r-process nucleosynthesis: conditions, sites, and heating rates

Transcription

1 r-process nucleosynthesis: conditions, sites, and heating rates Technische Universität Darmstadt August 14, 17

2 The (solar) r-process abundance pattern abundance proton number mass number N = 5 N = 8 N = neutron number log 1(T 1/ [s]) Uncertainties for r-process calculations: nuclear properties neutron capture cross sections β-decay rates fission rates & fragment distribution hydrodyn. conditions np n p+n n Y e = temperatures and densities expansion timescales

3 basic equations Ẏ i = j Ni j λ jy j + j,k N i j,k 1+δ jk ρn A σv j;k Y jy k + N i j,k,l j,k,l 1+ jkl ρ NA σv j;k;l Y jy k Y l nuclear statistical equilibrium: µ(z, N) = Z µ p + N µ n A 1 A3/ Y (Z, N) = G Z,N (ρn A ) i AiYi = 1 ZiYi = Ye i ( π A m ukt ) 3 (A 1) ( ) BZ,N exp Y N kt n Yp Z

4 (n, γ) (γ, n) equilibrium Y (Z,A+1) Y (Z,A) = σv n,γ (Z,A) G(Z,A+1) nn = λγ,n(z,a+1) G(Z,A) ( A+1 ) 3/ ( π ) 3/ A mu kt nn exp[s n(z, A + 1)/kT ] λ γ,n(z, A + 1) = ( G(Z,A) A ) 3/ ( mu kt ) 3/ G(Z,A+1) A+1 σv n,γ(z, π A) exp[ S n(z, A + 1)/kT ] Pb (Z=8) proton number, Z Yeq/Ycalc neutron number, N

5 Hot and cold r-process first defined by Wanajo (7) log( n n ) 5 original β-decays.5 β-decays temperature [GK] time [s] 1 Petermann et al. (1) Eichler et al. (15) tidal ejecta are a hot r-process scenario if nuclear heating is taken into account

6 Late-time heating from radioactive decays Hotokezaka et al. (16) Barnes et al. (16) see also Metzger (14), Lippuner & Roberts (15), Fernandez & Metzger (16), Rosswog et al. (17), Wollaeger et al. (17)

7 Survival timescales of heavy nuclei Möller et al. (3): proton number, Z proton number, Z neutron number, N Marketin et al. (15): neutron number, N log1 (min(t 1/ (α), T 1/ (β)) [s]) log1 (min(t 1/ (α), T 1/ (β)) [s])

8 Fission powering kilonova/macronova light curves experimentally known SF rates with 1 d < T 1/ < weeks proton number, Z neutron number, N log1 (min(t 1/ (α), T 1/ (β)) [s])

9 Phenomenological spontaneous fission rates proton number, Z Petermann et al. (1) log(t 1/ )[s] = 8.8B f neutron number, N ( log(t 1/ )[s] = Z A Z A proton number, Z Zagrebaev et al. (11) ) (.1 Z A neutron number, N log1 (min(t 1/ (α), T 1/ (β)) [s]) ) 3 + ( Z A )B f + C(Z, A) log1 (min(t 1/ (α), T 1/ (β)) [s])

10 Phenomenological spontaneous fission rates Based on ETFSI barriers (sets from I. Panov) log(t 1/ )[s] = 7.77B f 33.3 proton number, Z proton number, Z neutron number, N log(t 1/ )[s] = 1.145B f neutron number, N log1 (min(t 1/ (α), T 1/ (β)) [s]) log1 (min(t 1/ (α), T 1/ (β)) [s])

11 Spontaneous fission rates Based on BCPM EDF (Giuliani et al. 17) proton number, Z neutron number, N log1 (min(t 1/ (α), T 1/ (β)) [s])

12 Spontaneous fission rates proton number, Z Based on BCPM EDF (Giuliani et al. 17) neutron number, N based on these models very unlikely that spontaneous fission occurs on timescales between 1 day and weeks log1 (min(t 1/ (α), T 1/ (β)) [s])

13 from Meng-Ru s presentation (1.8.17)

14 MHD supernovae Winteler et al. (1)

15 Other models Nishimura et al. (17) see also Takiwaki et al. (9) Mösta et al. (14)

16 MHD supernovae in GCE Wehmeyer et al. (15)

17 Is there a demand for a reduced r-process network for hydro simulations?

18 Analytic formula for nuclear heating Korobkin et al. (1) Barnes et al. (16): f tot(t) =.36 only valid for FRDM! [ ] exp( at) + ln(1+btd ) bt d

19 Starting point: waiting point approximation Z + 1 Z Z 1 S crit n Ẏ (Z) = λ β (Z 1, N Z 1 )Y (Z 1) λ β (Z, N Z )Y (Z) Y (Z,A+1) Y (Z,A) S crit n = G(Z,A+1) G(Z,A) = kt ln [ ( A+1 ) 3/ ( π A n n G(Z,N+1) G(Z,N) ( A+1 A mu kt ) 3/ nn exp[s n(z, A + 1)/kT ] = 1 π mu kt ) 3/ ] ; S n(z, N Z ) > S crit n > S n(z, N Z + 1)

20 Decay to stability (first) idea: look at isobars and distribute nuclei into bins according to their β-decay timescales τ β < 1s 1 s < τ β < 1 1 s 1 1 s < τ β < 1 s 1 s < τ β < 1 3 s abundances of isobars stay constant for β-decays with P n =