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

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

Lewin & al., Space Sci. Rev., 62, 223, 1993 Kuulkers, NuPhS, 132, 466, 2004

40 s 2.7 h

2/12

Thermonuclear model of X-ray burst

Accretion

He H/He

C Fe C (X < 0.1) +heavy ashes above Fe

stable unstable rp-process

Strohmayer, Brown, ApJ, 566, 1045, 2002Schatz & al., Nuclear physics A, 718, 247, 2003

3/12

N.S.

C / RuHe / H

N.S.

C/FeHe

or

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