Urca processes in stellar degenerate cores Dag Fahlin Strömberg Structure and Reactions for Nuclear Astrophysics 22-24 November 2017 IPHC, Strasbourg December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 1 The fate of stars Heiko Möller, PhD Thesis (2017) December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 2 Degenerate ONe cores 16 20 23 24 25 I Main content after carbon burning: O, Ne, Na, Mg and Mg. I Mainly supported by degeneracy pressure 1=3 I Electron Fermi energy EF ∼ ρ increases when the core contracts I Electron capture (EC) when EF is larger than the Q value I This corresponds to a specific density threshold ρ I Thresholds (Arnett, Supernovae and Nucleosynthesis): −3 Nucleus EF [MeV] 2Yeρ [g · cm ] 25Mg 3.833 1.17 × 109 23Na 4.374 1.67 × 109 24Mg 5.513 3.16 × 109 20Ne 7.026 6.20 × 109 16O 10.42 1.90 × 1010 December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 3 Urca and double electron capture processes Heiko Möller, PhD Thesis (2017) December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 4 Urca cooling in acreeting ONe white dwarfs I We study the evolution of acreeting ONe white dwarfs up to oxygen ignition I Conditions at ignition important for final outcome 20 24 I Heating from double electron capture: Ne and Mg 25 25 23 23 25 25 I Schwab et al. (2017): Urca pairs Mg & Na, Na & Ne and Na & Ne I This was also studied in Heiko Möller’s PhD thesis I Both used the MESA (Modules for Experiments in Stellar Astrophysics) stellar evolution code December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 5 Urca cooling in acreeting ONe WD Schwab et. al, 2017. December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 6 Unexplored: Effect of metallicity in ONe cores I Non-zero metallicity in the progenitor =) additional nuclei in ONe core I Piersant et al. (2017): I Studied effects of initial metallicity on SNe Ia (i.e. acreeting CO white dwarfs) I Included EC processes on the corresponding nuclei I Simulation: increased density and neutronization at thermal runaway I Thus: metallicity affects light curve of SNe Ia I But the effects of metallicity in ONe cores remain unexplored I This is what we are currently investigating, i.e. including EC procceses on additional nuclei from initial metallicity December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 7 Nuclei considered in Piersanti et al. December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 8 Additional nuclei for ONe cores I Nuclei above should also matter for ONe cores I But: Oxygen ignites at higher densities than carbon I Consequently: EC on larger set of nuclei prior to runaway I Rough selection: Order by abundance and choose most abundant December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 9 Weak interaction rates I To include these effect we need accurate weak interaction rates I Traditional way: Tables of interaction rates, e.g. I Fuller, Fowler, and Newman (1980, 1982, 1985): sd & pf shells I Oda et al. (1994): sd shell I Langanke and Martínez-Pinedo (2001): pf shell I Suzuki et al. (2016): sd shell I Tables based on experimental data + shell model calculations I Problem: interpolation errors I Rates can quickly change several orders of magnitude I Newer tables (e.g. Suzuki et al.) have denser data points I But we still get issues at low temperatures (see Schwab et al. (2017)) December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 10 Example: The Urca pair 31P and 31Si T = 7. 0 108 K × Denser table 4 Oda et al. 6 ¢ ] 1 − s [ 8 λ ¡ g o l 10 12 7.0 7.2 7.4 7.6 7.8 8.0 3 log ρYe [g cm− ] ¡ ¢ December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 11 Alternative: Analytical determination I At these temperatures only low-lying excited states are relevant I Consequently the rates are typically determined by a few transitions I This means that we can compute the rates during the simulation I Phase space integrals can be approximated as an analytical expression (see Fuller, Fowler, and Newman (1985)) I This functionality has been implemented in the MESA stellar evolution code I We must identify relevant transitions December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 12 Urca pair 25Mg and 25Na: Experimental data 1/2+ 3/2+ 4.0 5/2+ 25Na 3.0 3/2+ 2.0 5/2+ 7/2+ Energy (MeV) 1.0 3/2+ 1/2+ 0.0 5/2+ 25Mg December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 13 Urca pair 25Mg and 25Na: Relevant transitions 1/2+ 3/2+ 4.0 5/2+ 25Na 3.0 3/2+ 2.0 5/2+ 7/2+ Energy (MeV) 1.0 3/2+ 1/2+ 0.0 5/2+ 25Mg December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 14 25Mg and 25Na: What is the difference? log(T/K) = 8. 6 3 4 5 ¢ ] 1 6 − s [ λ ¡ g 7 o l 8 9 Experimental data Selected transitions 10 8.5 8.6 8.7 8.8 8.9 9.0 3 log ρYe [g cm− ] ¡ ¢ December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 15 25Mg and 25Na: Are other transitions important? log(T/K) = 8. 6 3 4 5 ¢ ] 1 6 − s [ λ ¡ g 7 o l 8 9 Suzuki et al. Selected transitions 10 8.5 8.6 8.7 8.8 8.9 9.0 3 log ρYe [g cm− ] ¡ ¢ December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 16 Beta decay of 56Mn 1+ 4.0 2+ 3+ 0.111 MeV 56Mn 3.0 4+ 2.0 Energy (MeV) 1.0 2+ 0.0 0+ 56Fe December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 17 Beta decay of 56Mn log(T/K) = 8. 2 0 5 ¢ ] 1 − s [ 10 λ ¡ g o l 15 1 + 0 + → 2 + 2 + → 3 + 2 + → Total 20 8.0 8.2 8.4 8.6 8.8 9.0 3 log ρYe [g cm− ] ¡ ¢ December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 18 Forbidden transition from 20Ne 20 I Martinez-Pinedo et al. (2014): forbidden transition important for EC on Ne December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 19 Conclusions I Urca processes are important for the evolution of degenerate stellar cores I Rates are typically determined by few transitions — analytic determination of the rates I Accounting for initial composition of the star (metallicity) allows for additional EC processes that are currently being investigated 20 I Second forbidden transition from Ne still needs to be determined December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 20 Appendix X (2J + 1) exp(−E =kt) λEC = P λEC P = i i if if if P (2J + 1) exp(−E =kt) if j j j P k + EC ln 2 EC 2 h f j k σ tk j i i λif = Bif φ (qif ) Bif (GT ) = gA K 2Ji + 1 Z 1 EC 2 φ (qif ) = wp(qif + w) F(Z, w)Se(w)dw wl December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 21.