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Home , Thermal runaway

Urca processes in stellar degenerate cores Dag Fahlin Strömberg

Structure and Reactions for Nuclear 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 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) 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 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 (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 hψf | k σ tk |ψi i λif = Bif φ (qif ) Bif (GT ) = gA K 2Ji + 1 Z ∞ EC 2 φ (qif ) = wp(qif + w) F(Z, w)Se(w)dw wl

December 18, 2017 | IKP TUD | D. Fahlin Strömberg | 21