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

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 “neutronization 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 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 1.0 M(r) [M ] 0.5 1.0

nuclear matter nuclear matter

δ δ nuclei nuclei ( ∼> ο) 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 19

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 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 !!!!!!!!! !!!!!!!!!! !!!!!!!!! ~ 100 !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! Si !!!!!!!!!! Si !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! e !!!!!!!!!! !!!!!!!!! Fe, !!!!!!!!!! Ni Fe, Ni !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! e !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! M(r) [M ] M(r) [M ] 0.5 1.0 ~ M Ch 0.5 Mhc 1.0 heavy nuclei 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 Fe Fe Rs ~ 100 km e radius of e shock R formation !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! position of !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! shock !!!!!!!!!! Si ~ 10 !!!!!!!!! Si !!!!!!!!!! ~ 10 !!!!!!!!! e !!!!!!!!!! !!!!!!!!! formation !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! Fe !!!!!!!!! The shock stalls !!!!!!!!!! Fe, Ni !!!!!!!!! free n, !!!!!!!!!! !!!!!!!!! e !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! p !!!!!!!!!! !!!!!!!!! !!!!!!!!!! Ni !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! The shock uses up !!!!!!!!! some of its energy photodissociating !!!!!!!!!! nuclei along its !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! M(r) [M ] 0.5 1.0 M(r) [M ] 0.5 1.0 path. Thennuclear matter it stalls and becomes a standingnuclear matter accretion shock (SAS). nuclei nuclei Si−burning shell Si−burning shell

Shock Stagnation and ν Heating, R [km] Neutrino Cooling and Neutrino− R [km] Explosion (t ~ 0.2s) 10 5 Driven Wind (t ~ 10s) Rs ~ 200

4 νe,µ,τ ,ν e,µ,τ 10 e e

Ni R ~ 100 3 g free n, p Si 10 Si p R ~ 50 2 He ν νe n 10 r−process? νe,µ,τ ,ν e,µ,τ O e e νe 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

20 A protoneutron star is at the center The core is now has a radius of about 30-40km, and is called a proto- neutron star. The very center of the protoneutron star has temperatures of about a several tens of MeV, 1012K, and densities of about 1014 ∼ g/cm2. The exact composition is not known.

35 16 t = 1 s (a) pb 15 (b) 30 t = 2 s pb t = 7 s 14 pb 25 13 ]) 3 20 12 [g/cm

11 15 ( 10 10 log

Temperature [MeV] 10 9

5 8 νe - sphere 7 ν¯e - sphere 100 5 10 15 20 25 5 10 15 20 25 (c) 0.6 (d) 50 30 0.5 ] B 20 0.4 10 e

Y 0.3 5 3 0.2 2 Entropy per Baryon [k 0.1 1

0.5 5 10 15 20 25 5 10 15 20 25 Radius [km] Radius [km]

21 The proto-neutron star releases thermal neutrinos The proto-neutron star is so hot that everything is in thermal equilibrium, which means that thermal processes, e.g. neutrino bremsstahlung, produce neutrinos of all ﬂavors. Neutrinos come in three ﬂavors νe, νµ and ντ . These neutrinos scatter out of the proto-neutron star and then free stream. long mean free path ν core e νe

ννννµµτ τ

short mean free path

22 Neutrino diffusion: order of magnitude estimate How long does it take a 30 MeV neutrino to scatter out of a proto neutron star core? 1. 10 milliseconds 2. 10 seconds 3. 10 minutes 4. 10 days 5. 10 years some useful quantities: core size, R = 40 km; density, ρ = 1014gcm−3 2 4 2 2 Eν Gf me −44 2 weak cross section σ = σ0 2 , σ0 = ~4 = 1.76 10 cm mec 2 × R diffusion time tdiff = , where l is the mean free path lν c ν

23 Neutrino Scattering Neutrinos scatter from nucleons, nuclei: Scattering on neutrons, protons ν(¯ν)+ n n + ν(¯ν) • → − electron (neutrino) capture e + p n + νe • ↔ + positron (antineutrino) capture e + n p +ν ¯e • ↔ ν scattering on nuclei ν + A(Z,N) A(Z,N)+ ν • ↔ − νe capture on nuclei νe + A(Z,N) A(Z + 1,N 1) + e • ↔ − + ν¯e capture on nuclei ν¯e + A(Z,N) A(Z 1,N +1)+ e • ↔ −

24 Neutrino diffusion timescale The neutrino diffusion timescale depends on composition of the core. Here are a few predictions made from different equations of state.

The timescale on which neutrinos are emitted provides some information about the composition of the core.

25 Leptons above the protoneutron star Above the protoneutron star the neutrinos are free streaming - almost - a small amount of scattering still goes on. It is a reasonably good approximation to assume that the temperatures are frozen in at the decoupling surface, and the ﬂux declines roughly as 1/r2.

Above the proto-neutron star electrons and baryons are still thermally coupled and the temperature declines as you move away from the neutrino surface. The ﬂux is determined by thermal distributions.

26 Neutrino Decoupling Inside the core neutrinos scatter, and outside they free stream. The transition is called the decoupling surface. Which neutrinos have the lowest temperature at decoupling?

1. νe

2. ν¯e

3. νµ

4. ν¯µ some useful information: a proto-neutron star has more neutrons than protons the mass of an electron is 0.511 MeV the mass of a muon is 105.7 MeV

27 Neutrino spectra Spectra are determined by the physics at the surface of the proto-neutron star.

There is some uncertainty in the spectra. Diﬀerent opacities predict diﬀerent spectra.

28 R [km] Initial Phase of Collapse R [km] Neutrino Trapping (t ~ 0) R ~ 3000 R (t ~ 0.1s, c ~10¹² g/cm³) Fe Fe

R [km] Shock Propagation and Burst R [km] Bounce and Shock Formation e (t ~ 0.12s) R (t ~ 0.11s, c 2 o) R Fe Fe Rs ~ 100 km e radius of e shock R formation !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! position of !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! shock !!!!!!!!!! Si ~ 10 !!!!!!!!! Si !!!!!!!!!! !!!!!!!!! e !!!!!!!!!! !!!!!!!!! formation !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! Fe !!!!!!!!! !!!!!!!!!! Fe, Ni !!!!!!!!! !!!!!!!!!! !!!!!!!!! free n, !!!!!!!!!! !!!!!!!!! e !!!!!!!!!! !!!!!!!!! p !!!!!!!!!! !!!!!!!!! !!!!!!!!!! Ni !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! Neutrino diﬀusion !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! M(r) [M ] Neutrinos ﬁrst cool and then heat0.5 the 1.0 materialM(r) above[M ] the material above0.5 1.0 nuclear matter nuclear matter nuclei nuclei the protoneutron star. Si−burning shell Si−burning shell

Shock Stagnation and ν Heating, R [km] Neutrino Cooling and Neutrino− R [km] Explosion (t ~ 0.2s) 10 5 Driven Wind (t ~ 10s) Rs ~ 200

4 νe,µ,τ ,ν e,µ,τ 10 e e

Heating occurs when small numbers of neutrinos deposit energy in the region above the gain radius at a higher rate than the material produces neutrinos. 29 Re-energizing the stalled shock Neutrinos heat the material below the stalled shock, helping along the standing accretion shock instability.

30 R [km] Initial Phase of Collapse R [km] Neutrino Trapping (t ~ 0) R ~ 3000 R (t ~ 0.1s, c ~10¹² g/cm³) Fe Fe

R [km] Shock Propagation and Burst R [km] Bounce and Shock Formation e (t ~ 0.12s) R (t ~ 0.11s, c 2 o) R Fe Fe Rs ~ 100 km e radius of e shock R formation !!!!!!!!! !!!!!!!!!! !!!!!!!!! Explosion! !!!!!!!!!! e !!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! position of !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! shock !!!!!!!!!! !!!!!!!!! Si !!!!!!!!!! Si ~ 10 !!!!!!!!! e !!!!!!!!!! !!!!!!!!!Details of the explosion are still under !!!!!!!!!! investigation. But when the !!!!!!!!! formation !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! Fe !!!!!!!!! !!!!!!!!!! Fe, Ni !!!!!!!!! free n, !!!!!!!!!! !!!!!!!!!explosion occurs,e explosive nucleosynthesis !!!!!!!!!! occurs as well. !!!!!!!!! !!!!!!!!!! !!!!!!!!! p !!!!!!!!!! !!!!!!!!! !!!!!!!!!! Ni !!!!!!!!! !!!!!!!!!! e !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!!The energy of the shocked material allows !!!!!!!!!! nuclear burning, and a number !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! M(r) [M ] 0.5 1.0of elementsM(r) [M ] are produced. Lots0.5 of nickel,1.0 but smaller amounts of other nuclear matter nuclear matter nuclei nuclei elementsSi−burning shell as well, like titanium. 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 νe,µ,τ ,ν e,µ,τ

Ni R ~ 100 3 g free n, p Si 10 Si p R ~ 50 2 He e 10 α n r−process? ν ,ν e e O e,µ,τ e,µ,τ e R ns ~ 10 R ν M(r) [M ] n M(r) [M ] PNS1.3 gain layer 1.5 PNS 1.4 α, 9 3 n, p ,n, Be, cooling layer n, p α 12 C, seed

31 Why nickel? Nickel is a tightly bound iron group element that has equal numbers of neutrons and protons. Thus, nuclear statistical equilibrium favors nickel.

At high temperatures, e.g. T = a few 1010 K, the distribution of × elements is determined by their binding energies, not nuclear reactions. i.e. all nuclear reactions are balanced in nuclear statistical equilibrium.

32 Nickel-56 is important for the explosion Lots of nickel is produced in explosive burning and this is reﬂected in the light curve. The 56Ni beta decays to 56Co which decays to 56Fe. Gamma rays are produced at each step that thermalize. The timescale for these decays is months, which is reﬂected in the light curve.

4 I -18 R V -17 3 day 20 B -16

day 40 2

-15 Relative Flux U Absolute Magnitude -14 day 60

-13 day 80

0 50 100 150 200 Days Since Explosion 0 2000 4000 6000 8000 10000 Wavelength (Angstroms) Kasem and Woosley 2012

33 Other nucleosynthetic products As the shock moves out, it loses energy and the temperature drops. Nuclear burning will still occur, just not in nuclear statistical equilibrium. Nuclear burning also occurs in the neutrino driven wind. Ways to detect nucleosynthetic products supernova remnants • spectroscopy of gas clouds, stars • meteorites • Only elements that are made in large quantities can be seen in remnants

34 R [km] Initial Phase of Collapse R [km] Neutrino Trapping (t ~ 0) R ~ 3000 R (t ~ 0.1s, c ~10¹² g/cm³) Fe Fe

R [km] Shock Propagation and Burst R [km] Bounce and Shock Formation e (t ~ 0.12s) R (t ~ 0.11s, c 2 o) R 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 !!!!!!!!! Neutrino driven !!!!!!!!!! wind !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! !!!!!!!!! !!!!!!!!!! M(r) [M ] 0.5 1.0After theM(r) [M shock ] moves out, neutrinos0.5 1.0 deposit small amounts of energy nuclear matter nuclear matter nuclei nuclei nearSi−burning the shell surface of the proto-neutron star.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 νe,µ,τ ,ν e,µ,τ

35 Nucleosynthesis in hot outﬂows What matters? outﬂow timescale, milliseconds to seconds • entropy s 20 to s 400 • ∼ ∼ p electron fraction, Ye = , Ye 0.1 to 0.6, • n+p ∼

Electron fraction is set by the weak interactions: − + νe + n p + e , ν¯e + p n + e ↔ ↔

36 The weak interaction The only way to convert protons to neutrons and vice-versa − beta decay n p + e +ν ¯e • → − electron (neutrino) capture e + p n + νe • ↔ + positron (antineutrino) capture e + n p +ν ¯e • ↔ − νe capture on nuclei νe + A(Z,N) A(Z + 1,N 1) + e • ↔ − + ν¯e capture on nuclei ν¯e + A(Z,N) A(Z 1,N +1)+ e • ↔ −

37 p-process elements e.g. 92Mo Z = 42, N = 50 proton rich side of the valley of β stability → How do you make light p elements? Three possibilities:

Just the right Ye (around 0.485) • The right ﬂux of neutrinos on protons during element formation • The right ﬂux of neutrinos on nuclei during element formation • What are the candidate environments? Supernovae • Accretion disks •

38 The r-process elements e. g. Uranium-238 Z=92, N=146 need lots of neutrons →

A(Z,N)+ n A + 1(Z,N +1)+ γ ↔ Z − A(Z,N) A(Z + 1,N 1) + e +ν ¯e → − N rapid neutron capture as compared with beta decay Can the neutrino driven wind make the r-process? only if there are enough neutrons in the outﬂow • right neutrino/antineutrino ratios, entropy and timescale •

39 Distribution of elements in the solar system

0.1 scaled solar data

0.01

0.001 Abundance

0.0001

1e-05 40 60 80 100 120 140 160 180 200 A

Galactic chemical evolution is an area of study where all types of nucleosynthetic events are studied for the frequency in the universe and matched to the ﬁnal pattern.

40 Summary: cartoon of the supernova geometry

shock

proto neutron star core

41 Summary: where is the nuclear physics?

neutrino nucleosynthesis oscillations shock

neutrino scattering nuclear physics proto neutron star core & emission of core

42 Coming up next: Nucleosynthesis