Astrophysical Combustion
Elaine S. Oran
Laboratory for Computational Physics
US Naval Research Laboratory
30th International
Combustion Symposium
Chicago, July, 2004
SN 1994D in NGC 452626
Acknowledgments
Vadim N. Gamezo
Alexei M. Khokhlov
J. Craig Wheeler
Geraint Thomas
Naval Research Laboratory
University of Chicago
University of Texas, Austin
University of Wales, Aberystwyth
Michael Frenklach
Rowena Ball
K. Kailasanath
University of California, Berkeley
Australian National University
Naval Research Laboratory
Sponsors: NASA and ONR
D. Huw Edwards
University of Wales Aberystwyth
"... among the giants of
gasdynamics worldwide..."
"... an innovative experimentalist
with a deep understanding
of theory..."
(1925 ?? - 2003)
Combustion
Since the founding of the Combustion Institute, what
is considered "legitimate" combustion has become
more and more inclusive:
* Oxidation with energy release (emphasis on chemistry)
* Gases with exothermic chemical reactions
* Gas dynamics with exothermic chemical reactions
* Physics of flames - laminar and then turbulent
* Detonations, gaseous and condensed; propellants
* Often involving complex chemical reactions,
multiphase flow and reactions, that may produce
pollutants, soot, diamonds, fullerenes, nanoparticles ...
Now .... Combustion ... has come to mean:
The Result of Fluid Dynamics
Combined with Exothermic Reactions,
and Everything This Implies ...
A typical Symposium has representation from
Physics
Chemistry
Biology
Computer Science
Mechanical Engineering
Aerospace & Propulsion
Chemical Engineering
Electrical Engineering
Bioengineering
Environmental Sciences
Math, Applied Math
Materials Science
Atmospheric Sciences
Other (stray astrophysicist?)
The field has broadened,
become more inclusive and dynamic !
Outline
Evolving definition of combustion
Astrophysical combustion - Taking it to the limit
Thermonuclear combustion
Nucleosynthesis, Nuclear kinetics
Birth and death of stars - Stellar evolution
White dwarfs
Type Ia supernovae
Turbulent flames, detonations, and DDT
Astrophysical-terrestrial combustion analogies
Where is Exothermicity in Astrophysics?
Thermonuclear Reactions -
Big Bang - Nuclear reactions in an expanding background
Forms H, He, Li
Stars (Sun) - Nuclear fusion reactions
Burns H to He, He to C, O, etc.
Shell burning in supergiants; novae in white dwarfs
Supernovae - nuclear reactions to form higher Z elements
Chemical Reactions -
Interstellar Combustion - Dilute chemical reactions
Particle, soot formation. Multiphase flow
Relatively slow, exothermic
Quark-Baryon Transition - Exothermic?
Elementary particle reactions
In very early universe. An explosive transition?
Interstellar Dust and Particulates
(Table courtesy of M. Frenklach and A. Tielens)
Example
Observed Location
Red Giants1
ISM2
Meteorites
(June, 2004)
Formation
Mechanism
Mineral Carbides
4
8
4
Nucleation from gas
phase, T ~ 1000 - 3000 K
Aliphatics
4
4
4
Surface and gas-phase
reactions
Kerogens
8
??
4
Neutral reactions at
T ~ 1000 K
Aromatics
8
4
4
Cyclization by acetylene
additions at T ~ 1000 K
Amorphous Carbon
??
??
??
Deposition onto seed
particles at T > 1000 K
Diamonds
8
4
4
Excited or ionized
reactions
(SiC, TiC)
(polyyne chains)
(coals)
( PAHs,5 fullerenes
soot, graphite)
(DLC,3 HAC,4 glassy C
1. Cicumstellar envelopes around
carbon-rich giants
2. Interstellar Medium (ISM)
3. Diamond-like carbon (DLC)
4. Hydrogenated amorphous carbon (HAC)
5. Polycyclic aromatic hydrocarbon (PAH)
Interstellar Dust and Particulates
(June, 2004)
Where is Exothermicity in Astrophysics?
Thermonuclear Reactions -
Big Bang - Nuclear reactions in an expanding background
Forms H, He, Li
Stars (Sun) - Nuclear fusion reactions
Burns H to He, He to C, O, etc.
Shell burning in supergiants; novae in white dwarfs
Supernovae - nuclear reactions to form higher Z elements
Chemical Reactions -
Interstellar Combustion - Dilute chemical reactions
Particle, soot formation. Multiphase flow
Relatively slow, exothermic
Quark-Baryon Transition - Exothermic?
Elementary particle reactions
In very early universe. An explosive transition?
Nucleosynthesis
... the reactions by which atomic nuclei are transformed
to produce the observed abundances of elements
Thermonuclear
Supernovae
Stars, Core-Collapse SN
H, He, some Li made in Big Bang
Heavier than Li, made in stars
All stars burn H to He
Massive stars burn He to
C, O, Si, S, Fe
Big Bang
Above Fe, elements made in the
outer envelopes of supergiants
and in supernovae
Nuclear Kinetics
Over 100 species, Over 1000 reactions
Cross sections found from:
(1) Nuclear-reactor measurements or ion-beam experiments,
sometimes extrapolating to the right temperature range
(2) Theoretical estimates based on (1)
Number of Protons (Z)
100
Z=N
80
60
40
Very Unstable
20
0
0
20
40
60
80
100
120
140
Number of Neutrons (N = A - Z)
160
Birth and Death of Stars (1)
Molecular Clouds
Eagle Nebula -M16
HST 1995 (Hester and Scowen)
> Main Sequence Stars
Hertzsprung-Russell Diagram
Birth and Death of Stars
Molecular Clouds
< 0.08 M
Clouds ~
> Main Sequence Stars
with mass M0
> Brown Dwarf (these never ignite)
<8 M
M0 ~
> Red Giant
>8M
M0 ~
> Supergiant
{
>
> Planetary Nebula
> White Dwarf
> Thermonuclear
Supernova
> Core-Collapse Supernova
> Neutron Star or
Black Hole
> 200 M
Clouds ~
> ??? pulsate and blow apart ?
Birth and Death of Stars (3)
Molecular Clouds
<8M
M0 ~
> Main Sequence Stars
> Supergiants
>
>
Core-Collapse Supernovae
Betelguese
Neutron Star or Black Hole
1987A in Large Magellanic Cloud
(Progenitor ~ 20 solar masses)
Eta Carina NGC 3372
Birth and Death of Stars (2)
Molecular Clouds
> Main Sequence Stars
Arcturus
<8M
M0 ~
> Red Giants
>
>
White Dwarfs
Novae
>
Planetary Nebulae
V2487 Oph (1998)
>
HST, in M4
Thermonulcear
Supernovae
HST, NGC 6543, Cat's Eye
(~1000 years old)
SN 1994D in NGC 4536
White Dwarfs
f
f
f
f
f
Burned out stars
Mostly C and O
Radiate heat, eventually die
Mass approximately that of Sun
Size approximately that of Earth
f Many (>50%) are part of binary systems
f Accrete matter from their neighbor
f If they accrete just a small amount of
H or He from neighbor, this can burn
on the outside of the star and create flashes
called novae.
f If enough matter is accreted, so M0 approaches 1.4 M ,
density in the center increases, and star ignites.
Type Ia Supernovae
These do not just cook quietly, but burn explosively.
Before ...... NGC 4536
After
..... 1981B
Lifetime of WD: 108-1010 yrs
Explodes in 1 - 2 seconds
Bright as an entire galaxy ....
Releases 1051 ergs (1027 Mton)
Forms heavy elements ...
12C + 16O
heavier elements
Y
SN 1994D in NGC 4526
Type Ia Supernovae
Virgo Cluster
SN 1994D
Significance of SNIae
* Create and disperse higher Z elements
important to our way of life
* Provide "standard candles" for cosmological
measurements
* Laboratory for studying basic combustion
processes
Nuclear Kinetics
Leading Reaction (~50% energy release)
Over 100 species
Over 1000 reactions
∆ Unstable nuclides
40
Z
+ Very unstable
=
N
30
Ni
Co
Fe
20
Si
10
0
Triple alpha reaction (<10%, NSE relax)
12C
3 4He 3
O
C
0
10
20
....
Stable nuclides
....
Atomic Number (Z)
50
] 20Ne + 4He
12C + 12C
] 23Na + p
12C + 12C
] 23Mg + n
Pair Reactions (20-40%,quasiequil)
p + (Z,N) ] (Z+1, N)
n + (Z,N) ] (Z, N+1)
3He + (Z,N)
] (Z+2, N+2)
4He + (Z,N)
] (Z+1, N+2) + p
12C + 12C
30
Neutrons (N)
40
50
]
Electron capture, beta decay
56Ni
56Co
56Fe
Y
Y
Significance of SNIae
* Create and disperse higher Z elements
important to our way of life
* Provide "standard candles" for cosmological
measurements
* Laboratory for studying basic combustion
processes
Cosmological Significance of SNIae
The Best Standard Candles
Relative Brightness
(magnitude)
-20
Shape of light curve (brightness
vs time) is correlated to the
peak luminosity.
-19
-18
-17
Bright SNIa decline more slowly.
-16
-15
Scaling determined by Phillips
or luminosity width relation (LWR).
Scaled Magnitude
-20
-19
-18
-17
-16
-15
-20
0
20
Time (days)
40
60
Calan/Tololo Survey of SNIa
(Hamuy et al., 1996, Kim et al., 1997)
Candidate Standard Candles
Measure Velocity of Galaxies - not so hard ...
Calculate from the observed spectral redshift
Measuring Distances of Galaxies - so hard ...
Trigonometric parallax for nearby stars - Use earth
orbit as baseline to triangulate a star's distance
Cepheid variables - Good to ~100 Mparsecs
Stars with regularly pulsating atmospheres
Relation between luminosity and pulsation period
Elliptical and spiral galaxies - Good to ~200 Mparsecs
Spiral - rotational velocity correlated to luminosity
Eliptical - orbital velocity correlated to luminosity
Type II Supernovae - Good to ~300 Mparsecs
Not really a standard candle, but use (e.g.)
spectra of their expanding atmospheres
Type Ia Supernovae - Good to ~Gparsecs*
Peak luminosity correlated to shape of light curve
* 1 Gparsec ~ 3.2 x 109 Lt yrs ~ 3 x 1022 km
Cosmological Constraints
Friedmann Equation:
Hubble
parameter
mass
density
curvature
of the
universe
vacuum
energy
density
Implies a flat universe, the current idea
Use SNIae to determine H and
4% is regular matter; rest is dark matter
Significance of SNIae
* Create and disperse higher Z elements
important to our way of life
* Provide "standard candles" for cosmological
measurements
* Laboratory for studying basic combustion
processes
Combustion in SNIa - What do we know? (1)
Initial Conditions
T ~ 105 - 108 K
M ~ 2.8 x 1033 g (1.4 M )
ρc ~ 2 x 109 g/cc, radius ~2 x 108 cm = 2000 km
Binding energy ~ - 5 x 1050 ergs
cs~ 5 x 108 cm/s ~ 1/60 c
Explosion by a Thermal Instability
Normal stars are thermally stable and do not explodethey expand as their temperature rises
A degenerate WD does not expand when its
temperature rises -> Instability
Explosion takes 1-2 seconds
Energy released ~1.5 x 1051 ergs
Temperature reaches (8 - 9) x 109 K
Produces ~ M of Fe, ~ 0.6 M of radioactive 56Ni,
rest is Si-group
Velocities up to ~20,000-30,000 km/s in outer layers
>
Combustion in SNIa - What do we know? (2)
The Physical Model
Highly exothermic nuclear process
Binary reactions, no chain branching, typical rate is
R(T) ~ ρ2 exp(-Q/T1/3) or R ~ ρ2 exp(-Q/T),
Q/T ~ 10 - 50 (similar to hydrocarbon fuels)
T ~ 109 - 1010 K, ρ ~ 106 - 1010 g/cc
Among all nuclei from C to Ni, protons, neutrons, He
Heat conduction- very high: degenerate e-'s, photons
Viscosity - small - due to scattering e-'s, photons
Species diffusion - none (Lewis number = 0)
Equation of state - known to very high accuracy
Ideal gas of Fermi-Dirac e-'s and e+'s, Boltzmann gas
of ions, Planck radiation P = E / (γ - 1), γ ~ 4/3 to 5/3
These are the "ingredients" of flames and detonations!
Thermonuclear Detonation
Detonation speed: 1 - 1.4 x 109 cm/s
Detonation front thickness: 10-1 - 103 cm
Three fairly distinct burning regimes: Burn
C (50% of energy released), then form Si
(10-40% energy released), then form Fe
Structure is extremely sensitive to density!
The regimes are compressed at high density.
Detonation leaves behind a highly inhomogeneous mixture of
intermediate products of reaction and a complex multilevel
detonation structure (Gamezo et al., 1999)
Detonation cells form over a wide range of scales, depending on
the density and the burning regime.
Important Scales in White-Dwarf Deflagrations
Laminar flame-front thickness: 10-4 - 100 cm
Laminar flame speed: 107 - 104 cm/s (<< sound speed)
Flame is Rayleigh-Taylor unstable in gravitational field
Require a subgrid model to
account for flame stretching
and acceleration in cascade
regime and below.
Calculations show that St
does not depend on Sl, but
is determined primarily by
the Rayleigh-Taylor instability:
St = α (gLA)1/2,
α = 0.5,
g - graviational acceleration
L - length scale
A - Atwood number
Numerical Approach to Supernova Simulations
Solve unsteady, compressible fluid dynamics equations with:
Equation of state for a degenerate electron gas
Reduced kinetic mechanism for C+C burning, formation of Si
and Fe. Tracking method for nuclear flame
Fully Threaded Tree for adaptive mesh refinement
Effective resolution 20483, 108 cells, ∆x = 2.6x105 cm
Subgrid burning rate determined by gravity-related RayleighTaylor instability
Model one octant of the star.
Initial conditions: Hydrostatic equilibrium
Chandresekhar-mass C-O white dwarf
Spherical initial flame of radius 3x106 cm
3D SNIa Calculations ....
Deflagration Stage of the Explosion
Time (s)
Mass Fraction
Burned
Flame Surface
Gamezo, Khokhlov, Oran, Chtchelkanova, Rosenberg, Science, 2003
Converged Simulation of SNIa Explosion
0.576 s
1.257
1.393
1.487
1.531 s
1.573
1.613
1.652
1.724 s
1.760
1.883
1.902
The Hard Data on SNIa
Spectra: From spectral evolution, we can determine velocities
of material ejected, composition, and densities of the species,
as a function of depth in the ejected matter.
Light curves: From the rise and fall of these curves, we can
constrain the amount of Ni 56 produced by the explosion, the
values of density, and the expansion rate.
WD environment: From the type of the host galaxy, location
of the SNIa within the galaxy, and local environment in that
galaxy, we can determine something about the age of the WDs.
Nuclear Reaction Mechanism: Reasonable knowledge of
nuclear reactions and nucleosynthesis. There are three main
stages related to the burning of carbon, oxygen, and silicon.
Roles and scales of each of these differ by orders of magnitude.
Observations on Converged SNIa Simulations
(Science, January 2003)
This simulation is converged numerically ...
Varying resolution does not change the global features of the
results, e.g., the rate of expansion, final flame-surface area, ...
The size of the lobes formed is roughly the same at all scales
computed and for all converged resolutions.
Varied initial condition, e.g., different C/O ratios.
But the calculations do not produce the observed energy
release and spectra. The results do not (cannot?) show DDT.
Temperatures, densities in unreacted funnels are not high
enough to allow detonation ignition.
Approximations in model:
Expanding flame - not computed from a complete enough
model as we did for laboratory DDT computations.
Solution ?? - Microphysics of this flame?
Does Transition to Detonation Solve the Problem?
If so,
What is the Mechanism of DDT in SNIae?
How does a high-speed turbulent flame suddenly
become a supersonic reaction wave, a detonation?
This is a difficult problem in terrestrial combustion!!
Difficulty for experiments: Diagnostics of very
high-speed, 3D reactive flows
Difficulty for numerical simulations:
Disparity of scales ... Must resolve the flame front
structure and turbulent flame, in a large enough
system to see the interaction and watch evolution.
We can test whether DDT would solve the problem !!!!!!!
Simulation of a Type Ia Supernova Delayed Detonation
Simulation of a Type Ia Supernova Delayed Detonation
Deflagration
x1050
Etot (ergs)
b
Delayed Detonation
a
Deflagration
Time (s)
Delayed Detonation
Where and how can DDT occur?
How can detonation
ignition centers (hot
spots) form in a rapidly
expanding flame ?
Is the flame quenched
before DDT occurs?
The disparities between
the time and space
scales of the SN event
and hot-spot formation
are daunting.
Gamezo, Khokhlov, & Oran, 2001, 2002
Can we use laboratory
experiments and numerical
simulations to study how this
transition might occur?
High-resolution Computation of a Hot-Spot Explosion
µs
Density
868.4
867.1
866.5
Explosion transitions to a
detonation.
866.3
866.1
Hot spot explodes.
865.9
864.0
Time
860.7
859.0
857.6
Train of shocks runs through
unreacted material.
Flame brush contains regions
of unreacted material.
This is a Big Calculation ...
Current calculation: 19,000 cpu hours
SGI 3000; 48 or 128 processors
Initial grid evenly spaced, with
2x107 smaller cells at center
Use AMR, evolves to ~108 cells
∆xmin = 2.6x105 cm
To calculate DDT, need to resolve the
flame thickness, δf , with at
least 10 computational cells.
At ρ = 5 x 107 g/cm3, δf ~ 3.6x10-1cm
Therefore, need ∆xmin = 2.6x10-2 cm
This is 107 times smaller than current.
Using AMR, Ncells increases as N2, not N3 ; ∆t 107 times smaller.
Therefore, computer times increases by 107*3 = 1021~ 270.
Moore's Law: computer power doubles in 1.5 yrs
70x1.5 =
105 years until we can do this calculation in equivalent time!!
Astrophysical and Combustion Analogies
Astrophysical Object
Big Bang
Combustion Analogue
Explosion, He Formation
Weak ignition? Supersonic combustion?
Origin in space-time fluctuations?
Deflagration, detonation or SHS
Forms ordinary matter
Supersonic combustion
Main-Sequence Stars
Furnace, thermonuclear reactor
Red Giants
Supergiants
Multicomponent droplet burning,
with microexplosions
Multicomponent droplet burning
White Dwarfs
Decaying embers
Novae
Throwing a little fuel on embers
Type Ia Supernovae
Chemical plant explosion
Type II Supernovae
Structural collapse, shock propagation,
ignition, explosion
Smoldering combustion, soot formation
Quark-Hadron Transition
Interstellar Combustion
(To be taken with a very large grain of salt)
Several Concluding Thoughts ...
Astrophysics as a subfield of Combustion? The entire universe
and many of its most important astronomical components are
(very difficult) combustion systems.
An equivalently difficult combustion problem to many common
astrophysical problems: Try to explain what has happened in a
chemical-plant explosion from spectroscopic observations
taken a hundred miles away, as observed through the properties
of the observer's atmosphere.
An astrophysical laboratory... There are naturally occurring
combustion laboratories for testing models and theories over
a very wide range of time and space scales.
for testing combustion concepts ... Typical combustion phenomena,
such as ignition, laminar and turbulent flames, detonations,
multiphase flows, and particle and soot formation, are also
fundamental processes occurring in astrophysics.
under extreme conditions. The combustion concepts apply, but
the conditions under which they apply are usually quite different
and usually much more extreme in astrophysics.