Thermo and pycnonuclear burning in accreting neutron stars

1. Thermo and pycnonuclear burning in accreting neutron stars Leandro Gasques University of Lisbon

2. Michael Wiescher The Joint Institute for Nuclear Astrophysics (JINA) University of Notre Dame, USA Mary Beard The Joint Institute for Nuclear Astrophysics (JINA) University of Notre Dame, USA Dmitry Yakovlev Ioffe Physical Technical Institute St. –Peterbursg, Russia

3. Outline • Nuclear burning regimes in dense stellar matter • Single analytical equation for all regimes • Determination of astrophysical S-factors • Accreting NSs - Superbursts • Accreting NSs – Soft X-ray Transients • Summary

4. Physical Conditions MCP stellar matter: ions (fully ionized) + electrons (uniform background)

5. Classical Thermonuclear Reactions • The reacting ions behave as an almost perfect classical gas • Coulomb interactions with all the other nuclei and e- are neglected • Reaction rate depends mainly on T

6. Thermonuclear Regime with Strong Screening • Intermediate regime of density and temperature • Most of the nuclei are bound in a Coulomb lattice structure • Reacting pair of high-energy nuclei are still free created by neighboring plasma ions • Screening potential enhances R • Multiplicative factor in R

7. Pycnonuclear Reactions (T=0) • It operates at extremely low temperatures • Thermal effects are negligible • All the ions occupy gs in their potential wells • Coulomb penetration: ZPM vibrations

8. Pycnonuclear Reactions (T>0) • The majority of nuclei still occupy gs in their potential wells • Main contribution to R comes from nuclei in excited bound states

9. Intermediate Thermopycnonuclear Regime • Slightly unbound nuclei can move freely through dense matter • Those can fuse with the closest neighbours (pycnonuclear regime) • and with other nuclei (thermonuclear regime) • This regime is difficult for theoretical studies However... If the transition from the pycno to the thermonuclear regime is smooth  the rates are properly described by our single equation

10. Single Analytical Equation Gasques et al., PRC72, 025806 (2005) – OCP & Yakovlev et al., PRC74, 035803 (2006) - MCP

11. Single Analytical Equation but... the reaction rate depends on S-factor

12. Nuclear Potential First method: systematization of the nuclear densities  appropriate for reactions between stable nuclei Two-parameter Fermi distribution (2pF) Chamon et al., PRC66, 014610 (2002), and references therein

13. Systematization of the Nuclear Densities

14. Systematization of the Nuclear Densities

15. Nuclear Potential Second method: relativistic Hartree-Bogoliubov theory  appropriate for reactions between nuclei far from stability Afanasjev et al., Phys. Rev. C60 (1999) 051303

16. Coulomb VB E RB Radial distance Nuclear Barrier Penetration Model • 1-dim: the interaction only depends on the separation of the two nuclei • Potential: Coulomb + Nuclear + Angular Momentum (Hill-Wheeler) (WKB)

17. 12C + 12C Astrophysical S-factor

18. Neutron Rich Oxygen S-factor Gasques et al., Phys. Rev. C76, 045802 (2007)

19. All the Ingredients are there Beard et al., ADNDT (2009) – to be published

20. Accreting Neutron Stars (I) Superbursts (II) Soft X-ray Transients Accreted material falls onto the NS surface and undergoes many nuclear transformations: (e- capture, neutron emission & absorption, pycnonuclear) H → He → C → heavier elements

21. X-ray Bursts & Superbursts Superbursts: powered by 12C burning deep within the accreted layer 15s ~ 3 hours y ~1013 g cm-2 (4U 1820-30) • - Energetic ~ 1042 erg (more material accumulated?) • Long ~ hours (longer radiation transport?) • Recurrence ~ years (more time to accumulate?)

22. Ignition Conditions MNS = 1.6 M☼ RNS = 10.8 km dM/dt ~ 0.3 Eddington Typical ignition NS conditions: density ~ 2 x 109 g cm-3 temperature ~ 5.5 x 108 K yign ~ 8 x 1012 g cm-2 Cumming et al.: yign ~ (0.5-3) x 1012 g cm-2 temperature profile T(y) – Gupta et al. (2007): e- capture into excited states increases heating up by up to a factor of ~10

23. 108 Mass density (g cm-3) 1013 Soft X-ray Transients Hypothesis: quiescent thermal radiation in SXRTs is powered by the deep crustal heating of accreted matter in neutron stars Nuclear transformations in the accreted matter as it sinks into the crust under the weight of newly accreted material e- capture neutron emission neutron absorption neutron-rich nuclei which undergo pycnonuclear fusion reactions Ereleased ~ 1.1–1.5 MeV per accreted nucleon heating power ~ (6.6-9.0)x1033 Mdot erg s-1 (it explains the observed thermal luminosity of SXRTs in quiescence)

24. total energy generation power depends on the mass accretion rate Soft X-ray Transients Pycnonuclear reactions: 34Ne + 34Ne→ 68Ca (Haensel & Zdunik 1990,2003) Fuel: 40Mg(40Mg + 2e → 34Ne + 6n +2νe) at ρ* = 1.45x1012 g cm-3 34Ne burning time: crucial parameter (Maximum rate) (Optimal) (Minimum rate) Fig.: one-year cycle (accretion with constant rate in the first 2 months every year, followed by 10 months of quiescence).

25. Summary • Reaction rates in the thermonuclear regime are determined with good accuracy but are much less certain in other regimes • The unified equation can be easily improved when more information about the reaction rates become available • Our simple model allows the study of carbon ignition and deep crustal heating in accreting neutron stars • Nevertheless, fits to observed superburst lightcurves suggest that the ignition typically occurs at a column depth that is smaller than our predictions • The 34Ne burning time is currently very uncertain, ranging from milliseconds to a few years • The fastest burning may change the composition of the accreted crust while the slowest burning leads to a time-independent nuclear energy generation rate for a variable accretion

26. My primary research interest is in nuclear physics... but sometimes we have to stick our nose out there and jump into the fray! Thanks !!!

27. Systematization of the Nuclear Densities

28. nucleon distribution for ρ (a = 0.50 fm) finite-range approach M3Y – Reid or Paris matter distribution for ρ (a = 0.56 fm) zero-range approach Nuclear Potential

29. 12C + 12C Nuclear Potential  folding potential at energies of astrophysical interest (no energy dependence)

30. Carbon Burning Reaction Rates

31. General Ideas about Neutron Stars • NSs are the most compact stars known in the Universe. Their masses are tipically ~ 1.4 M☼ and their radii are ~ 10 Km • NSs are born hot after violent core collapse events and cool by emmiting neutrinos from their interior and photons from their surface • Cooling mechanisms depend on uncertain properties of dense matter (e.g. superfluidy, strong interactions, exotic particles, etc)