 2006,Tsujimoto & Bekki 2012, Brusadin et al. 2013,Mollá et al. 2015,Côté et al. 2016,Matteucci et al. 2016,Spitoni et al. 2017,Prantzos et al. 2018, Millán-Irigoyen et al. 2019 and references therein). Frequently used sets of yields, such as van den Hoek & Groenewegen (1997), Marigo (2001), Gavilán et al. (2005), or Gavilán et al. (2006) are based on a synthetic approach for the treatment of the thermally-pulsing Asymptotic Giant Branch, TP-AGB. Ventura & D’Antona (2005,2010), Siess (2010), Karakas (2010), Doherty et al. (2014a), Doherty et al. (2014b) and Ritter et al. (2018) presented detailed evolution and nucleosynthetic yield calculations of AGB and super-AGB stars2, but they did not study models below Z=10−4.Campbell & Lattanzio (2008) presented primordial to extremely metal-poor stars yields up to 3M.Iwamoto (2009) computed the evolution and nucleosynthesis of intermediate-mass models at Z=2×10−5.Cristallo et al. (2009,2011,2015) presented yields for low and intermediate mass stars in the metallicity range (-2.15 ≤[Fe/H] ≤+0.15). Chieffiet al. (2001) and Abia et al. (2001) computed yields of primordial stars in a wide mass range (between low and massive). The evolution and nucleosynthesis in the poorly-explored lowest-metallicity regime involve peculiar phenomena, such as double-shell and double-core flashes (Campbell & Lattanzio 2008), the corrosive second dredge-up (Gil-Pons et al. 2013, Doherty et al. 2014b) and the hot-third dredge-up (Chieffiet al. 2001,Goriely & Siess 2004,Herwig 2004,Gil-Pons et al. 2013, Straniero et al. 2014), which definitely deserve a proper analysis. From the point of view of observations of metal-poor stars, relevant for the understanding of the evolution of the primitive universe, it is important to recall the amount of data from big surveys, such as the HK objective-prism survey (Beers et al. 1992), the Hamburg-ESO survey (Christlieb et al. 2002), SkyMapper (Keller et al. 2007), the Sloan Extension for Galactic Understanding and Exploration, SEGUE (Yanny et al. 2009), and the Large Sky Area Multi-Object Fibre Spectroscopic Telescope, LAMOST (Cui et al. 2012) to be further expanded as WEAVE (Dalton et al. 2012), the PRISTINE survey (Starkenburg et al. 2014), and, especially, with the James Webb Space Telescope (Zackrisson et al. 2011). At present almost 1000 stars with [Fe/H].-3 have been detected in the Milky Way and dwarf galaxies. They tend to show high abundance dispersion, which reflects stochasticity in the nature of their progenitors: one CEMP star may show the signature of a single or very few stars, which makes them excellent laboratories to test early stellar nucleosynthesis. This work is aimed to address the problem of the scarcity of nucleosynthetic yield calculations in the EMP regime, to explore the effects of input physics, and to compare our theoretical results with observational data in the relevant metallicity regime. We present the yields of Z =10−5stars of initial masses between 3 and 7.5 M, slightly overlapping the upper mass limit presented in Campbell & Lattanzio (2008) (≤3M). This manuscript also represents an extension of the work by Do- 2Super-AGB stars are those which undergo a C-burning phase prior to the thermally pulsing phase, the TP-(S)AGB - for a recent review see Doherty et al. 2017. herty et al. (2014a,b), in which the nucleosynthesis of massive AGB and Super-AGB stars from Z =10−4to solar metallicity (Z=0.02) was analysed. Part of the stellar structure calculations upon which this work is based were presented in Gil-Pons et al. (2013). In order to quantify the effect of the uncertain wind massloss rates, we include new models computed with an alternative mass-loss prescription, and postprocess all the stellar structure results with a nucleosynthesis code. We also explore the main trends of evolution and yields with metallicity in the metal-poor regime. The results presented have potential interest in the context of stellar archaeology (see e.g. Frebel & Norris 2015), because comparison between theoretical gas yields and observations of CEMP stars in the Halo and dwarf galaxies may help to gain insight into the chemistry of the early universe, and into the nature of the early stellar populations. Such comparisons can also help constraining the uncertain input physics of CEMP stars, specifically, those related to the efficiency of stellar winds. They could help understand the pollution history of the intracluster medium and, eventually, the origin of multiple populations in globular clusters (Ventura et al. 2016). Used as inputs for Galactic chemical evolution (GCE) models, our yields can also help to understand the chemical evolution of the early universe, and to probe the Milky Way structure and formation history (Gibson et al. 2003). Our results can also be used as input physics for population synthesis, to help constrain the primitive IMF (Suda et al. 2013), and understand mass transfer in low and intermediatemass metal-poor stars (Abate et al. 2016). This manuscript is organised as follows. Section 2sum- marises the evolution of Z =10−5intermediate-mass EMP stars (IM EMPs), and describes trends with different wind prescriptions and metallicities. Section 3analyses the nucleosynthesis and the evolution of surface abundances of our computed models. Section 4presents our yields and production factors, Section 5explores the trends with metallicity and input physics of yields computed here and other existing in the literature, and Section 6presents a brief discussion of the binary channel for the formation of EMP stars, and a comparison to observational data. Finally, Section 7summarises and draws the main conclusions from our work. 2. Summary of the structural evolution of intermediate-mass EMP models We now briefly present the code and summarize the main results presented in Gil-Pons et al. (2013) in order to compare with the new calculations presented in this work. This new release includes a range of new models of initial masses between 3 and 7.5 M, computed with an alternative wind prescription during the AGB phase. We also intend to emphasize here the main characteristics of the evolution which ultimately determine the nucleosynthesis described in detail in the forthcoming sections. 2.1. Code and input physics description Our nucleosynthetic calculations are the result of postprocessing on existing structure profiles computed with the Monash-Mount Stromlo code MONSTAR (Frost & Lattanzio 1996,Campbell & Lattanzio 2008), and presented in Gil-Pons et al. (2013) and Gil-Pons et al. (2018). Its main characteristics involve the determination of convective boundaries using the Schwarzschild criterion, complemented with the attempt to search for neutrality approach (see, e.g. Castellani et al. 1971,Frost & Lattanzio Article number, page 2 of 18 P. Gil-Pons et al.: Nucleosynthetic yields of Z =10−5intermediate-mass stars Table 1. Main characteristics of the TP-(S)AGB of our Z=10−5models. Mini corresponds to the initial mass. NT P,τT P−(S)AGB and ∆tIP are, respectively, the number of thermal pulses, the duration of the TP-(S)AGB (given from the first thermal pulse until the end of our computations), and the interpulse period. Mc,ini,Nc,fand Menv,fare, respectively, the masses of the H-exhausted cores prior to the TP-(S)AGB, and the masses of the H-exhausted cores and the remnant envelopes at the end of the TP-(S)AGB. hTHeBS i,hTHBS i,hTBCE iare, respectively, the temperatures at the times of maximum luminosity for each pulse, given at the centre of the He-burning shell, at the H-burning shell and at the base of the convective envelope respectively, and averaged over the number of thermal pulses in each sequence Mtot dredge is the total mass dredged-up. hλiwas also averaged over the number of thermal pulses in each case, and h˙ Mwindiis the average mass-loss rates due to winds, that is, the envelope mass lost over the duration of the (S)AGB phase. Models were calculated using both the Vassiliadis & Wood (1993) and Bloecker (1995) with η=0.02 mass-loss rate prescription. The 6 Mmodel includes additional calculations with η=0.04 and η=1. Some of the entries for models between 4 and 7 M, computed with VW93, were presented in Tables 1 and 3 of Gil-Pons et al. (2013). We show them here to facilitate comparison. Mini NT P τT P−(S)AGB ∆tIP Mc,ini Mc,fMenv,fhTHeBS i hTHBS i hTBCEiMtot dredge hλi h ˙ Mwindi MMyr yr MMMMK MK MK MM/yr VW93 3 122 1.41 16148 0.81 0.87 0.10 345 83 68 0.70 0.98 4.0×10−7 4 197 1.19 6702 0.87 0.93 0.25 359 91 85 0.53 0.92 1.9×10−6 5 213 0.95 4382 0.91 0.97 0.54 357 95 88 0.40 0.91 3.7×10−6 6 372 0.87 1828 0.98 1.04 0.69 362 104 99 0.36 0.85 6.2×10−6 7 607 0.50 739 1.05 1.14 0.73 367 117 114 0.24 0.78 1.1×10−5 Blo95 3 23 0.45 17750 0.81 0.84 0.54 320 88 34 0.15 0.80 3.2×10−6 4 35 0.31 8285 0.87 0.89 0.62 328 95 62 0.14 0.88 8.3×10−6 5 43 0.26 5681 0.91 0.93 0.01 329 101 73 0.12 0.78 1.6×10−6 6 60 0.17 2574 0.96 0.98 0.20 330 110 89 0.09 0.72 2.8×10−5 6 (η=0.04) 41 0.13 2523 0.96 0.98 0.01 319 112 84 0.002 0.66 3.9×10−5 6 (η=1) 16 0.03 2393 0.96 0.97 0.01 283 111 54 0.001 0.33 2.0×10−4 7 82 0.11 1428 1.05 1.07 0.40 325 126 117 0.015 0.55 5.6×10−5 7.5 254 0.06 423 1.13 1.16 0.42 300 146 142 0.005 0.01 9.1×10−5 1996). The mixing-length to pressure scale height ratio αwas taken as 1.75. 2.1.1. Mass loss Mass-loss rates during the red giant branch are set to follow the prescription by Reimers (1975). Note however that mass loss in this part of the evolution is irrelevant at the considered initial metallicity (see Section 2.2). Mass-loss rates during the AGB or Super-AGB phase follow Vassiliadis & Wood (1993) (VW93 henceforth). These authors determined a direct relation between mass-loss rate and pulsation period from an analysis of CO microwave observations of AGB stars. To test the dependence of our results on this physical input, additional calculations are presented in this work, following Bloecker (1995) (Blo95 henceforth). Blo95 formulation is based on the Reimers (1975) massloss rate, and considers atmospheric calculations for Mira stars made by Bowen (1988). It includes a parameter ηto be determined by calibration. For instance Ventura et al. (2000) proposed a value η=0.02 based on observations of Li-rich giants in the Large Magellanic Cloud. This value for ηwas also used, for instance, in Ventura et al. (2001) and Doherty et al. (2014b). VW93 is the standard mass-loss prescription when MONSTAR (and similar versions of this code) is used. However, Reimers (1975) with ηvalues between 5 and 10 was used by Karakas (2010) to compute Z=10−4models, and Blo95 with η=0.02 is more frequently considered by authors computing very low-Z models (e.g. Herwig 2004). It is also commonly assumed that the mass loss rate depends on the metallicity. Pauldrach et al. (1989) proposed a scaling relation of the form: ˙ M(Zsurf)= Zsurf Z!n ˙ M(Z) (1) where Zsurf is the stellar metal surface abundance, and nis an exponent typically ranging between 0.5 and 0.7. However, the arguments for this scaling relation were derived from line-driven winds, and thus relevant for more massive and hotter stars than the ones we are considering. The characteristic higher luminosity of low-Z stars, their surface C-abundances, pulsations, and their possibility to form dust might allow for wind mechanisms (and rates) not so different from those of higher Z stars (e.g. Mattsson et al. 2008,Lagadec & Zijlstra 2008). Therefore, we opted for not introducing any Z-scaling. 2.1.2. Opacities and Initial composition Interior stellar opacities are from Iglesias & Rogers (1996). We use low-temperature opacities that take into account composition changes in C, N, and O. It has been shown that this is critical in this metallicity range, both for the duration of the TP-AGB phase, and for the overall efficiency of nucleosynthesis and mixing during this stage (see Constantino et al. 2014). Low-temperature opacity tables are from Lederer & Aringer (2009) and Marigo & Aringer (2009). Initial composition was solar scaled as in Grevesse & Noels (1993). EMP stars are known to have α-enhancements, however Article number, page 3 of 18 A&A proofs: manuscript no. aa_yields1e-5_ref we opted for keeping continuity with the existing grid in Doherty et al. (2014a,b) and defer α-enhanced calculations for a future work. Only the isotopes relevant for the energy generation were considered in the stellar structure calculations (1H, 3He, 4He, 12C, 14N, 16O, and Zother, which included all other species). Nuclear reaction rates were taken from Caughlan & Fowler (1988), and updated with NACRE (Angulo et al. 1999). 2.2. Evolution up to the TP-(S)AGB The details of the evolution of intermediate-mass Z=10−5stars were thoroughly described in Gil-Pons et al. (2013). Here we present a summary of the most relevant features for the nucleosynthesis, as well as additional sequences calculated both with the wind rate prescriptions by VW93, as in Gil-Pons et al. (2013), and by Blo95 with parameter η=0.02, 0.04 and 1. Our models experienced a pre-TP-(S)AGB evolution characteristic of IM EMPs of Z.10−5, with core H- and He-burning occurring before the first ascent of the giant branch and its associated dredge-up episode (Girardi et al. 1996;Chieffiet al. 2001). Our 7 and 7.5 Mmodels experience off-centre C-burning and eventually develop degenerate ONe cores surrounded by CO shells. This process is well known since the 1990s (see, for instance, Garcia-Berro & Iben 1994,Siess 2006,Gil-Pons et al. 2003,Doherty et al. 2010,Jones et al. 2013) Models of initial mass Mini between 3 and 6.5 Mexperience a standard second dredge-up (SDU) episode during which the convective envelope advances inwards and reaches regions of the star previously processed by H-burning via the CN-cycle. More massive models undergo the corrosive SDU in which the base of the convective envelope advances even deeper, and reaches regions processed by He-burning. Given that our models do not include rotation, the first event to alter the surface composition is the (corrosive) SDU. Recall that stars of metallicity Z =10−5do not experience a first dredge-up episode, but we keep the nomenclature SDU to refer to the dredge-up occurring during the Early- AGB, for consistency with the evolution of higher metallicity stars. 2.3. Evolution during the TP-(S)AGB Metallicity influences the evolution of the TP-(S)AGB of intermediate-mass stars mainly through its effects on mass-loss rates and thus, on the duration of this phase. Figure 1shows a summary of relevant parameters during the TP-(S)AGB stars of our Z=10−5sequences, compared to Z=10−4and Z=0.001 sequences which were computed with similar versions of monstar (see Section 2.1). Note that comparisons are not straightforwards, as the input physics in these versions of the code present some relevant variations. VW93 mass-loss rates are used in all the cases, except our Z=10−5models calculated with Blo95, and the Z=10−4sequences by Karakas (2010), who used the prescription by Reimers (1975), corrected with a multiplying parameter ηRvarying between 5 (for the 3 Mmodel), 7 (for the 4 Mmodel) and 10 (for models of Mini ≥5 M). Karakas (2010) also scaled mass-loss rates with metallicity as ˙ M=√Z/ZηR˙ MR, where ˙ MRrepresents the mass-loss rates exactly as in Reimers (1975). As we will see, these differences in wind prescriptions strongly affect the TP-AGB evolution and, ultimately, the nucleosynthetic yields. 2.3.1. Third dredge-up All our models experience third dredge-up (TDU) to varying extents. The efficiency of this process is described by the parameter λ=∆Mdredge ∆Mcore , where ∆Mdredge is the H-exhausted core mass dredged-up by the convective envelope after a thermal pulse, and ∆Mcore is the amount by which the core has grown during the previous interpulse period. λtends to increase during the first 10s thermal pulses, and remain almost constant during the remaining TP-(S)AGB. This parameter is known to decrease with increasing mass (Straniero et al. 2003). The reason is ascribed to the fact that more massive AGB stars have hotter and more compact cores. The temperature in the He-burning shell is higher, radiation pressure more important, and degeneracy consequently lower. These structural changes contribute to weaken the thermal pulses, and reduce both the duration of the instability and of the interpulse (for more details, see Siess 2010). Our models reproduce these trends, as seen in Table 1, and in Figure 1. The most massive EMP stars (Mini &5−6 M) also experience hot TDU (Chieffiet al. 2001;Herwig 2004) during which the H- burning shell is not completely extinguished and maintains high luminosities (up to 104−105L) during the thermal pulse. As a consequence the advance inwards of the base of the convective envelope is prematurely quenched. The effect of hot TDU can also be seen in Figure 1, as <λ>values for the Z=10−5mod- els of initial mass &5 Mtend to be lower than those of higher metallicity of analogous masses. It should be stressed that the TDU efficiency strongly depends on the treatment of convective boundaries and, specifically, on the implementation of overshooting (see, for instance, Freytag et al. 1996). We note that the TDU efficiency decreases with increasing Mini between λ∼1 and λ∼0.05. The latter low value corresponds to the 7.5 Mcase computed with Blo95, which has a very short TP-SAGB phase. Some authors obtained significant TDU for their primordial to very metal-poor massive AGB and Super-AGB models (Chieffiet al. 2001,Herwig 2004, Lau et al. 2008,Karakas 2010 and Gil-Pons et al. 2013), whereas others (Gil-Pons et al. 2003,2005;Siess 2010 and Suda & Fujimoto 2010) did not find any TDU. This issue is still controversial, particularly at the lowest metallicity regime. 2.3.2. Hot bottom-burning We can also see in Figure 1that the maximum temperature of the base of the convective envelope (TBCE) tends to increase with decreasing metallicity. This is once more related to the behaviour of core masses and, to a lesser extent, to the fact that lower metallicity models have lower C-abundances in their envelopes and thus need higher temperatures to keep up the CN-reaction rates required to maintain hydrostatic equilibrium. In Z=10−5mod- els with Mini ≥4M, the temperature at the base of the convective envelope exceeds &30 MK, and hot bottom burning (HBB) sets in (see, e.g. Dell’Agli et al. 2018, and references therein). The same happens in our 3 MVW93 model after 10 thermal pulses. Note that HBB is extremely sensitive to the metallicity, and particularly so in the stellar mass range considered in this work. All our models experience an overall increase in 12C surface abundances, either during the corrosive SDU or early thermal pulses. Indeed, despite the relatively high temperatures at the BCE, 12C is very efficiently replenished by TDU during the numerous thermal pulses. In addition, very short interpulse periods (Table 1and Figure 1) contribute to the formation of 14N but does not lead to a significant destruction of 12C. Article number, page 4 of 18 P. Gil-Pons et al.: Nucleosynthetic yields of Z =10−5intermediate-mass stars Fig. 1. Relevant TP-(S)AGB parameters for intermediate-mass models of different metallicities calculated with similar versions of the Monash- Mount Stromlo stellar evolution code. Mcore is the core mass at the end of the TP-(S)AGB calculations, λis the average TDU parameter, τT PAGB is the duration of the TP-(S)AGB phase, TBCE is the maximum temperature at the base of the convective envelope, NT P is the number of thermal pulses, tIP is the average interpulse period, LMAX is the maximum luminosity and ˙ Mis the average mass-loss rate during the TP-(S)AGB phase. Values are shown for our Z=10−5models (black); for Z=10−4models from Karakas (2010) (dotted orange), and from Doherty et al. (2014b, 2015) (solid orange); for Z=10−3models for Fishlock et al. (2014) (thin green) and Doherty et al. (2014b,2015) (thick green). Sequences calculated with the wind prescriptions by VW93, Reimers (1975), and Blo95 are shown, respectively, with solid, dotted and dashed lines. 2.3.3. Effects of mass-loss rates Mass-loss rates (which tend to decrease with decreasing metallicity) are the key factor which determines the main differences between models in Figure 1, that is, the variation in duration of the TP-(S)AGB and interpulse period. Unfortunately, the mass-loss rates is very uncertain for the evolution and nucleosynthesis of TP-(S)AGB stars, and especially so in the low-Z regime (Gil-Pons et al. 2018 and references therein). EMP stars are more compact and hotter than higher metallicity stars of similar masses, and thus yield very low massloss rates when using the prescription by VW93, (which depends strongly on stellar radius and has a negative dependence with the Article number, page 5 of 18 A&A proofs: manuscript no. aa_yields1e-5_ref Fig. 2. Left panels: evolution of mass-loss rates (upper) and total luminosities (lower) for the 3 MZ=10−5model computed with the prescriptions of Vassiliadis & Wood (1993) (blue) and Bloecker (1995) with η=0.02 (orange). Right panel: same for the 7 MZ=10−5models. effective temperature). As shown by Doherty et al. (2014b), using the prescription by Blo95 (with η=0.02), which has a very strong dependence on surface luminosity, dramatically shortens the duration of the TP-(S)AGB phase of Z=10−4stars with respect to the sequences calculated with VW93. When the Z=10−5 models are considered with the Blo95 prescription instead of VW93, the duration of the TP-(S)AGB is shortened by a factor 3 in the 3 Mmodel, and a factor 5 in the 7 Mmodel. The maximum surface luminosity during the TP-(S)AGB also decreases (see Figure 1), because the cores have less time to grow as massive as in the VW93 case. Because the Blo95 prescription is based on Reimers (1975) formulation, the behaviour of mass-loss rates with luminosity is very similar in models computed with these prescriptions. Note that the implementation of VW93, which includes a relatively strong dependence on the effective temperature yields considerably lower mass-loss rates in the most massive Z=10−5cases, which are more compact and hotter than their higher Z counterparts. The cooler 7 and 7.5 M of Z=10−4and Z=10−3computed with VW93 have average mass-loss rates similar to the Z=10−5models of the same mass computed with Blo95. Due to the shorter duration of the TP-(S)AGB in models computed with the wind prescription by Blo95, the number of thermal pulses and the amount of dredged-up matter during the TDU also decrease (see Table 1and Figure 1). The effect is naturally more dramatic when the parameter values η=0.04 and 1 are used. In these cases the duration of the TP-AGB is reduced by approximately a factor 7 and a factor 30 respectively for the 3 and 7 Mmodels. With increasing mass-loss rate, fewer TDU episodes occur and the surface enrichment is consequently reduced. As a result, the average efficiency hλiis lower in our sequences calculated with Blo95 compared to those using the VW93 prescription (see Table 1and Figure 1). We also note that the rise in < λ > with thermal pulse number is almost independent of the mass loss rate prescription. The maximum efficiency is reached at about the same pulse number and its value is also very comparable. Note finally that a shorter TP-(S)AGB phase leads to a lower HBB efficiency, because it operates over a shorter time and on top of a less massive cores, which implies lower BCE temperatures. We can see in Figure 1, that the effect of mass-loss rates on TBCE is very mild between 4 and 7 M, but becomes significant for our lowest-mass models. The 3 Mmodels are actually close to the lower mass threshold required for the occurrence of HBB, and thus, the model calculated with Blo95, which evolves rapidly on the TP-AGB can not develop an efficient HBB by the time most of its envelope is lost. Article number, page 6 of 18 P. Gil-Pons et al.: Nucleosynthetic yields of Z =10−5intermediate-mass stars Fig. 3. Evolution of the surface abundances of some selected isotopes for the 3 MZ=10−5model computed with the Vassiliadis & Wood (1993) mass-loss rates. When considering the effects of mass-loss rates on the TPAGB evolution at various metallicities (Figure 1), we must recall that the mass-loss rates used for the Z=10−4models are an adapted version of Reimers (1975), which leads to considerably shorter TP-AGB phases than those resulting from the prescription by VW93. For a comparison, the Z=10−4, 5 Mmodel calculated with Reimers (1975) undergoes 69 thermal pulses, whereas the same model computed with VW93 undergoes 138 thermal pulses (see Karakas & Lattanzio 2007). As a consequence of the different wind prescription, the duration of the TPAGB phase of Z=10−4models becomes even shorter than that of Z=0.001 of analogous masses. The upper left panel of Figure 1shows that the initial-to- final mass relation of Z=10−5models is less steep than that of higher metallicity cases. Due to the significantly longer TP-AGB phases of Z=10−5cases, the 3 and 4 Mmodels develop more massive cores than their higher Zcounterparts, regardless of the wind prescription. We also note that faster evolving super-AGB models (Mini &7 M) yield very similar final core masses that are almost independent of metallicity, when the same (VW93) prescription is used. The use of Blo95, which leads to even faster evolution, yields final cores of masses between 0.03 and 0.08 M lower. As a summary, due to the SDU and early TP-(S)AGB evolution, the metallicity (in terms of Z) is increased to near-solar, and the subsequent TP-(S)AGB evolution of our initially EMP models is qualitatively very similar to that of metal-rich stars. However, it is interesting to note some relevant quantitative differences. Compared to higher metallicity models, EMP stars have: Fig. 4. Evolution of the surface abundances of some selected isotopes for the 3 MZ=10−5model, using mass-loss rates as in Bloecker (1995) (see main text for details). –longer duration of the TP-(S)AGB, determined mainly by the relative weakness of winds at lower metallicity; –shorter interpulse periods ∆tIP as a consequence of their larger core masses; –a higher number of thermal pulses (both because of the shorter ∆tIP and the longer duration of the TP-(S)AGB); –thinner intershell mass; –higher convective intershell temperatures (&360 MK); –higher temperatures at the base of the convective envelope (average TBCE &33 MK). We finally note that just like metal-rich stars, model convergence is lost prior to the complete ejection of the H-rich envelope (remnant envelope mass may be as high as &1 Mfor our more massive models). This failure is related to the development of an Fe-opacity peak near the base of the convective envelope, and was analysed in Lau et al. (2012). It is also interesting to note that the remaining envelope mass at the end of our calculations is lower when higher wind rates are used. Indeed, the instability described in Lau et al. 2012 seems to be favoured by the higher density and temperature at the BCE which are achieved in models with slower mass-loss rates (and thus more massive final H- exhausted core). The immediate evolution of the star after this instability remains a subject of debate. Article number, page 7 of 18 A&A proofs: manuscript no. aa_yields1e-5_ref Fig. 5. Evolution of the surface abundances of some selected isotopes for the 7 MZ=10−5model computed with the mass-loss rates by Vassiliadis & Wood (1993). 3. Nucleosynthesis and evolution of isotopic surface abundances 3.1. Code description Detailed nucleosynthetic calculations were performed using monsoon, the postprocessing code developed at Monash University (Cannon 1993;Lugaro et al. 2004;Doherty et al. 2014a). monsoon takes as inputs the basic structure profiles of the models computed with monstar (temperature, density, convective velocity at each mass point). It calculates abundance variations due to nuclear reaction rates and time-dependant convection using a “donor cell” scheme (Cannon 1993;Henkel et al. 2017). monsoon builds its own mesh-point distribution for each new model, which allows higher resolution in regions with large abundance variations. Nuclear reaction rates are mostly from the JINA reaction library (Cyburt et al. 2010). p-captures for the NeNa-cycle and MgAl chain are from Iliadis et al. (2001), p-captures on 22Ne are from Hale et al. (2002), α-captures on 22Ne are from Karakas et al. (2006), and p-captures on 23Na are from Hale et al. (2004). The version of monsoon used for the present work includes 77 species, up to 32S and Fe-peak elements. Additionally, it includes a ’g’ particle (Lugaro et al. 2004), which is a proxy for s-process elements. Eventual neutron captures on nuclides which are not present in our network are accounted for by assigning a cross section to n-captures on 62Ni which corresponds to an average of cross sections of n-captures up to 209Bi. This neutron-sink ap- Fig. 6. Evolution of the surface abundances of some selected isotopes for the 7.5 MZ=10−5model computed with the mass-loss rates by Bloecker (1995). proach was used by Jorissen & Arnould (1989); Lugaro et al. (2003); Herwig et al. (2003). Note that the use of a postprocessing code does not allow the feedback of detailed composition on the evolution. The effects on the equation of state (through the mean molecular weight), energy generation and on the opacities are however expected to be very limited since we are dealing with trace elements. 3.2. Surface composition changes during the standard and corrosive second dredge-up During a standard SDU a very strong surface enrichment in 4He abundance, Xsurf(4He), occurs. Our models have an initial Xsurf(4He) =0.248. In the case of our 3 Mmodel computed with VW93, Xsurf(4He)=0.277 after the SDU, and 0.308 at the end of the evolution. Surface 4He enhancement is even higher for more massive models. For our 6 Mmodel, Xsurf(4He) values at the end of the SDU and at the end of the evolution are, respectively, 0.339 and 0.373. Because the SDU is so efficient at increasing the surface 4He, models computed with Blo95 also produced high yields of this isotope, in spite of their shorter TPAGB. This is one of the main reasons why IM stars can be considered as good candidates for the pollution of the intracluster medium that gave rise to the formation of multiple stellar populations in globular clusters, that are characterised by different He over-abundances (see, e.g. Milone et al. 2012,Milone et al. 2014,Piotto et al. 2012, and Piotto et al. 2013). Note also that helium mass fractions close to 0.4 have been reported (e.g. Norris 2004;Piotto et al. 2007;Bellini et al. 2013). The effects of Article number, page 8 of 18 P. Gil-Pons et al.: Nucleosynthetic yields of Z =10−5intermediate-mass stars SDU on isotopes beyond 4He are also significant. Regardless of the wind prescription 14N surface abundances at the end of this episode increase by a factor 5-6 with respect to their initial values. Surface abundances of 18O are moderately enhanced and to a lesser extent 21Ne and 23Na. Simultaneously, 12C is depleted and the abundances of 16O and 22Ne slightly decreased (Figures 3and 4). Models of initial mass Mini &7 Mundergo the corrosive SDU (CSDU). Like a normal SDU, it causes a high increase in He (e.g. Xsurf(4He) is 0.364 at the end of the CSDU, and 0.456 at the end of the evolution of our model computed with VW93). In addition, mild enhancements occur for 13C, 22Ne (through 14N(α, γ)18F(β+, ν)18O(α, γ)22Ne), 23Na and 27Al (see Figures 5 and 6). Interestingly surface Xsurf(7Li) is clearly enhanced. It is created by e-capture on 7Be which is itself formed by α-capture on 3He (Cameron & Fowler 1971). Shortly afterwards 7Li is destroyed by p-captures. The distinctive signature of the corrosive SDU is the additional pollution with He-burning products, mainly 12C, which contributes to increase the envelope opacity and in turn the mass loss rate (see, for instance, Marigo & Girardi 2007,Nanni 2018). 3.3. Nucleosynthesis during the TP-(S)AGB evolution 3.3.1. Third dredge-up episode The TDU allows the transport to the surface of isotopes synthesised in the convective zones associated with thermal pulses. All our models experience TDU whose efficiency, as shown in Section 2, decreases with increasing initial mass (see Table 1). The TDU raises Xsurf(12C) by 3 orders of magnitude for the 3 M model calculated with VW93 (which reaches Xsurf(12C)=10−3) and by 2 orders of magnitude for the 5 Mmodel calculated with VW93 (up to Xsurf(12C)=2×10−4). The enhancement in 4He and 12C are the most significant signatures of the occurrence of TDU, but He-burning in the pulse-driven convective zone also contributes to the synthesis of 12C(α, γ). To a lesser extent, 16O also forms via 13C(α,n)16O and 13N(α,p)16O, and 20Ne is slightly produced by 16O(n,γ)17O(α,n)20Ne. Besides, 21Ne is created through 16O(n,γ)17O(α, γ)21Ne and 20Ne(n,γ)21Ne. 22Ne forms from 14N(α,γ)18F(β+,ν)18O(α,γ)22Ne. 25Mg and 26Mg are synthesised via (α,n) and (α, γ) reactions on 22Ne, respectively. It is important to recall that in IM EMP stars the H burning shell remains active during the development of the thermal pulse, with luminosities up to 104-105L. This allows 4He, 13C, 14N and 15N to be created above the He-flash driven convective zone while flashes are occurring. Note however that, because the H-burning and He-burning regions are not mixed until the subsequent TDU episode occurs, the matter synthesised in the H burning shell cannot fuel He-burning during the current flash. Neutrons, relevant for the occurrence of s-process nucleosynthesis, are produced mainly via 22Ne(α,n)25Mg (Straniero et al. 1997) within the thermal pulse if the temperature at the base of the pulse exceeds &3.5×108K. This source is activated in our most massive Z=10−5models. Right panels of Figures 3to 6show the evolution abundances of selected isotopes during the TP-(S)AGB phase. 3.3.2. Hot bottom burning The temperature at the base of the convective envelopes of our model stars is between 30 MK and &140 MK, and thus their TPAGB phase is mostly dominated by the occurrence of the HBB, in particular by the onset of the CN and NeNa-cycles and the MgAl-chain. Note however that, as mentioned above, our lowest Mini case (3 M) does not develop significant HBB until its envelope has been sufficiently enriched in metals (Zenv .10−3) due to efficient early TDU episodes (see Figures 3and 4). From the nucleosynthetic point of view, the main result of HBB is an enrichment of the stellar envelope in 4He (which was also enhanced by SDU). The onset of the CN-cycle also produces a significant increase in 14N and 13C, and milder enhancements in 15N, at the expense of 12C, 16O and 18O. Despite the occurrence of HBB, overall the surface abundances of 12C and 16O reach near equilibrium values and even increase along the TP- (S)AGB phase because of the efficient TDU replenishing these isotopes. Also, the surface 12C/13C ratio remains nearly constant around its equilibrium value of 4 during most of the TP-(S)AGB evolution, and all our stars become C-rich. Through the NeNa-cycle the surface abundance of 20Ne increases at the expense of 21Ne, 22Ne, and 23Na abundances. Because TBCE values are higher (and thus the NeNa-cycle more efficient) for more massive models, 20Ne enhancement is more significant. This can be seen by comparing Figures 3 and 5.21Ne is quickly destroyed by p-capture during HBB, regardless of the initial mass. 22Ne is converted into 20Ne (22Ne(p,γ)23Na(p,α)20Ne), and into 26Mg by α-captures. However, 22Ne is efficiently replenished by TDU raising its surface abundance and feeding the NeNa-cycle. The implementation of the fastest Blo95 mass-loss rate decreases the time during which the NeNa-cycle is active. It also reduces the number of TDU episodes, the final core mass and incidentally TBCE . As a consequence, the enhancement of 23Na all the Ne isotopes is significantly diminished. This can be seen by comparing Figures 3and 4, which show the surface abundance evolution of 3 Mmodels with VW93 and Blo95 respectively, and by comparing 5and 6), which show analogous information for the 7 Mcases. The temperatures at the BCE are also high enough for the activation of the MgAlSi-chain. 26Al and 27Al increase at the expense of Mg isotopes via subsequent proton captures and βdecays. 24Mg(p,γ)25Al(β+,ν)25Mg(p,γ)26Al(p,γ)27Si(β+,ν)27Al. All our models computed with VW93 reach TBCE high enough to allow for the formation of significant amounts of Al and Si isotopes, and the higher the initial mass (and thus the average TBCE ), the higher the Al and Si yields. Note that these isotopes are relevant for the formation of grains and can ultimately the impact stellar wind. As it happens with the NeNa-cycle, the shorter TP- (S)AGB duration and lower TBCE of Blo95 models significantly reduce the yields of all the isotopes involved in the MgAlSichain. It is important to recall that, given the high TBCE values of our models, uncertainties in the rates of the reactions involved in the NeNa-cycle and in the MgAlSi-chain are expected to have an important effect on the corresponding nucleosynthetic yields (Izzard et al. 2006), specially on those of 22Ne, 23Na and 26Al. With higher mass loss rate prescriptions, the effect of HBB is reduced mainly because of the shorter duration of the TP- (S)AGB phase. The enrichment in 14N and, to a less extent, of 13C and 18O are smaller. Actually, both TDU and HBB acting during shorter times, significantly reduce the surface enhancement of all isotopes above 20Ne, with respect to the cases computed with VW93. Note also that 12C is only weakly affected by the different wind prescriptions because its abundance is maintained at its equilibrium value. Figures 3and 4show the effect of different mass-loss rates on the surface abundance evolution of the most abundant isotopes. Article number, page 9 of 18 A&A proofs: manuscript no. aa_yields1e-5_ref parts, produce positive (although low) yields of 21Ne, 24Mg and 32S. The presented yields point to the potential relevance of our models as contributors of 4He and 14N, regardless of the wind prescription used. If real mass-loss rates are biased to low values, our sequences would also contribute to 16O, 22Ne, heavy Mg isotopes, 27Al, and 28Si, although the production of 16O and 28Si is mostly due to massive stars. Actually, the yields of all the isotopes mentioned above are about one order of magnitude higher when computed with VW93 than when computed with Blo95 (with η=0.02). These differences would impact Galactic chemical evolution models. In terms of isotopic ratios of 12C/13C and 25,26Mg/24Mg, the effects of the mass-loss rates are also crucial. We suggest that, once future observations of 25,26Mg/24Mg extend below [Fe/H]=-2.5, they could provide a useful tool to help constraining mass-loss rates in the EMP regime. The crucial effects of different wind prescriptions on the stellar yields presented hampers the detection of a clear trend with metallicity, and emphasize the importance of using consistent grids of nucleosynthetic yields as inputs for GCE models. Comparison of yields from IM EMPs with nitrogen-rich CEMP-s stars from the Halo is promising enough to further study. Our models provide a better match to observations when the mass-loss rates by Blo95 with η=0.02, more efficient than VW93, are used. The uncertain physics of mixing, possibly affected by magnetic buoyancy (Nucci & Busso 2014), gravity waves (Denissenkov & Herwig 2003;Battino et al. 2016), and rotation (Herwig 2005;Straniero et al. 2015;Cristallo et al. 2015), also plays a determining role in the evolution and yields, and its effects should be explored. The environment where Z=10−5stars formed showed the specific signature of one or a few individual objects, rather than the mixture of a large number of stellar yields. Therefore it is important to increase the number of observational counterparts, and perform a detailed exploration of extended nucleosynthesis (including s-process), and of the parameter space of theoretical models, probably combining both the initial compositions corresponding to the yields of primordial objects and the yields of our early generation models. 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The abundance patterns of selected elements in terms of [X/Fe], which may facilitate comparison with observational data and with other theoretical calculations, are presented in table A.1. Note that the results corresponding to our actual yields were presented in Figure 7, and those corresponding to the hypothetical cases in which 1% of the matter ejected by our models was homogeneously mixed in the 0.2 Menvelope of an unevolved Z=10−5star, were presented in Figures 11 and 12. Table A.1. Abundances pattern of selected elements in terms of [X/Fe] as given by the ejecta, or under the assumption that 1% of this matter was homogeneously diluted in the surface 0.2 Mof an unevolved Z=10−5star. Lithium abundance is shown as <log10(7Li)>=Log10(N(Li)/N(H))+ 12. Results using the Vassiliadis & Wood (1993) and Bloecker (1995) with the indicated ηvalues are shown. Mini/M<log10(7Li)>C N O F Ne Na Mg Al Si P S VW93 3.0 -0.49 3.19 4.97 2.30 3.74 3.85 3.95 3.73 3.35 2.15 2.62 0.29 3.0-dil -0.04 2.14 3.91 1.27 2.69 2.80 2.90 2.68 2.30 1.13 1.57 0.02 4.0 -0.13 3.14 4.91 2.36 2.95 3.48 3.66 3.77 3.56 2.28 3.06 0.65 4.0-dil -0.03 2.07 3.84 1.31 1.89 2.42 2.59 2.71 2.49 1.24 2.00 0.11 5.0 -0.44 2.98 4.85 2.20 2.66 3.31 3.41 3.61 3.70 2.24 3.03 0.63 5.0-dil -0.05 2.18 4.04 1.41 1.86 2.51 2.61 2.81 2.90 1.45 2.23 0.18 6.0 -0.46 2.78 4.75 2.04 1.93 2.96 2.92 3.39 3.64 2.04 2.76 0.43 6.0-ms -0.06 2.07 4.03 1.34 1.24 2.25 2.21 2.67 2.92 1.34 2.05 0.12 7.0 -0.49 2.69 4.54 1.87 1.46 2.49 2.36 3.07 3.35 1.95 2.55 0.34 7.0-dil -0.07 2.04 3.88 1.23 0.85 1.84 1.71 2.42 2.69 1.31 1.90 0.10 Blo95 3.0 2.58 3.61 3.67 1.61 3.37 2.51 2.36 2.28 1.56 0.57 0.88 5.6×10−3 3.0-dil 1.55 2.59 2.65 0.68 2.35 1.50 1.36 1.28 0.64 0.10 0.21 5.4×10−3 4.0 1.50 2.72 4.18 1.54 2.46 2.26 2.26 2.20 1.68 0.55 1.03 9.2×10−3 4.0-dil 0.68 1.85 3.30 0.74 1.59 1.40 1.39 1.34 0.86 0.13 0.36 9.2×10−3 5.0 0.94 2.42 3.99 1.30 1.77 1.90 1.91 1.92 1.64 0.38 0.94 8.0×10−3 5.0-dil 0.32 1.65 3.22 0.62 1.03 1.15 1.16 1.17 0.91 0.09 0.36 1.4×10−3 6.0 (η=0.02) 0.49 2.23 3.88 1.43 1.81 1.45 1.29 1.70 1.60 0.31 0.76 5.8×10−3 6.0-dil (η=0.02) 0.12 1.54 3.18 0.79 1.14 0.81 0.68 1.03 0.94 0.08 0.29 1.2×10−3 6.0 (η=0.04) 0.67 2.22 3.71 1.13 1.42 1.24 1.14 1.32 1.26 0.16 0.49 2.1×10−3 6.0-dil (η=0.04) 0.23 1.53 3.02 0.54 0.78 0.63 0.55 0.70 0.64 0.04 0.15 4.2×10−4 6.0 (η=1) 2.16 1.17 2.67 0.17 -0.37 0.02 0.41 0.10 0.29 0.03 0.20 4.1×10−5 6.0-dil (η=1) 1.47 0.58 1.98 0.04 -0.05 0.00 0.12 0.02 0.08 0.01 0.05 8.4×10−6 7.0 -0.32 2.41 3.49 1.00 1.00 1.00 0.94 1.37 1.14 0.50 0.59 6.9×10−3 7.0-dil -0.07 1.77 2.85 0.49 0.49 0.49 0.44 0.79 0.59 0.17 0.22 1.6×10−3 7.5 -0.55 1.08 3.79 -0.46 -0.80 -0.11 -0.97 -1.00 -0.90 0.49 -0.31 7.9×10−3 7.5-dil -0.09 0.56 3.17 -0.07 -0.10 -0.02 -0.11 -0.11 -0.10 0.18 -0.06 1.9×10−3 Article number, page 18 of 18