Impact of a revised 25 Mg(p, γ ) 26 Al reaction rate on the operation of the Mg-Al cycle
O. Straniero, G. Imbriani, F. Strieder, D. Bemmerer, C. Broggini, A. Caciolli, P. Corvisiero, H. Costantini, S. Cristallo, A. DiLeva, A. Formicola, Z. Elekes, Zs. Fülöp, G. Gervino, A. Guglielmetti, C. Gustavino, Gy. Gyürky, M. Junker, A. Lemut, B. Limata, M. Marta, C. Mazzocchi, R. Menegazzo, L. Piersanti, P. Prati, V. Roca, C. Rolfs, C. Rossi Alvarez, E. Somorjai, F. Terrasi, H.P. Trautvetter
aa r X i v : . [ a s t r o - ph . S R ] N ov Impact of a revised Mg(p, γ ) Al reaction rate on the operationof the Mg-Al cycle
O. StranieroINAF-Osservatorio Astronomico di Collurania, Teramo, Italy, and INFN Sezione di Napoli,Napoli, Italy [email protected]
G. ImbrianiDipartimento di Scienze Fisiche, Universit`a di Napoli ”Federico II”, and INFN Sezione diNapoli, Napoli, ItalyF. StriederInstitut f¨ur Experimentalphysik, Ruhr-Universit¨at Bochum, Bochum, GermanyD. BemmererHelmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr 400, GermanyC. BrogginiIstituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, via Marzolo 8, 35131Padova, ItalyA. CaciolliIstituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, via Marzolo 8, 35131Padova, Italy and Legnaro National Laboratory (INFN), Legnaro (Padova), ItalyP. CorvisieroUniversit`a di Genova and INFN Sezione di Genova, Genova, ItalyH. Costantini 2 –Universit`a di Genova and INFN Sezione di Genova, Genova, ItalyS. CristalloINAF-Osservatorio Astronomico di Collurania, Teramo, Italy, and INFN Sezione di Napoli,Napoli, ItalyA. DiLevaDipartimento di Scienze Fisiche, Universit`a di Napoli ”Federico II”, and INFN Sezione diNapoli, Napoli, ItalyA. FormicolaINFN, Laboratori Nazionali del Gran Sasso (LNGS), Assergi (AQ), ItalyZ. ElekesInstitute of Nuclear Research (ATOMKI), Debrecen, HungaryZs. F¨ul¨opInstitute of Nuclear Research (ATOMKI), Debrecen, HungaryG. GervinoDipartimento di Fisica Universit`a di Torino and INFN Sezione di Torino, Torino, ItalyA. GuglielmettiUniversit`a degli Studi di Milano and INFN, Sezione di Milano, ItalyC. GustavinoINFN, Laboratori Nazionali del Gran Sasso (LNGS), Assergi (AQ), ItalyGy. Gy¨urkyInstitute of Nuclear Research (ATOMKI), Debrecen, Hungary 3 –M. JunkerINFN, Laboratori Nazionali del Gran Sasso (LNGS), Assergi (AQ), ItalyA. Lemut Universit`a di Genova and INFN Sezione di Genova, Genova, ItalyB. LimataDipartimento di Scienze Fisiche, Universit`a di Napoli ”Federico II”, and INFN Sezione diNapoli, Napoli, ItalyM. Marta Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr 400, GermanyC. MazzocchiUniversit`a degli Studi di Milano and INFN, Sezione di Milano, ItalyR. MenegazzoIstituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, via Marzolo 8, 35131Padova, ItalyL. PiersantiINAF-Osservatorio Astronomico di Collurania, Teramo, Italy, and INFN Sezione di Napoli,Napoli, ItalyP. PratiUniversit`a di Genova and INFN Sezione di Genova, Genova, ItalyV. Roca 4 –Dipartimento di Scienze Fisiche, Universit`a di Napoli ”Federico II”, and INFN Sezione diNapoli, Napoli, ItalyC. RolfsInstitut f¨ur Experimentalphysik, Ruhr-Universit¨at Bochum, Bochum, GermanyC. Rossi AlvarezIstituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, via Marzolo 8, 35131Padova, ItalyE. SomorjaiInstitute of Nuclear Research (ATOMKI), Debrecen, HungaryF. TerrasiSeconda Universit`a di Napoli, Caserta, and INFN Sezione di Napoli, Napoli, ItalyH.-P. TrautvetterInstitut f¨ur Experimentalphysik, Ruhr-Universit¨at Bochum, Bochum, GermanyJanuary 30, 2018Received ; accepted present address: Lawrence Berkeley National Laboratory, Berkley, CA 94720 USA present address: GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, 64291 Darm-stadt, Germany 5 – ABSTRACT
Proton captures on Mg isotopes play an important role in the Mg-Al cycleactive in stellar H-burning regions. In particular, low-energy nuclear resonancesin the Mg(p, γ ) Al reaction affect the production of radioactive Al gs as wellas the resulting Mg/Al abundance ratio. Reliable estimations of these quantitiesrequire precise measurements of the strengths of low-energy resonances. Basedon a new experimental study performed at LUNA, we provide revised rates ofthe Mg(p, γ ) Al gs and the Mg(p, γ ) Al m reactions with corresponding uncer-tainties. In the temperature range 50 to 150 MK, the new recommended rateof the Al m production is up to 5 times higher than previously assumed. Inaddition, at T= 100 MK, the revised total reaction rate is a factor of 2 higher.Note that this is the range of temperature at which the Mg-Al cycle operates inan H-burning zone.The effects of this revision are discussed. Due to the significantly larger Mg(p, γ ) Al m rate, the estimated production of Al gs in H-burning regions isless efficient than previously obtained. As a result, the new rates should imply asmaller contribution from Wolf-Rayet stars to the galactic Al budget. Similarly,we show that the AGB extra-mixing scenario does not appear able to explain themost extreme values of Al/ Al, i.e. > − , found in some O-rich presolargrains. Finally, the substantial increase of the total reaction rate makes thehypothesis of a self-pollution by massive AGBs a more robust explanation forthe Mg-Al anticorrelation observed in Globular-Cluster stars. Subject headings:
Nuclear reactions, nucleosynthesis, abundances — Stars: AGB andpost-AGB — Stars: Wolf-Rayet — globular clusters: general
1. Introduction
Many important astronomical phenomena are related to the occurrence of the Mg-Alcycle in stellar interiors. In past decades several potential stellar sites with an active Mg-Alcycle have been identified. In particular, this cycle is active in the deepest layer of aH-burning zone provided the temperature is sufficiently large (T >
40 MK). Therefore, thenecessary conditions are fulfilled in the core of massive main sequence stars (M >
30 M ⊙ ) aswell as in the H-burning shells of red giant branch (RGB), asymptotic giant branch (AGB)and red super-giant stars. The Mg-Al cycle is also active during explosive H-burning events,such as Nova like outbursts.In these stars the H burning is often coupled to extended mixing episodes, suchas mixing powered by convection or other physical processes, e.g. rotational inducedinstabilities, so that the products of the internal nucleosynthesis may appear at the stellarsurface and can be directly observed. In addition, these stars undergo intense massloss episodes and, thus, they provide an important contribution to the pollution of theinterstellar medium. The presence of radioactive Al (ground state half-live t / ≈ × yr) in different astronomical environments may be a trace of the operation of the Mg-Al cyclein stellar interiors. For example, the detection of the 1.809 MeV γ -ray line demonstratesthat a few M ⊙ of this isotope is presently alive in the galactic disk (see Diehl et al. 2006).On the other hand, the excess of Mg in the solar system material, proves that someradioactive Al has been injected into the presolar nebula shortly before the solar systemformation, about 4.5 Gyr ago (Lee et al. 1977; Gallino et al. 2004). Furthermore, a Mgexcess has also been found in several presolar grains, such as SiC grains belonging to theso-called mainstream type (Zinner et al. 1991). These grains most likely condensed inatmospheres of C-rich AGB stars and, therefore, are believed to be fingerprints of thechemical composition of these stars. Finally, an evidence of the operation of the Mg-Al 7 –cycle is commonly found in Globular Cluster stars, which show a clear anticorrelationbetween Mg and Al (Kraft et al. 1997; Gratton et al. 2001). This anticorrelation is usuallyascribed to an early pollution (occurred about 13 Gyr ago) of the intra-cluster gas causedby massive AGB, perhaps super-AGB stars An accurate understanding of the stellar sites where the Mg-Al cycle takes place mayprovide solutions for many open issues in stellar evolution, stellar nucleosynthesis as well aschemical evolution. Spectroscopic observations of Al and Mg coupled to information of the Al radioactive decay derived from direct observations, e.g. γ -ray astronomy, or indirectmeasures, e.g. isotopic analysis of solar system and presolar material, may constrain stellarmodels in a wide range of stellar masses and evolutionary phases. These correlations provideunique opportunities to study the coupling between mixing processes and nuclear burning.However, this work requires a precise evaluation of the nuclear reaction rates of theMg-Al cycle. As part of a long-lasting experimental campaign on H-burning reactions,the LUNA collaboration has recently measured the Mg(p, γ ) Al rate at the GranSasso National Laboratory (Strieder et al. 2012). In the present work we use this newmesurements to revise the rate of this important Mg-Al cycle reaction. In the next sectionwe briefly review the status of the experimental data in the relevant astrophysical energy In the following, with massive AGB we refer to stars with initial mass between ∼ ∼ ⊙ . After the core-He burning, they form a degenerate C-O core and experience anAGB phase. With super-AGB we refer to stars with initial mass between ∼ ∼
10 M ⊙ .These stars ignite carbon in the degenerate core (usually it is an off-center ignition, due to theplasma neutrino cooling), form an O-Ne core and enter the super-AGB phase (Ritossa et al.1996). Note that the exact values of these mass limits depend on the chemical compositionand their theoretical derivation is significantly affected by the uncertainties of several inputsphysics. 8 –region and recommend a set of nuclear physics parameters that should be used for thereaction rate calculations. As shown in Figure 3, the proton capture on Mg may produce Al in two different states, namely the ground state and the isomeric state at E x = 228 keV.The corresponding reaction rates are provided in section 3 as a function of temperature. Afinal discussion follows, where some of the possible astrophysical applications are addressed.
2. Experimental Studies of the reaction Mg(p, γ ) Al The astrophysical reaction rate of Mg(p, γ ) Al (Q = 6.306 MeV) is dominated bynarrow resonances. These resonances have been studied in previous experiments down to alow-energy limit of E = 189 keV (Champagne et al. 1983a,b, 1986, 1989; Endt et al. 1986,1988; Endt & Rolfs 1987; Iliadis et al. 1990; Endt 1990; Iliadis et al. 1996; Powell et al.1998). The known Al level structure suggested the existence of additional low-lyingresonances at E = 37, 57, 92, 108, and 130 keV, among which the 92 keV resonance appearsmost important for astrophysical temperatures from 50 to 120 MK. These low-energyresonances, indeed, were identified in indirect experiments through transfer reaction studies(see Iliadis et al. 1996, and references therein).Recently, in an experiment at the underground 400 kV LUNA (Laboratory forUnderground Nuclear Astrophysics) accelerator in the Laboratori Nazionali del Gran Sasso(Costantini et al. 2009; Broggini et al. 2010) the resonance at 92 keV was for the firsttime observed in a direct study (Strieder et al. 2012). The resonance strengths of the 92,189, and 304 keV resonances have been measured with unprecedented sensitivity takingfull advantage of the extremely low γ -ray background level in the Gran Sasso laboratory.The Gran Sasso underground laboratory, where an average rock coverage of 1400 m (3800meter water equivalent) reduces the γ -ray background signal by several orders of magnitude(Costantini et al. 2009), is the ideal location for measurements of many astrophysically 9 –important nuclear reactions. In spite of tremendous experimental efforts in backgroundreduction, target sample preparation as well as improvements in γ -ray detection, otherlow-energy resonances are still unaccessible for direct detection. The strength of a resonance is defined in terms of nuclear resonance parameters: ωγ = 2 J + 1(2 j + 1)(2 j + 1) Γ a Γ b Γ (1)with J , j , j the spins of resonance, projectile and target nucleus, respectively, and Γ a ,Γ b , Γ the partial widths for the entrance and exit channel, and the total resonance width atthe resonance energy, respectively. The resonance strength for narrow resonances as in thecase of Mg(p, γ ) Al can be measured directly in the thick-target yield approximation (seeRolfs & Rodney 1988, for details). Alternatively, the resonance parameters, e.g. the protonpartial width Γ p of the entrance channel, can be obtained from indirect experiments (seebelow).The determination of weak low-energy resonance strengths from direct measurementsis usually extremely difficult. Small target contaminations, e.g. oxygen, as well asstoichiometry changes under heavy proton bombardment may have a large effect on theabsolute determination. A measurement relative to a well-known resonance can often avoidsuch difficulties. In Strieder et al. (2012) the low-energy resonances have been normalizedto the 304 keV resonance which in turn was precisely measured with several differentexperimental techniques (Limata et al. 2010). The resonance strength values used for thepresent reaction rate calculation are summarized in Table 1 and compared to NACRE(Angulo et al. 1999) and a more recent compilation by Iliadis et al. (2010a). Additionally, 10 –the ground state feeding probability and the electron screening correction for directlymeasured ωγ values are listed. The NACRE (Angulo et al. 1999) rate at low temperatures (resonances below 130 keV)is mainly based on a reanalysis (Iliadis et al. 1996) of proton partial width values from olderproton stripping data (Betts et al. 1978; Champagne et al. 1989; Rollefson et al. 1990).The same source of information was used in Iliadis et al. (2010a).The proton width of the 92 keV resonance calculated from the recent direct experiment,Γ p = (5 . ± . × − eV (Strieder et al. 2012), deviates from the value used in thecompilations, Γ p = (2 . ± . × − eV (Iliadis et al. 2010b), by 1.8 σ . Therefore, atthe 90 % confidence level the two values are incompatible, while the proton width ofStrieder et al. (2012) is in good agreement with the original value of Rollefson et al. (1990),Γ p = (5 . ± . × − eV. In contrast to the 92 keV resonance where a large spread ofthe indirect data is obvious (see Table II in Iliadis et al. (1996)), the proton width data forthe 37 and 57 keV resonances from different experiments are in much better agreement andwe used the value quoted in Iliadis et al. (2010b) for the present work. As a general rule wehave used data from direct experiments whenever available and the results from indirectmeasurements were included only where no direct data exists. The Mg(p, γ ) Al resonances decay through complex γ -ray cascades either to the 5 + ground state or the 0 + isomeric state at E x = 228 keV. The ground state feeding is ofparticular relevance for astronomy since the Al ground state decays into the first excited 11 –state of Mg with the subsequent γ -ray emission observed by the satellite telescopes. Theisomeric state of Al decays (T / = 6 . Mg and doesnot lead to the emission of γ -rays. Therefore, a precise determination of the ground statefeeding probability f is important for the reaction rate calculation.For the 189 and 304 keV resonances this parameter could be reinvestigatedexperimentally in a high resolution study using a high purity germanium detector(Limata et al. 2010; Strieder et al. 2012). A high precision determination for the low-energyresonances was impossible and the ground state feeding probabilities for these resonancesrely mainly on previous literature information. The main source of information onthe feeding probability is Endt & Rolfs (1987), which is to a large extent based on theexperimental work published in Endt et al. (1988). For resonances at 37 and 57 keVthe feeding probability seems to be well grounded while for the 92 keV resonance thereis no experimental information from Endt et al. (1988). Unfortunately, the alternativeliterature information in case of the 92 keV resonance is contradictory. A probability of80 ±
15 % was deduced from the experimental branching ratio determination measured inthe Mg( He,p γ ) Al reaction (Champagne et al. 1983a,b). However, in Champagne et al.(1986), the same authors quote a value of 61 %, while the compilation of Endt & Rolfs(1987) gives 85 %. The origin of this large discrepancy is unknown, but may be attributedto different assumptions on the secondary branching ratios. Recent measurements(Strieder et al. 2012) suggested a stronger feeding of Al states that predominately decayto the isomeric state reducing the ground state fraction. Therefore, a ground state feedingprobability of 60 +20 − %, as reccommended by Strieder et al. (2012), has been used in thepresent work for the 92 keV resonance. In general, the small uncertainty, e.g. 1 %, quotedin Endt & Rolfs (1987) seems questionable due to the disagreement for certain resonancesand a larger uncertainty has been assigned to these values (see Table 1). 12 – In astrophysical environments nuclear reactions usually take place at energies farbelow the Coulomb barrier where the probability for the incoming particle to overcomethe repulsive force of the interacting partner decreases steeply with decreasing energy(Rolfs & Rodney 1988). In laboratory studies the target nuclei are in most cases in theform of atoms or molecules while projectiles are usually in the form of positively chargedions. The atomic (or molecular) electron clouds surrounding the reacting nuclei act asa screening potential reducing the Coulomb barrier effectively seen by the penetratingparticles. Thus, the penetration through a shielded Coulomb barrier at a given projectileenergy E is equivalent to that of bare nuclei at energy E eff = E + U e . This so called electronscreening effect (Assenbaum et al. 1987) becomes very important for large nuclear chargesat low energies.In general, a resonance strength ωγ is proportional to the penetration probabilitythrough the Coulomb barrier, the penetrability P l (E) of the orbital angular momentum l : ωγ ∝ Γ p ∝ P l (E). Thus, the enhancement factor f es of the entrance channel can beexpressed as: f es = ωγ screen ωγ bare = P l (E + U e )P l (E) (2)and for small l the approximation f es ≈ exp( πη U e / E) is valid (Assenbaum et al. 1987)where η is the Sommerfeld parameter (Rolfs & Rodney 1988). The screening potential U e is usually calculated in the approximation that the projectile velocity is much smaller thanthe Bohr velocity of the electrons (Shoppa et al. 1993). This approximation representsthe so called adiabatic limit where the electrons remain in the lowest energy state of thecombined projectile and target system with the same quantum numbers as the originalsystem. Consequently, the screening potential is given by the difference in atomic bindingenergy between the original system and the single positively charged combined system. 13 –The atomic binding energies can be found in literature, e.g. Huang et al. (1976).In case of Mg(p, γ ) Al in the adiabatic limit a value of U e = 1 .
14 keV was calculatedleading to enhancement factors f es quoted in Table 1. However, in most cases experimentalinvestigations of the electron screening potential resulted in larger values compared tothe adiabatic limit (see e.g. Strieder et al. 2001). This discrepancy is still far from beingsolved and certainly deserves further studies. It is worth noting that alternative approacheshave been discussed in the literature (Liolios 2001, 2003) which lead to slightly differentvalues for the screening potential. In order to account for this ambiguity in the theoreticalcalculation of the electron screening potential, we assign an uncertainty to the adiabaticlimit enhancement factor equal to 30 % of the difference between its value and unity.Note that the electron screening effect is already sizeable for the 304 keV resonance buthas been totally neglected in previous compilations, e.g. Angulo et al. (1999); Iliadis et al.(2010a), when low-energy resonance parameters from direct studies were used.
3. The reaction rate calculation
The Maxwellian-averaged two-body reaction rate can be calculated fromRolfs & Rodney (1988): N A h σv i = N A (8 /π ) / µ / ( kT ) / ∞ Z σ ( E ) Ee − E/kT dE (3)where N A is the Avogadro number, µ the reduced mass, k the Boltzmann constant, T thetemperature, σ ( E ) the cross section at the center-of-mass energy E , and v the relativevelocity of the reactants.For narrow resonances, the reaction cross section can be expressed in the Breit-Wigner 14 –approximation and when N A h σv i is given in cm mol − s − , this leads to N A h σv i = 1 . × ( µT ) / X i f i ωγ i e − . E i /T (4)where the energies E is in MeV, µ is in amu, T is the temperature in GK, and ( ωγ ) i and f i are the strength (in units of MeV) and ground state feeding probability of the i -thresonance, respectively.The fractional reaction rate with the contributions of individual resonances is shown inFigure 1. The reaction rate in the temperature window between 50 and 300 MK is nearlyentirely determined by the resonances measured in recent LUNA experiments (Limata et al.2010; Strieder et al. 2012) with a small contribution from the 57 keV resonance at thelower edge of this window. At larger temperatures, namely T >
300 MK, the contributionof high-energy resonances becomes significant (see Figure 1), but this temperature range isbeyond the scope of the present work.The reaction rate uncertainty was investigated following the Monte Carlo approach ofLongland et al. (2010) randomly varying the ωγ values entering the calculation within theirexperimental uncertainties. In Tables 2 and 3 the calculated reaction rates for ground stateand isomeric state are shown together with the associated lower and upper limits which aredefined by the 68 % confidence level of the obtained distribution. These new reaction ratesare compared with the results of NACRE (Angulo et al. 1999) and Iliadis et al. (2010a) inFigure 2.The present reaction rates are higher than previously found because of higher ωγ srecommended for the 92 and 189 keV resonances. In particular, the reaction rate for theisomeric state feeding increased by a factor 3-5 for temperatures between 50 and 150 MKwhile the ground state reaction rate is larger by 30-40 % in the same temperature window.The larger effect on the isomeric state reaction rate arises from the revised ground statefeeding probability for the 92 keV resonance (see Sect. 2.3 and Table 1). The uncertainty 15 –at temperatures higher than T >
100 MK is significantly reduced now due to the newaccurate determination of the 304 keV resonance while at lower temperatures a sizeableuncertainty is still present. However, the parameters for the reaction rate calculation havebeen deeply revised in the present work and indirect data have been replaced by directmeasurements when possible. Therefore, the present recommended reaction rates appear tobe more robust than the results from previous work.
4. Discussion
The new rate of the Mg(p, γ ) Al is expected to produce major effects in thetemperature range 50 < T <
150 MK. These conditions are typically found in the core ofmassive main sequence stars as well as in the H-burning shell of RGB and AGB stars. Inthis section we review three scientific cases related to the operation of the Mg-Al cycle inthese stellar environments. Our aim is to identify interesting problems of stellar evolutionand nucleosynthesis whose solution requires an accurate evaluation of the Mg(p, γ ) Alrate.To illustrate these scientific cases, we will make use of a bare nuclear network code, i.e.an appropriate set of differential equations describing the evolution of the abundances of allthe isotopes of the Mg-Al cycle solved under constant temperature and density conditions.The equations are linearized and the resulting set of linear equations is solved by means ofa Newton-Rhapson algorithm. The initial abundances of Mg, Al and Si isotopes are takenfrom Lodders et al. (2009) and properly scaled to the adopted metallicity. To mimic theeffect of an extended convective mixing, the H mass fraction is maintained constant. Theadopted nuclear network is illustrated in Figure 3.Although a quantitative study of all the implications of the new rate would require the 16 –computation of appropriate stellar models, where the coupling of mixing and burning maybe accurately accounted, a bare network calculation is adequate for most of the purposes ofthe present discussion. We also make use of previous results of stellar models calculations,published in the recent literature, where the effects of a change of the reaction rates havebeen discussed in some details.In the following, bare network calculations obtained by means of the new rate arecompared to the ones obtained by means of the rate reccommanded by Iliadis et al. (2010a).Note that in the quoted temperature range, the Iliadis et al. (2010a) rates for the twochannels of the Mg(p, γ ) Al practically coincide with the corresponding NACRE rates. Al in the wind of Wolf-Rayet stars
Since the 1980s, the observations of the 1.809 MeV gamma-ray line emitted in starforming regions of the Milky Way have raised interesting questions about the origin ofthe galactic pollution of Al (Mahoney et al. 1984; Diehl et al. 1995, 2006). Althoughit is commonly accepted that massive stars, i.e. those ending their life as core-collapsesupernovae, are the main source of the galactic Al, the precise nucleosynthesis scenario isstill matter of debate. Favoreable conditions are expected during the advanced phases ofthe evolution of such massive stars. In particular, a significant contribution should comefrom the pre-explosive as well as the explosive nucleosynthesis occurring in the C- andNe-burning shells (Arnett & Wefel 1978; Woosley & Weaver 1980). Nevertheless, extanttheoretical models show that an additional contribution may come from Wolf-Rayet (WR)stars (Dearborn & Blake 1985). In this case, the Al is produced within the core of verymassive main sequence stars (M >
30 M ⊙ ), where the temperature exceeds 50 MK. Since themain sequence phase, these stars experience a huge mass loss. In such a way, even materiallocated on the top of the H-convective core, which is enriched with the ashes of the Mg-Al 17 –cycle, may be ejected. The actual contribution of the WR stars to the galactic budgetof Al is rather controversial. While Palacios et al. (2005) find that these stars providebetween 20 to 50% of the whole galactic Al, Limongi & Chieffi (2006) conclude that thecumulative yield of WRs is negligible when compared to that from C and Ne burning shells.Figure 4 illustrates the nucleosynthesis scenario for the core-H burning phase of a WRprecursor. The burning timescales of Mg, Mg, and Al gs are reported as a function ofthe temperature and defined as: τ i = 1 XρN A < σv > i (5)where i denotes for Mg, Mg, and Al gs with the corresponding reaction rates for Mg(p, γ ) Al, Mg(p, γ ) Al tot , and Al gs (p, γ ) Si, respectively. We have assumed ahydrogen mass fraction X = 0 . ρ = 100 g/cm . All the reaction ratesare from the NACRE compilation except for Mg(p, γ ) Al where we have used both thepresent work and the Iliadis et al. (2010a) rates. The thick solid line represents the residualtime for an 80 M ⊙ stellar models (Limongi & Chieffi 2006, from), i.e. the fraction of themain-sequence lifettime during which the central temperature is larger than a given value.During most of the main sequence lifetime, the Mg(p, γ ) Al is the fastest processof the Mg-Al cycle. As already found by Limongi & Chieffi (see also Iliadis et al. 2011),the corresponding Mg burning timescale is sufficiently short to ensure that all the Mgavailable in the convective core is converted into Al. Note that only at the end of themain sequence, when the central H is close to the complete exhaustion and the temperatureis about 80 MK, the burning rate of Mg becomes as short as that of Mg. As a result,the burning of Mg provides a negligible contribution to the Mg abundance in the core,and, in turn, to the Al production. The Al gs accumulated in the convective core ismarginally depleted by the subsequent proton captures, because its burning timescale is 18 –about 2 orders of magnitude larger than that of the Mg. Finally, since the Al gs lifetimeis comparable to the stellar lifetime, its radioactive decay have to be considered.In summary, the amount of Al accumulated in the convective core of a massive stardepends, essentially, on the original Mg content and on the branching ratio between thetwo output channels of the Mg(p, γ ) Al reaction. Indeed, due to the competition betweenthe Mg(p, γ ) Al gs and the Mg(p, γ ) Al m , only a fraction of the original Mg is actuallyconverted into Al gs . A comparison between the previous (Iliadis et al. 2010a) and therevised branching ratio shows that at temperatures of the core H-burning, the new ratesimply a substantial increase of the competitive channel, i.e. the isomeric state production,than previously assumed (Figure 2). As a consequence, the Al gs production in theconvective core of H-burning massive stars is less efficient than believed so far. Note thatthis finding does not necessarily imply that the contribution of WR stars to the galactic Al is neglogible. A reliable evaluation of this contribution still resides, for example, onthe poorly-known mass range of these stars, which is significantly affected by mass lossuncertainties.
The chemical analysis of presolar grains, dust particles found in pristine meteorites witha size smaller than a few microns, reveals a variety of isotopic compositions. These presolargrains, e.g. mainstream SiC and O-rich grains (see Hoppe & Zinner 2000; Clayton & Nittler2004, for a review), represent fossil records of the parent star atmospheres and provideunique information on stellar nucleosynthesis.Mainstream SiC grains are believed to condense in the C-rich atmospheres surroundinglow-mass (M < ⊙ ) AGB stars of different metallicity (0 . < Z < . Mg excess observed in SiC as well as O-rich grains from AGB stars is interpretedas the signature of an in-situ decay of Al (Zinner et al. 1991; Nittler et al. 1994) andcurrent theoretical models predict that low-mass AGB stars may deliver a substantialamount of Al. The Al is produced in the H-burning shell of an AGB star, accumulatedin the H-exhausted region and mixed by convection powered by thermal pulses to regionsof higher temperatures. In case the maximum temperature remains below the thresholdfor the activation of the Ne( α ,n) Mg reaction (T <
300 MK), the Al survives and, lateron, may be dredged up to the stellar surface. Contrarily, the Al is destroyed by neutroncaptures occurring at the bottom of the convective zone and only Al above this zone canbe dredged up (Mowlavi & Meynet 2000; Cristallo et al. 2009). Basing on full networkstellar model calculations, Cristallo et al. (2011) found values of Al/ Al up to 5 × − ,in good agreement with those measured in mainstream SiC grains and several O-rich grains.However, in some O-rich grains values larger by up to one order of magnitude have beenobserved.These extreme excesses of Al are often explained by invoking an AGB extra-mixingwhich connects the bottom of the convective envelope to the hottest H-burning zone, wherethe Mg-Al cycle is at work. Note that the extra-mixing scenario provides a widely acceptedexplanation of the C and O isotopic ratios measured in the atmospheres of low-mass RGBstars (Boothroyd et al. 1994; Charbonnel 1995; Denissenkov & Weiss 1996) and O isotopicratios found in a large sample of presolar grains suggest that extra-mixing should be at 20 –work also during the AGB phase (Nollett et al. 2003). Nevertheless, a reliable mechanismfor such an extra-mixing has not been yet identified, possible candidates are rotationalinduced instabilities, magnetic pipes, gravity waves and thermohaline mixing.The AGB extra-mixing hypothesis implies that parent stars of O-rich grains with large Al excess never attain the C-star stage, because otherwise one should expect also SiCgrains showing similarly large values of Al overabundance: this occurrence is considereda major drawback of the proposed scenario. However, as pointed out by Straniero et al.(2003), there is a lower limit for the mass of AGB stars with C / O > ⊙ at solar metallicity, while it is only 1.3 M ⊙ at Z= 0 . Al.In a recent work Palmerini et al. (2011) showed that the O-rich grains with extreme Mg excess can be explained by AGB stellar models with particularly deep extra-mixing,provided that i) the initial mass is lower than 1.5 M ⊙ and ii) the Mg(p, γ ) Al gs reactionrate is enhanced by a factor of 5 with respect to the and Iliadis et al. (2010a) rates.The coupling between nuclear burning and mixing makes a quantitative analysis of theimpact of the new rates on the isotopic composition of O- and C-rich presolar grains difficultand would require the computation of stellar models with an extended nuclear network.This effort is beyond the purpose of the present work, but some qualitative considerationmay be drawn on the basis of bare network calculations. According to Palmerini et al.(2011), the maximum temperature attained by the extra-mixing is between 40 and 50 MKcorresponding to an energy range where the Mg proton capture rate is dominated by the 21 –57 keV resonance (see Figure 1). In Figure 5 we report the evolution of the Al/ Al ratiofor material exposed to a constant temperature of 40 MK (lower panel) and 50 MK (upperpanel), respectively. In this energy range the recommended new rate for the Mg(p, γ ) Al gs is only about 10 % larger with respect to Iliadis et al. (2010a), while the competing channel, Mg(p, γ ) Al m , is about 40% larger. As a consequence, the resulting Al/ Al isotopicratio at T = 50 MK is even lower than previously found, although the total rate is larger.Moreover, in spite of the large uncertainty of the dominant 57 keV resonance contribution,we can definitely exclude an increase of a factor 5 of the Mg(p, γ ) Al gs rate.In conclusion, AGB models without extra-mixing may account for Al/ Al up to5 × − , values commonly found in mainstream SiC grains as well as in many O-rich grainsfrom AGB stars. Larger values of Al/ Al may be in part explained by a deep extra-mixing(T ≥
50 MK), but even in the upper limit of the Mg(p, γ ) Al gs rate, it is unlikely thatthe extra-mixing scenario could produce aluminum isotopic ratios with Al/ Al > − . For many years, Globular Clusters (GCs) have been considered as simple stellarsystems, made of nearly coeval stars and formed from a chemically homogeneous preexistinggas nebula. Nevertheless, a growing amount of photometric and spectroscopic observationsindicate that many GCs actually harbor multiple stellar populations characterized bystar-to-star chemical variations. Such chemical variations include the well-known O-Na andMg-Al anticorrelations which are usually coupled to a nearly constant value of C+N+O.This chemical pattern is a carachteristic signature for H-burning, where the Ne-Na andthe Mg-Al cycles are active. The first evidence of these ”anomalies” was found in brightred giant stars (Kraft et al. 1997; Ivans et al. 1999). As it is well known, RGB starshave an extended convective envelope, but the innermost unstable layer does not reach 22 –the H-burning zone. Therefore, an extra-mixing was initially invoked to explain theobserved anticorrelations. Nonetheless, this hypothesis is in contrast with the more recentdiscovery of O-Na and the Mg-Al anticorrelations in less evolved turn-off and sub-giantstars (Gratton et al. 2001; Yong et al. 2003). These observations definitely rule out thehypothesis that the anticorrelations are the result of an in-situ physical process and provethat they were already present in the gas nebula from which these stars formed about13 Gyr ago. Among the proposed alternative hypothesis, the pollution of the primordialgas by an early generation of massive AGB stars (perhaps super-AGB) appears promising(Cottrell & Da Costa 1981; Dantona et al. 1983; Ventura & D’Antona 2005). In thesemassive AGB stars, the convective envelope penetrates the regions where the H burningtakes place: this phenomenon is usually called hot bottom burning (Renzini & Voli 1981).Then, the relatively low-velocity wind of these stars ensures the required pollution of theintra-cluster medium. According to this scenario, stars with low Mg and high Al (or lowO and high Na) would represent a second generation of cluster stars, formed after theintermediate mass stars of the first generation passed through the AGB phase and pollutedthe intra-cluster gas with ashes of H-burning.However, the attempts made so far to simultaneously reproduce the observed O-Naand Mg-Al anticorrelations have produced controversial results (Fenner et al. 2004;Ventura & D’Antona 2005). Recently, Ventura et al. (2011) showed that an increase of the Mg(p, γ ) Al reaction rate by a factor of 2, coupled to a more sophisticated treatmentof the convective energy transport under super-adiabatic conditions, may reduce thediscrepancy between the theoretical expectations and the observed cluster abundances ofMg and Al.In order to illustrate the influence of the newly recommended reaction rates on theMg-Al cycle operating in the H-burning shell of a massive AGB star, we have performed 23 –some bare network calculations. Values for the metallicity, the H mass fraction, thetemperature and the density representative of the innermost layers of the convectiveenvelope of a massive AGB star have been selected, namely: Z= 0 . .
6, T=100 MKand ρ = 10 g/cm . The result is shown in Figure 6, where the upper panel refers to thecalculation obtained by means of the new reaction rates for the Mg(p, γ ) Al, while thebottom panel corresponds to the calculations obtained by adopting the Iliadis et al. (2010a)rates. The NACRE compilation has been used for all the other reactions of the Mg-Al cycle,while for the Al gs decay rate we have assumed the terrestrial value ( λ = 2 . × − s − ). The increase of the new total Mg(p, γ ) Al reaction rate by a factor 2 with respectto Iliadis et al. (2010a) is indeed very close to the value found by Ventura et al. (2011)and support the massive AGB self-pollution scenario. It should be noted that the largestvariations in the evolution of the Mg and Al isotopic abundances are caused by the larger Mg(p, γ ) Al m rate. This variation favors a prompt destruction of Mg and a fast increaseof the Al production. In Figure 7, the Al (elemental) abundance is compared to thecorresponding Mg abundance, for the T= 100 MK calculations. The new rate implies asteeper anticorrelation and a significant increase of the maximum Al abundance. Note thesimilarity of this figure with figure 4 of Ventura et al. (2011) based on the result of AGBstellar models obtained under different assumptions for the Mg(p, γ ) Al rate.
5. Summary and Conclusions
The Mg(p, γ ) Al reaction rate has been revised on the basis of new measurementsof the key resonances at E=92, 189 and 304 keV. Particular efforts have been devotedto review all experimental parameters, e.g. resonance strengths, ground state branchingratio fractions, and electron screening, in order to reduce the systematic uncertainty of thisreaction rate in the temperature range present in stellar H-burning zones. Note that in 24 –previous works the input parameter uncertainties were partly underestimated, e.g. presentuncertainties on ground state branching ratio and electron screening were not considered.We have found a significant variation of the rate for temperature 50 < T <
150 MK withrespect to previous studies. The revised total reaction rate is about a factor of 2 larger thansuggested by NACRE and Iliadis et al. (2010a), while the production rate of the isomericstate, which decays almost instantly into Mg, is up to a factor of 5 larger. As a result, theexpected production of Al gs in stellar H-burning zones is lower than previously estimated.This implies, in particular, a reduction of the estimated contribution of WR stars to thegalactic production of Al. We have also investigated the possible effect on the Mg andAl isotopic composition of presolar grains originated in AGB stars. The most importantconclusion is that the deep AGB extra-mixing, often invoked to explain the large excess of Al in some O-rich grains, does not appear a suitable solution for Al/ Al > − .On the other hand, the substantial increase of the total reaction rate makes theGlobular Cluster self-pollution caused by massive AGB stars a more reliable scenario forthe reproduction of the Mg-Al anticorrelation.In summary, we have demonstrated that a considerable improvement of our knowledgeof the nuclear reaction rates involved in the Mg-Al cycle allows to constrain nucleosynthesisand stellar evolution models as well as the interplay between nuclear burning and mixingprocesses operating simultaneously in stellar interiors. In this context, further experimentalstudies are required to improve the analysis reported in section 4 and to derive more firmconclusions on the operation of the Mg-Al cycle in stellar interiors. Some input parametersstill carry a significant uncertainty, e.g. the ground state branching ratio of each nuclearresonance. Partially, as in case of the 92 keV resonance, these branching ratios are basedon experiments with rather low statistics and, therefore, we recommend a reinvestigation ofthese parameters in a dedicated experiment. In addition, other key reactions of the Mg-Al 25 –cycle, such as the Mg(p, γ ) Al, deserve more attention. Note that Mg is the mostabundant isotopes among those involved in the Mg-Al cycle and at T >
80 MK this reactionis faster than Mg(p, γ ) Al, thus providing additional fuel for the Al production. The ratetabulated by NACRE is essentially based on the experimental result by Trautvetter & Rolfs(1975). At low energy, the cross section is dominated by a resonance at 214 keV. Anexperiment performed by of the TUNL group (Powell et al. 1999) resulted in a 25%higher resonance strength than recommended by NACRE. Note that this result has beenincorporated by Iliadis et al. (2010a) in their revised reaction rate. However, Limata et al.(2010) derive a value for the strength of the 214 KeV resonance that agrees with the oldresult by Trautvetter & Rolfs (1975). Further studies are required to disentangle thesecontroversial results. Concerning the production of Al gs , a key role is played by the Al gs (p, γ ) Si reaction. The only available direct measurement has been discussed inVogelaar et al. (1996). Recently, the 184 keV resonance has been measured at TRIUMFwith the Recoil Mass Separator (Ruiz et al. 2006). An up-to-date analysis of the reactionrate has been presented by Iliadis et al. (2010a). The difficulties of these measurements arerelated to the radioactivity of Al gs . Also in this case further experimental investigationsare mandatory.The present work has been supported by INFN and in part by the EU (ILIAS-TARII3-CT-2004-506222), OTKA (K101328), and DFG (Ro 429/41). We are grateful toM. Limongi for the enlightening discussions on the Al production in massive stars.A. Di Leva, G. Imbriani, L. Piersanti and S. Cristallo aknowledge the support of theItalian Ministry of Education, University and Research under the FIRB2008 program. O.Straniero, L. Piersanti and S. Cristallo have been supported by INAF under the PRIN2010program. A. Caciolli aknowledges financial support by Fondazione Cassa Di Risparmio diPadova e Rovigo. 26 –
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B., Mitchell, L. W., Kavanagh, R. W., et al. 1996, Phys. Rev. C, 53, 1945Woosley, S. E., & Weaver, T. A. 1980, Astroph. J., 238, 1017Yong, D., Grundahl, F., Lambert, D. L., Nissen, P. E., & Shetrone, M. D. 2003, Astron.Astroph., 402, 985Zinner, E., Amari, S., Anders, E., & Lewis, R. 1991, Nature, 349, 51This manuscript was prepared with the AAS L A TEX macros v5.2. 31 –Table 1. The new recommended Mg(p , γ ) Al resonance strengths (uncorrected forscreening) and corresponding ground state fractions f . The parameters for resonances notlisted here were taken from Iliadis et al. (2010b). The electron screening enhancementfactor f es was calculated according to Assenbaum et al. (1987). present work Iliadis et al. (2010a) Angulo et al. (1999)(NACRE) a E (keV) b ωγ (eV) f es f ωγ (eV) f ωγ (eV)37.0 (4 . ± . × − - 0 . ± . e (4 . ± . × − . +21 . − . ) × − . ± . × − - 0 . ± . e (2 . ± . × − . +1 . − . ) × − . ± . × − . ± .
08 0 . +0 . − . (1 . ± . × − . +1 . − . ) × − . ± . × − . ± .
03 0 . ± . f (7 . ± . × − . ± . × − . ± . × − . ± .
01 0 . ± . g (3 . ± . × − . ± . × − the numerical values used for the ground state feeding probability are not provided b from Endt & Rolfs (1987), the uncertainty is less than 0.2 keV in all cases c from Endt & Rolfs (1987) d from Iliadis et al. (2010b) e from Endt & Rolfs (1987) where a larger uncertainty than originally quoted was assumed f from Strieder et al. (2012) g from Limata et al. (2010)
32 –Table 2. Reaction rate for Mg(p , γ ) Al gs (cm mol − s − ).T (GK) lower limit recommended value upper limit0.010 8 . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × −
33 –Table 2—ContinuedT (GK) lower limit recommended value upper limit0.140 1 . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . ×
34 – 35 –Table 3. Reaction rate for Mg(p , γ ) Al m (cm mol − s − ).T (GK) lower limit recommended value upper limit0.010 2 . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × −
36 –Table 3—ContinuedT (GK) lower limit recommended value upper limit0.140 3 . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . ×
37 – 38 – N < v > i / N < v > p r e s en t T (GK)
37 keV57 keV 92 keV189 keV 374 keV418 keV304 keV
Fig. 1.— Ratios of individual reaction rate contributions and total recommended rate of Mg(p, γ ) Al. The dominant individual contributions are labeled while the dashed lineindicates the summed contributions of weak resonances as well as resonances above E =420 keV. The grey shaded area represents the temperature range for which the major revisionshave been accounted in the present work. 39 – < v > i / < v > p r e s en t ground state0.00.20.40.60.81.01.21.4 isomeric state0.01 0.1 10.00.20.40.60.81.01.21.4 total T (GK)
Fig. 2.— Comparison between the present recommended reaction rates of Mg(p, γ ) Aland those reported by NACRE (dashed lines, Angulo et al. (1999) and Iliadis et al. (2010a)(solid lines). Shaded and hatched areas represent the estimated 1 σ uncertainties of thepresent work and Iliadis et al. (2010a), respectively. Note that in Iliadis et al. (2010a) theuncertainties on the ground state feeding factors are not considered. 40 –Fig. 3.— The Mg-Al cycle: solid and dashed lines refer to stable and unstable isotopes,respectively. 41 –Fig. 4.— Burning timescales of Mg versus temperature, as obtained by adopting therecommended Mg(p, γ ) Al reaction rate (solid line) and the Iliadis et al. (2010a) rate (dot-dashed line). The hatched areas represent the uncertainties due to the total reaction rate.The burning timescales of Mg and Al gs are also reported, dashed and long-dashed lines,respectively. The thick-solid line represents the residual main-sequence time for a 80 M ⊙ models (see text for more details). 42 –Fig. 5.— Evolution of the aluminum isotopic ratio for material exposed to a temperature of40 MK (lower panel) and 50 MK (upper panel). Solid lines represent the calculation madeby means of the recommended rate of the Mg(p, γ ) Al reaction, while the dashed lineshave been obtained by means of the corresponding Iliadis et al. (2010a) rate. In all casesthe density is 1 g/cm , X= 0 .
7. Hatched areas represent the cumulative uncertainties dueto both channels of the Mg(p, γ ) Al reaction. 43 –Fig. 6.— Evolution of Mg and Al isotopes. Temperature and density are mantained con-stant, namely: T=100 MK and ρ = 10 g/cm , respectively. At t=0, the composition isscaled solar and Z=0.001. The H mass fraction is X=0.6. The various lines represent thefollowing isotopes: Mg (solid), Al (dashed), Al (long dashed) and Si (dotted). Thecalculation shown in the upper panel has been obtained by using the recommended rates ofthe Mg(p, γ ) Al reactions. The hatched area represents the cumulative uncertainty on the Al gs abundance due to both channels of the Mg(p, γ ) Al. For comparison, the resultsobtained by means of the Iliadis et al. (2010a) rates are shown in the lower panel. 44 –Fig. 7.— Al abundance versus Mg abundance for the same case shown in figure 6. The solidand the dashed lines refer to the calculations made by means of the new (recommended)and the Iliadis et al. (2010a) rates of the Mg(p, γ )26