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# 5.3 Supernovae explosions

Over its lifetime, a high-mass star is supported against collapse by the thermal energy derived from converting hydrogen to iron, via intermediate species. Some of this energy is radiated away by the surface of the star over its long lifetime. Then, at the end of its life, it reverses that entire process by breaking apart the iron nuclei into their constituents. At the end of its life, a high-mass star will emit a similar amount of energy in a few seconds to that which it has emitted over its entire main-sequence lifetime!

Therefore, in a stellar core composed largely of iron, photodisintegration and neutronisation reactions trigger a rapid collapse, which will continue until the core reaches a density comparable to that of an atomic nucleus.

- Given that a nucleus of mass number A has a radius , what is its density?

- The density where the mass and the volume . Hence and therefore

This is equivalent to around 200 million tonnes per cubic centimetre! When the core approaches nuclear densities, nuclear forces resist any further compression and the collapsing core will rebound. This sends a shockwave through the infalling material, which causes much of the stellar envelope to be ejected. This is a supernova explosion (see Figure 4).

Figure 4 Two images of the same galaxy taken 41 days apart, with the location of a supernova highlighted by the white lines in the right-hand image.

Over the course of a year or so, the optical light output of a supernova is typically about 1042 J. However, it can also be observed that a further 1044 J of energy is carried away as the kinetic energy of the exploding debris, at velocities of tens of thousands of kilometres per second, to form a supernova remnant. These are certainly vast amounts of energy, but it turns out that they do not tell the whole story of the energy release during a supernova.

As you saw earlier, the gravitational potential energy released in the collapse of a stellar core is . This is 100 times greater than the observed energy carried away by the expanding debris, and it is at least 10 times the energy required to photodisintegrate the iron core, and 10 times the energy that can be carried away by neutronisation. So where does all the gravitational potential energy released by a supernova actually go?

In fact, there is an intermediate stage between the iron core and the production of a compact remnant. This takes the form of a hot, dense plasma of neutrons, protons, electrons, neutrinos and photons. At a temperature of 1011 K and a density of 1014 kg m-3 this plasma is opaque to electromagnetic radiation, but not to neutrinos; it is believed that neutrino/antineutrino pairs are produced in the plasma, and carry away most of the gravitational binding energy of the collapsing core.

- Quantify the ways in which energy is carried away from a supernova.

- Photons provide the least effective means of removing the energy: only ~ 1042 J over the first year or so after the explosion. The expansion of the ejected material carries 100 times as much as kinetic energy, ~ 1044 J. However, the binding energy of the neutron star is , so much more energy must be removed than is carried by the photons and kinetic energy. The majority is thought to be carried away by neutrinos.

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