Supernovae

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Supernovae Type Ia
A really good explosion.
http/www.supersci.org
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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. For several weeks
their luminosity rivals that of a large galaxy.
HST
SN 1994D
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• 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 Type Ia supernova spectrum at peak light is
dominated by lines of singly ionized Si, Ca, S,
Mg, Fe. The late time spectrum (not shown) has
strong emission lines of singly and doubly
ionized Co and Fe.
Filippenko, (1996), Ann. Rev. Astron. Ap
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Possible Type Ia Supernovae in Our Galaxy
SN D(kpc) mV
185 1.2-0.2
-8-2 1006 1.4-0.3
-9-1 1572 2.5-0.5
-4.0-0.3 1604 4.2-0.8
-4.3-0.3
Expected rate in the Milky Way Galaxy about 1
every 200 years, but dozens are found in other
galaxies every year. About one SN Ia occurs per
decade closer than 5 Mpc.
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Spectra are similar from event to event
Spectra of three Type Ia supernovae near peak
light courtesy Alex Filippenko
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The B-band (blue) light curves of 22 Type Ia
supernovae (Cadonau 1987). Broadly speaking they
are quite similar.
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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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Some Critical Issues

• How do Type Ia supernovae explode. Can we
  understand the outcome from first principles?
  Yes, maybe someday
• Why is there a width-luminosity relation?
  Its the opacity.
• Could there be evolutionary corrections that
  must be applied to the use of Type Ia
  supernovae as standard candles?
  Dont know, but it is surprising that the
  light curves can be described to high
  accuracy as a single parameter family
  (56Ni mass)

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Leading Model
Accretion and growth to the Chandrasekhar Mass
(1.38 solar masses) Degenerate thermonuclear
explosion. (Hoyle and Fowler, 1960).
Explains

• Lack of H in spectrum
• Association with old population
• Regularity
• Large production of 56Ni and a light curve
  dominated by radioactivity.

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In order for the white dwarf to grow and
reach the Chandrasekhar Mass the accretion rate
must be relatively high (to avoid the nova
instability). This must be maintained for
millions of years.
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Progenitor
Arnett (1968, 1969) Nomoto, Sugimoto, Neo (1976)

Ignition occurs as the highly screened carbon
fusion reaction begins to generate energy faster
than 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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Ignition Conditions

• Supernova preceded by 100 years of convection
  throughout most of its interior
• 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 x 109 g cm-3
Burning 0.05 solar masses can cause expansion by
a factor of three
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Conditions in a Chandrasekhar Mass white dwarf as
its center runs away following about a
century of convection.
Vertical bars denote convective regions
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Convection for 100 years, then formation of a
thin flame sheet.
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
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Laminar Flame Speed
km/s
nb. these speeds are slower than 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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(Starting from 1.38 solar masses of carbon and
oxygen)
A Successful Model Must

• 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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Laminar Flame Speed
km/s
cm
Timmes and Woosley, (1992), ApJ, 396, 649
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Model W7
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 01
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)
Brachwitz et al. (2000)
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For over 25 years the search has been for the
correct physics that would describe this
solution, i.e., a little burning at high density
and a lot of burning at low density.

• Rayleigh-Taylor Instability
• Turbulence
• Delayed Detonation
• Pulsational Detonation
• Off-center burning

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Kercek, Hillebrandt, Truran (1998)
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Rogers, Glatzmaier, and Woosley (2002)
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Combustion Rate
In 1D for an undeformed flame
but in general in 3D
Bottom half is burning less fuel than top half
where r and l are the largest and smallest scales
of the distortion and D is the fractal dimension
(D 2 for a plane, 3 for space filling of radius
l). In the supernova D starts near2 and grows as
a consequence of instabilities.
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One of the most effective ways of
increasing surface area is turbulence.
l
L
Big whorls have little whorls that feed on their
velocity....
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The Gibson Length
For a standard Kolmogorov picture of turbulence
lGib is defined by
This is the smallest length scale that can be
deformed by turbulence before burning first.
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If use this for the smallest length scale and
D2.33for Kolmogorov turbulence
The flame moves with an effective speed equal to
that of the largest (local) turbulent
eddy. This also turns out to be true for other
for other representations of turbulence. e.g.
Niemeyer and Kerstein, New Astron, (1997), 2,
239 for Bolgiano-Obukhov scaling.
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Unlike the laminar flame speed which slows with
time (density), the turbulent speeds and sizes of
the largest eddies increase with time
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A simple toy model ...
"Sharp-Wheeler Model"
g
Model OK, but deficient in Si, S, Ar, Ca
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Speculation

How many points and when and where each ignites
may have dramatic consequences for the supernova
(origin of diversity?)
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Igniting the star at a single point off
center gives very different results than
igniting precisely at the center or in a
spherical volume.
This "single point ignition" model did not
produce a supernova (pulsation would have
ensued)
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Ignition at 5 points did produce a
successful supernova with 0.65 solar masses of
burned material, 0.5 solar masses of which
was 56Ni.
Note - this was a 2D calculation.
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Reinecke et al. (2002)
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Reinecke, Hillebrandt, Niemeyer, et al. (2002)
MPA
0.4 solar masses Fe 4.5 x 1050 erg
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slides from Martin Reinecke
converged??
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slide from Martin Reinecke
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Light Curve
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 108 to 1015 cm.
During that time, the internal energy goes down
from 1051 erg to 1044 erg. The internal energy
is totally inadequate to power the light curve.
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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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More 56Ni implies a larger luminosity at
peak. (Arnett's rule)
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
"Photon Splitting" than less ionized Fe
Hence hotter implies more optical opacity
(actually less optical efficiency)
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Left a single supernova model (energy, density
structure, etc) in which only the mass of 56Ni
has been varied. Also shown are the standard
template of light curves displaying the
width-luminosity relation.
Pinto Eastman, (2001), New Astron,
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Light Curves
What matters?

• The mass of 56Ni -- contributes explosion
  energy, radioactive energy, and opacity.
• The mass of 54Fe, 58Ni, and other stable members
  of the iron group -- contribute opacity
  and explosion energy, but no radioactive
  energy.
• The mass of SiSArCa -- contribute to the
  explosion energy, but not the opacity or
  radioactive energy.
• The explosion energy -- depends on the ignition
  density (hence accretion rate) and C/O ratio
  as well as all the above masses.
• Mixing

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An idealized model
Assume a starting mass of 1.38 solar masses, a
central density of 2 x 109 g cm-3 and a C/O ratio
of 12 For a given starting density, the final
composition (three variables, plus mixing) then
defines the model.
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The final velocity distribution is not very
sensitive to how the energy is
deposited (especially for the iron containing
region).
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Conclusions

• A first principles understanding of how Type Ia
  supernovae explode is still lacking, but
  progress is being made
• It may be that detonation plays no role in the
  explosion though this issue is not
  conclusively resolved. SN Iae explode by a
  carbon deflagration in which instabilities and
  turbulence play a key role.
• The width-luminosity relation is a consequence
  of the atomic physics of the explosion, in
  particular a temperature- dependent escape
  probability. The most important parameter is
  the mass of 56Ni.
• But there are four other parameters that ought
  to affect the light curve at some level.
  Evolutionary corrections could enter in this
  way.