We study the effect of uncertainties in the proton-capture reaction rates of
the NeNa and MgAl chains on nucleosynthesis due to the operation of hot bottom
burning (HBB) in intermediate-mass asymptotic giant branch (AGB) stars. HBB
nucleosynthesis is associated with the production of sodium, radioactive Al26
and the heavy magnesium isotopes, and it is possibly responsible for the O, Na,
Mg and Al abundance anomalies observed in globular cluster stars.
  We model HBB with an analytic code based on full stellar evolution models so
we can quickly cover a large parameter space. The reaction rates are varied
first individually, then all together. This creates a knock-on effect, where an
increase of one reaction rate affects production of an isotope further down the
reaction chain. We find the yields of Ne22, Na23 and Al26 to be the most
susceptible to current nuclear reaction rate uncertainties.Comment: Presented at NIC-IX, International Symposium on Nuclear Astrophysics
  - Nuclei in the Cosmos - IX, CERN, Geneva, Switzerland, 25-30 June, 200

Iliadis, Christian

Izzard, Robert

Karakas, Amanda

Lugaro, Maria

English

arXiv

We study the effect of uncertainties in the proton-capture reaction rates of the NeNa and MgAl chains on nucleosynthesis due to the operation of hot bottom burning (HBB) in intermediate-mass asymptotic giant branch (AGB) stars. HBB nucleosynthesis is associated with the production of sodium, radioactive 26Al and the heavy magnesium isotopes, and it is possibly responsible for the O, Na, Mg and Al abundance anomalies observed in globular cluster stars. We model HBB with an analytic code based on full stellar evolution models so we can quickly cover a large parameter space. The reaction rates are varied first individually, then all together. This creates a knock-on effect, where an increase of one reaction rate affects production of an isotope further down the reaction chain. We find the yields of 22Ne, 23Na and 26Al to be the most susceptible to current nuclear reaction rate uncertainties

Izzard, R.G.

Lugaro, M.

Iliadis, C.

Karakas, A.

Carolina Digital Repository

arXiv:astro-ph/0607536v1  24 Jul 2006Reaction Rate Uncertainties: NeNa and MgAl inAGB StarsRobert G. Izzard∗University of UtrechtE-mail: R.G.Izzard@phys.uu.nlMaria LugaroUniversity of UtrechtE-mail:M.Lugaro@phys.uu.nlChristian IliadisUniversity of North CarolinaE-mail: iliadis@unc.eduAmanda KarakasMcMaster UniversityE-mail: karakas@physics.mcmaster.caWe study the effect of uncertainties in the proton-capture reaction rates of the NeNa and MgAlchains on nucleosynthesis due to the operation of hot bottomburning (HBB) in intermediate-massasymptotic giant branch (AGB) stars. HBB nucleosynthesis is associated with the production ofsodium, radioactive26Al and the heavy magnesium isotopes, and it is possibly responsible for theO, Na, Mg and Al abundance anomalies observed in globular cluster stars.We model HBB with an analytic code based on full stellar evoluti n models so we can quicklycover a large parameter space. The reaction rates are variedfirst individually, then all together.This creates a knock-on effect, where an increase of one reaction rate affects production of anisotope further down the reaction chain. We find the yields of22Ne,23Na and26Al to be the mostsusceptible to current nuclear reaction rate uncertainties.International Symposium on Nuclear Astrophysics — Nuclei in the Cosmos — IXJune 25-30 2006CERN, Geneva, Switzerland∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licen. http://pos.sissa.it/Reaction Rates and NeNa/MgAl Robert G. Izzard1. IntroductionThe Asymptotic Giant Branch (AGB) is the final evolutionary phase of stars with a mass lessthan about 8M⊙. The core of an AGB star has exhausted its supply of hydrogen and helium bynuclear burning and is made of carbon, oxygen, neon and perhas m gnesium, the main helium-burning products. A thin helium layer separates it from the convective stellar envelope which ismostly hydrogen. Hydrogen burning in a shell at the base of the envelope dominates the stellarluminosity, which is many thousands of times that of the Sun,b t is punctuated by thermal pulsesdue to ignition of the helium layer. At each pulse the third dredge-up may occur, in which helium-burnt material is mixed into the stellar envelope, polluting t with helium, carbon,22Ne and heavys-process elements. The lifetime of an AGB star is dominated by rapid mass-loss which limits it toabout a million years, after which the stellar envelope is eject d into the interstellar medium and aCO white dwarf remains.In AGB stars more massive than about 4M⊙ the hydrogen burning shell, at a temperature of 60to 100 million K, extends into the convective envelope, a process calledhot-bottom burning(HBB).The envelope composition is directly affected by the various hydrogen-burning cycles: CNO, NeNaand MgAl. The effect is to convert carbon and oxygen to nitrogen, neon to sodium and magnesiumto aluminium. The abundance anomalies seen in globular cluster stars, for example the oxygen-sodium anticorrelation, may be due to HBB in AGB stars [1]. The combination of third dredge-upof carbon with HBB is an important source of primary nitrogen, specially at low-metallicity.Stellar models of hot-bottom burning rely on nuclear reaction rates that are inherently uncer-tain due to both experimental limits and extrapolation intothe low-energy stellar regime. Our aimis to determine the effect of considering the rate uncertainties on the stellar abundances, and hencethe chemical yields from AGB stars undergoing HBB. We have sel ct d the NeNa and MgAl pro-ton capture reactions primarily because these are modelleddir ctly by our synthetic AGB model.It is not possible to vary the CNO reactions because they contribute significantly to the stellar lu-minosity, so affect the stellar structure, while we are assuming that changes in the NeNa/MgAlreaction rates donot affect the stellar structure.2. ModelOur synthetic AGB model is described in detail in [2] but has been extended to include theNeNa and MgAl cycles (Izzard et al 2006,in preparation) as well as the CNO cycle. We modelburning in the convective envelope by replacing the burn/mix/burn/mix. . . cycle with a singleburn/mix event (see Figure 1) where the amount of material burnt, and the time it is burnt for, iscalibrated to detailed AGB models [3].We analytically solve the differential equations for the abundances of20,21,22Ne,23Na,24,25,26Mgand26g,26m,27Al in the burning region so we can follow the surface abundances as a function of time.The NeNa cycle is solved by an eigenvalue method (assuming noinput to or output from the cycle,which is justified as23Na(p,γ)24Mg is usually slow and input from19F is negligible comparedto the amount of20Ne present), then23Na is decayed explicitly into24Mg. The MgAl cycle thenconsists only of forward reactions if we ignore27Al(p,α)24Mg, which is always justified at thetemperature of HBB (log10T/K ∼ 7.7− 8.0), so each rate equation is easily solved analytically.2Reaction Rates and NeNa/MgAl Robert G. Izzard+ + + + + + . . . ≈ N×Figure 1: Schematic view of our hot-bottom burning model. The detailed stellar models show that only athin layer at the base of the convective envelope is hot enough to burn. In reality, and in the detailed models,the thin layer is continously mixed over hundreds of convecti turnover timescales, but our synthetic modelcan reproduce the effect by burning a large fraction of the stellar envelope for a short time.Reaction Lower limit Upper limit Reference20Ne(p,γ)21Na(β+)21Ne −50% +50% Iliadis et al. 2001 [5]=NACRE [4]21Ne(p,γ)22Na(β+)22Ne −20% +20% Iliadis et al. 2001 [5]22Ne(p,γ)23Na −50% ×2000 Hale et al. 2001 [5]23Na(p,α)20Ne −30% +30% Rowland et al. 2004 [6]23Na(p,γ)24Mg /40 ×10 Rowland et al. 2004 [6]24Mg(p,γ)25Al(β+)25Mg −17% +20% Iliadis et al. 2001 [5] = Powell et al. 1999 [7]25Mg(p,γ)26Alg(β+)26Mg −50% ×1.5 Iliadis et al. 2001 [5]26Mg(p,γ)27Al /4 ×10 Iliadis et al. 2001[5]26Mg(p,γ)27Al −25% ×3 Iliadis et al. 2001[5]26Alg(p,γ)27Si(β+)27Al −50% ×600 Iliadis et al. 2001[5]Table 1: Nuclear reaction rates in our network and their uncertainties.Beta-decays except that of26Alg are treated as instantaneous, we do allow for27Al(p,α)24Mg byexplicit decay of27Al (the rate of this reaction is always negligible) and the chain is terminatedat 27Al because27Al(p,γ)28Si is very slow. The nuclear reactions, rate uncertainties in the HBBtemperature range and references are found in Table 1.We have constructed two sets of models in which:1. Each reaction is varied individually,2. All reactions are varied at the same time.When comparing the yield of an isotope, which we define simplyas the mass ejected as that isotope,we use a control model where all the reaction rates are set to their recommended values (i.e. theirrate multipliers are all 1.0). We useM = 5,6M⊙ andZ= 0.02,0.004 to test the effect of increasingmass and decreasing metallicity, both of which increase theamount of hot-bottom burning.3. ResultsFigure 2 shows the effect on chemical yields of the NeNa and MgAl isotopes of varying theproton-capture nuclear reaction rates. The values shown are percentage differences from the controlvalues, where positive values indicate extra production, negative values extra destruction, and zeromeans no change.The main effects are:3Reaction Rates and NeNa/MgAl Robert G. Izzard-100%-10% 0 +10% +100% +1000% +10000%  27Al  26Al  26Mg  25Mg  24Mg  23Na  22Ne  21Ne  20NeM=5  Z=0.02 M=6  Z=0.02 M=5  Z=0.004 M=6  Z=0.004 Figure 2: Uncertainty ranges for chemical yields as the difference from the control value as a functionof isotope for our four sets of model. Dark colours are the maxi um uncertainty ranges for varying eachreaction individually, the light colours give the uncertainty when all the reactions are varied together.• Complete conversion of22Ne to23Na, or not, due to the large uncertainty in the22Ne(p,γ)23Narate. The yield of23Na can be boosted by a factor of about 40 atZ = 0.004, in both the 5 and6M⊙ models. This sodium isprimary;• A very large uncertainty in26Al production, ranging from×0 to ×2. This stems from the×600 range of the26Al(p,γ)27Si rate. There is a corresponding knock-on effect on27Al;• Most other isotopes vary by at most about 10−20%.It is sometimes necessary to consider changing all the reaction rates together. The yields of themagnesium isotopes atZ = 0.004 show this clearly, as they are affected by the preceding NeNacycle rate changes followed by23Na(p,γ)24Mg . . . (p,γ)25Al(β+)25Mg . . .(p,γ)26Al(β+)26Mg.4. ConclusionsWe have showed that changes in yields from hot-bottom burning stars due to nuclear reac-4Reaction Rates and NeNa/MgAl Robert G. Izzardtion rate uncertainties can be significant, particularly for 22Ne, 23Na, the magnesium isotopes andaluminium. The effect of reaction rate uncertainty becomesstronger as the hydrogen burning tem-perature increases i.e. at higher mass and/or lower metallicity. For some isotopes, especially thoseof magnesium, it is important to consider changingall the uncertain reaction rates at the same time,as simply changing the proton capture rate on each isotope does n t give an accurate error rangefor the yield.It remains to be seen if, say, a higher22Ne(p,γ)23Na rate can help to solve the problem of theglobular cluster abundance anomalies, which show excessive odium and lower oxygen, particu-larly as we have not tried to change the CNO cycle rates here. It is also possible that the yields ofprimary sodium could be constrained by galactic chemical evo ution models, which in turn wouldgive us an upper limit for the22Ne(p,γ)23Na rate, although we will also have to examine carefullythe role of massive stars in23Na production.Factor of two changes in the magnesium yields in our low-metallici y models may be importantfor fine-structure constant (α) variation studies because∆α/α is a steep function of(25Mg+26Mg)/24Mg (see Fig. 1 of [8]).References[1] R. Gratton, C. Sneden, E. Carretta,Abundance Variations Within Globular Clusters, Annual Review ofAstronomy & Astrophysics42 385[2] R. G. Izzard et al.,A New Synthetic Model for AGB Stars, Monthly Notices of the RAS350 407-426[3] A. I. Karakas, J. C. Lattanzio and O. R. PolsParameterising the Third Dredge-up in Asymptotic GiantBranch Stars, Publications of the Astronomical Society of Australia19 515-526[astro-ph/0210058][4] C. Angulo, M. Arnould, M. Rayet and P. DescouvemontA compilation of charged-particle inducedthermonuclear reaction rates, Nuclear Physics A656 3[5] C. Iliadis et al.,Astrophysical Journal Supplement Series134 151[6] C. Rowland et al.,Astrophysical Journal615 L7[7] D. C. Powell et al.,Nuclear Physics A, 660 349[8] Y. Fenner, M. T. Murphy and B. K. Gibson,On variations in the fine-structure constant and stellarpollution of quasar absorption systems, Monthly Notices of the RAS358 468-4805

Reaction rate uncertainties: NeNa and MgAl in AGB stars

Reaction Rate Uncertainties: NeNa and MgAl in AGB Stars

Reaction Rate Uncertainties: NeNa and MgAl in AGB Stars

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