1. Hydrodynamical simulation of detonations in superbursts. Noël Claire (I.A.A., U.L.B.) Thesis advisors : M. Arnould (I.A.A., U.L.B.) Y. Busegnies (I.A.A., U.L.B.) In collaboration with : M. Papalexandris (U.C.L.) V. Deledicque (U.C.L.) A. El messoudi (I.A.A., U.L.B.) P. Vidal (L.C.D., Poitiers) S. Goriely (I.A.A., U.L.B.) UNIVERSITE LIBRE DE BRUXELLES

2. Observational properties of X-ray bursts and superbursts X-ray burst Superburst L max  10 38 ergs s -1 E tot  10 39 ergs t burst  10s – several min t rec  5min - days L max  10 38 ergs s -1 E tot  10 42 ergs t burst  several min – several hours t rec  years Lewin & al., Space Sci. Rev., 62, 223, 1993 Kuulkers, NuPhS, 132, 466, 2004 40 s 2.7 h 2/12

3. Thermonuclear model of X-ray burst Accretion HeH/He CFe C (X < 0.1) + heavy ashes above Fe stableunstable rp-process Strohmayer, Brown, ApJ, 566, 1045, 2002 Schatz & al., Nuclear physics A, 718, 247, 2003 3/12

4. N.S. C / Ru He / H N.S. C/Fe He or Thermonuclear model of superburst Thermally unstable ignition of 12 C at densities of about 10 8 – 10 9 g cm -3 N.S. Crust 100 m 10 m C/Fe/Ru H/He burning Atmosphere Accretion stream ~ 10 5 g cm -3 ~ 10 9 g cm -3 4/12

5. All previous studies of superbursts are 1D, they correctly reproduce the total energy, peak luminosity, recurrence time, and duration of the superburst. But superbursts are multi-D phenomena !!! - Accretion - Accretion is not uniform on the surface -Ignition -Ignition conditions not reached at the same time everywhere Importance of the study of the propagation of the combustion Spitkovsky & al., ApJ, 566, 1018, 2002 Moreover the propagation phase has never been studied, even in 1D detonation Weinberg & al. (ApJ Letters, 650, 119, 2006) suggest that the way of propagation of the combustion in superburst phenomena is a detonation. 5/12

6. A new finite volume method, parallelised algorithm for modeling astrophysical detonations. A new finite volume method, parallelised algorithm for modeling astrophysical detonations. (Noël & al., A&A, 470, 653, 2007) Finite volume method - Finite volume method algorithm (MUSCL type) Unsplit dimentionally - Unsplit dimentionally Time-splitting - Time-splitting is included to be able to solve the very stiff nuclear network equations (Strang J., SIAM J. Num. Anal. 5, 506, 1968). - Parallel code - Parallel code (mpi) The equations: 2 dimentional euler equations with a general astrophysical equation of state and a 13 species nuclear reaction network. 6/12

7. - Astrophysical equation of state (tabulated): ions + radiation + electrons partially degenerate and partially relativistic + electrons/positrons pairs We had to write an adapted Riemann solver based on Colella, Glaz, JCP,59,264,1985. The E.O.S. is not a gamma law - Nuclear reaction network: 13 species ( 4 He, 12 C, 16 O,…, 56 Ni) nuclear reaction network : 11 (  ) reactions from 12 C  16 O to 52 Fe  56 Ni, the corresponding 11 photodesintegration reactions, 3 heavy-ions reactions : 12 C( 12 C,  20 Ne, 12 C( 16 O,  24 Mg and 16 O( 16 O,  28 Si, and the triple alpha-reaction and its inverse. - Test case : Reactive shock tube LR Comparaison with (Fryxell, Muller, Arnett, MPA 449,1989) LR  (g cm -3 ) 2.5 10 9 10 9 T (K)8 10 9 8 10 7 V (cm s -1 )5 10 8 0 NiC P (g s -2 cm -1 ) 7/12

8. Detonation in pure 12 C at T = 10 8 K and  = 10 8 g cm -3 1D steady-state calculations (ZND model) are made by A. El Messoudi - characteristic time-scales of the detonation - characteristic length-scales of the detonation - reaction-zone structure - set the initial parameters and boundary conditions in the time-dependent calculations - allow to compare 1D time-dependent results with the steady-state solution LR  (g cm -3 ) 3.01 10 8 10 8 T (K)4.46 10 9 10 8 V (cm s -1 )8.07 10 8 0 NiC Mass fractions 8/12

9. Temperature (in K), velocity (in cm s -1 ), density (in g cm -3 ) and pressure (in erg cm -3 ) profiles of a detonation front in pure 12 C at T =10 8 K and  = 10 8 g cm -3 at time = 5 10 -6 s. X is in cm. Nuclear energy generation (erg g -1 s -1 ) profile + same simulation in a mixture C/Fe: X C =0.3 X Fe =0.7 Temperature Velocity Density Pressure Energy generation 9/12

10. Detonation in a mixture 12 C/ 96 Ru (X C =0.1; X Ru =0.9) at T = 10 8 K and  = 10 8 g cm -3 Nuclear reaction network extension: 9 species ( 64 Ni, 68 Zn,…, 96 Ru) and 16 nuclear reactions are added : 8 (  ) and the corresponding 8  reactions. Effective rates are introduced in order to reproduce the energy production of a reference network of 14758 reactions on 1381 nuclides. Energy generation Temperature Density (  ) and  rates: Nuclear energy generation (erg g -1 s -1 ), temperature (K), density (g cm -3 ) and mass fractions profiles. Z is the distance to the shock in cm. Energy production (erg g -1 ) 10/12

11. Energy generation Temperature Density Nuclear energy generation (erg g -1 s -1 ), temperature (K), density (g cm -3 ) and mass fractions profiles. Z is the distance to the shock in cm. Full network calculation + same simulation in a mixture : X C =0.2 X Ru =0.8 Effective (  ) and  rates: 11/12

12. Conclusions -We have developed a multi-D algorithm able to study astrophysical detonations with a nuclear reaction network and an astrophysical equation of state. - Our algorithm is robust to test cases. - We have been able to simulate a detonation in conditions representative of superbursts in pure He accretors and in mixed H/He accretors. - We have constructed a new reduced nuclear reaction network. - Multi-D simulations are in progress. 12/12

13. Perspectives - 1D simulation of the propagation of the detonation in inhomogeneous medium -Multi-D simulations Pure He detonation which goes through an Fe buffer Collision of two C detonations Temperature He C Si Fe Ni X X He C S Fe Ni 12/13

14. Detonation on the neutron star surface Weinberg & al. (ApJ Letters, 650, 119, 2006) suggest that the way of propagation of the combustion in superburst phenomena is a detonationmulti-D detonation. Detonations are intrinsically multi-D phenomena. burned gas Reaction zone shock Desbordes LCD-CNRS Small perturbations disturb the detonation front. The planar front is replaced by incident shocks, transverse waves, and triple points. cellular pattern These high-pressure points trajectories give rise to the cellular pattern. P. Vidal (LCD, Poitiers) 6/14

15. Detonation in a mixture 12 C/ 96 Ru at T = 10 8 K and  = 10 8 g cm -3 Nuclear reaction network extension: 68 Zn(  ) 64 Ni 64 Ni(  ) 68 Zn 72 Ge(  ) 68 Zn 68 Zn(  ) 72 Ge 76 Se(  ) 72 Ge 72 Ge(  ) 76 Se 80 Kr(  ) 76 Se 76 Se(  ) 80 Kr 84 Sr(  ) 80 Kr 80 Kr(  ) 84 Sr 88 Zr(  ) 84 Sr 84 Sr(  ) 88 Zr 92 Mo(  ) 88 Zr 88 Zr(  ) 92 Mo 96 Ru(  ) 92 Mo 92 Mo(  ) 96 Ru full network : 14758 reactions, 1381 nuclides net0 : 0 net1 : 0 + 1 + 6 rmax(64Ni-96Ru) : 0 + 1 + 6 + 0 + 1 + 6 rmax(16O-96Ru) : 0 + 1 + 6 + 0 + 1 + 6 Reverse rates are estimated making use of the reciprocity theorem.

16. Hydra : the new Scientific Computer Configuration at the VUB/ULB Computing Centre HP XC Cluster Platform 4000, composed of 32 nodes Nodes HP Proliant DL585, each composed of - 4 CPUs AMD Opteron dual-core @ 2.4 GHz - 32 GB RAM - 73 GB hard drive

17. Same simulation in a mixture C/Fe: X C =0.3 X Fe =0.7 Pure C : D = 1.3 10 9 cm s -1, produces mainly He C/Fe : D = 1.21 10 9 cm s -1, produces mainly Ni