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.) UNIVERSITE LIBRE DE BRUXELLES
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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.,
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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.)
UNIVERSITE LIBRE DE BRUXELLES
Observational properties of X-ray bursts and superbursts X-ray burst Superburst
Thermonuclear model of superburstThermally unstable ignition of 12C at densities of about 108 – 109 g cm-3
N.S. Crust
100 m
10 m
C/Fe/Ru
H/He burning
Atmosphere
Accretion stream
~ 105 g cm-3
~ 109 g cm-3
4/12
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 !!!
- AccretionAccretion is not uniform on the surface-IgnitionIgnition 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 1DWeinberg & al. (ApJ Letters, 650, 119, 2006) suggest that the way of propagation of the combustion in superburst phenomena is a detonationdetonation.
5/12
A new finite volume method, A new finite volume method, parallelised parallelised
algorithm for modeling astrophysical algorithm for modeling astrophysical detonations.detonations.
(Noël & al., A&A, 470, 653, 2007)- Finite volume methodFinite volume method algorithm (MUSCL type)- Unsplit dimentionallyUnsplit dimentionally- Time-splittingTime-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.
0. dSdVdt
dSV u
0 . dSpdSdVdt
dSSV uuu
0 . dVdSpdSEdVEdt
d nucVStStV uu
2
2ueEt
speciesnuciViSiV niRdSYY
dt
d,...,1 0 . u
i
i
YTee
YTpp
,,
,,
6/12
- 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 (4He, 12C, 16O,…, 56Ni) nuclear reaction network : 11 () reactions from 12C16O to 52Fe56Ni, the corresponding 11 photodesintegration reactions, 3 heavy-ions reactions : 12C(12C,20Ne, 12C(16O,24Mg and 16O(16O,28Si , and the triple alpha-reaction and its inverse.- Test case : Reactive shock tube
L R
Comparaison with (Fryxell, Muller, Arnett, MPA 449,1989)
L R
(g cm-3)
2.5 109 109
T (K) 8 109 8 107
V (cm s-
1)5 108 0
Ni C
1
p
e
P (
g s
-2 c
m-1)
7/12
Detonation in pure 12C at T = 108K and = 108 g cm-31D 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
L R
(g cm-3)
3.01 108
108
T (K) 4.46 109
108
V (cm s-
1)8.07 108
0
Ni C
Mass fractions
8/12
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 = 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
Temperature
Velocity
Density
Pressure
Energy generation
9/12
Detonation in a mixture 12C/96Ru (XC=0.1; XRu=0.9)
at T = 108K and = 108 g cm-3Nuclear reaction network extension: 9 species (64Ni, 68Zn,…, 96Ru) 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.
Energygeneration Temperature
Density
(() and ) and rates: 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
Energygeneration
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
Effective (Effective () and ) and rates: rates:
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- 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
HeCSiFeNi
X
X
HeCSFeNi
12/13
Detonation on the neutron star surfaceWeinberg & al. (ApJ Letters, 650, 119, 2006) suggest that the way of propagation of the combustion in superburst phenomena is a detonationdetonation. Detonations are intrinsically multi-Dmulti-D phenomena.
burned gas
Reaction zone shock
Desbordes LCD-CNRS
Small perturbations disturb thedetonation front.
The planar front is replaced by incident shocks, transverse waves, and triple points. These high-pressure points trajectories give rise to the cellular cellular patternpattern.
P. Vidal (LCD, Poitiers)
6/14
Detonation in a mixture 12C/96Ru at T = 108K and = 108 g cm-3
Nuclear reaction network extension:
68Zn()64
Ni
64Ni()68Zn
72Ge()68
Zn
68Zn()72
Ge76Se()72
Ge
72Ge()76
Se80Kr()76S
e
76Se()80
Kr84Sr()80K
r
80Kr()84Sr
88Zr()84Sr
84Sr()88Zr
92Mo()88
Zr
88Zr()92
Mo96Ru()92
Mo
92Mo()96
Ru
full network : 14758 reactions, 1381 nuclidesnet0 : 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.
Hydra : the new Scientific Computer Hydra : the new Scientific Computer Configuration Configuration
at the VUB/ULB Computing Centreat the VUB/ULB Computing CentreHP 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
Same simulation in a mixture C/Fe: XC=0.3 XFe=0.7
Pure C : D = 1.3 109 cm s-1, produces mainly HeC/Fe : D = 1.21 109 cm s-1, produces mainly Ni