Constraints on CEMP-no progenitors from nuclear astrophysics
Arthur Choplin, André Maeder, Georges Meynet, Cristina Chiappini
AAstronomy & Astrophysics manuscript no. choplin c (cid:13)
ESO 2018October 3, 2018
Constraints on CEMP-no progenitors from nuclear astrophysics
Arthur Choplin , André Maeder , Georges Meynet , and Cristina Chiappini Geneva Observatory, University of Geneva, Maillettes 51, CH-1290 Sauverny, Switzerland Leibniz-Institut für Astrophysik Potsdam, An der Sternwarte 16, 14482, Potsdam, GermanyReceived / Accepted
ABSTRACT
Context.
The CEMP-no stars are long-lived small mass stars presenting a very low iron content and overabundances of carbon withno sign or only very weak signs for the presence of s- or r-elements. Although the origin of that abundance pattern is still a matter ofdebate, it was very likely inherited from a previous massive star, that we shall call here the source star.
Aims.
We rely on a recent classification of CEMP-no stars arguing that some of them are made of a material processed by hydrogenburning that was enriched in products of helium burning during the nuclear life of the source star. We examine the possibility offorming CEMP-no stars with this material.
Methods.
We study the nucleosynthesis of the CNO cycle and the Ne-Na Mg-Al chains in a hydrogen burning single zone whileinjecting the helium burning products C, O, Ne and Mg. We investigate the impact of changing the density and temperature,as well as the injection rate. The nuclear reaction rates involving the creation and destruction of Al are also examined.
Results. N, Na, Mg and Al are formed when injecting C, O, Ne and Mg in the hydrogen burning zone. The C / Cratio is constant under various conditions in the hydrogen burning zone. The predicted [Al / Fe] ratio varies up to ∼ Al.
Conclusions.
The experiments we carried out support the view that some CEMP-no stars are made of a material processed byhydrogen burning, coming from a massive star experiencing mild-to-strong rotational mixing. During its burning, this material waslikely enriched in helium burning products. No material coming from the carbon-oxygen rich core of the source star should be addedto form the daughter star, otherwise the C / C ratio would be largely above the observed range of values.
Key words. nuclear reactions, nucleosynthesis, abundances − stars: chemically peculiar − stars: abundances
1. Introduction
The content of iron at the surface of a star is often used as an in-dication of the chemical enrichment of its environment. A verysmall amount of iron relatively to the sun indicates a region sim-ilar to the early universe, where only few nucleosynthetic eventshappened. A way to obtain new clues on stars in the early uni-verse is then to examine the most iron deficient objects. Carbon-Enhanced Metal-poor Stars (CEMP) are a subclass of iron de-ficient stars, with an excess of carbon relatively to the sun, aswell as oxygen and nitrogen in general. Although it can vary abit from an author to another, the two common criteria defin-ing a CEMP are [Fe / H] < − . / Fe] > . / Fe] covers ∼ . / Fe] = . / Fe] = .
26 for HE1327-2326 (Norris et al. 2013; Allenet al. 2012). The frequency of CEMP seems to rise toward lower[Fe / H] (Lee et al. 2013), but also with increasing distance fromthe Galactic plane (Frebel et al. 2006) or moving from inner toouter halo (Carollo et al. 2012). The so-called CEMP-no sub-class is characterized by its low content in s- or r-elements, con-trary to the other sublasses of CEMP: CEMP-s, CEMP-r andCEMP-r / s (Beers & Christlieb 2005). CEMP-no stars are of par-ticular interest since they dominate at [Fe / H] (cid:46) − [X / Y] = log ( N X / N Y ) - log ( N X (cid:12) / N Y (cid:12) ) with N X , Y the number den-sity of elements X and Y, (cid:12) denoting the abundances in the sun. ing and fallback" scenario (Umeda & Nomoto 2002, 2005; Tom-inaga et al. 2014). The later explains CEMP-no with a modelof faint supernovae from Pop III stars with mixing and fallback.The mixing considered in these models occurs just before or dur-ing the explosion. The zone of mixing as well as the mass cut are free parameters of the models adjusted di ff erently in each starto reproduce observed abundance patterns of CEMP-no stars.According to the "spinstar" scenario, CEMP-no formed in aregion previously enriched by material coming from low metal-licity, rotating massive stars. During their nuclear lifetime, spin-stars experienced mass loss and strong mixing triggered by ro-tation. As developed in Maeder et al. (2015), although di ff er-ent, these two models appear more complementary than contra-dictory. Processes like strong internal mixing in the source star,winds or faint supernova may have all happened. Lately, Taka-hashi et al. (2014) presented results based on rotating modelswith strong fallback (but no mixing in the sense of the works byUmeda & Nomoto) and tried to deduce the initial rotation of thesource stars from comparisons with observed abundance patternsfrom 3 CEMP-no stars.Recently, Maeder et al. (2015) proposed the idea that the va-riety of observed ratios is likely due to material having been pro-cessed back and forth by hydrogen and helium burning regionsin the spinstar. In other words, these two burning regions are ex-changing material between them. These exchanges are triggeredby the rotational mixing. In a first step, the helium burning prod- The mass cut delimits the part of the star which is expelled from thepart which is kept into the remnant. Article number, page 1 of 13 a r X i v : . [ a s t r o - ph . S R ] J un & A proofs: manuscript no. choplin
Fig. 1.
Schematic view of the ’back and forth’ process at work in the spinstar. It occurs during the core helium burning phase and it is an exchangeof chemical species between the helium burning core and the hydrogen burning shell. ucts di ff use into the hydrogen burning shell. More specifically, C and O synthesized in the helium core di ff use in the hy-drogen burning shell, boosting the CNO-cycle and creating pri-mary N and C (see the left panel of Fig.1). In their turn, theproducts of the hydrogen burning shell (among them N) dif-fuse back in the helium core. The isotope Ne is synthesizedthrough the nuclear chain N( α, γ ) F(, e + ν e ) O( α, γ ) Ne. Theisotope Mg can also be synthesized thanks to the reaction Ne( α, γ ) Mg (see the middle panel of Fig.1). Also some Mgcan be created through the reaction Ne( α, n ) Mg. Neon andmagnesium can enter again in the hydrogen burning shell, boost-ing the Ne-Na and Mg-Al chains and therefore creating sodiumand aluminium (see the right panel of Fig.1). Through such backand forth exchanges between the hydrogen and helium burningregions, an all series of isotopes can be formed. The abundancescan vary a lot depending on the strength and on the number ofthose exchanges and thus such models can easily account forthe variety of the abundance ratios observed at the surface ofCEMP-no stars. For a given initial mass and rotation rate, the ro-tational mixing responsible for the exchanges described above isstronger at low metallicity. This e ff ect is mainly due to the highercompactness of low metallicity stars (Maeder & Meynet 2001).Putting aside the complexity of stellar models, we realizein this work simple nuclear experiments in order to illustratethe idea of Maeder et al. (2015) and to constrain the conditionsneeded in the source stars that would lead to the appropriate nu-cleosynthesis required to form CEMP-no stars. We study the im-pact of injecting C, O, Ne and Mg in a hydrogen burningsingle zone at typical temperatures and densities of the hydro-gen burning shell of a 20 −
60 M (cid:12) source star model at very lowmetallicity ( Z = − ). Di ff erent sets of nuclear rates are testedfor the three main reactions involving Al. We compare our re-sults with a subsample of 5 CEMP-no stars which have a simi-lar metallicity than the metallicity considered in our models andwhich are, according to Maeder & Meynet (2015), made of a ma-terial processed by hydrogen burning, coming from the sourcestar. Note that the active hydrogen burning shell in the source star can be enriched in products of helium burning, as explainedpreviously. Although limited, these numerical experiments, byfocusing mainly on the nucleosynthesis of the problem, allow usto explore what just nuclear physics can do and how the resultsare sensitive to only some nuclear aspects of the problem. As weshall see, even these very simple numerical experiments allow usto obtain very interesting constraints on the sources of CEMP-nostars, constraints that are particularly strong since based on themost simple numerical experiments that we can imagine to do.In Sect. 2, we recall briefly the classification of CEMP-nostars made by Maeder & Meynet (2015) and select the subsampleof CEMP-no stars used in this work. The experiments we carriedout are described in Sect. 3 and results obtained in Sect. 4. Sect.5 and 6 are dedicated to a discussion about the C / C ratio, thelithium and aluminium abundances. In Sect. 7, we discuss thepossible astronomical origin of the CEMP-no stars considered.Conclusions are given in Sect. 8.
2. The CEMP-no stars of classes 2 and 4
Maeder & Meynet (2015) provided a method to classify theabundance patterns observed at the surface of CEMP-no starsbased mainly on two ideas: the first idea is that some materialcan be exchanged between the hydrogen and helium burning re-gions inside the star. As already noted in the previous section, thehydrogen burning reactions can transform the material enrichedin helium burning products. This will boost the abundance ofsome isotopes as for instance N. This N can at its turn dif-fuse into the helium burning region where it is transformed into Ne, and Ne can migrate into the hydrogen burning region,being transformed (at least in part) into Na. Focusing on hy-drogen burning regions, we shall speak of secular mixing of firstorder when the CNO cycle will process material enriched by thenormal products of helium burning (typically C and O), of sec-ond order when the CNO cycle will process material enrichedin helium burning products resulting from material that was en-riched in hydrogen burning products (typically Ne, resulting
Article number, page 2 of 13. Choplin et al.: Constraints on CEMP-no progenitors from nuclear astrophysics
Table 1.
Type (MS if T ef f ≥ g ≥ .
25, RGB otherwise), class and abundance data for the CEMP-no stars considered in this work.
Star Type Class [Fe / H] [C / Fe] [N / Fe] [O / Fe] [Na / Fe] [Mg / Fe] [Al / Fe] [Si / Fe] [ C / C] A(Li) Ref.CS 22945-017 MS 4 ++ -2.52 2.28 2.24 < < + -3.97 1.06 2.16 1.98 2.10 1.38 0.02 0.77 -1.35 < < < -0.05 7, 9CS 30322-023 RGB 4 ++ -3.39 0.80 2.91 0.63 1.04 0.80 - 0.58 -1.35 < -0.3 1, 4, 5, 6HE 0057-5959 RGB 2 + Na -4.08 0.86 2.15 < > -1.65 - 7HE 1300 + < > -1.47 1.06 2, 6, 7HE 1310-0536 RGB 2 + -4.15 2.36 3.20 < < < ++ -5.76 4.26 4.56 3.70 2.48 1.55 1.23 - > -1.25 < + + -2.52 2.33 2.94 2.56 - 0.33 - - -1.47 - 4, 6HE 1419-1324 RGB 4 ++ -3.05 1.76 1.47 < < ++ < -7.1 > > References . 1 - Masseron et al. (2006); 2 - Frebel et al. (2007); 3 - Frebel et al. (2008); 4 - Masseron et al. (2010); 5 - Masseron et al. (2012); 6 - Allen et al. (2012); 7 - Norris et al. (2013);8 - Keller et al. (2014); 9 - Roederer et al. (2014); 10 - Hansen et al. (2014); 11 - Hansen et al. (2015). from α -captures on N). Similar definitions can be made forthe helium burning region. Just due to these back and forth ex-changes, di ff erent families of abundance patterns resulting fromhydrogen and helium burning and secular mixing of various or-ders can result.The second idea is that a second type of mixing can be envis-aged: this one occurs between the stellar ejecta, when the nuclearreactions have stopped. We shall call this type of mixing stellarejecta mixing . Typically, some CEMP-no stars show signs of be-ing made of material processed by hydrogen and helium burningand then mixed once ejected into the ISM. The material pro-cessed by hydrogen burning can result from secular mixing ofvarious orders.Using such lines of reasoning, Maeder & Meynet (2015) di-vided the CEMP-no class in 5 subclasses. – Class 0: the CEMP-no is made of a material processed by hy-drogen burning but which was not enriched in helium burn-ing products (no secular mixing, no mixing of the ejecta). – Class 1: the CEMP-no is made of a material processed by he-lium burning but which was not enriched in hydrogen burn-ing products (no secular mixing, no mixing of the ejecta). – Class 2: the CEMP-no is made of a material processed byhydrogen burning, which has been enriched in the normalproducts of helium burning (secular mixing of first order, nomixing of the ejecta). – Class 3: the CEMP-no is made of a mixture of ejecta in-volving material processed by both hydrogen and heliumburning. The material processed by hydrogen burning resultsfrom a secular mixing of first order, and the material pro-cessed by helium burning results from a secular mixing ofsecond order (that means that the material processed by he-lium burning has been enriched by hydrogen burning prod-ucts having transformed helium burning products). For in-stance large amounts of N and C, coming from transfor-mation of C and O, enter by mixing in the helium core.Then, successive α -captures on N create some Ne and , Mg. – Class 4: the CEMP-no is made of a material processed by hy-drogen burning (no mixing of the ejecta) resulting from sec-ular mixing of second order. This means that the hydrogenburning transforms material that was processed two times byhelium burning. Typically, neon and magnesium enter againin the hydrogen shell, boosting the Ne-Na and Mg-Al chains.In each of the classes presented before, refinements are madedepending on how advanced is the nuclear burning. For instance,the Mg-Al chain may have more or less acted in the source star so that more or less aluminium has been be created. A sign ’ + ’after the class number indicates a material more processed. Amaterial even more processed is indicated with a sign ’ ++ ’ afterthe class number. We see that classes 1 and 3 are, at least partly,made of helium burning products while classes 0, 2 and 4 aremade of hydrogen burning products. Maeder & Meynet (2015)attributed a class to 30 out of 46 CEMP-no stars: 4 belonging tothe class 2, 17 to the class 3 and 9 to the class 4.In the present work, we focus on CEMP-no of classes 0, 2and 4, i.e. made of a material processed by hydrogen burningthat was eventually enriched in helium burning products. A char-acteristic shared by both stars in classes 2 and 4 (there are not yetobserved CEMP-no of class 0) is a relatively low C / C ratio,between 2 and 12 with a mean of 5.1. This value is characteristicof the CNO processing. The other CEMP-no stars have gener-ally a higher C / C (up to 50). Part of the helium burning re-gion ( C-rich and C-poor) expelled by the source star is usedto form the classes 1 and 3, explaining the higher C / C ratiosfor class 3 CEMP-no stars (there are not yet observed CEMP-noof class 1).Our subsample is finally made of 13 CEMP-no stars ofclasses 2 and 4 with a mean [Fe / H] of − .
9. Table 1 gives thetype, the class and the abundances data for the sample of CEMP-no stars considered in this work. We note the class 2 + Na for HE0057-5959. ’Na’ stands because of the high [Na / Fe] ratio. Theinterpretation is the following: owing to a su ffi ciently high tem-perature, a significant amount of Ne was synthesized in the he-lium burning core of the source star. Some of it have di ff used inthe hydrogen burning shell, boosting the Ne-Na chain and there-fore creating some Na.Note that among those 13 CEMP-no stars, 5 are dwarfs (MS,cf Table 1) and 8 are giants (RGB, cf Table 1), according to thefollowing criteria: the stars with T e f f ≥ g ≥ C surface abundances and in-creases the C and N surface abundance. The abundances ofO, Ne, Na, Mg and Al elements will not change since the temper-ature inside the hydrogen burning shell of such a low mass star islikely too low to activate the ON, Ne-Na and Mg-Al cycles. If welook at the plots [C / Fe] and [N / Fe] versus log g for the observedCEMP-no stars (c.f. Choplin et al. 2016, Fig. 1) we see that thedispersion of the carbon and nitrogen abundances with respectto iron are quite similar for MS and RGB stars. This means thatthe e ff ect of the first dredge-up does not change significantly theabundance of carbon and nitrogen with respect to the changesrelated to the dispersion of the initial abundances (about 4 dex). Article number, page 3 of 13 & A proofs: manuscript no. choplin
Fig. 2. M r as a function of X c ( He), the central mass fraction of He for arotating 60 M (cid:12) model at a metallicity Z = − (similar to a Kippenhahndiagram). Shown in color is the temperature T in MK (upper panel) andthe density ρ in g cm − (lower panel) in the convective hydrogen burningshell, during the core helium burning phase, from X c ( He) = .
98 to X c ( He) = Based on stellar evolution models, Placco et al. (2014) have de-termined a correction ∆ [ C / Fe ] = [ C / Fe ] ini − [ C / Fe ] after 1DUp (1)to apply to the [C / Fe] ratio of 505 Metal-Poor stars in order torecover their initial [C / Fe]. This correction corresponds to thee ff ect of the first dredge-up (if any). Any dredge-up would de-crease [C / Fe] so that ∆ [C / Fe] ≥
0. Note that ∆ [C / Fe] = ∆ [C / Fe] < .
1, one ∆ [C / Fe] = .
31 (CS 29498-043)and one ∆ [C / Fe] = .
74 (CS 22949-037). These corrections aresmall compared to the observed range of [C / Fe] ratios.Also, the fact that the CNO equilibrium value of C / C isobtained at the surface of the MS stars implies that such lowvalues, at least in these stars, cannot be due to a dredge upevent. Moreover, the highest C / C belong to HE 1419-1324,a RGB CEMP, showing that the RGB feature is not necessar-ily associated with a low C / C ratio, as expected by the ef-fect of the dredge up. Correcting the CNO abundances of theevolved CEMP-no stars is of course important in general butin the framework of the present work we focus on the range ofobserved abundances rather than of individual stars, and hencethese small corrections have no impact on our conclusions.
3. Presentation of the experiment
The conducted experiment consists in injecting products synthe-sized in the helium burning core of massive stars like C, O, Ne or Mg in a hydrogen burning single zone of 1 M (cid:12) (H-boxthereafter) with a constant temperature T and density ρ . The H-box reproduces schematically the convective hydrogen burningshell during the core helium burning phase of the source star.To set the initial conditions in the H-box, we rely on a ro-tating 60 M (cid:12) model computed with the Geneva code. The ini-tial metallicity is Z = − . It corresponds to [Fe / H] = − . α -enhanced). The initialabundances in the H-box are taken from the hydrogen burningshell of this model, at the beginning of the core helium burning phase, when the mass fraction of He in the core X c ( He) = . r is the mass coordinate, X c ( He) the central mass fraction of He. We see from this figurethat T and ρ in the convective hydrogen burning shell take valuesof 30 −
80 MK and 1 − − respectively. For a 20 M (cid:12) model,the ranges of T and ρ are 30 −
60 MK and 1 −
10 g cm − . As afirst step, we fix T =
50 MK and ρ = − in the H-box. Dif-ferent temperatures and densities in the H-box are discussed ina second time. The simulation is stopped either when the hydro-gen in the box is exhausted (when the mass fraction of hydrogenin the H-box X ( H) < − ) or when the time t exceeds 10 Myr.Note that depending on the stellar model chosen for setting theinitial abundances in the H-box, we can have a slightly di ff erentinitial chemical composition in the H-box. This will depend onthe chemical composition of the model in its hydrogen burningshell, at the core helium burning ignition ( X c ( He) = . (cid:12) to a 60 M (cid:12) model. The abundances of neon, sodium, magnesiumand aluminium do vary a bit more. It is due to the di ff erenceof temperature that implies a slightly di ff erent nucleosynthesisin the hydrogen burning shell, at the very beginning of the corehelium burning phase.Regarding the nuclear reaction rates, we took the ones usedin the Geneva code (see Ekström et al. 2012). Those rates aremainly from Angulo et al. (1999) for the CNO-cycle but almostall rates for Ne-Na Mg-Al chains are from Hale et al. (2002).Only Ne( p , γ ) Na and Ne( p , γ ) Na are taken from Anguloet al. (1999) and Iliadis et al. (2001), respectively. Note that thefinal abundance of Al in the H-box is added to the one of Mgsince Al is a radioactive isotope ( t / = . × yrs).In order to reproduce schematically the di ff usion of C, O, Ne and Mg from the helium core to the hydrogen shell, weinject a constant mass per year in the H-box, coming from areservoir composed only of the considered specie ( C, O, Neor Mg). We consider injection rates of 10 − , 10 − and 10 − M (cid:12) yr − for C and O and 10 − , 10 − and 10 − M (cid:12) yr − for Ne and Mg. More details about the method for inject-ing the species and the justification of the adopted injection ratesare given in the Appendix. Four cases are tested in the presentexperiment: – no injection is made in the H-box, – C and O are injected, – C, O, and Ne are injected, – C, O, Ne and Mg are injected.Note that in a real star, the mass is conserved and thus any in-jection into the hydrogen burning shell implies that some matterhas to di ff use out from that region. In complete stellar models,the elements that are more abundant in the hydrogen burningshell than in one of the two adjacent regions will di ff use out inthe region(s) where this element is less abundant. However tokeep the model as simple as possible we do not consider thatcomplication here. The present work can be seen as a numericalexperiment and not as an attempt to model in all details whathappens in stars. Indeed, the most important gradients of abun-dances are those coming from the di ff erence in the abundancesbetween the helium core and the hydrogen burning shell. Di ff u-sion from the helium core to the hydrogen burning shell is there-fore clearly the dominant feature, blurring all the other di ff usionprocesses. In complete stellar models, injection of nitrogen intothe helium core occurs dominantly by convection when the he-lium core slightly grows in regions left over by the hydrogen Article number, page 4 of 13. Choplin et al.: Constraints on CEMP-no progenitors from nuclear astrophysics
Fig. 3.
Abundances in the H-box as a function of the logarithm of X ( H ) − X ( H ). The four panels correspond to the four considered cases: whenno injection is made, when C and O are injected, when C, O and Ne are injected and when C, O, Ne and Mg are injected. Densityand temperature in the box are ρ = − and T =
50 MK. burning shell, not by di ff usion from the hydrogen to the heliumburning region. Also, as we will see, the results of our simplebox model well fit qualitatively the results obtained from com-plete stellar models following in a consistent way the mixing ofthe elements. Thus we are quite confident that our simple ap-proach grasp the essential of the process.Let us also mention that the origin of the iron is not inves-tigated in the present work. By choosing a non-zero metallicity,we assume that the small iron content observed at the surface ofthe CEMP-no stars is already present in the source star (and inthe H-box). Our sample of classes 2 and 4 CEMP-no stars is ex-pected to be made of a material processed by hydrogen burningthat comes from the source star, i.e. of the outer layers of this star.The iron abundance in those outer layers is likely not a ff ected bythe nucleosynthesis and stays equal to its initial value. As a con-sequence, a comparison of the models with the observed ratioslike [C / Fe] or [N / Fe] can be made, provided that the iron con-tent in the models (the [Fe / H] ratio) is similar to the iron contentof the CEMP-no stars. In our models, [Fe / H] = − .
4. Results of the experiment
Fig. 3 shows the mass fraction of elements as a function oflog( X ( H ) − X ( H )) (i.e. the logarithm of the initial mass frac-tion of hydrogen minus the current hydrogen mass fraction inthe H-box) for the four cases presented in Sect. 3. The initialmass fraction of H in the box is equal to 0.33, the temperatureand density are set to T =
50 MK and ρ = − and theinjection rates are 10 − M (cid:12) yr − for C and O and 10 − M (cid:12) yr − for Ne and Mg. – When no injection is made (first left panel of Fig. 3), only4.28 × − of hydrogen (in mass fraction) is consumedat the end of the limited time, which we fixed at 10 Myr.No transient regime is seen for the CNO elements since theCNO-cycle is already at equilibrium at t =
0. The mass frac-tion of sodium, X ( Na) first increases slightly due to thee ff ect of the Ne-Na chain. It finally drops, like X ( Ne), infavor of X ( Mg) owing to the reaction Na( p , γ ) Mg. At T =
50, since the Mg( p , γ ) Al reaction is weak, it doesnot succeed in transforming e ffi ciently the Mg synthesizedso that the Mg abundance increases. A little amount of Al is destroyed when little H remains in the shell and is transformed either in Si through Al( p , γ ) Si, or in Mgthrough Al( p , α ) Mg, both channels being almost equal atthis temperature. – Injecting C and O boosts the CNO cycle and createsprimary N and C (second left panel of Fig. 3). TheCNO elements being more and more abundant, more andmore hydrogen is burnt and it is finally exhausted after ∼ C, Cand N. Since the reaction O( p , γ ) F is much slower,the injected O accumulates before being destroyed into F. Those two regimes can be seen on the second leftpanel of Fig. 3: the curve showing O first increases untillog( X ( H ) − X ( H )) ∼ − − < log( X ( H ) − X ( H )) < − O destruction be-comes important). No permanent regime is attained for O. C and O rise dramatically at the end since the hydrogenis almost exhausted: the CNO cycle works less and less, im-plying an accumulation of the injected C and O. Regard-ing the other elements, we see that Ne decreases in favorof Na but the duration of the simulation is too short in thiscase for the Ne-Na and Mg-Al chains to operate significantly. – Doing the same experiment but injecting also some Neallows the synthesis of Na and Mg through the reac-tions Ne( p , γ ) Na and Na( p , γ ) Mg (see Fig. 3, thirdleft panel). Also some Ne is created when the reaction Na( p , α ) Ne occurs. At this temperature and for the se-lected rates, the ( p , α ) channel is 1.6 higher than the ( p , γ )channel so that Na is almost equally destroyed in Ne and Mg. The reaction Mg( p , α ) Al is too slow to activatethe Mg-Al chain. Since neon, sodium and magnesium staymuch less abundant than the CNO elements, the hydrogen isnot burnt significantly quicker than in the case 2 describedjust before, when injecting only C and O. – The last case is when injecting Mg as well (right panel ofFig. 3). The di ff erence with the previous case is the increaseof Al by ∼ Mginto Al thanks to a proton capture. For the temperature,density and time of simulation considered, the Al destruc-tion through either the ( p , α ) or ( p , γ ) channels is not signif-icant.Fig. 4 shows the [X / Fe] ratios for the four cases presentedin Fig. 3. Plotted are the initial abundance pattern in the H-box(lines with squares) and the final one (lines with triangles). The
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Fig. 4. [X / Fe] ratios in the H-box for the four considered cases. The [ C / C] ratio is also shown (i.e. C / C ratio relatively to the sun, inlogarithm). The red points show the CEMP-no stars of Table 1 with [Fe / H] = − . ± .
3. The abundance patterns in the box at t = , respectively. The green pattern on the second(third) panel shows the composition in the hydrogen burning shell at the end of the core helium burning phase of a complete 20 M (cid:12) stellar modelat 30% (70%) of the critical velocity on the ZAMS. Density and temperature in the box are ρ = − and T =
50 MK. grey area corresponds to the range of values covered during thesimulation. The dotted lines correspond to the final patterns inthe H-box when the rates of injection are divided and multipliedby 100 respectively. The red points represent the observed ratiosin CEMP-no stars of similar metallicities ([Fe / H] = − . ± .
3) asthe metallicity considered in our numerical experiment ([Fe / H] = − . / Fe] ratios predicted by the models.Without injection, the abundance pattern in the H-box doesnot change very much and all the [X / Fe] ratios (except [N / Fe]and [Al / Fe]) stay below the observed values. It is not surprisingsince the observed values correspond to classes 2 and 4 while thepresent experiment (no injection) would rather correspond to theCEMP-no of class 0. This class is made of a material processedonly by hydrogen burning and where no mixing occurred be-tween the hydrogen and helium burning regions. Injecting some C and O enhances the corresponding [X / Fe] ratios, as wellas [N / Fe] (Fig. 4, second left panel). Increasing or decreasingthe rate of injection by a factor of 100 (dotted lines) changes thefinal pattern in the box but not dramatically: from the lower tothe upper dotted line, the rate of injection is multiplied by 4 dexwhile the di ff erence in [X / Fe] values does not exceed 2 dex (forC, N and O). This is because when injecting more C and Oin the H-box, the hydrogen is burnt more rapidly so that hydro-gen exhaustion occurs earlier. We have here a negative feedbackprocess: increasing the rate of injection increases the amountof injected species but at the same time reduces the availabletime for injecting those new chemical species in the H-box. Thisexplains qualitatively why injecting C and O at a rate 10 higher does not lead to an increase of 4 dex of the final [C / Fe],[N / Fe] and [O / Fe] ratios. The third case shows enhancements of[Ne / Fe], [Na / Fe] and [Mg / Fe] ratios: protons captures on the in-jected Ne create Na and then Mg. The final patterns of thefourth case present enhancements of [Mg / Fe] and [Al / Fe] ratioscompared to the case 3: due to the injection of Mg, the Mg-Alchain is boosted, hence creating some Al.Changing the temperature and the density in the H-box leadsto the results presented in Fig. 5. We tested temperatures of T =
50, 60 and 80 MK at a constant density ρ = − (left panel) and densities of ρ =
1, 10 and 100 g cm − at a con-stant temperature T =
50 MK (right panel). For both cases, theinjected species are C, O, Ne and Mg and the injectionrates are 10 − M (cid:12) yr − for C and O and 10 − M (cid:12) yr − for Ne and Mg. In addition to the other [X / Fe] ratios, [Si / Fe] isalso shown. Increasing either the temperature or the density leadsto lower [X / Fe] ratios at hydrogen exhaustion (except howeverfor the [Si / Fe] ratio at T =
80 MK). When raising the densityfor instance, the rates of the nuclear reactions increase, allow-ing a quicker synthesis of the chemical species than at lowerdensities. At the same time, the hydrogen is burnt more rapidlyso that hydrogen exhaustion occurs earlier, letting less time toinject new species. Summing those two opposite e ff ects finallyleads to lower [X / Fe] ratios at hydrogen exhaustion. For the samereasons, similar results are found when varying the temperature,although the dependance of the nuclear rates on temperature ismuch stronger than the dependance on the density. This is thereason why the various temperatures spanning a relatively smallrange of values (see Fig. 5) change the [X / Fe] ratios much moresignificantly than the various densities, that cover yet a muchlarger range of values.The initial [Si / Fe] ratio in the box is about 1 and it is littlea ff ected by changes of temperature and density. However, in-creasing the temperature up to T =
80 MK leads to about 0.5dex more silicon at the end. The first reason is that the nuclearrates associated to Mg, Al and Si are generally 3-4 dex higherat T =
80 MK than at T =
50 MK, allowing the synthesis ofsome Si. The second reason is the following: Al is destroyedeither to form Si thanks to the Al( p , γ ) Si reaction, either toform Mg owing to the reaction Al( p , α ) Mg. When Al isdestroyed into Mg, the Mg-Al chain operates and synthesizesagain Al. On the opposite, Al is definitely destroyed when itis transformed into Si. At T =
50 and 60 MK, both channelsare roughly equal. At T =
80 MK, the ( p , γ ) channel is ∼ p , α ) one. This tends to reduce Mg and Aland to increase Si.Also shown on Fig. 4 and 5 is the [ C / C] ratio, i.e.log( C / C) - log( C / C) (cid:12) . The isotopic ratio in the Sun istaken from Lodders (2003). Whatever the case, the [ C / C] ra-tio does not vary more than 0.5 dex, always staying around -1.5.This is because the equilibrium value is quickly reached whenthe CNO cycle operates. After each injection of C, the equi-librium ratio is reached again quasi instantaneously compared to
Article number, page 6 of 13. Choplin et al.: Constraints on CEMP-no progenitors from nuclear astrophysics the current timestep. Especially, [ C / C] reaches similar finalvalues under all the explored temperatures and densities. Whenthe CNO cycle operates, the [ C / C] equilibrium ratio is indeedalmost temperature and density independent.We see that the observed [X / Fe] ratios are best covered wheninjecting C, O and Ne (see the grey area in the third panelof Fig. 4). We note however that the models always give too highvalues for the [Al / Fe] ratios (this point will be discussed on Sect.6). For all the other ratios, our very simple numerical experimentconfirms the need for some mixing between the helium and hy-drogen burning zones in the source star to explain the generalpattern observed in CEMP-no stars of classes 2 and 4. The factthat the injection of Ne seems to be needed supports the viewthat a strong mixing might be at work in the source star: Necan enter in the hydrogen burning shell if C and O have firstdi ff used in the hydrogen burning shell, but also if the created Nhave entered at its turn in the helium burning core. For most ofthe ratios, however, we note that the grey region is wider thanthe ranges covered by the observations. We think that this is nota very serious problem when considering that CEMP-no starsare not made of pure hydrogen shell material. For being used toform new stars, this matter needs to be ejected either by windsor at the time of the supernova. In this process, the region wherethe CNO-cycle was active (hydrogen shell) will be mixed withother layers of the star as well as eventually with some inter-stellar medium. For instance, any mixing with the outer layersof the star where the iron has the same abundance as in the hy-drogen shell but where the CNO abundances are smaller, closeto their initial values ( ∼ − for a model with Z = − ) willshift the nitrogen abundance downward. Therefore, in order toobtain the observed nitrogen abundances in CEMP-no stars, it islikely needed that much higher abundances are reached in the hy-drogen burning shell. While our box experiments provide someinteresting constraints about the nuclear processes that might beneeded to reproduce the peculiar abundance patterns of CEMP-no stars, only the computation of complete stellar models withthe account for the ejection mechanism (both through winds andthrough the supernova explosion) and for some possible mixingwith the circumstellar material can provide abundances ratiosthat might be compared with the observed ratios in CEMP-nostars. This has to be kept in mind when interpreting the compar-ison shown in Fig. 4.Note also that injecting some Mg raises the [Al / Fe] ratiofar above the observed range. In stellar models, Mg comesfrom the transformation of Ne which occurs at the very endof the core helium burning phase. Thus, Mg could be injected(if any) only at the very end or after the core helium burningphase, leaving little time for nuclear burning to transform this Mg into Al in the hydrogen burning shell. In that respect, thepresent numerical experiments injecting Mg regularly all alongthe burning of the hydrogen shell clearly overestimates what oc-curs in real stars. Thus, the no Mg injection hypothesis is byfar not unrealistic.It is interesting to note that detailed stellar models are quali-tatively well enough reproduced by this simple one zone model.The two green patterns on Fig. 4 show the [X / Fe] ratio in thehydrogen burning shell of a complete stellar model at the end ofthe core helium burning phase. The abundances are taken in thehydrogen shell, where the energy released by hydrogen burningis the highest. The two stellar models are 20 M (cid:12) , Z = − starscomputed at 30% (second panel) and 70% (third panel) of thecritical velocity on the ZAMS. It corresponds to an initial equa-torial velocity of 280 and 610 km s − respectively. Increasingthe initial velocity can be modeled, in the single zone model, by increasing the injection rate and injecting some Ne in additionto the C and O. By comparing the two green patterns, it isalso interesting to see the strong impact of the initial rotation onthe [X / Fe] ratios in the hydrogen burning shell at core heliumexhaustion. This shows that the stellar rotation at low metallicityis likely a non-negligible process.One point that deserves more discussion is the constant valuefound for the C / C ratio under various conditions. What canbe learnt from this ratio? How could it be used in stellar evolu-tion models? The lithium content at the surface of the CEMP-nostars can give interesting constraints as well. Also a deepest in-vestigation on the [Al / Fe] ratio seems worthwhile, because of thediscrepancy we found between models and observations. Whichconditions or assumptions will favor a lower [Al / Fe] ratio, closerto the observed values?
5. Dilution with material processed by heliumburning and with initial ISM
In the previous section we have investigated the secular mixingbetween the hydrogen and helium burning regions, during thenuclear life of the source star. We will now discuss the mixingevents that can happen outside from the star, when the nuclearreactions are not active anymore. Di ff erent kinds of materialscan be ejected by the source star in the ISM. Let us consider twoof them: (i) the material that was processed by hydrogen burningand (ii) the one that was processed by helium burning. Outsidefrom the star, those materials can be mixed together and / or withthe ISM. We distinguish 2 kinds of dilutions: – the dilution between the material processed by hydrogenburning and the one processed by helium burning. This cor-responds to a mixing between di ff erent parts of the star. Bymixing we mean mixing of the ejecta (or stellar ejecta mix-ing as defined in Sect. 2), hence outside of the star, withoutnuclear reactions. – the dilution of the whole material ejected by the source star(no matter if it was processed by hydrogen or helium burn-ing) with the initial ISM, in which the source star formed.This is a mixing of the stellar ejecta with the initial ISM.Based on considerations on the C / C ratio and the lithiumabundance, we investigate the possibility of constraining thosetwo kinds of mixing events. C/ C ratio to constrain the amount of ejecta processed by helium burning
The C / C ratio of the selected CEMP-no stars gives a strongconstraint on the kind of material needed to form those stars. Aswe see in Fig. 4, this ratio is very close to the one found in a CNOprocessed material. We see from Fig. 4 and 5 that injecting some C in a hydrogen burning region does not change the C / Cratio, under various densities, temperatures and rates of injec-tion. However, if switching o ff the nuclear reactions (this is whathappen when the material is ejected from the source star) andmixing the CNO processed material with part of the region pro-cessed by helium burning, this ratio will no longer stay aroundthe observed values.This point can be illustrated with a simple experiment. Onecan mix together the two kind of material ejected by the sourcestar: the ejecta that was processed by hydrogen burning and theone by helium burning (H-ejecta and He-ejecta hereafter). The Article number, page 7 of 13 & A proofs: manuscript no. choplin
Fig. 5.
Left : same as figure 4 but for 3 di ff erent temperatures in the H-box. Also the [Si / Fe] ratio is shown. Only the final abundance patterns inthe box are plotted. The injected species are C, O, Ne and Mg. Density is unchanged (1 g cm − ) and the injection rate is 10 − M (cid:12) yr − for C and O and 10 − M (cid:12) yr − for Ne and Mg).
Right : same as the left panel but for 3 di ff erent densities in the H-box. The temperature is setto 50 MK. [ C / C] ratio can be followed as adding more and more He-ejecta to the H-ejecta. The left panel of Fig. 6 shows [ C / C]as a function of f mix defined as the fraction of He-ejecta added tothe H-ejecta. For instance, f mix = − means 1% of He-ejectawith 99% of H-ejecta. We tested two compositions for the H-ejecta. The first one has mass fraction of C and C equal to1.11 10 − and 3.10 10 − . It is called C-poor H-ejecta . Thosemass fractions are the ones in the H-box at t =
0. The secondmixture has a C mass fraction of 2.01 10 − and a C one of5.45 10 − . We call it C-rich H-ejecta . Those values correspondto the mass fractions of C and C in the H-box, a few timebefore hydrogen exhaustion, when C is injected. – The
C-poor H-ejecta corresponds to the low rotational mix-ing case. Few C has di ff used from the helium core to thehydrogen shell so that the mass fractions of C and C inthe hydrogen burning shell stay around their initial value, i.e.around 10 − . When this part of the star is expelled, we get anejecta poor in carbon. – The
C-rich H-ejecta corresponds to the strong rotationalmixing case. A lot of C has di ff used in the hydrogen burn-ing shell, raising its abundance and the one of C far abovetheir initial values. At the time of the ejection, this materialis enriched in carbon compared to the previous case.From what regards the carbon abundances in the He-ejecta,we took characteristics values in the helium burning core. We setX
Heb ( C) = Heb ( C) = f mix = − ) of the He-ejecta with 99% of a C-rich H-ejectaleads to a [ C / C] of − . C / C] ratio of 2.6, far abovethe observed range. It seems that whatever the C-richness of theH-ejecta, hence the amount of helium products that entered in the hydrogen burning shell during the life of the source star, the finalcontribution of the material processed by helium burning com-ing from the the source star should be null to form the CEMP-nostars of classes 2 and 4. This strongly support the idea that theCEMP-no stars of classes 2 and 4 are only made of the hydro-gen envelope of the source star. More generally, since C / Cis highly sensitive to the burning region considered (it is low fora hydrogen burning and high for a helium burning region), thisratio could be used to constrain the mass cut of spinstar modelsat the time of the supernova: the mass cut could be chosen inorder to reproduce the observed C / C ratio of the consideredCEMP-no star.The grey histogram in the right panel of Fig. 6 shows thedistribution of all observed [ C / C] ratios at the surface ofCEMP-no stars. It contains the 13 CEMP-no stars of Table 1plus 15 other CEMP-no stars with a measured C / C ratio.Some CEMP-no stars (not considered in this work) have higher[ C / C] ratios, suggesting the need for a small amount of mate-rial processed by helium burning to form them. We see howeverthat the amount of material processed by helium burning neededshould stay small in any case ( f mix (cid:46) . C / C] ratio (3 out of 12 in our sub-sample). An accurate determination of this ratio for those starswould be interesting to validate the previous statement regardingthose stars.
In the previous section, we discussed the mixing of the stellarejecta: the regions processed by hydrogen and helium burningejected by the source star can be mixed together, when the nu-clear burning has stopped. The following discussion is related tothe mixing (or the dilution) of the whole stellar ejecta with theinitial ISM, in which the source star formed.The lithium is an interesting element to obtain pieces of in-formations on the amount of ISM that should be mixed with the
Article number, page 8 of 13. Choplin et al.: Constraints on CEMP-no progenitors from nuclear astrophysics
Fig. 6.
Left : [ C / C] ratio as a function of the mixing factor f mix ,which represents the fraction of material processed by helium burningmixed with the material processed by hydrogen burning. Two composi-tions are tested for the material processed by hydrogen burning: a C-richcomposition (red line) and a C-poor composition (black line). Right : thegreen histogram shows the distribution of the CEMP-no stars used inthis work. They belong to the class 2 or 4. The grey histogram shows allknown CEMP-no stars with a measured C / C ratio. source star ejecta to form the CEMP-no stars. The abundance oflithium A(Li) in the pristine ISM is equal to 2.72 according toCyburt et al. (2008). It is totally destroyed in massive stars. Asa consequence, as soon as the ejecta of the massive source staris mixed with the ISM, the abundance of lithium is raised (inthe mixture made of initial ISM and source star ejecta). If oneassumes that the lithium content at the surface of the CEMP-nostar reflect the one in the cloud where it formed, then the higherthe lithium content at the surface of the CEMP-no star, the morethe source star ejecta was diluted with the ISM. The dilution fac-tor for mixing the progenitor ejecta with the ISM can be chosenin order to obtain the observed A(Li) value of the consideredCEMP-no star.A di ffi culty is that the lithium at the surface of the CEMP-nostar can be depleted by internal mixing processes in the CEMP-no star itself. However, such processes might not be able to ex-plain the low content of lithium observed at the surface of someCEMP-no stars. Meynet et al. (2010) pointed out that the maxi-mal depletion predicted by the models of Korn et al. (2009) (1.2dex) is unable to account for the A(Li) value observed at the sur-face of HE 1327-2326 (A(Li) < = . − . = .
52 at minimum, i.e.the WMAP content minus the maximal predicted depletion fac-tor. We see that the depletion mechanism has di ffi culties to ac-count for the lowest observed A(Li) values. The alternative forHE 1327-2326 is that it formed with a Li-poor material.The A(Li) values (or upper limits) for 9 of the consideredCEMP-no stars are shown on Table 1. The lower panel of Fig.3 in Meynet et al. (2010) shows the dilution factor M ISM / M eje vs. A(Li). According to this figure and if we consider that thelithium was not depleted by the CEMP-no stars themselves, thedilution factor should be less than ∼ . < C, N and O in the H-box when injecting C and O is at least 10 − (see Fig. 3). The mass fraction of the CNO elements in a Z = − ISM is about 10 − . 90% of 10 − with 10% of 10 − gives ∼ − .The dilution is not playing a significant role in that case.Let us suppose now that the lithium was depleted by theCEMP-no stars. We take the maximum depletion factor (1.2 dex)from Korn et al. (2009) and we add it to the observed A(Li) inorder to get the initial A(Li) value, before the depletion process.The two highest A(Li) belong to CS 22945-017 ( < .
71) andCS 22958-042 ( < . ∼
2. There is still notenough ISM for the dilution to have a significant e ff ect, excepthowever for CS 22945-017. One must stay cautious on thosesimple statements about the dilution between ejecta and ISM butin the framework of our simple model, we see that the dilutionwith the initial ISM might play only a limited role. This is be-cause the metal abundances in the region processed by hydrogenburning are much higher than the ones in the initial ISM and be-cause the dilution factors derived from the lithium abundance aresmall in most of the cases.
6. The effects impacting the Al and Si abundances
The experiments presented in Sect. 4 show that the [Al / Fe] ratioin the H-box at hydrogen exhaustion lies always above the ob-served range of values. Even the initial [Al / Fe], taken from thehydrogen burning shell of a 60 M (cid:12) model at the beginning ofthe core helium burning phase is just above the observed range(see lines with squares on Fig. 4). We investigate now 3 e ff ectsimpacting the aluminium abundance: the injection (species andrate), the temperature and the nuclear reaction rates. First of all, one expects a lower final [Al / Fe] ratio if no Mgis injected. If it is injected, some Al is created through the re-action Mg( p , γ ) Al. This is illustrated in the third and fourthpanels of Fig. 4. We see indeed that injecting Mg leads to ahigher final [Al / Fe] than if no Mg is injected.Fig. 7 shows [Al / Fe] as a function of R Ne , the rate of in-jection of Ne at T =
50 MK (left panel) and T =
80 MK(right panel). The injected species are C, O and Ne. Theblue, black and green lines are associated to 3 sets of nuclear re-actions rates that we tested and that will be discussed on Sect.6.3. Let us focus on the case 2 (black lines) that corresponds tothe nuclear rates used until now. The horizontal black line showsthe initial [Al / Fe] ratio in the H-box and the black line with tri-angles shows the final ones. We see that the final [Al / Fe] ratio at T =
80 MK (right panel of Fig. 7) is lower when less Ne isinjected. When the injection rate is low enough, the Al is glob-ally more destroyed than created. We see that some aluminiumis created at the end if R Ne > − M (cid:12) yr − for the consid-ered case. This aluminium comes mainly from the injected Nethanks to successive proton captures.Those two arguments suggest that a moderate amount of Ne coming from the helium burning core to the hydrogen burn-ing shell together with no Mg would probably play in favor ofa lower final [Al / Fe] ratio.
Article number, page 9 of 13 & A proofs: manuscript no. choplin
Fig. 7. [Al / Fe] ratios in the H-box as a function of R Ne , the rate of injection of Ne ( C and O are also injected). The temperature is T = T =
80 MK (right), the density ρ = − and C, O and Ne are injected. The three lines with triangles show the final [Al / Fe]ratios in the H-box when considering three di ff erent sets of nuclear rates for the 3 principal reactions implying Al (see text for explanations).The horizontal blue, black and green lines corresponds to the initial [Al / Fe] in the H-box for the 3 considered cases. Observed [Al / Fe] are shownby the red dashed lines for the CEMP-no stars that have [Fe / H] = − . ± . The final abundance of aluminium depends on the strength ofthe nuclear reactions rates that create and destroy it. The nu-clear rates for the Ne-Na and Mg-Al cycles are generally 3-4 dexhigher at T =
80 MK than at T =
50 MK so that the synthesisof aluminium is slower at T =
50 MK. Fig. 7 shows that in-deed, the final [Al / Fe] ratios deviate only little from their initialvalues at T =
50 MK (left panel) while the di ff erence is muchmore significant at T =
80 MK (right panel). Note however thatthe ’case 3’ pattern at T =
50 MK stands largely below its ini-tial value (horizontal green line) but this is due to the Al thathas decayed into Mg at the end of the simulation (this reduces[Al / Fe] by about 1 dex). Also the green triangle at the abscissa10 − M (cid:12) yr − deviates from the others. The considered nuclearrates in that case disfavor the synthesis of Al (see discussion onSect. 6.3). This together with the low injection rate that imply alonger time before hydrogen exhaustion, allow a larger depletionof Al than at higher injection rates.Also, we saw on Sect. 4 (see also Fig. 5, left panel) that in-creasing the temperature leads to a lower final [Al / Fe] ratio (anda higher [Si / Fe]). This stays true as long as some Mg is in-jected: if Ne is injected but not Mg (as in Fig. 7), [Al / Fe]can be higher when increasing the temperature. It can be seen bycomparing the left and right panels of Fig. 7 at the abscissa 10 − M (cid:12) yr − for instance. In that case, no Mg is injected so that Al comes mainly from the successive proton captures on theinjected Ne. The chain leading to Al is longer if starting from Ne than from Mg. In that chain, the rate of Mg( p , γ ) Al at T =
50 MK is very low compared to the other reaction rates.This reaction tends to stop the chain at T =
50 MK so that thefinal content in Al is generally close to the initial one, evenwith high injection rates of Ne. Injecting some Mg is a wayto avoid this bottleneck reaction and synthesize some aluminum, even at T =
50 MK (see the fourth panel of Fig. 4). The rate of Mg( p , γ ) Al strongly increases from T =
50 to 80 MK (byabout 7 dex) so that the chain leading to Al (and Si) is nomore blocked at T =
80 MK.A moderate temperature in the hydrogen shell ( ∼
50 MK)is likely more compatible with a lower [Al / Fe] under variousamounts of Ne coming from the helium core to the hydrogenshell. In the strong mixing case (high R Ne ) and at high temper-atures, this could lead to a very high [Al / Fe] ratio (Fig. 7, rightpanel).
A point that deserves to be investigated is the uncertainties ofthe nuclear rates. In a hydrogen burning region, the two reac-tions destroying Al are Al( p , γ ) Si and Al( p , α ) Mg. Thereaction which create Al is Mg( p , γ ) Al. The 3 nuclear ratesassociated to these reactions are very uncertain at the consideredtemperatures. To illustrate this point, we compared 3 sets of nu-clear rates for the 3 mentioned reactions involving Al. We usedrates provided by the JINA REACLIB database (Cyburt et al.2010). – Case 1: the best scenario for the Al synthesis. We took themaximum rate (at T =
80) for Mg( p , γ ) Al (Cyburt et al.2010). The minimum rate was taken for both Al( p , γ ) Siand Al( p , α ) Mg (van Wormer et al. 1994). – Case 2: we used the rates taken for this work (see Sect. 3). – Case 3: the best scenario for Al destruction. The minimumrate for Mg( p , γ ) Al is from Angulo et al. (1999) andthe maximum rates for Al( p , γ ) Si and Al( p , α ) Mg arefrom Cyburt et al. (2010).To be consistent, we computed 2 other complete stellar mod-els from the ZAMS to core helium burning ignition with the
Article number, page 10 of 13. Choplin et al.: Constraints on CEMP-no progenitors from nuclear astrophysics / Fe] ratios taken in the H-boxare shown by the blue (case 1), black (case 2) and green (case3) horizontal lines. We see that the scatter is significant. Thisis because the Mg-Al cycle is already operating in the core ofthe complete stellar model during the Main-Sequence so that thealuminum abundance is a ff ected if changing the nuclear rates.Depending on the set of nuclear rates, it finally leads to a dif-ferent aluminum content in the hydrogen shell at core heliumburning ignition, hence in the H-box.The lines with triangles correspond to the final [Al / Fe] ratiosin the H-box for the 3 cases. We verify that the rates consideredin this work (case 2) lead to a final [Al / Fe] ratios in between thetwo extreme cases. Whatever the injection rate, at least 1.5 dexseparates the blue from the green pattern, the green one givinglower [Al / Fe] since this is the case where Al is the most de-stroyed and the less synthesized. A word of caution: for the case3, the abundance of Al is higher than the one of Al during theburning, so that [Al / Fe] is significantly a ff ected when decayingthe Al into Mg. For the cases 1 and 2, Al is more abundantso that decaying Al at the end reduces only a little [Al / Fe].4 out of 5 CEMP-no stars with [Fe / H] = − . ± . / Fe]. Those ratios are represented by the red dashedlines on Fig. 7. The scatter of the observed [Al / Fe] ratio is wellenough covered by the case 3 (green pattern) if relying on dif-ferent values for R Ne , the injection rate of Ne. If we selectthat set of rates, our model indicates that (i) the CEMP-no starswith [Al / Fe] (cid:38) ∼
50 MK would not lead to a high enough aluminiumcontent (see left panel of Fig. 7) and (ii) only a high enoughinjection rate of Ne can account for Al-enhanced CEMP-nostars. The four stars considered here do not show such a high[Al / Fe] ratio (except CS 29498-043 however, but with a modestenhancement). This might tend to disfavor the progenitors wherethe mixing is really strong (very high initial velocity) and witha high temperature in the hydrogen shell ( (cid:38)
60 M (cid:12) stars). Thetwo left possibilities are either a high temperature ( ∼
80 MK) inthe hydrogen shell but a weak mixing (a low R Ne ), or a mod-erate temperature in the hydrogen shell ( ∼
50 MK) with a weakto strong mixing. A moderate temperature in the hydrogen shellis more likely achieved in ∼
20 M (cid:12) progenitors (30 −
60 MK)rather than in ∼
60 M (cid:12) ones (30 −
80 MK, see Fig. 2).
The silicon abundance is also a ff ected when changing the injec-tion, temperature or nuclear reaction rates. In the explored rangeof parameters (temperature, injection rate and nuclear reactionrates, see Fig. 7) and for the injected species considered ( C, O and Ne), the final [Si / Fe] ranges from 1 to 1.8.At T =
50 MK, the final [Si / Fe] ratio depends very weaklyon the injection rate. This is because the Ne-Si chain is stoppedby the Mg( p , γ ) Al reaction (see Sect. 6.2). In that case, the fi-nal [Si / Fe] ratio is almost equal to the initial value, which rangesfrom 1 (case 1, lowest rate for Al( p , γ ) Si) to 1.2 (case 3, high-est rate for Al( p , γ ) Si).At T =
80 MK, the final abundance of silicon is always en-hanced compared to the initial one. The Mg( p , γ ) Al reactiondoes not block the Ne-Si chain anymore so that the injected Nesynthesizes some Si. The final [Si / Fe] ratios range between 1.2and 1.8. Three CEMP-no stars with [Fe / H] = − . ± . / Fe]. The values are 0.77, 0.82 and 0.87. Those valuesbeing closer to the results given by the model at T =
50 MK(1 < [Si / Fe] < T (cid:39)
50 MK), consistent withthe discussion in Sect. 6.3.
7. The possible astronomical sources of classes 2and 4 CEMP-no stars
Through the present work, we suggest that the high observedabundances of C together with that of N, O, Na and Mg at thesurface of the CEMP-no stars are the signature of a mixing be-tween the helium and hydrogen burning regions of the sourcestar, during its nuclear life. What are the objects able to expe-rience such a mixing process? In the framework of our resultsbut also in a more global context, we speculate on the possibleprogenitors of classes 2 and 4 CEMP-no stars.
AGB stars are known contributors to s-process elements. Theyare generally believed to be responsible for the enrichment,by mass transfer, in s-elements observed at the surface of theCEMP-s stars. In addition to the abundances, the models haveto reproduce the period of the binary system for instance, whichcan give tight contraints but increase also the di ffi culty of findingmodels matching the observations (see, e.g., Abate et al. 2015).In AGB stars, there is a mixing between the two shells. Itcould also in principle be enhanced by rotation or at least rotationmay change the chemical structure of the star at the beginning ofthe AGB phase (see the 7 M (cid:12) model in Meynet et al. 2010, forinstance).It seems however that there are at least 2 di ffi culties in thisscenario to explain the CEMP-no stars. Firstly, the AGB stars areexperiencing the s-process and by definition, the CEMP-no classis not (or weakly) enriched in s-elements. This feature wouldbe di ffi cult to explain relying on AGB stars. Secondly, it seemsdi ffi cult to account for the CEMP-no stars having [Fe / H] (cid:46) − Tominaga et al. (2014) discussed the scenario of faint supernovaefrom Pop. III stars with mixing and fallback. In such models,only the outer layers are ejected from the progenitor. It is indeedneeded to explain the observed CNO abundance patterns, as wellas the low C / C ratios. This is in line with the discussion aboutthe mixing of the ejecta: we saw in Sect. 5 that no (or a few)material processed by helium burning coming from the sourcestar should be mixed to the hydrogen rich envelope, when thenuclear life of the star is finished. In other words, mainly thehydrogen rich envelope of the progenitor would be needed toform the future CEMP-no star.On the other hand, these models are generally non-rotating,leading to some di ffi culties in explaining the high nitrogen abun-dance observed in some CEMP-no stars without invoking anextra mixing process in the progenitor. Rotating models werehowever considered in Takahashi et al. (2014), predicting higherN / Fe ratios in the ejecta, quite in line with the observed ones at
Article number, page 11 of 13 & A proofs: manuscript no. choplin the surface of two out of the three CEMP-no stars they consid-ered (HE 0107-5240 and HE 1327-2326).
Limongi et al. (2003) proposed a two steps scenario: a normal ∼
15 M (cid:12) supernova responsible for the iron-peak elements, fol-lowed by a fainter one experiencing strong fallback, comingfrom a ∼
35 M (cid:12) . The second progenitor, more massive, enrichesthe ISM in light elements: C, N, Na and Mg. These elements areproduced thanks to a partial mixing between hydrogen and he-lium burning shells that can occur in Z = C / C ratio of 240 for this two stepsmodel. The predicted [ C / C] ratio is 0.4 and this is not com-patible with the values of the CEMP-no stars considered here(see Fig. 6, right panel). We note however that 3 out of 12 haveonly a lower limit for the C / C ratio (see Table 1) so that sucha high predicted C / C could be consistent with these CEMP-no stars.
Several signatures of fast rotation at low metallicity were foundover the past years. One strong signature is that the large nitrogenabundances as well as the low C / C ratios observed in normalVery Metal-Poor (VMP) stars are much better reproduced by lowmetallicity chemical evolution models if including fast rotators,also called spinstars (Chiappini et al. 2006, 2008). Because ofthe high rotation, the injection process we have investigated hereoperates in the spinstar and it could be a way to obtain a materialenriched in C, N, O, Na and Mg together with a low C / C,that will ultimately form a CEMP-no star of class 2 or 4.The spinstars and more generally the objects experiencing amixing between hydrogen and helium burning regions appear asinteresting candidates for being the classes 2 and 4 CEMP-noprogenitors.
8. Conclusions
We studied the possibility of forming CEMP-no stars with a ma-terial processed by hydrogen burning coming from the sourcestar. We carried out nuclear experiments where the convectivehydrogen burning shell of the source star was modeled by a hy-drogen burning single zone (H-box). The mixing between thehelium burning core and the hydrogen burning shell was mim-icked by injecting the products of helium burning C, O, Neand Mg in the H-box. N, Na, Mg and Al are synthesizedwhen injecting those species in the hydrogen burning zone. The C / C ratio is constant under various densities, temperatures inthe H-box, and also under various injection rates. The [Al / Fe]ratio in the hydrogen burning zone lies generally above the ob-servations. Using di ff erent nuclear reaction rates found in the lit-erature for the reactions involving Al leads to a better coverageof the observed [Al / Fe] scatter. The high observed [Al / Fe] ratiosare reproduced at su ffi ciently high hydrogen burning tempera-ture (80 MK) and if the injection rate of Ne is high enough.This might point toward a massive (high temperature) and fastrotating (high injection rate) progenitor.Through this work, we suggest that the high observed abun-dances of light elements at the surface of the CEMP-no starsare the signature of a mixing between the helium and hydrogen burning regions of the progenitor, during its nuclear life. It sup-ports the CEMP-no star formation scenario of Maeder & Meynet(2015) for classes 2 and 4. This scenario states that those starsare made of a material processed by hydrogen burning only butwhere products of helium burning coming from the helium coreof the source star di ff used into the hydrogen burning shell thanksto the rotational mixing. This arrival of new elements boosts thenucleosynthesis in the hydrogen burning shell. Considerationson the C / C ratio confirmed that the CEMP-no stars of classes2 and 4 are made of a material that was only processed by hydro-gen burning in the source star. This corroborate the assumptionstating that the CEMP-no stars formed mainly with the hydro-gen rich envelope of the source star. The C / C ratio is highlysensitive to the burning region considered in the source star (hy-drogen or helium burning region). It could be used to constrainthe part which is expelled from the source star at the time of thesupernova in order to reproduce the observed C / C ratio at thesurface of the CEMP-no stars.The spinstars are interesting candidates for being the class2 and 4 CEMP-no progenitors because of their rotation that in-duces exchanges of material between the hydrogen and heliumburning regions. This is giving some support to the idea that therotation played an important role in the early chemical evolutionof galaxies.
Acknowledgements.
The authors thank the anonymous referee who helped toimprove this paper through very constructive remarks. This work was supportedby the Swiss National Science Foundation (project number 200020-160119).
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9. Appendix
Let us consider a box of initial mass m = (cid:12) where X i denotesthe mass fraction of the element i . We consider also a reservoircomposed only of the element e , so that its mass fraction X (cid:48) e inthe reservoir is 1. During a time ∆ t , we inject a mass ∆ m = R e ∆ t (2)from the reservoir into the box. R e is the injection rate of the el-ement e expressed in M (cid:12) yr − . After the injection, the new massfraction X ne w e of the injected element in the box is X ne w e = X e m + X (cid:48) e ∆ mm + ∆ m = X e m + R e ∆ tm + R e ∆ t . (3)The new mass fraction of the other elements in the box can beexpressed as X ne w i (cid:44) e = X i mm + R e ∆ t . (4)Note that the initially 1 M (cid:12) H-box is growing in mass due tothe injection. Its final mass is generally similar to the initial oneand does never exceed ∼ . (cid:12) for the presented results, whichstays relatively close to 1M (cid:12) .The point is now to estimate R e the injection rate. Let us con-sider the example of the carbon. In stellar models, the primary N is synthesized through the di ff usion of C and O fromthe helium core to the hydrogen burning shell. The secondary N is formed with the initial CNO elements in the star. One canroughly quantify M prim N the mass fraction of primary N formedduring the core helium burning phase : M prim N = (cid:32)(cid:90) M X N ( M r ) d M r (cid:33) Y c = − ( X C , ini + X N , ini + X O , ini ) M (5)where Y c is the central He mass fraction, X N ( M r ) the massfraction of N at coordinate M r , X C , ini , X N , ini , X O , ini the massfractions of the CNO elements at the ZAMS and M the total massof the star at the end of the core helium burning phase. M prim N is defined as the total amount of N in the star at core heliumexhaustion minus the amount of N that can be formed with theinitial CNO content (secondary N). We suppose that all the Cand O di ff using from the helium core to the hydrogen shell aretransformed into N. In that case, to get a mass M prim N of primarynitrogen in the star at the end of core helium burning, one needan average injection rate of ( C + O) in the hydrogen shell of R C + O = M prim N τ HeB (6)where τ HeB is the duration of the core helium burning phase. Fora 60 M (cid:12) model at Z = − and at 70 % of the critical velocityat the ZAMS, we find R C + O = − M (cid:12) yr − .The amount of primary nitrogen synthesized (hence the valueof R C + O ) can change significantly depending on the rotation,the mass of the model or the prescription for the rotational mix-ing for instance. In the present work we consider 10 − < R C < − M (cid:12) yr − (the chosen values are 10 − , 10 − and 10 − M (cid:12) yr − ). Also, we set R C = R O and R Ne = R M g = R C / Ne and Mg are ∼
100 times less abundant than C and O in the helium burning core of a low metallicity mas-sive stellar model, so that ∼