Nuclear Astrophysics Lecture 1 Gail McLaughlin North Carolina State University 1 Neutrino Astrophysics What are the fundamental properties of neutrinos? • What do they do in astrophysical environments? • What do neutrinos in a core collapse supernova do? • What do neutrinos in a black hole accretion disk do? • Nuclear Astrophysics What is the origin of the elements? • Where are the heaviest elements made? • What elements are made in compact object mergers/ stellar explo- • sions? 2 Outline Lecture 1: Introduction • Lecture 2: Nucleosynthesis • Lecture 3: The r-process • 3 Gas clouds that make stars As a gas cloud is made primarily of hydrogen and helium, with trace amounts of other elements. The small amounts of other elements were made in the Big Bang (Li, Be, B) or else were ejecta in prior stellar explosions (carbon and heavier). Stars are formed when a gas cloud collapses. Very old stars have mostly Big Bang elements, whereas newer stars have more heavier elements (although hydrogen and helium still dominate). 4 Stars As the cloud collapses, the density and temperature increase. If the cloud is large enough, then the nuclear reactions begin. Hydrogen starts a series of reactions, the pp chain, the burn hydrogen to helium. Hydrogen burning occurs at around 107K. + p + p D + e + νe → D + p 3He + γ (pp I, 86%) → 3He +3 He 4He + p + p → 5 Stars: what do we see? Light is the primarily and traditional tool of astronomy, and we use it to look at stars. Light has many excellent features it doesn’t change identity • it travels in a straight line (w/o GR) • it is easy to detect • it contains spectral information • Light has one less excellent feature: it is not very penetrating • Even very dilute matter is opaque to light, and this prevents us from seeing inside stars. It takes 10,000 years for a photon to random walk its way out of the center of the sun. 6 Stars and Neutrinos In order to use light to test for nuclear reactions in the sun, we need a model e.g. John Bahcall’s standard solar model. There is a lot of physics in between the nuclear reactions and the surface emission of the sun. Another tool is the neutrino: The neutrino has many excellent features: it is very penetrating • it travels in a straight line (w/o GR) • Neutrinos have a few less excellent features: they change identity • they are hard to detect • 7 Neutrinos from the sun that are detected here on earth have traveled straight from the nuclear reaction in which they were produced and were emitted just a few minutes before they were detected. Reconstruction of the sun from neutrinos, SuperK collaboration 8 Detecting neutrinos from the sun - p + p D + e + + ν p + e + p D + ν e e (pp: 99.75%) (pep: 0.25%) D + p3 He + γ 3 3 α 3 4 7 γ 3 + ν He + He + 2p He + He Be + He + p α + e + e (pp-I: 86%) (HeP: 0.00002%) - 7 7 8 ( 7Be) 7 Be + e Li + ν Be + p B + γ e 8 7Li + p 2 α 8 B Be* + e+ + ν 8 e ( B) (pp-II: 14%) 8 Be* 2 α (pp-III: 0.02%) Detectors like SuperKamiokande and SNO have/had higher thresholds and see primarily Boron-8 neutrinos. To see other neutrinos, a detection reaction and a detector with a low threshold is required, e.g. Borexino. 9 Experiments measure deficit of νe (Homestake, Gallex, Sage, Kamiokande, SuperK, SNO) Homestake − νe + Cl e + Ar → SAGE, GALLEX − νe + Ga e + Ge → SuperK − − νe + e νe + e → 10 Neutrino Oscillations Neutrinos come in different flavors νe,νµ,ντ ,... Flavor eigenstates = mass eigenstates Pontecorvo (1957) 6 The rest is just quantum mechanics ... Consider two flavors νe,νµ νe = cos θ ν1 + sin θ ν2 | i | i | i νµ = sin θ ν1 + cos θ ν2 | i − | i | i Flavor eigenstates νe,µ Mass eigenstates ν1,2 | i ↔ | i 11 Matter Enhanced (MSW) Oscillations Neutrino propagation in matter: forward scattering on electrons leads to effective potential e e CC+NC Ve Vx ν ν V = − = 2√2G N (r) e e 2 F e G F e e electron density Ne(r) NC ν ν Wolfenstein (1978) µ,τ µ,τ G Mikheyev-Smirnov (1985) F Modified wave equation 2 2 V δm cos(2θ) δm sin(2θ) ~ d 4E 4E i c ψν = − 2 2 ψν dr δm sin(2θ) V + δm cos(2θ) 4E − 4E Consider eigenstates of RHS (“matter eigenstates”) 12 Start at high density matter eigenstates flavor eigenstates ≃ Resonance occurs if diagonal element vanishes. Possibilities 2 2 1) νe ν1 non adiabatic P (νe) cos θ, P (νµ) sin θ → − ∼ ∼ 2 2 2) νe ν2 adiabatic P (νe) sin θ, P (νµ) cos θ → ∼ ∼ ν ~ | e > m 2 2E | ν 2 > MSW resonance ρ 13 Boron-8 neutrinos undergo MSW oscillations pp neutrinos undergo vacuum oscillations 14 Helium burning When the core of our sun runs out of hydrogen, it will start to burn helium. It contracts until the temperature reaches around 108K. α + α + α 12C → α +12 C 16C → Unfortunately this happens when the sun becomes a red giant and incinerates the earth. Luckily that is five billion years away. Our sun is will not become hot enough to burn past carbon and will end its like as a carbon-oxygen white dwarf. 15 Burning past carbon and oxygen A bigger star can get hotter and burn past oxygen. It develops either an oxygen-neon magnesium core ( 8 solar mass star) or an iron core (10 ∼ solar masses). The later burning stages occur at around 109K. 16 Iron core collapse Iron is tightly bound and no more energy can be released as it burns past iron. The iron core becomes larger and larger and is supported by electron degeneracy pressure. At some point it can no longer maintain hydrostatic equilibrium and it begins to collapse. Specifically, the iron starts to disso- R [km] Initial Phase of Collapse R [km] Neutrino Trapping (t ~ 0) R ~ 3000 R (t ~ 0.1s, c ~10¹² g/cm³) ciate and electrons capture on the Fe Fe e νe !!!!!!!!!! !!!!!!!!! !!!!!!!!!! protons. !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! ~ 100 !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! Si !!!!!!!!!! Si − !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! ν !!!!!!!!!! e + p n + ν !!!!!!!!! e Fe, !!!!!!!!!! Ni e !!!!!!!!! !!!!!!!!!! Fe, Ni !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! → !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! νe !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! Once initiated, the process runs !!!!!!!!! !!!!!!!!!! M(r) [M ] M(r) [M ] 0.5 1.0 ~ M Ch 0.5 Mhc 1.0 heavy nuclei away due to energy losses. Si−burning shell Si−burning shell R [km] Shock Propagation and Burst R [km] Bounce and Shock Formation e (t ~ 0.12s) R (t ~ 0.11s, c 2 o) R 17 Fe Fe Rs ~ 100 km e radius of e shock R !!!!!!!!! formation !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! position of !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! shock !!!!!!!!!! !!!!!!!!! Si !!!!!!!!!! Si ~ 10 !!!!!!!!! e !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! formation !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! Fe !!!!!!!!! !!!!!!!!!! Fe, Ni !!!!!!!!! free n, !!!!!!!!!! !!!!!!!!! e !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! p !!!!!!!!!! !!!!!!!!! !!!!!!!!!! Ni !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! M(r) [M ] 0.5 1.0 M(r) [M ] 0.5 1.0 nuclear matter nuclear matter nuclei nuclei Si−burning shell Si−burning shell Shock Stagnation and Heating, R [km] Neutrino Cooling and Neutrino− R [km] Explosion (t ~ 0.2s) 10 5 Driven Wind (t ~ 10s) Rs ~ 200 4 e e 10 e e Ni R ~ 100 3 g free n, p Si 10 Si p R ~ 50 2 He e n 10 r−process? e e O e e e R ns ~ 10 R M(r) [M ] n M(r) [M ] PNS1.3 gain layer 1.5 PNS 1.4 9 3 n, p ,n, Be, cooling layer n, p 12 C, seed Neutronization burst The neutrinos produced in this way during collapse are called the “neu- tronization burst”. − e + p n + νe → 18 R [km] Initial Phase of Collapse R [km] Neutrino Trapping (t ~ 0) R ~ 3000 R (t ~ 0.1s, c ~10¹² g/cm³) Fe Fe e !!!!!!!!! e !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e The core rebounds and !!!!!!!!! creates a shock !!!!!!!!!! !!!!!!!!! ~ 100 !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! Si !!!!!!!!!! Si !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! e Fe, !!!!!!!!!! Ni The core collapses to very high density !!!!!!!!! and then rebounds. The details !!!!!!!!!! Fe, Ni !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! e !!!!!!!!!! of the bounce depend on the equation !!!!!!!!! of state. !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! M(r) [M ] M(r) [M ] 0.5 1.0 ~ M Ch 0.5 Mhc 1.0 Material moving outward collides with material moving inwaheavyrd nuclei creating Si−burning shell Si−burning shell a shock. R [km] Shock Propagation and Burst R [km] Bounce and Shock Formation e δ δ (t ~ 0.12s) R (t ~ 0.11s, c ∼< 2 o) R Fe Fe Rs ~ 100 km e radius of νe shock R !!!!!!!!! formation !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! position of !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! shock !!!!!!!!!! !!!!!!!!! Si !!!!!!!!!! Si ~ 10 !!!!!!!!! νe !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! formation !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! Fe !!!!!!!!! !!!!!!!!!! Fe, Ni !!!!!!!!! free n, !!!!!!!!!! !!!!!!!!! νe !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! p !!!!!!!!!! !!!!!!!!! !!!!!!!!!! Ni !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! M(r) [M ] 0.5