On the stability of thermonuclear flames in type Ia supernova explosions [Elektronische Ressource] / Friedrich Konrad Röpke

Friedrich Konrad Röpke

Sujets

• Astronomie

Informations

• Publié par: technische_universitat_munchen
• Publié le: 01 janvier 2003
• Nombre de lectures: 120
• Langue: English
• Poids de l'ouvrage: 13 Mo

Extrait

Max-Planck-Institut für Astrophysik
On the Stability of Thermonuclear Flames
in Type Ia Supernova Explosions
Friedrich Konrad Röpke
VollständigerAbdruckdervonderFakultätfürPhysikderTechnischenUniversitätMünchen
zur Erlangung des akademischen Grades eines
Doktors der Naturwissenschaften
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr. L. Oberauer
Prüfer der Dissertation:
1. Hon.-Prof. Dr. W. Hillebrandt
2. Univ.-Prof. Dr. M. Lindner
Die Dissertation wurde am 3. 7. 2003 bei der Technischen Universität München einge-
reicht und durch die Fakultät für Physik am 24. 7. 2003 angenommen.The phenomenon of combustion exerts
a lifelong fascination over us.
— Ya. B. Zel’dovich (1980)Contents
1. Prologue 1
1.1. Observational facts on Type Ia supernovae . . . . . . . . . . . . . . . . . 2
1.2. Astrophysical implications . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1. Conclusions from the observations . . . . . . . . . . . . . . . . . 3
1.2.2. Constraints for the astrophysical models . . . . . . . . . . . . . . 4
1.2.3. Possible progenitor scenarios . . . . . . . . . . . . . . . . . . . . 4
1.2.4. Pre ignition evolution . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.5. Astrophysical relevance of Type Ia supernovae . . . . . . . . . . 7
1.3. Current status of Type Ia supernova research . . . . . . . . . . . . . . . . 8
1.4. Objectives of this work . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5. Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2. Theoretical Considerations 15
2.1. Reactive fluid dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1. General form of a balance equation . . . . . . . . . . . . . . . . 16
2.1.2. The Euler equations . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.3. The Navier Stokes equations . . . . . . . . . . . . . . . . . . . . 18
2.1.4. General reactive flow . . . . . . . . . . . . . . . . . . 18
2.1.5. Nondimensional representation of the general
reactive flow equations . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.6. Source terms for nuclear reactions . . . . . . . . . . . . . . . . . 21
2.2. Combustion theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1. The discontinuity approximation of burning fronts and modes of
propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2. Internal structure of detonation and deflagration waves . . . . . . 27
2.2.3. Laminar flames . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.4. Phenomenological description according to Markstein . . . . . . 31
2.2.5. Thermonuclear deflagration in C+O white dwarf matter . . . . . 31
2.3. Flame instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.1. Linear stability analysis . . . . . . . . . . . . . . . . . . . . . . 34
2.3.2. Corollaries from the flame instabilities . . . . . . . . . . . . . . . 40
2.4. Analytical studies of nonlinear flame propagation . . . . . . . . . . . . . 44
2.4.1. Stability analysis after Zel’dovich . . . . . . . . . . . . . . . . . 44
2.4.2. The Sivashinsky equation . . . . . . . . . . . . . . . . . . . . . 44
vContents
2.4.3. Pole decomposition . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.5. Fractal descriptions of flame fronts . . . . . . . . . . . . . . . . . . . . . 48
2.6. Turbulent combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.6.1. Basic concepts of turbulence theory . . . . . . . . . . . . . . . . 51
2.6.2. Turbulent burning regimes and resulting length scales . . . . . . . 52
2.6.3. Active turbulent combustion . . . . . . . . . . . . . . . . . . . . 54
2.7. Deflagration to detonation transition . . . . . . . . . . . . . . . . . . . . 54
3. Astrophysical background 57
3.1. Thermonuclear combustion in Type Ia Supernovae . . . . . . . . . . . . 57
3.1.1. Models for the explosion mechanism . . . . . . . . . . . . . . . 57
3.1.2. Turbulent combustion in Type Ia supernova explosions . . . . . . 59
3.2. Hydrodynamical considerations . . . . . . . . . . . . . . . . . . . . . . 61
3.2.1. The equation of state for white dwarf matter . . . . . . . . . . . . 61
3.2.2. External forces: gravity . . . . . . . . . . . . . . . . . . . . . . . 62
4. Numerical implementation 63
4.1. Fluid dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.1.1. Operator splitting . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.1.2. Discretization on a computational grid . . . . . . . . . . . . . . . 65
4.1.3. Numerical solution of the Euler equations . . . . . . . . . . . . . 65
4.1.4. Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . 68
4.1.5. Implementation of the hydrodynamics solver . . . . . . . . . . . 69
4.2. Equation of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3. Thermonuclear reactions . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4. Flame model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4.1. The level set technique . . . . . . . . . . . . . . . . . . . . . . . 70
4.4.2. The G equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.4.3. Re initialization . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5. Flame/flow coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5.1. Geometrical information . . . . . . . . . . . . . . . . . . . . . . 72
4.5.2. In cell reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 73
4.5.3. Flux splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5.4. Treatment of the source terms . . . . . . . . . . . . . . . . . . . 75
5. Results and discussion 79
5.1. Some verification tests of the implementation . . . . . . . . . . . . . . . 79
5.2. Problems with the numerical . . . . . . . . . . . . . . . 82
5.3. Flame propagation into quiescent fuel . . . . . . . . . . . . . . . . . . . 85
5.3.1. Passive vs. complete implementation . . . . . . . . . . . . . . . 86
5.3.2. Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.3.3. General features of flame evolution . . . . . . . . . . . . . . . . 90
5.3.4. The linear regime of flame ev . . . . . . . . . . . . . . . . 97
viContents
5.3.5. The nonlinear regime of flame evolution . . . . . . . . . . . . . . 99
5.3.6. Increase in flame surface and acceleration of the flame . . . . . . 99
5.3.7. Influence of the initial flame shape and the boundary conditions . 103
5.3.8. Flame stability at different fuel densities . . . . . . . . . . . . . . 104
5.4. Flame interaction with a vortical flow . . . . . . . . . . . . . . . . . . . 109
5.4.1. Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.4.2. What can be expected? . . . . . . . . . . . . . . . . . . . . . . . 111
5.4.3. Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.4.4. A Parameter study . . . . . . . . . . . . . . . . . . . . . . . . . 116
6. Epilogue 127
6.1. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.2. Comparison with experiments . . . . . . . . . . . . . . . . . . . . . . . 129
6.3. Implications for SN Ia models . . . . . . . . . . . . . . . . . . . . . . . 131
6.4. Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
A. Derivation of the Sivashinsky equation for a
hydrodynamical model of the flame 135
B. Vectors of the general reactive flow equation 139
C. Nomenclature 141
Bibliography 145
vii1. Prologue
One evening, when, as usual, I was contemplating the
heavenly dome whose face was so familiar to me, I saw
with inexpressible astonishment a radiant star of extraor-
dinary magnitude.
Struck with surprise, I could hardly believe my eyes. Its
brightness was greater than that of Sirius, and Jupiter. It
could only be compared with that of Venus. People gifted
with good eyesight could see this star in daylight, even at
noon.
— Tycho Brahe on the 1572 supernova encounter
Transient phenomena in the sky have attracted the attention of mankind for millennia and
still today cosmic explosions pertain to the most fascinating objects of astrophysics. The
observation of supernova explosions, which belong to the brightest astrophysical events,
played an outstanding role in the history of astronomy. Ancient records provide obser-
vational data of astonishing accuracy, sometimes even allowing for the reconstruction of
the light curve of historical supernovae (Stephenson & Green 2002, Green & Stephenson
2003). The dawn of modern European astronomy coincides with the systematic observa
tion of two supernovae conducted by Tycho Brahe in 1572 (Brahe 1573) and by Johannes
Kepler in 1604. The term supernova was introduced by Baade & Zwicky (1934) to dis
tinguish these events from classical novae. Supernovae are astrophysical objects whose
luminosity raises on timescales of a few days to weeks and then decreases over several
42 43 −1years after reaching a peak luminosity up to 10 – 10 erg s , equivalent to the lumi
nosity of an entire galaxy. The overall energy release of supern