Pr

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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.)

5th JETSET School on High Performance Computing
in Astrophysics, January 8th - 13th 2008
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Observational properties of X-ray bursts and
superbursts
X-ray burst
Superburst
40 s
Lewin al., Space Sci. Rev., 62, 223, 1993
Kuulkers, NuPhS, 132, 466, 2004
Lmax ? 1038 ergs s-1 Etot ? 1039 ergs
tburst ? 10s several min trec ? 5min -
days
Lmax ? 1038 ergs s-1 Etot ? 1042 ergs
tburst ? several min several hours trec
? years
2/12
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Thermonuclear model of X-ray burst
Accretion
He
H/He
stable
unstable
rp-process
C (X lt 0.1) heavy ashes above Fe
C
Fe
Strohmayer, Brown, ApJ, 566, 1045, 2002
Schatz al., Nuclear physics A, 718, 247, 2003
3/12
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Thermonuclear model of superburst
Thermally unstable ignition of 12C at densities
of about 108 109 g cm-3
4/12
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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 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., ApJ, 566, 1018, 2002
Moreover the propagation phase has never been
studied, even in 1D Weinberg al. (ApJ Letters,
650, 119, 2006) suggest that the way of
propagation of the combustion in superburst
phenomena is a detonation.
5/12
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A new finite volume method, parallelised
algorithm for modeling astrophysical
detonations.(Noël al., AA, 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 a
13 species nuclear
reaction network.
6/12
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- Nuclear reaction network 13 species (4He, 12C,
16O,, 56Ni) nuclear reaction network 11 (a,g)
reactions from 12C(a,g)16O to 52Fe(a,g)56Ni, the
corresponding 11 photodesintegration reactions, 3
heavy-ions reactions 12C(12C,a)20Ne,
12C(16O,a)24Mg and 16O(16O,a)28Si , and the
triple alpha-reaction and its inverse.
- Test case Reactive shock tube
L R
r (g cm-3) 2.5 109 109
T (K) 8 109 8 107
V (cm s-1) 5 108 0
Ni C

P (g s-2 cm-1)
7/12
Comparaison with (Fryxell, Muller, Arnett, MPA
449,1989)
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Detonation in pure 12C at T 108K and r 108 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

Mass fractions
L R
r (g cm-3) 3.01 108 108
T (K) 4.46 109 108
V (cm s-1) 8.07 108 0
Ni C
8/12
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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 12C 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 XC0.3
XFe0.7
9/12
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Detonation in a mixture 12C/96Ru (XC0.1
XRu0.9) at T 108K and r 108 g cm-3
Nuclear reaction network extension 9 species
(64Ni, 68Zn,, 96Ru) 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
nuclides.
(a,g) and (g,a) rates
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 distance to the
shock in cm.
10/12
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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 XC0.2 XRu0.8
11/12
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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
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• 1D simulation of the propagation of the
  detonation in inhomogeneous medium
• Multi-D simulations

Perspectives
Pure He detonation which goes through an Fe
buffer
Collision of two C detonations
12/13
Temperature
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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
detonation. Detonations are intrinsically
multi-D phenomena.
burned gas
Small perturbations disturb the detonation
front. The planar front is replaced by incident
shocks, transverse waves, and triple points.
These high-pressure points trajectories give
rise to the cellular pattern.
Reaction zone
shock
Desbordes LCD-CNRS
P. Vidal (LCD, Poitiers)
6/14
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Detonation in a mixture 12C/96Ru at T 108K and
r 108 g cm-3
Nuclear reaction network extension
68Zn(g,a)64Ni 64Ni(a,g)68Zn
72Ge(g,a)68Zn 68Zn(a,g)72Ge
76Se(g,a)72Ge 72Ge(a,g)76Se
80Kr(g,a)76Se 76Se(a,g)80Kr
84Sr(g,a)80Kr 80Kr(a,g)84Sr
88Zr(g,a)84Sr 84Sr(a,g)88Zr
92Mo(g,a)88Zr 88Zr(a,g)92Mo
96Ru(g,a)92Mo 92Mo(a,g)96Ru
Reverse rates are estimated making use of the
reciprocity theorem.
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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 _at_ 2.4 GHz
- 32 GB RAM - 73 GB hard drive
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Same simulation in a mixture C/Fe XC0.3 XFe0.7
Pure C D 1.3 109 cm s-1, produces mainly
He C/Fe D 1.21 109 cm s-1, produces mainly
Ni