– 1 –1. Nucleosynthetic Yields From Various SourcesIn this section we discuss the various sites for producing the heavy elements, and givea guide to the literature and to sources for the yields for each process. Talbot & Arnett(1973, ApJ, 186, 69) defined a stellar production matrix, which describ es the productionof each isotope in a star of initial mass m. One element of this matrix, Qij(m), representsthe fraction of the stellar mass which was originally present in the form of species j andis eventually ejected by the star in the form of element i, so Qij(m) = (mej)ij(m)/(mXj),where Xjis the abundance by mass of element j already present in the star when it firstformed.Then the to t al contribution of a star of mass M to the ejected mass of the element i,both newly formed, and originally present, is given by(Mej)i=Xj=1,nQij(M) XjM.In most modern calculations, the yield for element i is given without the detail of whatwas the initial form o f i before nucleosynthesis, i.e. the production yield pim= (Mej)i/M.The dependence on j is treated by carrying out the calculation of yields for various stellarmetallicities at each stellar mass.Galactic yields yiare then the sum over a stellar generation with a specific IMF, takinginto account the minimum mass that dies (usually set to 1M⊙) and the remnants (whitedwarfs, neutron stars, black holes) f or each species i.Remember tha t the mass of a highly evolved star is its initial mass − mass lost duringevolution through winds. This early lost material has a chemical inventory close to oridentical to that of the star when it was formed. Then there is t he mass ejected nearthe end of the star’s lifetime (during the supernova, nova, etc), which will contain highly– 2 –processed material f rom the stellar interior as well as the outer layers of the star. Thus tocalculate the yields you need a detailed understanding of the last stages of stellar evolution,of the explosion tha t might occur, and of the mass cutoff for ejection, as well as the nuclearreaction network itself.1.1. The Neutron ExcessNaively one might think that the nuclear reaction rates depend only on T , ρ, and theinitial chemical composition. But there is another important parameter, related to theintitial chemical composition, the neutron excess.Neutrons and pro t ons can interconvert via weak interactions, and these conversionsoccur during decays. The second reaction listed below, when only the right arrow holds, iselectron capture, while the third is β-decay.p +ν⇀↽n + e+, p + e−⇀↽n + ν, n⇀↽p + e−+ν.Free neutrons decay with a mean lifetime of ∼15 min via the last o f the three reactionslisted above.Depending on whether there is enough time for the various unstable isotopes thatmay be produced to decay, one can end up with different isotopic compositions. Thisis not only the case for the neutron capture processes, but also for nuclear reactions inexplosions, where the timescale may be so short that β-decays cannot happen. In addition,the formation of neutron-rich isotopes, be they stable or unstable, is more rapid if there a reexcess neutrons.We must have a constant total number of nucleons. If weak interactions (decays)– 3 –cannot occur fast enough, we will have a constant number of protons and a constant numberof neutrons, Nn+ Np=PiNiAi, where Aiis the atomic mass of the isotope and the sum isover all isotopes i present.The neutron excess per nucleon, η, is (Nn− Np)/(Nn+ Np). By charge neutrality, theelectron number is the total number of protons, and, since the material is fully ionized,Ye=PiYiZi, where Yeis the fraction of electrons in a fixed mass of the plasma and Ziisthe charge of each isotope i. By definition,PiYiAi= 1, so one can show that η = 1 − 2Ye.Thus the neutron excess is related to a deficit of free electrons in the plasma.Consider He burning in a convective core at T ∼ 108K.18O, with 8 protones and10 neutrons, can be produced by14N(α, γ)18F, followed by decay of18F to18O. This isimportant because it converts a relatively abundant nucleus with no neutron excess (14N)into a nucleus with a neutron excess o f (2/18) = 0.111. For solar abundances, at this stageof stellar evolution and nuclear processing in the core, this gives a total neutron excess ofη ≈ 1.5 × 10−3.Primordial gas is mostly H, which has only one proton, and no neutrons, a nd hencethe initial neutron excess is negative. As H burning proceeds, H is converted into4He and12C, both of which have a neutron excess of 0. Then, after He burning, η becomes slightlypositive as a small neutron excess builds up through production of18O.Since decays cannot happen during explosive nucleosynthesis (i.e. in modeling SNII),the input neutron excess is identical to that of the final burned products that are eventuallyejected. Using the value η = 1.5 × 10−3in explosive nucleosynthesis calculations reproducesthe r atios of neutron-rich nuclei to their neighbors in the periodic ta ble for the solarcomposition. If a value significantly different is chosen, the predicted final isotopic ratios donot match those for the Sun.– 4 –2. SNIaSNIa are usually believed to be explosions of white dwarfs that have approached theChandrasekhar limit (Mch∼ 1.39M⊙) through accretion from a companion in a binarysystem, although in his recent colloquium Martin van Kerkwijk suggested a somewhatdifferent mechanism, the merging of two C-O white dwarfs. The white dwarfs are disruptedby thermonuclear fusion of C and O from accreted material heated up by packing evenmore accreted material on top of the white dwarf. Thus the details depend on the accretionrate from the companion, among other parameters. Given these issues, SNIa yields are veryhard t o calculate.SNIa are used as standard candles in cosmology, and it therefore behooves us tounderstand the explosion mechanism, and the resulting nucleosynthesis, well.SNIa contribute very significantly to the Fe- peak elements. Their production of lighterelement is considerably less important. They produce very little of elements lighter thanAl. The first yield calculations were by Iwamoto, Brachwitz, Nomoto et al (1999, ApJS,125, 439). Recently Travaglio, Hillebrandt, Reinecke & Thielemann (2004, A&A, 425 , 1029)present 2D and 3D hydrodynamical models of SNIa and a new set of nucleosynthesis yields.The latest calculations of SNIa detonations are given by Woosley, Kerstein, Sankaran& Ropke (2009, ApJ, 704, 255). These are