Download Introduction to Astrophysics Tutorial 4: Supernovae

Introduction to Astrophysics
Tutorial 4: Supernovae
Iair Arcavi
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Three Ways for Stars to End Their Lives
1. Low-mass single stars: create white dwarf, remains below Chandrasekhar mass, cools down
slowly.
2. Low-mass stars in a binary system: create white dwarf, accrete mass from companion, approach
Chandrasekhar mass, explode (supernova of type Ia).
3. High-mass stars: collapse, degenerate core exceeds Chandrasekhar mass, explode (supernovae of
all other types).
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The Evolution of Massive Stars (Final Stages)
• Massive stars (M & 10M ) go through sequential stages of burning all the way to Fe. Shell
burning proceeds rapidly (for 15M star for e.g., H → He takes about 11 · 106 years while
Si → F e only some 18 days).
• Mass loss plays an important role (the higher the mass, the greater the mass loss), but is poorly
understood. Wolf Rayet stars are an example of high mass loss rates, ejecting most or all of the
H and exposing the He core.
• Cores are not degenerate until the nal burning stages. Only when Fe core contracts, do they
become degenerate, but because the mass is larger than MCh , degeneracy pressure can not
withstand self-gravity, and star continues to contract. Three processes then increase the collapse
rate:
1.
Electron capture
onto heavy nuclei rob from degeneracy pressure, and energy by the
inverse beta decay.
2. Degeneracy pressure has very low sensitivity to temperature, so temperature can rise unrestrained, leading to photodisintegration of Fe which robs an additional 2M eV per
nucleon:
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F e → 134 He + 4n − 124M eV
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3. Increasing temperatures then allow photodisintegration
neutrons causing losses of 6M eV per nucleon.
4. Additional inverse beta causes neutronization:
of He
into free protons and
p+e→n+ν
robbing more energy (which goes to the neutron mass and escapes with the neutrino) and
decreases electron pressure.
• Finally, at ρ ∼ 1015 gr/cm3 , neutron degeneracy pressure sets in halting the collapse. A ∼ 20km
neutron-rich core at atomic densities is formed.
• The remaining outer layers fall onto the core, but are bounced out and ejected at velocities up
to 10, 000km/s.
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Core Collapse Supernovae
3.1
The Energy Budget
The energy we have at our disposal, is that released by gravitational contraction of the core (Mc ∼
1.5M ) from its initial radius Rc ∼ 0.01R to its nal radius Rnc ∼ 20km:
∆Egrav
GMc2
GMc2
−
−
2
Rc2
Rnc
GMc2
2
Rnc
= −
≈
≈ 3 · 1053 erg
Where does this energy go?
1. The nuclear processes absorb approximately:
≈
∆Enuc
≈
Mc
MHe
2 · 1052 erg
7M eV
2. The radiation observed (of ∼ 3 · 1010 L for about one year) uses up:
∆Erad ≈ 3 · 1051 erg
3. The mass seen ejected requires
∆Ebind
GMc (M − Mc )
Rc
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5 · 10 erg
=
≈
2
to unbind from the star, assuming M ∼ 10M and an additional:
∆Ekin
1
2
(M − Mc ) vexp
2
1052 erg
=
≈
to account for the observed vexp ∼ 10, 000km/s.
Together this accounts for only 10% of the gravitational energy released. Where does the rest go?
And what mechanism deposits the energy in the envelope? The answer to both questions is neutrinos,
thanks to their enormous numbers (∼ 1057 ) and the extremely high densities of the surrounding
matter allow for enough neutrino pressure. This idea was conrmed experimentally with the detection
of neutrinos from SN1987A which went of in the LMC, a few hours before the light was seen.
3.2
Light Emission from Supernovae
When the shock breaks through the surface, a are up of radiation in the UV is released. As the
envelope expands and cools, the radiation shifts to the optical and becomes visible. As the shock
sweeped through the mantle it heated it up to temperatures up to ∼ 5 · 109 K which can allow for
nuclear statistical equilibrium within seconds. This causes fusion to 56 N i (not Fe since the fuel is at
Z/A ∼ 1/2 and there is no time for beta decays to change this ratio). Once the shock reaches the
Ne-O layer, the temperature reaches ∼ 2 · 109 K and nucleosynthesis stops.
N i is an unstable element which decays (with a half life of 6.1 days) to 56 Co, also an unstable
element which itself decays (with a half life of 77.1 days) to 56 F e. These decays power the supernova
light curve for a few months and dictate its decline rate. The amount of 56 N i produced can thus be
deduced from the light curve. For e.g. SN1987A produced some 0.075M of 56 N i.
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Detections of 1.8M eV photons (gamma rays) in the ISM which come from the decay of 26 Al to 26 M g
tell us that nucleosynthesis and the dispersion of heavy elements is going on continuously, since the
half life of this decay is 7.2 · 105 years.
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Type Ia Supernovae
A second channel for stellar explosions involves an accreting white dwarf. When it approached MCh
(but before actually reaching it), its C is ignited. Because of the high degeneracy (i.e. pressure weakly
depends on temperature), the fusion process is a runaway one, burning the entire white dwarf, and
producing a spectacular explosion. This process implies that all explosions of this type are very similar,
since the mass, composition and conditions are the same for every case (unlike for the massive stars'
core collapse explosions). This makes type Ia supernova ideal standard candles (in addition to the fact
that they are extremely bright events).
In fact this could also happen when two white dwarfs merge. It is now known which (if not both)
possibilities are realized in nature.
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