Nuclear Astrophysics: Supernova Evolution and Explosive Nucleosynthesis
Gabriel Martínez Pinedo
Advances in Nuclear Physics 2011 International Center Goa, November 9 – 11, 2011 Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Outline
1 Introduction
2 Astrophysical reaction rates
3 Hydrostatic Burning Phases Hydrogen Burning Advanced burning stages
4 Core-collapse supernova Neutrinos and supernovae
5 Nucleosynthesis heavy elements Neutrino-driven winds Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements A new Era for Nuclear Astrophysics
Improved observational capabilities Improved supernovae models
New radioactive ion beam facilities (RIBF, SPIRAL 2, FAIR, FRIB) are being built or developed that will study many of the nuclei produced in explosive events. Hydrostatic burning phases studied in underground labs (LUNA) We need improved theoretical models to fully exploit the potential offered by these facilities. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements What is Nuclear Astrophysics?
Nuclear astrophysics aims at understanding the nuclear processes that take place in the universe. These nuclear processes generate energy in stars and contribute to the nucleosynthesis of the elements and the evolution of the galaxy.
Hydrogen mass fraction X = 0.71 3. The solar abundance distribution Helium mass fraction Y = 0.28 Metallicity (mass fraction of everything else) Z = 0.019 Heavy Elements (beyond Nickel) mass fraction 4E-6 a-nuclei Disk solar abundances: Gap 12C,16O,20Ne,24Mg, …. 40Ca general trend; less heavy elements B,Be,Li Elemental 0 10 Halo (and isotopic) 10-1 composition 10-2 + Sun + of Galaxy at 10-3 location of solar -4 n r-process peaks (nuclear shell closures) system at the time o 10 Bulge
i
t -5
c 10 of it’s formation
a -6
r
f
10 r -7 e 10 s-process peaks (nuclear shell closures) b -8
m 10
u -9
n 10 10-10 10-11 Fe peak U,Th -12 (width !) 10 Fe Au Pb 10-13 0 50 100 150 200 250 mass number
K. Lodders, Astrophys. J. 591, 1220-1247 (2003) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Cosmic Cycle
8 4...6 10 y M~10 Mo
dense molecular star formation (~3%) condensation clouds
interstellar 106-1010 y medium stars star M > 0.08 Mo s
infall dudustst winds SN explosion
mixing SNR's & ~90% hot bubbles Galactic compact remnant SNIa (WD, halo 102-106y NS,BH) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Nucleosynthesis processes
In 1957 Burbidge, Burbidge, Fowler and Hoyle and independently Cameron, suggested several nucleosynthesis processes to explain the origin of the elements.
νp-process “neutrino-proton process” s-process 184 rp-process “slow process” via chain of stable nuclei through “rapid proton process” 162 via unstable proton-rich nuclei neutron capture through proton capture Pb (Z=82)
Proton dripline 126 (edge nuclear stability) Number of protons
Sn (Z=50)
r-process “rapid process” via Ni (Z=28) 82 unstable neutron-rich nuclei
Neutron dripline 50 (edge nuclear stability) 28 Fusion up to iron 20 Big Bang Nucleosynthesis 2 8 Number of neutrons Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Composition of the Universe after Big Bang Ma tt e r C o m po sit io n 80 76 after Big Bang Nucleosynthesis 70.683 in Solar System
60 ) % (
on i
act 40 r F ass
M 27.431
24
20
1.886 8.00E-08 0 HHeMetals
Stars are responsible of destroing Hydrogen and producing “metals”. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Star formation
Stars are formed from the contraction of molecular clouds due to their own gravity. Contraction increases temperature and eventually nuclear fusion reactions begin. A star is born. Contraction time depends on mass: 10 millions years for a star with the mass of the Sun; 100,000 years for a star 11 times the mass of the Sun.
The evolution of a Star is governed by gravity Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements What is a star?
A star is a self-luminous gaseous sphere. Stars produce energy by nuclear fusion reactions. A star is a self-regulated nuclear reactor. Gravitational collapse is balanced by pressure gradient: hydrostatic equilibrium. mdm dF = G = [P(r + dr) P(r)]dA = dF grav − r2 − pres dm = 4πr2ρdr mρ dP G = − r2 dr Further equations needed to describe the transport of energy from the core to the surface, and the change of composition (nuclear reactions). Supplemented by an EoS: P(ρ, T). Star evolution, lifetime and death depends on mass. Two groups Stars with masses less than 9 solar masses (white dwarfs) Stars with masses greater than 9 solar masses (supernova explosions) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Core evolution
Hydrostatic equilibrium together with properties equation of state determines the evolution of the star core.
red: transition from relativistic to non-relativistic electrons. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Where does the energy come from? Energy comes from nuclear reactions in the core. 1 4 + 4 H He + 2e + 2νe + 26.7 MeV →
E = mc2
The Sun converts 600 million tons of hydrogen into 596 million tons of helium every second. The difference in mass is converted into energy. The Sun will continue burning hydrogen during 5 billions years. Energy released by H-burning: 18 1 6.45 10 erg g− = 6.7 MeV/nuc × 33 1 Solar Luminosity: 3.85 10 erg s− × Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Nuclear Binding Energy
Liberated energy is due to the gain in nuclear binding energy. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Type of processes
Transfer (strong interaction)
15 12 N(p, α) C, σ 0.5 b at Ep = 2.0 MeV ' Capture (electromagnetic interaction)
3 7 6 He(α, γ) Be, σ 10− b at Ep = 2.0 MeV ' Weak (weak interaction)
+ 20 p(p, e ν)d, σ 10− b at Ep = 2.0 MeV ' 2 24 2 b = 100 fm = 10− cm Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Types of reactions
Nuclei in the astrophysical environment can suffer different reactions: Decay 56 56 + Ni Co + e + νe 15O +→γ 14N + p → dn a = λ n dt − a a In order to dissentangle changes in the density (hydrodynamics) from changes in the composition (nuclear dynamics), the abundance is introduced:
na ρ Ya = , n = Number density of nucleons (constant) n ≈ mu dY a = λ Y dt − a a Rate can depend on temperature and density Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Types of reactions
Nuclei in the astrophysical environment can suffer different reactions: Capture processes a + b c + d → dn a = n n σv dt − a bh i
dYa ρ = YaYb σv dt −mu h i decay rate: λ = ρY σv /m a bh i u 3-body reactions: 3 4He 12C + γ → dY ρ2 α Y3 = 2 α ααα dt −2mu h i decay rate: λ = Y2ρ2 ααα /(2m2) α α h i u Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Reaction rates
Consider na and nb particles per cubic centimeter of species a and b. The rate of nuclear reactions a + b c + d → is given by: rab = nanbσ(v)v, v = relative velocity In stellar environment the velocity (energy) of particles follows a thermal distribution that depends of the type of particles. Nuclei (Maxwell-Boltzmann) ! m 3/2 mv2 N(v)dv = N4πv2 exp dv = Nφ(v)dv 2πkT −2kT Electrons, Neutrinos (if thermal) (Fermi) g 4πp2 N p dp dp ( ) = 3 (E(p) µ)/kT (2π~) e − + 1 photons (Bose) 2 4πp2 N(p)dp = dp (2π~)3 epc/kT 1 − Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Stellar reaction rate
The product σv has to be averaged over the velocity distribution φ(v) (Maxwell-Boltzmann) Z σv = ∞ φ(v)σ(v)vdv h i 0 that gives: ! m 3/2 Z mv2 m m σv = 4π ∞ v3σ(v) exp dv, m = 1 2 h i 2πkT 0 −2kT m1 + m2
or using E = mv2/2
!1/2 8 1 Z E σv = ∞ σ(E)E exp dE 3/2 h i πm (kT) 0 −kT Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Neutron capture (compound picture)
A + n B + γ → 2 2 2 σn πo B + γ HII C C HI A + n o Tγ(En + Q)Tn(En) ≈ |h | | ih | | i| ∝ T transmision coefficient, E neutron energy, Q = m + m m = S (B), n A n − B n Q En. 2 σn o Tn(En), Tn(En) vnPl(En) ∝ n ∝ Pl(En), propability tunneling through the centrifugal barrier of momentum l. Normally s-wave dominates and P0(En) = 1. 1 1 σn 2 vn = , σnv = constant ∝ vn vn h i Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Charged-particle reactions Stars’ interior is a neutral plasma made of charged particles (nuclei and electrons). Nuclear reactions proceed by tunnel effect. For the p + p reaction the Coulomb barrier is 550 keV, but the typical proton energy in the Sun is only 1.35 keV.
Cross section given by: 2 r 1 2πη Z1Z2e m b σ(E) = e− S (E), η = = E ~ 2E E1/2 Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements S factor
S factor makes possible accurate extrapolations to low energy. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Gamow window
Using definition S factor: !1/2 " # 8 1 Z E b σv = ∞ S (E) exp dE 3/2 1/2 h i πm (kT) 0 −kT − E Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Gamow window Assuming the S factor is constant over the gamow window and approximating the integrand by a Gaussian one gets: !1/2 ! 2 ∆ 3E σv = S (E ) exp 0 h i m (kT)3/2 0 − kT with !2/3 bkT E = = 1.22(Z2Z2AT 2)1/3 keV 0 2 1 2 6
4 p 2 2 5 1/6 ∆ = E0kT = 0.749 (Z1 Z2 AT6 ) keV √3 6 (A = m/mu and T6 = T/10 K) Examples for solar conditions (T = 15 106 K): × reaction E0 (keV) ∆/2 (keV) exp( 3E0/kT) T dependence − 6 3.6 p + p 5.9 3.2 1.1 10− T 14 × 27 20 N + p 26.5 6.8 1.8 10− T 12 × 57 42 C + α 56.0 9.8 3.0 10− T 16 16 × 239 182 O + O 237.0 20.2 6.2 10− T × Reaction rate depends very sensitively on temperature Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Rate Examples: (p, γ)
1010 109 64 27 −3 Ga(p,γ) np = 10 cm 108 65Ge(γ,p) 107
) 106 −1 105 104 Rate (s 103 102 101 100 0.1 1 10 Temperature (GK) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Rate Examples: (α, γ)
103 94 27 −3 102 Kr(α,γ) nα = 10 cm 98Sr(γ,α) 101
0
) 10 −1 10−1
Rate (s 10−2
10−3
10−4
10−5 0.1 1 10 Temperature (GK) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Rate examples: (n, γ)
1010 109 130 22 −3 Cd(n,γ) nn = 10 cm 108 131Cd(γ,n) 107 130Cd beta decay
) 106 −1 105 104 Rate (s 103 102 101 100 0.1 1 10 Temperature (GK) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Hertzspung-Russell diagram Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Hydrogen burning: ppI-chain
Step 1: p + p 2He (not possible) → + p + p d + e + νe Step 2: d + p → 3He → d + d 4He (d abundance too low) → Step 3: 3He + p 4Li (4Li is unbound) → 3He + d 4He + n (d abundance too low) → 3He + 3He 4He + 2p →
d + d not going because Yd is small and d + p leads to rapid destruction. 3 3 He + He goes because Y3He gets large as nothing destroys it. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements The relevant S-factors + 25 p(p, e νe)d: S 11(0) = (4.00 0.05) 10 MeV b ± × calculated p(d, γ)3He: S (0) = 2.5 10 7 MeV b 12 × − measured at LUNA 3 3 4 He( He, 2p) He: S 33(0) = 5.4 MeV b measured at LUNA
Laboratory Underground for Nuclear Astrophysics (Gran Sasso). Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Reaction Network ppI-chain
dYp 2 ρ ρ 2 ρ = Yp σv pp YdYp σv pd + Y3 σv 33 dt − mu h i − mu h i mu h i 2 dYd Yp ρ ρ = σv pp YdYp σv pd dt 2 mu h i − mu h i
dY3 ρ 2 ρ = YdYp σv pd Y3 σv 33 dt mu h i − mu h i 2 dY4 Y3 ρ = σv 33 dt 2 mu h i Stiff system of coupled differential equations. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements pp chains
Once 4He is produced can act as catalyst initializing the ppII and ppIII chains. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements The other hydrogen burning: CNO cycle
4 2He 1.7 MeV (max) 1 1H ν + + + γ e 12 + + 1 6C + 1H
e+ Electron (+)
15 e- Electron (–) 13 7N 7N γ Photon
ν Neutrino
Neutron
Proton
+ 14 γ 7 + + 15 N 13 8O 6C e+ + + 1 1 1 H ν 1H 1.2 MeV (max) + γ
requires presence of 12C as catalyst. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Neutrino spectrum (Sun)
This is the predicted neutrino spectrum ]
1 Gallium Chlorine SuperK − 1012 s 2 − pp 1010 ±1%
8 13 10 N 7 ) [for lines, cm 15 Be pep 1 O − ±10% ±1.5%
6 MeV 10 +20% 1 17 8 − F B –16% s 2 − 104
± hep ? 102
0.10.2 0.5 12 5 10 20 Flux at 1 AU (cm Neutrino energy (MeV) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Energy generation: CNO cycle vs pp-chains Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Consequences
Stars slightly heavier than the Sun burn hydrogen via CNO cycle. CNO cycle goes significantly faster. Such stars have much shorter lifetimes Mass (M ) lifetime (yr) 0.8 1.4 1010 × 10 )'*+",-..% 1.0 1 10 .(- .%/0#10/2% 1.7 2.7× 109 #!(#%(+/%*'-!( 3 -!4+ 3.0 2.2 × 108 × 5.0 6 107 !"#$$%&#'!( × 7 9.0 2 10 5#6",-..% 16.0 1 × 107 .(- .%.('11%#!% × 6 (+/%,-'!% 25.0 7 10 ./7/!4/ 40.0 1 × 106 × Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Helium Burning
Once hydrogen is exhausted the stellar core is made mainly of helium. Hydrogen burning continues in a shell surrounding the core. 4 5 22 He + p produces Li that decays in 10− s. Helium survives in the core till the temperature become large enough (T 108 K) to overcome the coulomb barrier for 4 4 ≈ 8 16 He + He. The produced Be decays in 10− . However, the lifetime is large enough to allow the capture of another 4He: 3 4He 12C + γ → Hoyle suggested that in order to account for the large abundance of Carbon and Oxygen, there should be a resonance in 12C that speeds up the production. 12C can react with another 4He producing 16O 12C + α 16O + γ → These two reactions make up helium burning. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Hoyle State and tripple α reaction
Red giant structure Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Influence 12C(α, γ) in nucleosynthesis Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements End of helium burning
Nucleosynthesis yields from stars may be divided into production by stars above and below 9 M .
stars with M . 9 M These stars eject their envelopes during helium shell burning producing planetary nebula and white dwarfs. Constitute the site for the s process. stars with M & 9 M These stars will ignite carbon burning under non-degenerate conditions. The subsequent evolution proceeds in most cases to core collapse. These stars make the bulk of newly processed matter that is returned to the interstellar medium. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Stellar Evolution Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Stellar life
Nuclear burning stages (e.g., 20 solar mass star)
Main T Time Main Fuel Secondary Product Product (109 K) (yr) Reaction
14 7 CNO H He N 0.02 10 4 H Æ 4He
18 22 4 12 O, Ne 6 3 He Æ C He O, C s-process 0.2 10 12C DJ)16O Ne, 3 12C + 12C C Mg Na 0.8 10 20Ne JD)16O Ne O, Mg Al, P 1.5 3 20Ne DJ)24Mg Cl, Ar, 16O + 16O O Si, S K, Ca 2.0 0.8 Ti, V, Cr, 28Si JD)… Si Fe Mn, Co, Ni 3.5 0.02 Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Supernova types Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements SN1987A
53 Type II supernova in LMC neutrinos Eν 2.7 10 erg 50.0 ≈ × ( 55 kpc) Kamiokande II ∼ 40.0 IMB
30.0
20.0 Energy (MeV)
10.0
0.0 0.0 5.0 10.0 15.0 Time (seconds) light curve
E 1053 erg grav ≈ E 8 1049 erg rad ≈ × E 1051 erg = 1 Bethe kin ≈ Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Presupernova Star
Star has an onion like structure. Iron is the final product of the different burning processes. As the mass of the iron core
56 86 9 40 Fe Kr 107 127 24 Ca Ag I grows it becomes unstable and Mg 174Yb 16 208Pb 8 O 238U 12C collapses when it reaches 7 4He 6 around 1.4 M . 6Li 5 A
/ b
E 4 3 3He 2 1 2H 0 1H 0 50 100 150 200 250 A Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Schematical Evolution
ν Progenitor (~ 15 M ) M M ν (Lifetime: 1 ~ 2 107 y) ν ν− Sphere M M H O/Si Hot 13 Fe ν Extended Mantle ~10 cm Dense He 7 10 cm Core ν ν Early ν ν "Protoneutron" ~0.1−1 Sec. Star M 6 Dense 10 cm ν Core ν ν ν Late Protoneutron Star (R ~ 20 km) Shock
Supernova ν 3 10 8 cm e ~1 Sec. ν Collapse of e + p n + e and Core (~1.5 M ) Photodisintegration of Fe Nuclei "White Dwarf" 30000 − 60000 km/s ν e (Fe−Core) (R ~ 10000 km) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Early iron core
The core is made of heavy nuclei (iron-mass range A = 45–65) and electrons. Composition given by Nuclear Statistical Equilibrium. There are Ye electrons per nucleon.
The mass of the core Mc is determined by the nucleons. There is no nuclear energy generation which adds to the pressure. Thus, the pressure is mainly due to the degenerate electrons, with a small correction from the electrostatic interaction between electrons and nuclei. 2 As long as Mc < Mch = 1.44(2Ye) M (plus slight corrections for finite temperature), the core can be stabilized by the degeneracy pressure of the electrons. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Onset of collapse
There are two processes that make the situation unstable: 1 Silicon burning is continuing in a shell around the iron core. This adds mass to the iron core increasing Mc. 2 Electrons can be captured by protons (free or in nuclei):
e− + A(Z, N) A(Z 1, N + 1) + νe. → − This reduces the pressure and keep the core cold, as the neutrinos leave. The net effect is a reduction of Ye and consequently of the Chandrasekhar mass (Mch) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Nuclear Statistical Equilibrium
At high temperatures compositium can be aproximated by Nuclear Statistical Equilibrium. Compositium is given by a minimum of the Free Energy: F = U TS . Under the constrains of conservation of number of − nucleons and charge neutrality. It is assumed that all nuclear reactions operate in a time scale much shorter than any other timescale in the system. Nuclear Statistical Equilibrium favors free nucleons at high temperatures and iron group nuclei at low temperatures. Production of nuclei heavier than iron requires that nuclear statistical equilibrium breaks at some point. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Nuclear Statistical Equilibrium
The minimum of the free energy is obtained when:
µ(Z, A) = (A Z)µn + Zµp − implies that there is an equilibrium between the processes responsible for the creation and destruction of nuclei:
A(Z, N) Zp + Nn + γ
Processes mediated by the strong and electromagnetic interactions proceed in a time scale much sorter than any other evolutionary time scale of the system. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Nuclear abundances in NSE
Nuclei follow Boltzmann statistics:
2 !3/2 2 n(Z, A) 2π~ µ(Z, A) = m(Z, A)c + kT ln GZ,A(T) m(Z, A)kT
with GZ,A(T) the partition function:
X π Ei(Z,A)/kT G (T) = (2J + 1)e− exp(akT)(a A/9MeV) Z,A i 6akT i ≈ ∼ Results in Saha equation:
3/2 !A 1 2 !3(A 1)/2 GZ,A(T)A ρ − Z A Z 2π~ − B(Z,A)/kT Y(Z, A) = A Yp Yn − e 2 mu mukT
Composition depends on two parameters: Yp, Yn. They are determined from the conditions: P i YiAi = 1 (conservation number nucleons) P i YiZi = Ye (charge neutrality) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Composition
T= 9.01 GK, l= 6.80e+09 g/cm3, Y =.0.433 45 e
40
35
30
25
20
15 Z (Proton Number)
10 Log (Mass Fraction)
5 ï5 ï4 ï3 ï2 0 0 10 20 30 40 50 60 70 80 90 N (Neutron Number)
T= 17.84 GK, l= 3.39e+11 g/cm3, Y =.0.379 45 e
40
35
30
25
20
15 Z (Proton Number)
10 Log (Mass Fraction)
5 ï5 ï4 ï3 ï2 0 0 10 20 30 40 50 60 70 80 90 N (Neutron Number) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Composition
log X 0 9 •3 50 T = 9.01 GK, ρ = 6.80 × 10 g cm , Ye = 0.433 •1
40 •2
•3 30 •4
20 •5 Proton number •6 10 •7
0 •8 0 10 20 30 40 50 60 70 80 Neutron number log X 0 11 •3 50 T = 17.84 GK, ρ = 3.39 × 10 g cm , Ye = 0.379 •1
40 •2
•3 30 •4
20 •5 Proton number •6 10 •7
0 •8 0 10 20 30 40 50 60 70 80 Neutron number Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Initial conditions
The dominant contribution to the pressure comes from the electrons. They are degenerate and relativistic:
P neµe = neεF ≈
µe is the chemical potential, fermi energy, of the electrons:
1/3 ρYe µe 1.11(ρ7Ye) MeV, = ne ≈ mu
7 3 For ρ7 = 1 (ρ = 10 g cm− ) the chemical potential is 1 MeV, reaching the nuclear energy scale. At this point is energetically favorable to capture electrons by nuclei. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements How to determine the evolution
Composition determined by NSE, function of temperature, density and Ye.
Weak interactions are not in equilibrium (µe + µp , µn + µν). Change of Ye has to be computed explicitly: X Ye = YiZi i
X i X i Y˙e = λ Yi + λ Yi ec β− − i i Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Presupernova evolution
T = 0.1–0.8 MeV, 7 10 3 ρ = 10 –10 g cm− . R [km] Initial Phase of Collapse (t ~ 0) Composition of iron group nuclei. R Fe ~ 3000 Important processes: ν e electron capture: e +(N, Z) (N +1, Z 1)+ν − e → − Si β− decay: ν e Fe, Ni (N, Z) (N 1, Z+1)+e− +ν¯e → − ν e Dominated by allowed transitions M(r) [M ] 0.5 1.0 ~ MCh (Fermi and Gamow-Teller) Si−burning shell Evolution decreases number of electrons (Ye) and Chandrasekar 2 mass (Mch 1.4(2Ye) M ) ≈
Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Laboratory vs. stellar electron capture
15 15 Laboratory 15 Supernova 10 10 10 5 Low−lying Strength 0 Gamow−Teller 5 5 Resonance σ τ+ electron distribution (Z,A) 0 0 (Z−1,A) (Z−1,A) (Z,A)
Capture of K-shell electrons to Capture of electrons from the high energy tail of tail of GT strength distribution. the FD distribution. Capture to states with large Parent nucleus in the ground GT matrix elements (GT resonance). Thermal state ensemble of initial states. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Beta-decay
Electron capture
Beta decay 20 15
15 10
10 E (MeV) E (MeV) 5 GT− 5 Finite T F 0 (Z,A) GT+ 0 (Z+1,A)
GT+ and GT sum rules related by Ikeda sum rule: − S S + = 3(N Z) − − − Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements GT in charge exchange reactions
GT strength could be measured in Charge-Exchange reactions: GT proved in (p, n), (3He, t). − 3 2 GT+ proved in (n, p), (t, He), (d, He).
Mathematical relationship (Ep 100 MeV/nucleon): ≥ dσ (0◦) f (Ex)B(GT) dΩdE ≈
g2 X B(GT) = A f σk tk i 2 2J + 1|h || ±|| i| i k Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Independent Particle Model
58 Independent particle model. GT+ strength in Ni measured in (n, p). 1.5 f5/2 58 p Ni (El-Kateb et al, 1994) 1/2 p FFN 3/2 f7/2 1.0 στ + ν π
f5/2 p
GT Strength 1/2 0.5 p 3/2 f5/2 p f7/2 1/2 ν π p 3/2 58 f 0.0 Ni 7/2 -2 0 2 4 6 8 10 ν π E (MeV) 58Co
The IPM allows for a single transition ( f7/2 f5/2). It does not → correctly reproduce the fragmentation of GT strength (correlations). To account for correlations, it is necessary to explicitly consider the “residual” interaction between nucleons. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Gamow-Teller strength and rates
1.0 0.5 0 56 10 56 54 51 -3 Fe FFN V 10 Fe Ni 0.8 Exp 0.4 SM -6 -1 0.6 0.3 10 10 -9 0.4 0.2 10 LMP -2 -12 FFN 10 10 0.2 0.1 ρ =10.7 ρ =4.32 -15 7 7 10 -3 0.0 0.0 10 56 55 55 59 Fe Mn Co -1 Co 0 10 0.6 10 0.4 ) -2 1 -1 10 − 10 0.4 -3 (s 10 -2 ec 10 -4 0.2 λ 10 0.2 -3 GT Strength 10 ρ -5 ρ 7=4.32 10 7=33 0.0 0.0 -4 -6 10 54 10 60 58Ni 59Co Mn Co -1 0 0.6 10 10 1.0
-2 -2 0.4 10 10 0.5 0.2 -3 -4 10 ρ 10 ρ 7=10.7 7=33 -4 -6 0.0 0.0 10 10 1 4 7 10 1 4 7 10 -2 0 2 4 6 8 10 12 -2 0 2 4 6 8 10 12 E (MeV) E (MeV) T9 T9
2 2 GF Vud i, f E F Z E B GT E2 P Ei/kT σi, f ( e) = 4 3 ( , e) i, f ( ) ν i, f (2Ji + 1)e− λec 2π~ c ve Z λec = P E /kT 1 ∞ (2J + 1)e i i, f p2 f E T E dE i i − λec = 2 3 e ( e, , µe)σi, f ( e) e π ~ Qi f Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements KVI results using (d, 2He)
−2 C. Bäumer et al. PRC 68, 031303 (2003) 10 −3 LMP ) 10 2 + 0.4 (d, He) 51V(d,2He)51Ti 10−4 ) B(GT 0.3 −1 10−5
(s 1.4 λ 1.2 −6 0.2 10 1 0.8 −7 10 0.6 0.1 0 2 4 6 8 10 10−8 0 2 4 6 8 10 T (109 K) Old (n, p) data 0.1 0.5 51V(n,p) Alford et al. (1993) 0.2 0.4 )
+ 0.3 large shell model 0.3 calculation B(GT+) 0.2 B(GT 0.4 0 1 2 3 4 5 6 7 0.1 Ex [MeV]
0 0 2 4 6 8 10
GT strength in 48Sc, 50V, 58Ni, 64Ni also measured. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Consequences weak rates
A. Heger et al., PRL 86, 1678 (2001)
8 1011 T
15 M 25 M ) 6 T 10 3 ⊙ ⊙ 10 − K) 9 4 109 (g cm T (10 2 ρ ρ ρ 108 0.50
0.48 WW LMP e
Y 0.46
0.44
10−3
) −4 1 10 LMP−EC − β − −5 LMP− (s 10 e 10−6 dt dY −7 10 10−8 106 105 104 103 102 101 100 105 104 103 102 101 100 Time till collapse (s) Time till collapse (s) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Collapse phase
R [km] Neutrino Trapping Important processes:
R (t ~ 0.1s, cδ ~10¹² g/cm³) RFe Neutrino transport ν e (Boltzmann equation):
ν + A ν + A (trapping) ν e ν + e− ν + e− (thermalization) ~ 100 Si 2 cross sections E ν Fe, Ni ν ∼ e electron capture on protons: e + p n + ν − e 0.5 M 1.0 M(r) [M ] hc electron capture on nuclei: heavy nuclei e +A(Z, N) A(Z 1, N+1)+ν Si−burning shell − − e
Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements (Un)blocking electron capture at N=40
Independent particle treatment g9/2 Unblocked g9/2 Correlations N=40 Finite T f Blocked 5/2 GT p GT f5/2 1/2 p p 1/2 3/2 p3/2 f7/2 neutrons protons f7/2 neutrons protons Core Core Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Electron capture: nuclei vs protons
Electron capture rates Energetics 106 40 105 104 103 30
) 2
1 10 − µe 1 (s 10 1H ec 0 68 20 λ 10 Ni 69 (MeV) -1 Ni 10 76 -2 Ga 10 79 Ge 10 〈Q〉 = µn−µp 10-3 89Br 10-4 1010 1011 1012 Qp − ρ (g cm 3) 0 1010 1011 1012 Abundances ρ (g cm−3) 100
10−1 Yn
Yh 10−2 P Yα Rh = i Yiλi = Yh λh 10−3 h i Abundance Rp = Ypλp, Yi = ni/n Yp 10−4
10−5 1010 1011 1012 ρ (g cm−3) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Effects Realistic calculation
With Marek, Rampp, Janka & Buras (Approx. General Relativistic model) 15 M presupernova model from A. Heger & S. Woosley
0.45 106
Bruenn 105 LMSH 0.40
) 104 0.5 −1 s11-SLMS Ylep s15-SLMS 0.35 103 0.4 s20-SLMS lep,c e
Y s25-SLMS , 50 Y ,c
e 2
Y 10 0.30 40 0.3 Ylep + 0.03
30 Ye −emission (MeV s ν 1 (MeV) E
10 〉
ν 20 0.2 9 10 11 12 13 14 15 E
〈 10 10 10 10 10 10 10 0.25 10 ρ [g/cm3] 100 Bruenn 0 Ye 10 12 14 LMSH 10 10 −310 ρc (g cm ) 0.20 10−1 1010 1011 1012 1013 1014 1010 1011 1012 1013 1014 −3 −3 ρc (g cm ) ρc (g cm ) Electron capture on nuclei dominates over capture on protons All models converge to a “norm” stellar core at the moment of shock formation. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Neutrino interactions in the collapse
Bruenn and Haxton (1991) Based on results for 56Fe
Elastic scattering: ν + A ν + A (trapping) Absorption: ν + (N, Z) e + (N 1, Z + 1) e − − ν-e scattering:
ν + e− ν + e− (thermalization) Inelastic ν-nuclei scattering:
ν + A ν + A∗ Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Neutrino trapping in supernovae
During the collapse of the core of a massive star the densities become so large that even neutrinos become dynamically trapped in the collapsing core at densities 1012 g cm 3. ∼ − The neutrino mean free path (λν = 1/nσ) can be estimated from the expression for the cross section (assume matter composed of nuclei with A = 110 Z = 40).
2 GF 2 h 2 i2 σ(Eν) = E N (1 4 sin θW )Z 4π~4c4 ν − − ρG2 1/λ = F E2N2 2.5 10 9ρ E2N2/A ν 4 ν − 12 ν 4π(~c) Amu ≈ × λν 220 m (Eν = 20 MeV) ≈ The diffusion time for a distance of 30 km is: 3L2 t = 41 ms cλν ≈ Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Importance trapping
After trapping and thermalization, neutrinos becomes degenerate. They are described by a Fermi-Dirac distribution with chemical potential µν given by the weak equilibrium condition:
µν = µe (µn µp) − − The presence of neutrinos stops electron capture processes and a sizable electron fraction survives the collapse. The inner core collapses as a homologous unit. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Homologous collapse
R [km] Neutrino Trapping
(t ~ 0.1s, cδ ~10¹² g/cm³) RFe ν e
ν e ~ 100 Si Fe, Ni ν e M(r) [M ] 0.5 Mhc 1.0 heavy nuclei Si−burning shell
After thermalization an inner homologous core forms in which the local sound velocity is larger than the infall velocity.
Matter in the outer core falls at supersonic velocities. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements
Bounce and νe burst
R [km] Bounce and Shock Formation
δ < δ (t ~ 0.11s, c ∼ 2 o) RFe ν radius of e shock
Collapse continues until central density formation becomes around twice nuclear matter Si ν ~ 10 e density. Fe, Ni ν e Sudden increase in nuclear pressure stops 0.5 1.0 M(r) [M ] the collapse and a shock wave is launched
nuclear matter
δ ( δ > ) nuclei ∼ ο Si−burning shell at the sonic point. The energy of the shock depends on the Equation of State.
ν R [km] Shock Propagation and e Burst (t ~ 0.12s) The passage of the shock dissociates RFe ν Rs ~ 100 km e nuclei into free nucleons which costs Rν
ν e 8 MeV/nucleon. Additional energy is ν position of ∼ e shock Si lost by neutrino emission produced by formation ν e Fe electron capture (ν burst). e free n, p ν Ni e Shock stalls at a distance of around 0.5 1.0 M(r) [M ] 100 km. nuclear matter nuclei Si−burning shell Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Spherical simulation Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Spherical simulation Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Spherical simulation Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Spherical simulation Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Spherical simulation Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Spherical simulation Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Spherical simulation Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Spherical simulation Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Neutrino burst
400 s11-SLMS 300
] s15-SLMS s / g r s20-SLMS e
51 200 s25-SLMS 10 [ e ν L 100
0 -10 0 10 20 50 100 150 200 t [ms]
Burst is produced when shock wave reaches regions with densities low enough to be transparent to neutrinos Burst structure does not depend on the progenitor star. Future observation by a supernova neutrino detector. Standard neutrino candles.
Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Delayed explosion mechanism: neutrino heating
Shock Stagnation and ν Heating, R [km] Explosion (t ~ 0.2s) Main processes: Rs ~ 200
ν ,ν e,µ,τ e,µ,τ νe + n p + e− + ν¯e + p n + e R ~ 100 g free n, p Si
p R ν ~ 50 ν Concept of gain radius due to Bethe. e n ν ,ν ν e,µ,τ e,µ,τ e Corresponds to the region where cooling (electron positron capture) and heating PNS 1.3gain layer 1.5 M(r) [M ] cooling layer (neutrino antineutrino absorption) are equal.
!6 kT Cooling: 143 MeV/s 2 MeV
2 2 Lνe,52νe Lν¯e,52ν¯e 110 Y + Y MeV/s Heating: 2 n 2 p r7 r7 Gravitational energy of a nucleon at 100 km: 14 MeV Energy transfer induces convection and requires multidimensional simulations. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Nucleosynthesis beyond iron
The stable nuclei beyond iron can be classified in three categories depending of their origin: s-process
Charge Number r-process p-process (γ-process)
Neutron Number Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Nucleosynthesis beyond iron
Three processes contribute to the nucleosynthesis beyond iron: s-process, r-process and p-process (γ-process).
10 2
80 1 10 s r s ] 0 70 p-drip 6 10 r 10 -1 60 -2 Z 10 50 10 -3 115 Sn 180 p n-drip -4 138 W 40 10 La Abundances [Si=10 152 10 -5 Gd 30 164 180 m Ta 10 -6 Er 40 60 80 100 120 80 100 120 140 160 180 200 N A
10 12 3 s-process: relatively low neutron densities, nn = 10 − cm− , τn > τβ 20 3 r-process: large neutron densities, nn > 10 cm− , τn < τβ. p-process: photodissociation of s-process material. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements The r-process
The r-process is responsible for the synthesis of half the nuclei with A > 60 including U, Th and maybe the super-heavies.
250 Known mass Known half−life r−process waiting point (ETFSI−Q)
100 200 98 96
94
92
90
88 Solar r abundances 86 84 188 190 186 82
80
78 184 180 182 76 178 176 74 164 166 168 170 172 174 150 72 162 70 160 N=184 68 158
66 156 154 64 152 150 62 140 142 144 146 148 1 60 138 134 136 58 130 132 0 128 10 56 54 126 124 10 −1 52 122 120 50 116 118 10 −2 48 112 114 110 46 −3 108 10 100 106 N=126 44 104 100 102 42 10 98 96 40 92 94
38 88 90 86 84 r−process path 36 82 34 80 78 32 74 76
30 72 70 28 66 68 64 26 62 N=82 28 60 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58
Main parameter determining the nucleosynthesis is the neutron-to-seed ratio ns.
A f = Ai + ns Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements r-process and metal-poor stars Cowan & Sneden, Nature 440, 1151 (2006) Stars rich in heavy r-process elements (Z > 56) and poor in iron (r-II stars, [Eu/Fe] > 1.0). 0 Robust abundance patter for Z > 56,
ε consistent with solar r-process abundance. −2 These abundance seems the result of events −4 that do not produce iron. [Qian & Wasserburg, Relative log Phys. Rept. 442, 237 (2007)] −6 Astrophysical scenario is unknown. It should −8 30 40 50 60 70 80 90 involve ejection of very neutron-rich matter. Atomic Number 0.5 (b) Sr 0 Zr translated pattern of CS 22892-052 (Sneden et al. 2003) Stars poor in heavy r-process elements but Ru -0.5 Mo with large abundances of light r-process Pd -1 ) Y Z
elements (Sr, Y, Zr) (
ε -1.5 Nb log Production of light and heavy r-process -2 Ag elements seems to be decoupled. -2.5 Possible astrophysical scenario: -3 HD 122563 (Honda et al. 2006) Eu -3.5 40 50 60 70 80 neutrino-driven wind in core-collapse Atomic Number (Z) supernova Honda et al, ApJ 643, 1180 (2006) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Evolution composition: assuming NSE
Adiabatic expansion from high temperatures:
6 3 s = 50, T = 10 GK, ρ = 8.47 10 g cm− , Ye = 0.48 × log Y 50 0 •2 40 •4 •6 30 •8 •10 20 •12 Proton number •14 10 •16 •18 0 •20 0 10 20 30 40 50 60 Neutron number Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Evolution composition: assuming NSE
Adiabatic expansion from high temperatures:
6 3 s = 50, T = 8 GK, ρ = 3.78 10 g cm− , Ye = 0.48 × log Y 50 0 •2 40 •4 •6 30 •8 •10 20 •12 Proton number •14 10 •16 •18 0 •20 0 10 20 30 40 50 60 Neutron number Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Evolution composition: assuming NSE
Adiabatic expansion from high temperatures:
6 3 s = 50, T = 6 GK, ρ = 1.44 10 g cm− , Ye = 0.48 × log Y 50 0 •2 40 •4 •6 30 •8 •10 20 •12 Proton number •14 10 •16 •18 0 •20 0 10 20 30 40 50 60 Neutron number Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Evolution composition: assuming NSE
Adiabatic expansion from high temperatures:
5 3 s = 50, T = 4 GK, ρ = 3.76 10 g cm− , Ye = 0.48 × log Y 50 0 •2 40 •4 •6 30 •8 •10 20 •12 Proton number •14 10 •16 •18 0 •20 0 10 20 30 40 50 60 Neutron number Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Evolution composition: assuming NSE
Adiabatic expansion from high temperatures:
4 3 s = 50, T = 2 GK, ρ = 3.47 10 g cm− , Ye = 0.48 × log Y 50 0 •2 40 •4 •6 30 •8 •10 20 •12 Proton number •14 10 •16 •18 0 •20 0 10 20 30 40 50 60 Neutron number Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Impact of light nuclei Nuclei with A = 5 and A = 8 are not stable.
Nuclei heavier than A = 7 can only be produced by 3-body reactions: 3 4He 12C + γ → 2 4He + n 9Be + γ → suppressed due to low densities (Probability ρ2) and high temperatures (destruction ρT 3). ∼ ∼ Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements α-rich freeze out
Previous discussion assumes that nuclear reactions responsible for the build up of heavy nuclei proceed faster than the expansion timescale. It needs to be compared with the timescale for destruction of alpha particles by the 3α reaction:
1 1 dY ρ2 α Y2 = = 2 α ααα τα Yα dt 2mu h i
2 11 6 2 1 5 3 T = 6 GK, ααα /m = 7.6 10− cm g− s− , ρY = 2.5 10 g cm− h i u × α × τα = 0.4s
For faster expansions build up of heavy nuclei is suppressed leaving substantial amounts of free protons or neutrons. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements
Sensitivity to entropy and Ye
s 7 photon-to-baryon ratio (B. S. Meyer, Phys. Rept. 227, 257 (1993)) γ ∼ Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements
Contours constant Qα
α separation energies determine the heaviest nuclei that are build before α-rich freeze out.
From Woosley & Hoffman, Astrophys. J. 395, 202 (1992). Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Evolution Abundances
t/τdyn Calculation assuming: s = 250 k, Ye = 0.4, τdyn = 8 ms, T(t) = T0e−
100 3 2 10−1 1 0 −2 10 ) −1
seed −2 Y
−3 /
10 n
Y −3
Abundance −4 10−4 log( neutrons −5 10−5 alpha −6 heavy −7 10−6 −8 10 9 8 7 6 5 4 3 2 1 0 0.001 0.01 0.1 1 10 Temperature (GK) Time (s) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Evolution Abundances
100 3 2 10−1 1 0 −2 10 ) −1
seed −2 Y
−3 /
10 n
Y −3
Abundance −4 10−4 log( neutrons −5 10−5 alpha −6 heavy −7 10−6 −8 10 9 8 7 6 5 4 3 2 1 0 0.001 0.01 0.1 1 10 Temperature (GK) Time (s) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Neutron to seed in adiabatic expansions
1 10 20 50 100 150 250
0.48 0.48
0.46 0.46
0.44 0.44
ce
0.42 0.42
0.4 0.4
bundan
A 0.38 0.38
n
ro 0.36 0.36
ct
e 0.34 0.34
El
0.32 0.32
0.3 0.3
100 200 300 0 1 2 Entropy (linear scale) Entropy (log scale)
IG Y Y S Y F . 9.È n/ seed in a contour plot as a function of initial entropy and e for an expansion timescale of 0.05 s as expected from SNe II conditions
From Freiburghaus et al., Astrophys. J. 516, 381 (1999) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Neutron to seed in adiabatic expansions
3 3 t/τdyn ns s /(Y τdyn), T(t) = T0e− ∼ e
0.5
τ dyn = 0.0039 s 0.039 s 0.195 s
0.4 e Y
0.3
0.2 0 100 200 300 400 500 600 S
Combinations Ye, s, and τdyn necessary for producing the A = 195 peak. From Y.-Z. Qian, Prog. Part. Nucl. Phys. 50, 153 (2003) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Nuclear physics needs
Fission rates and distributions: • n-induced • spontaneous E-delayed n-emission • E-delayed branchings (final abundances)
E-decay half-lives (abundance and process speed) n-capture rates • for A>130 in slow freezeout • for A<130 maybe in a “weak” r-process ?
Q-physics ? Seed production rates (DDD,DDn, D2n, ..) Masses (Sn) (location of the path) figure from H. Schatz Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Classical r-process, (n, γ) (γ, n) equilibrium
Need: • mix of suitable heavy seed nuclei (A=56-90) and neutrons • sufficient large number density of neutrons (max at least ~1e24 cm-3) • sufficient large neutron/seed ratio (at least ~100)
Temperature: ~1-2 GK Density: 300 g/cm3 (~60% neutrons !) neutron capture timescale: ~ 0.2 µs
r
e Rapid neutron
b
m capture β-decay
u
n
n
o
t
o Seed
r
P Equilibrium favors (γ,n) photodisintegration “waiting point” Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements (n, γ) (γ, n) equilibrium
If the r-process occurs in (n, γ) (γ, n) equilibrium:
µ(Z, A + 1) = µ(Z, A) + µn
2 !3/2 !3/2 " # Y(Z, A + 1) 2π~ A + 1 G(Z, A + 1) S n(Z, A + 1) = nn exp Y(Z, A) mukT A 2G(Z, A) kT The maximum of the abundance defines the r-process path: ! T 3 S 0(MeV) = 9 34.075 log n + log T n 5.04 − n 2 9
21 3 For n = 5 10 cm− and T = 1.3 GK corresponds at S = 3.23 MeV, n × n S 2n = 6.46 MeV Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Dynamical r-process calculations
Dynamical calculations show that the r-process can occur under two different regimes with quite different demands from nuclear physics. [A. Arcones, GMP, Phys. Rev. C 83, 045809 (2011)] High temperature “hot” r-process [classical (n, γ) (γ, n) equilibrium]
Low temperature “cold” r-process [competition between (n, γ) and β−, Blake & Schramm, ApJ 209, 846 (1976)]
unmodified 4 2.0 10 Trs =1GK 3 no Rrs 10 K] ]
9 2 1.5 3
10 10 cm 1 10 1.0 0 10 -1 density [g/ density 10 unmodified temperature[ 0.5 -2 Trs =1GK 10 no Rrs -3 0.0 -2 -1 0 10 -2 -1 0 10 10 10 10 10 10 time [s] time [s] Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements hot vs. cold r-process Hot r-process Cold r-process
3 3 10 10 photodissiociation
1 1 10 10
-1 beta decay -1 10 10 beta decay
-3 -3 time scale [s] 10 time scale [s] 10 photodissociation neutron capture -5 -5 10 neutron capture 10 -7 -7 10 -2 -1 0 10 -2 -1 0 10 10 10 10 10 10 time [s] time [s]
-4 -4 10 10
-5 -5 10 10
-6 -6 10 10
abundance -7 -7 abundance 10 10
-8 -8 10 FRDM 10 FRDM ETFSI-Q ETFSI-Q HFB-14 HFB-14 Duflo Zuker Duflo Zuker -9 -9 10 120 130 140 150 160 170 180 190 200 210 10 120 130 140 150 160 170 180 190 200 210 A A Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Why such a large differences?
Currently available mass models show big differences in the predicted masses before and after the neutron shell closures, where one expects transitions from deformed to spherical nuclei.
FRDM 12 ETFSI−Q Data FAIR reach 10−4 8 Impact on abundances (MeV) r•process region 2n −5 S Cd (Z=48) Isotopes 10 4
10−6 0 125 130 135 140 145 150 155 160 Mass Number −7 16 10 FAIR reach Abundance
12 −8 Solar Abundances 10 FRDM
r•process region ETFSI−Q 8 (MeV)
2n −9 S Er (Z=68) Isotopes 10 110 120 130 140 150 160 170 180 190 200 210 4 FRDM ETFSI−Q Mass Number Data 0 160 165 170 175 180 185 190 195 200 205 Mass Number (A. Arcones & GMP, Phys. Rev. C 83, 045809 (2011)) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements FAIR: a new era in our understanding of the r-process
the FAIR reach for nuclear masses.
82
masses measured at the FRS-ESR
65 r-process 126 path
58
50 rp-process path Will be measured with 82 SUPER-FRS-CR-NESR
28
stable nuclei 20 50
8 nuclides with 28 known masses 20 8 Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Neutrino emission from the proto-neutron star Neutrino detection from SN1987A 50.0 ν , ν− , ν , ν − µ µ τ τ − Kamiokande II νe 40.0 IMB νe 30.0 20.0 Energy (MeV) 10.0 T ~ 1/R 0.0 0.0 5.0 10.0 15.0 Time (seconds) Gravitational binding energy: E GM2/R 1053 erg. grav ≈ ∼ Neutrino emission lasts around 10 s with energies Eν 10 MeV. ∼ Enormous neutrino fluxes around the neutron star surface: 43 2 1 Φν = 10 cm− s− at 20 km. Gravitational binding energy nucleon 100 MeV. ∼ With Eν 10 MeV the typical neutrino-nucleon cross section is 41 ∼2 10− cm− . This results in interaction times of 10 ms. Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Influence of neutrinos on nucleosynthesis
Main processes:
νe + n p + e− Early times (up to 1-2 seconds): ν¯ + p → n + e+ e → proton-rich ejecta (νp-process). Neutrino interactions determine the proton Later times: to neutron ratio, the ejecta are proton rich if: neutron-rich ejecta (r-process)?? < 4(m c2 m c2) 5.2MeV ν¯e − νe n − p ≈ 20 Marek & Janka, ApJ 694, 664 (2009) 18 ] V
e 16 M
[ 2.5 MeV 14 gy r e
n 12 e e
g 10 a r ν e e
v 8 a ν¯e 6 νµ ,ντ 0 200 400 600 time [ms] Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Long term evolution neutrino luminosities and average energies
Long-term simulations of the collapse and explosion of an 8.8 M ONeMg core,
0 4 10 L/10 Accretion Phase Cooling Phase ν ] e -1 3 νe νµ/τ -1 erg s 2 10 52 1 L [10 -2 0 10
12 10 > [MeV]
ε 10 <
8 5 0 0.05 0.1 0.15 0.2 2 4 6 8 Time after bounce [s] Hüdepohl et al., PRL 104, 251101 (2010)
Fischer et al, A&A 517, A80 (2010) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Neutrino driven wind
Neutrino cooling and Neutrino-driven wind At T = 10 GK starts the formation 105 of α-particles (4He).
ν , ν Between T = 8 GK and T = 3 GK, 104 e,µ,τ e,µ,τ
the formation of seeds occurs. m in k Dominating reactions are: R Ni 103 12 3α C + γ Si (proton-rich ejecta) 9 He 2α + n Be + γ 102 νp-process 9 12 ν , –ν Be + α C + n r-process O e,µ,τ e,µ,τ R (neutron-rich→ ejecta). ns ~10
Rν At lower temperatures proton PNS 1.4 α, p α, p, nuclei 3 M(r) in M (νp-process) or neutron (r-process) n, p α, n α, n, nuclei captures take place. GMP, Physik Journal 7, 51 (2008) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements Impact of neutrino interactions on proton-rich ejecta
Once neutrino interactions are consistently included in the nucleosynthesis network, nuclei with A > 64 are produced.
104 Without ν With ν 103 ⊙ i, 2
/Y 10 i Y
101
100 40 45 50 55 60 65 70 75 80 85 90 95 100 Mass Number A Antineutrino absorption and expansion time scales are similar ( 1 s) ∼ Neutrinos speed-up the matter flow + ν¯e + p e + n n + 64Ge→ 64Ga + p 64Ga + p → 65Ge ... → These reactions constitute the νp-process C. Fröhlich, et al., PRL 96, 142502 (2006)
Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements The νp-process
Without neutrino interactions proton-rich ejecta form N = Z iron-group nuclei with A < 64. 65As However, nucleosynthesis occurs at the presence of substantial (p, γ ) S = −90(85) keV neutrino fluxes. p
64Ge β+ 63.7 s
64Ga Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements The νp-process
Without neutrino interactions proton-rich ejecta form N = Z iron-group nuclei with A < 64. 65As 66As However, nucleosynthesis occurs at the presence of substantial (p, γ ) neutrino fluxes. Antineutrino absorption and 64 65 expansion time scales are similar Ge Ge ( 1 s) ∼ ()n,p (p, γ ) Neutrinos speed-up the matter flow ~ 10 ms + ν¯e + p e + n n + 64Ge→ 64Ga + p 64Ga 64Ga + p → 65Ge ... → These reactions constitute the νp-process C. Fröhlich, et al., PRL 96, 142502 (2006) Introduction Astrophysical reaction rates Hydrostatic Burning Phases Core-collapse supernova Nucleosynthesis heavy elements The νp-process
Without neutrino interactions proton-rich ejecta form N = Z iron-group nuclei with A < 64. However, nucleosynthesis occurs at the presence of substantial neutrino fluxes.
Antineutrino absorption and 102 Sr Ru Kr expansion time scales are similar Mo Se Pd ( 1 s) 1
) 10 ⊙
∼ i,
X Zr
ej Ge Br Nb Neutrinos speed-up the matter flow Zn Ga Rb Cd
/(M As + i Y ν¯e + p e + n M 0 10 Cu n + 64Ge→ 64Ga + p 64Ga + p → 65Ge ... Rh 10−1 → 60 70 80 90 100 110 120 These reactions constitute the νp-process Mass number A C. Fröhlich, et al., PRL 96, 142502 (2006) Trajectories from supernova simulation (Janka)