UNIVERSITE LIBRE DE BRUXELLES Hydrodynamical simulation of detonations

UNIVERSITE LIBRE DE BRUXELLES 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. )

Observational properties of X-ray bursts and superbursts X-ray burst Superburst 40 s Lewin & al. , Space Sci. Rev. , 62, 223, 1993 2. 7 h Kuulkers, Nu. Ph. S, 132, 466, 2004 Lmax 1038 ergs s-1 Etot 1039 ergs Etot 1042 ergs tburst 10 s – several min tburst several min – several hours trec 5 min - days trec years 2/12

Thermonuclear model of X-ray burst Accretion He stable C H/He unstable Fe Strohmayer, Brown, Ap. J, 566, 1045, 2002 rp-process C (X < 0. 1) + heavy ashes above Fe Schatz & al. , Nuclear physics A, 718, 247, 2003 3/12

Thermonuclear model of superburst Thermally unstable ignition of 12 C at densities of about 108 – 109 g cm-3 He C/Fe N. S. He / H C / Ru or N. S. Accretion stream Atmosphere ~ 105 g cm-3 H/He burning 10 m C/Fe/Ru 100 m ~ 109 g cm-3 N. S. Crust 4/12

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

A new finite volume method, parallelised algorithm for modeling astrophysical detonations. (Noël & al. , A&A, 470, 653, 2007) - Finite volume method algorithm (MUSCL type) - Unsplit dimentionally - 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 (mpi) The equations: 2 dimentional euler equations with a general astrophysical equation of state and 13 species nuclear reaction network. 6/12

- Astrophysical equation of state (tabulated): ions + radiation + electrons partially degenerate and partially relativistic + electrons/positrons pairs The E. O. S. is not a gamma law We had to write an adapted Riemann solver based on Colella, Glaz, JCP, 59, 264, 1985. - Nuclear reaction network: 13 species (4 He, 12 C, 16 O, …, 56 Ni) nuclear reaction network : 11 (a, g) reactions from 12 C(a, g)16 O to 52 Fe(a, g)56 Ni, the corresponding 11 photodesintegration reactions, 3 heavy-ions reactions : 12 C(12 C, a)20 Ne, 12 C(16 O, a)24 Mg and 16 O(16 O, a)28 Si , and the triple alpha-reaction and its inverse. - Test case : Reactive shock tube L R r (g cm-3) 2. 5 109 T (K) 8 109 8 107 V (cm s 1) 5 108 0 Ni C R P (g s-2 cm-1) L Comparaison with (Fryxell, Muller, Arnett, MPA 449, 1989) 7/12

Detonation in pure 12 C at T = 108 K and r = 108 g cm-3 1 D 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 1 D time-dependent results with the steady-state solution Mass fractions L R r (g cm-3) 3. 01 108 T (K) 4. 46 109 108 V (cm s 1) 8. 07 108 0 Ni C 8/12

Temperature Energy generation Velocity Density Pressure 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 =108 K and r = 108 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: XC=0. 3 XFe=0. 7 9/12

Detonation in a mixture 12 C/96 Ru (XC=0. 1; XRu=0. 9) at T = 108 K and r = 108 g cm-3 Nuclear reaction network extension: 9 species (64 Ni, 68 Zn, …, 96 Ru) and 16 nuclear reactions are added : 8 (a, g) and the corresponding 8 (g, a) reactions. Effective rates are introduced in order to reproduce the energy production of a reference network of 14758 reactions on 1381 (a, g ) nuclides. and (g, a) rates: (a, g) and (g, a) rates: Energy generation Temperature Density Energy production (erg g-1 ) Nuclear energy generation (erg g-1 s-1) , temperature (K), density (g cm-3) and mass fractions profiles. Z is the 10/12

Effective (a, g) and (g, a) rates: 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 : XC=0. 2 XRu=0. 8 11/12

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

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

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

Detonation in a mixture 12 C/96 Ru at T = 108 K and r = 108 g cm-3 Nuclear reaction network extension: 68 Zn(g, a)64 Ni(a, g)68 Zn 72 Ge(g, a)68 Zn(a, g)72 Ge 76 Se(g, a)72 Ge(a, g)76 Se 80 Kr(g, a)76 Se(a, g)80 Kr 84 Sr(g, a)80 Kr(a, g)84 Sr 88 Zr(g, a)84 Sr(a, g)88 Zr 92 Mo(g, a)88 Zr(a, g)92 Mo 96 Ru(g, a)92 M 92 Mo(a, g)96 R o u full network : 14758 reactions, 1381 nuclides net 0 : l 0 net 1 : l 0+ l 1+ l 6 rmax(64 Ni-96 Ru) : l 0+ l 1+ l 6 +l 0+ l 1+ l 6 rmax(16 O-96 Ru) : l 0+ l 1+ l 6 +l 0+ l 1+ l 6 Reverse rates are estimated making use of the reciprocity theorem.

Hydra : the new Scientific Computer Configuration at the VUB/ULB Computing Centre HP XC Cluster Platform 4000, composed of 32 nodes Nodes HP Proliant DL 585, each composed of - 4 CPUs AMD Opteron dual-core @ 2. 4 GHz - 32 GB RAM - 73 GB hard drive

Same simulation in a mixture C/Fe: XC=0. 3 XFe=0. 7 Pure C : D = 1. 3 109 cm s-1, produces mainly He C/Fe : D = 1. 21 109 cm s-1, produces mainly Ni