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I was watching a video (https://www.youtube.com/watch?v=IZ59_akUUBs) about massive explosions and came across 2007bi. The video stated that this SN happened due to gamma-ray driven antimatter creation.

Apparently, its core being made mostly of oxygen began releasing energetic photons which decayed into electron/positron pairs. Their mutual annihilation caused the core to collapse and triggered the supernova.

I have a couple of questions concerning this.

  1. Pair-instability supernova happens when a star is about 130 solar masses, but the star here was only at 100 solar masses.... (per Wiki "These stars are large enough to produce gamma rays with enough energy to create electron-positron pairs, but the resulting net reduction in counter-gravitational pressure is insufficient to cause the core-overpressure required for supernova. Instead, the contraction caused by pair-creation provokes increased thermonuclear activity within the star that repulses the inward pressure and returns the star to equilibrium. It is thought that stars of this size undergo a series of these pulses until they shed sufficient mass to drop below 100 solar masses, at which point they are no longer hot enough to support pair-creation. Pulsing of this nature may have been responsible for the variations in brightness experienced by Eta Carinae in 1843, though this explanation is not universally accepted.") [https://en.wikipedia.org/wiki/SN_2007bi ]

Is it more likely the size of the star was wrong, or the that it can happen at lower mass or possibly there was something else at work here?

  1. Why wouldn't the extra energy from the electron/positron annihilation add more energy to the star's core? It seems counter-intuitive that adding energy reduces the internal supporting pressure. Can someone explain this?
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Pair instability supernovae are thought to end the lives of stars with initial masses $>130 M_{\odot}$.

For SN2007bi, the relevant paper by Gal-Yam et al. (2010) deduced that they had seen the explosion of a $100M_{\odot}$ helium core and they infer that such a massive core would have arisen in a star with an initial mass of $\sim 200M_{\odot}$. So there is no contradiction here between theory and observation.

The core of a very massive star relies on radiation pressure as a means of support. Pair production removes gamma ray photons that were providing pressure support and replaces them with the rest masses of (relatively) slowly-moving electrons and positrons, which do not.

What matters here (for the pressure) is the kinetic energy density, not the total energy density - which is roughly constant. Pair production has the effect of turning the pure kinetic energy density of photons into the rest-mass of electrons and positrons, thus reducing the pressure.

Of course, the matter and anti-matter also annihilate giving back the photons, but it is an equilibrium process such that once a population of (albeit short-lived) matter/anti-matter pairs are created, they reduce the radiation pressure. The idea is that in the cores of particularly massive stars this is a runaway process, with core contraction leading to greater pair production, more contraction... And ultimately a supernova that blows up the whole star.

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  • $\begingroup$ Your answer was very helpful. Thanks 1 final question: So would 2007bi shed the extra 30+ solar masses as ejections? IF so, how long would this period last? $\endgroup$
    – Rick
    Mar 3 '19 at 13:00
  • $\begingroup$ @Rick It has probably shed more than that if it started as a 200 solar mass star. The only mass estimate here is of the core of the star that exploded. $\endgroup$
    – ProfRob
    Mar 3 '19 at 14:59
  • $\begingroup$ @Rick These stars have lifetimes of a few million years, but I would think most mass loss would be in the final ~million years or less. $\endgroup$
    – ProfRob
    Mar 3 '19 at 18:15
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Does gravity or pressure get stronger faster?

Suppose a star is in equilibrium between pressure and gravity. If it compresses slightly, the core is compressed adiabatically and it's pressure increases. But gravity also increases. If gravity increases more, the equilibrium is unstable and the collapse will accelerate.

How much does gravity increase? Consider a the pressure added from the weight of a shell 1cm thick and 1000km across. If the shell compresses to 500km (8-fold volume reduction of the core), it experiences 4 times as much gravity on a quarter of area (16 times the pressure). Thus $P_{grav}$ ~ $V^{-4/3}$ [because 8^(4/3) = 16].

For ideal gases/plasmas at moderate temperatures (enough to be fully ionized) the pressure is $P_{cold}$ ~ $V^{-5/3}$. This is a steeper power-law ("stiffer" equation of state) than gravity and the gas is stable.

At high temperatures photons support most of the pressure. Photon pressure have a power-law of $P_{rad}$ ~ $V^{-4/3}$. This is right on the boundary of (in)stability. But since the gas pressure still contributes slightly, the actual power law is slightly more negative than -4/3 and the star is slightly stable. But it doesn't take much to destabilize things.

In all stars the core is heating and compressing over time as the fuel gets used. When the core gets within a factor of 5 or so of 511 keV, or 5.9 Giga Kelvin, electrons and positrons start being produced. Some of the heat of compression is "wasted" as pair creation rather than making more energetic photons or increasing particle kinetic energies. This makes the power-law "softer" and makes the core unstable.

Once electron-positron pairs (but not actual anti-protons) are created en-masse the core destabilizes and collapses. Temperature, pressure, and gravity are all increasing, but gravity is rising faster than pressure.

The sudden increase in temperature and pressure causes fusion to massively accelerate. Fusion is releasing much more heat, 7 MeV per nucleon, than the thermal energy which is well less than 1 MeV. If the collapse were mild, fusion would gently stop the collapse and the star would reach a new equilibrium. But the collapse is severe. Fusion has to drive pressure far higher than gravity to reverse the inertia of the in-falling matter. At the point of minimum core size, pressure far exceeds gravity and fusion is occurring faster and faster in a thermal runaway. A violent explosion ensues that leaves no remnant behind.

The energy source is fusion, not antimatter, but the pair-production allows gravity to (temporary) win and set the stage for runaway fusion.

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