Physics 250Neutrino/Nuclear AstrophysicsSpring 2011Chapter 1Big Bang Nucleosynthesis1.1 Elemental abundancesOne of the most important clues about the origin and subsequent evolution of our universecomes from nuclear physics, the elemental abundances we can measure on the sun’s surface,on the surfaces of distance stars (including elements dredged up from the interior by mixing),and in the interstellar medium. One can divide the elements into roughly five groups:a) The dominant elements in our universe are hydrogen and helium, which account for almostall of the known baryons. Their abundances by mass are1H ∼ 0.754He ∼ 0.25We will see that these elements owe their abundances primarily to nuclear and weak inter-action processes occuring in the first few minutes after the big bang. Because of this, theirabundances are powerful probes of cosmology. We will also see that these abundances canalso be tied to cosmological physics at quite a different era, the era of recombination, whenelectrons, protons, and other bare nuclei recombined, forming atoms. At that point the uni-verse became transparent to photons. Measurement of the cosmic microwave background,the radiation that decoupled at this time, provides another test of the baryon abundance inour universe, because that bayon number influences the density fluctuations that grew overthe first 400,000 years of the universe’s evolution.b) In contrast to the abundance of H and He, the lighter “1p-shell” nuclei — those heavierthan He but lighter than C – are relatively rare. Relative to H and He, their abundances arelower by 8-10 orders of magnitude:6Li ∼ 7.75E-107Li ∼ 1.13e-89Be ∼ 3.13E-1010B ∼ 5.22E-1011B ∼ 2.30E-9These rare elements have a fascinating heritage. We will see that7Li can be produced in theBig Bang. Li, Be, and B can also be produced in the interstellar medium, when energeticcosmic-ray protons collide with elements like C, N, and O. This process thus connects to twoimportant chapters in this course – one on the origin of cosmic rays, the other on supernovae1Mass Numberlog10 Abundance [Si=106]Solar Abundances0 20 40 60 80 100 120 140 160 180 200-2024681012Fig T h e ab u n d an ces of is otop es in th e s olar s y s tem as a f u n ction of atom ic m as s[3,4]. The abundances are normalized so that the total abundance of silicon is 106.nuclear reaction played in the synthesis of the elements. In 1957, Burbidge,Burbidge, Fowler & Hoyle [1] and Cameron [2] wove these threads into a co-hesive theory o f nucleosynthesis, demonstrating how the solar isotopic abun-dances (displayed in Fig. 1) bore the fingerprints of their astrophysical o r ig ins.Today, investigations refine our answers to these same two questions, how arethe elements that make up our universe formed, a nd how do these nucleartransformations, and the energy they release, affect their astrophysical hosts.In this article, we will concentrate on summarizing the two basic numericalmethods used in nucleosynthesis studies, the tracking of nuclear transmuta-tions via rate equations and via equilibria. We will also briefly discuss workwhich seeks to meld these methods together in order to overcome the limita-tions of each. To properly orient readers unfamiliar with nuclear astrophysicsand to briefly describe the differing physical conditions which influence theoptimal choice o f abundance evolution method, we begin with a brief intr o-duction to the background astrophysics (§2), before discussing the form thatthe ra t e equations take (§3). In §4 we will discuss the difficulties inherent insolving these rat e equations. §5 describes the equations of nuclear equilibriaas well as the limitations of their use. Finally in §6 we will discuss hybridschemes which seek to use local equilibria to simplify the r ate equations.2Figure 1: The solar system abundances of the elements (these elements were incorporatedinto the solar system 4.7 b.y. ago) as a function of A=Z+N. Note: a) the large abundancesof H and He; b) the deep “hole” coresponding to Li/Be/B; c) a series of peaks, particularlyprominent for the α nuclei, corresponding to the products of stellar burning between mass12 and mass ∼ 40; d) a mass peak near Fe, A ∼ 56-60; e) rare heavier elements, but withmass peaks near A ∼ 130 and A ∼ 195. From Hix and Thielemann, astro-ph/9906478/.2F ig ur e 12Figure 2: The evolution of galactic Li as a function of metallicity. Stellar metallicity servesas a clock, with low-metallicity stars having formed early, high metallicity later (when theinterstellar medium was enriched in metals from previous generations of stars). The [Fe/H]is the metallicity measure, relative to solar. Note the Li abundance plateau – called the Spiteplateau – at low metallicity, indicating that some baseline of Li existed when the first starswere formed. This is assumed to be the primordial value. Note the great spread of values forstars of solar metallicity. The two circles correspond to the expected standard solar modelLi (the high value) and the measured Li. The sun managed to destroy mosts of its Li – mostlikely by dredging Li to depth (to high temperatures, where it can be burned) – during somepast epoch. Also shown are various theoretical mechanisms proposed for synthesizing Li.From Ryan et al., astro-ph/9905211/.360 80 100 120 140 160 180 200 220MASS NUMBER−3.00−2.50−2.00−1.50−1.00−0.500.000.501.001.50log εSS s−ProcessSS r−ProcessSeSrTeXeBaEuPbOsPtAuF ig . — The s - pr o cess a nd r - pr o cess a bunda nces in so la r syst em ma t t er , ba sed up o n t hewor k by K¨appeler et al. (1989). Note the distinctive s-process signatures at masses A ≈ 88,138, and 208 and the corresponding r-process signatures at A ≈ 130 and 195, all attributableto closed shell effects on neutron capture cross sections. It is the r-process pattern thusextracted from solar system abundances that can be compared with the observed heavyelement patterns in extremely metal-deficient stars. The total solar system abundances forthe heavy elements are those compiled by Anders and Grevesse (1989).Figure 3: A more detailed view of solar system heavy element abundances. Note that the twomass peaks mentioned earlier are double peaks. We will see that the peak components areproduced by different neutron-capture mechanisms. From Truran et al., astro-ph/0209308/.4(which on exploding enrich the interstellar medium with the products of stellar burning,such as C, N, and O).