Michael Zingale

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Lecture 17
Michael Zingale
Type Ia Supernovae
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SN 1998dh
SN 1998aq
SN 1998bu
Type Ia supernovae are the biggest thermonuclear
explosions in the universe. Twenty billion,
billion, billion megatons (1051 erg). For
several weeks their luminosity rivals that of a
large galaxy.
HST
SN 1994D
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Observational Facts

• Very bright, regular events, peak L 1043
  erg s-1
• Associated with an old stellar population
  (found in ellipticals, no clear association
  with spiral arms)
• No hydrogen in spectra strong lines of Si,
  Ca, Fe
• Not strong radio sources
• Total kinetic energy 1051 erg (no compact
  remnant)
• Higher speed, less frequent than Type II

SN 1994D
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The Phillips Relation (post 1993)
Broader Brighter
Can be used to compensate for the variation in
observed SN Ia light curves to give a calibrated
standard candle.
Note that this makes the supernova luminosity at
peak a function of a single parameter e.g.,
the width.
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Type Ia supernovae at large distances seem to be
fainter, for their observed red shift, than what
would be expected in any cosmology without a
cosmological constant. Bottom panel shows
difference between the distance modulus and
that expected for a universe with no cosmological
constant and Omega matter 0.3
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Models that have been Suggested

• All based upon accreting white dwarfs to
  explain association with old population,
  absence of hydrogen, regularity, etc.
• (Hoyle and Fowler 1960)
• Merging white dwarfs High
  accretion rate leads to ignition at the edge
  Flame burns stably to center,
  converts dwarf to NeO
  Collapse to a neutron star. But see also Yoon et
  al. (2007, MNRAS, 380,
  933)
• Sub-Chandrasekhar mass models
• Accretion at about 3 x 10-8
  solar masses/yr Build a
  thick He layer of about 0.15 to 0.20 solar
  masses on top of a
  carbon-oxygen white dwarf
  of 0.7 0.9 solar masses
  He detonation induces a detonation of the CO
  core? Problems with
  spectrum and difficulty detonating CO
  Does produce some missing isotopes
  (Woosley and Weaver, 1994,
  ApJ, 423, 371)
• SN0.1a - Bildsten et al.
  (2007, ApJ, 662, L95)

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SN Ia Progenitor Systemsexplosions of
carbon/oxygen white dwarf stars
merging double white dwarf binary
accreting white dwarf near the Chandrasekhar
limit (1.4 Msun)
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Chandraskhar Mass Model

• Accretion and growth to almost he Chandrasekhar
  Mass (1.38 solar masses)
• corrected for Coulomb effects but usually
  relativity effects are ignored.
• Ye 0.50

In order to avoid the nova instability must
accrete at a rate 10-7 solar masses per year.
This must be maintained for millions of years.
Possible observational counterpart
supersoft x-ray sources (controversial)
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Ignition
Arnett (1968, 1969) Nomoto, Sugimoto, Neo (1976)

Ignition occurs as the highly screened carbon
fusion reaction begins to generate energy faster
than (plasma) neutrino losses can carry it away.
At a given temperature, the plasma neutrino
lossesfirst rise with density and then decline
when
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Neutrino Losses

Itoh et al 1996, ApJS, 102, 411, see
also Beaudet, Petrosian, Salpeter 1967, ApJ,
147, 122
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The ignition conditions depend weakly on the
accretion rate. For lower accretion rates the
ignition density is higher. Because of the
difficulty with neutron-rich nucleosynthesis, lowe
r ignition densities (high accretion rates) are
favored.
Ignition when nuclear energy generation by
(highly screened) carbon fusion balances
cooling by neutrino emission.
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Conditions in the Star

• Supernova preceded by 100 years of convection
  throughout most of its interior. Energy goes into
  raising the temperature of the white dwarf
  (not expansion, not radiation).
• Last "good convective model" is when the central
  temperature has risen to 7 x 108 K

Pressure scale height 400 km Nuclear time
scale 102 sConvective time scale 102 s
Convective speed 50 km s-1 Binding energy 4 x
1050 erg Density 2.7 x 109 g cm-3
Burning 0.05 solar masses can cause expansion by
a factor of three
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Central T 7 x 108 K (just before runaway)
Ma et al (2009)
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Dependence on Rotation
If ignition farther off center correlates with
greater Ni production in the detonation,
as seems likely, then the brightness of a SN Ia
will correlate inversely with its rotation rate.
?????????????????????????????Ignition radius
(rad/s) (km) 0 120 0.167
80 0.84 35 2.52
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Zingale et al. (2009)
xyz slices of a low Mach number calculation
of ignition (3843 zones). 0.5 MCPUhr at
ORNL. Reynolds Number implies barely
turbulent. Each increase of factor of 10 in
resolution costs 104 in CPU.
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Convection for 100 years, then formation of a
thin flame sheet. First bubbles
Note that at 7 x 108 K the burning time
and convection time become equal.
Cant maintain adiabatic gradient
anymore 1.1 x 109 K, burning goes faster
than sound could go a pressure scale
height Burning becomes localized
T
0
radius
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Fuel
Diffusion
Burning
Ash
Temperature

• This is the conductive
• or sometimes laminar
• flame speed.

l
A laminar flame
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Laminar Flame Speed
km/s
nb. these speeds are comparable to the
convective speeds prior to runaway
cm
Timmes and Woosley, (1992), ApJ, 396, 649
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Heat Capacity
Nuclear burning to the iron group gives qnuc 7
x 1017 erg/gm
silicon group 5 x 1017 erg/gm
Above about 107 gm cm-3 burning will go to
nuclear statistical equilibrium and make only
iron group elements
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At 10 billion K burning always goes to
completion and makes iron. Only below four
billion K (few x 107 gm cm-3) does one begin to
make Si, S, Ar, Ca, Mg, etc. Almost all the
initial white dwarf is more dense than
that. So, naive physics gives us a flame that
burns the star slowly to iron, experiences a lot
of electron capture, and barely unbinds the star
maybe after several pulses
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But actually A Successful Model Must
(Starting from 1.38 solar masses of carbon and
oxygen)

• Explode violently

• Produce approximately 0.6 solar masses of
  56Ni (0.1 to 1 Msun )
• Produce at least 0.2 solar masses of
  SiSArCa
• Not make more than about 0.1 solar masses of
  54Fe and 58Ni combined
• Allow for some diversity

For the light
For the spectrum
For the nucleosynthesis
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These requirements are in conflict with the basic
physics outlined so far

• Such a vastly subsonic speed will not give a
  powerful explosion or much 56Ni
• Burning much fuel at 109 g cm-3 will result in
  copious electron capture and lots of 54Fe and
  58Ni
• The flame will slow to almost a halt at the
  densities where SiSArCa might be made.
• The origin of diversity is not clear

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It has been known empirically for some time
that the way to get around these problems and
agree with observations is with a flame that
starts slowly, pre-expands the star (so as to
avoid too much electron capture) then moves very
rapidly when the density is around 107 108 gm
cm-3.
Unfortunately the laminar flame has just the
opposite behavior and a prompt explosion
(detonation) would turn the whole star to
iron (in conflict with the spectrum).
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Model W7 an empirical model
that works
Thielemann, Nomoto, and Yokoi (1986), AA,
158, 17 and (1984), ApJ, 286, 644

• 0.0 s
• 0.60 s
• 0.79 s
• 1.03 s
• 1.12 s
• 1.18 s
• 1.24 s
• 3.22 s

Half of the time is spent burning the first 0.1
solar masses.
Note the long time spent at going slow near the
center. The flame accelerates to nearly sound
speed at the end
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The fact that W7, an empirical parameterized model
agrees so well with observations suggests that
the correct SN Ia model should have similar
properties.
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Nucleosynthesis compared to the Sun
(normalized to 56Fe 1)
some problems with 58Ni indicate too
much electron capture in the explosion.
Brachwitz et al. (2000)
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But how to get a flame that moves at
greater than about 30 the sound speed?

• Rayleigh-Taylor Instability The ashes are
  from 20 to100 less dense than the fuel.
  geff 109 cm s-2. The float speed can be 1000
  km/s after just a tenth of a second
• Turbulence The RT instability leads
  to Kelvin-Helmholtz instability and
  turbulence
• Delayed Detonation At late times the
  flame may accelerate to supernonic speeds and
  become a self-sustaining detonation wave

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MULTI-D MODELS
Explosion - Burning and Propagation
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Vorticity Burning Floating Bubble 500x500x2048
0.5 MCPUHr so far
Aspden et al (2009)
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10243 zone calculation in Munich. The SNOB Run.
Barely resolves integral scale for the
turbulence
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Transition to Detonation Turbulence or Colliding
Waves?
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Asymmetric Delayed Detonation

• PPM based code
• Use level set for flame tracking

• subgrid model for turbulence (Pocheau 1994
  Schmidt et al 2006ab)

Roepke, Woosley, and Hillebrandt (2007)
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White dwarf expands less than in the Röpke et al.
model, so the collision on the far side occurs at
higher density and with less geometrical dilution.
In the Chicago version, the temperature is
sufficient to ignite a detonation that consumes
the rest of the star. The answer depends on the
subgrid model
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Spontaneous transition to detonation?

• Rising plumes create shear which drives
  turbulence
• After the turbulence cascades down one order of
  magnitude in length scale it is Kolmogorov
  and isotropic. On small scales, the flame
  sees this turbulence and is moved around by
  it.
• Later transition to supersonic burning?
  (Detonation)

The Reynolds Number is very large
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Transition to detonation?
1.5 x 107
1.0 x 107
0.667 x 107
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Kerstein (1988, 1989, 1990)
The Linear Eddy Model (LEM) is a 1D stochastic
simulation of 3D turbulence

• Assume background of isotropic
  Kolmogorovturbulence
• Turbulent advection represented by randomly
  sampled eddy events on a1D grid
• Each event is an instantaneous rearrangement of
  property profiles triplet map

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The triplet map is a 1D procedure that emulates
3D eddy kinematics
Kerstein (1988, 1989, 1990)
The triplet map captures compressive strain and
rotational folding effects, and causes no
property discontinuities
The triplet map is implemented numerically as
a permutation of fluid cells
This procedure emulates the effect of a 3D
eddy on property profiles along a line of sight
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Summary - MCh model

• Characteristics of the explosion are set by the
  location and frequency of the ignition
  points, the flame model used for the
  deflagration stage, and the conditions assumed
  for the transition to detonation.
• First principles calculations are advancing but
  arent there yet. Need higher resolution
• The observable properties of the supernova will
  also be affected by the ignition density
  (affects both the binding energy and electron
  capture), the C/O ratio, the metalicity,
• and the rotation rate

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2-D Delayed Detonation Model(calculations by
Röpke, Kasen, and Woosley) 0.7 Msun of 56Ni
density
composition
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strong deflagration weak detonation
weak deflagration strong detonation
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Light Curves
After the white dwarf has expanded a few times
its initial radius its internal energy (and
entropy) will be chiefly due to radiation, that
is -
Before the radiation can diffuse out the
supernova has expanded from a 2 times 108 to
1015 cm. During that time, the internal energy
goes down from 1051 erg to 1044 erg. The
remaining internal energy is totally inadequate
to power the light curve (1049 erg).
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Energy from explosion
E 1051 erg T 1010
K R few x 108 cm Light can
escape when
But then adiabatic expansion implies that the the
interior temperature has dropped by 106 and the
interior energy is negligible. Radioactivity is
essential to keep the supernova hot and shining!
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Radioactivity
q 3.0 x 1016 erg/gm
q 6.4 x 1016 erg/gm
0.6 solar masses of radioactive Ni and Co can
thus provide 1.1 x 1050 erg at late times after
adiabatic expansion is essentially over.
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Qualitative Type Ia Supernova Light Curve
56Ni 56Co decay
Diffusion and expansion time scales approximately
equal
Luminosity
1043
Optical light curve
.
gamma-ray escape
1042
0 20
40 60
t (days since peak)
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Why is there a Philipps Relation?
Pinto Eastman (2001) New Astronomy
Broader Brighter
Photons must diffuse through a forest of lines
in a differentially expanding medium.
Doppler shift causes a migration from line to
line.
13,000 K at peak light
The trapped radiation is mostly uv and the uv
optical depth is very large.
Photons escape chiefly by fluorescence.
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Pinto and Eastman, (2000), ApJ, 530, 757
Blackbody peak near maximum light
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The decline is faster in B than in other bands.
Some of the energy that is lost from B appears
in R
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Dan Kasens explanation of the Phillipps
Relation
More 56Ni implies a larger luminosity at
peak.
But more 56Ni also implies higher temperature
in the interior. This in turn implies that Fe,
Co, Ni are more highly ionized (III rather than
II)
The more highly ionized Fe is less effective at
redistributing the blue light into the red
because it has fewer lines.
Hence hotter implies more optical opacity
(actually less optical efficiency)
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Light Curve Comparison2D delayed detonation
model compared to SN 2003du
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Spectral Time Series
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Model Width Luminosity Relation2-D delayed
detonation models (angle averaged)
Compare to current observational data set (SN
Factory, SDSS) Plan for future missions
(LSST/JDEM)
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3-D supernova spectrum calculationpure
deflagration model from Roepke et al, 2007
Calculation on 1000 cores Cray XT4 Jaguar _at_ ORNL
spatial resolution 150 x 150 x
150 wavelength resolution 1 angstrom (2x104
points) memory usage 1 TB execution time
10,000 CPU-hours
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