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# 5 Supernovae

In this section, you’ll see what happens to a star whose final core mass exceeds the Chandrasekhar limit, and subsequently, discover what remnant it may leave behind.

A star with a main-sequence mass will complete all the stages of nuclear fusion that are available. Silicon burning will result in a core composed mainly of iron-56, surrounded by concentric shells of silicon, oxygen, neon, carbon, helium and hydrogen. No energy can be released by the thermonuclear fusion of iron, so the core collapses and the degenerate electrons within it become more and more relativistic. When the mass of the core exceeds the Chandrasekhar limit (about ), the degenerate electrons are no longer able to support the core, and a catastrophic collapse follows. The core will essentially collapse on a free-fall timescale, liberating gravitational potential energy.

- The free-fall timescale is given by . Calculate the free-fall timescale for a stellar core with a density of .

- Putting in the numbers to the equation above,

- The gravitational potential energy released in the collapse of a stellar core of mass M, from an initial radius R1 to a final radius R2, is . Calculate the gravitational potential energy released when a stellar core of mass collapses to a radius of about 10 km.

- In this case, the final radius is very small, so , and we can neglect the initial gravitational potential energy as it is so small. Therefore the gravitational potential energy released is . So the energy released by the collapse of a stellar core is

As the previous two questions show, the collapse of the core is very rapid and it liberates a vast amount of energy.

The initiation of exothermic (energy-liberating) fusion reactions provides pressure support for stars during their long-lasting burning phases. However, the initiation of endothermic (energy-absorbing) reactions draws kinetic energy out of the material and hence eliminates the pressure support. There are two processes that can absorb energy in the collapsing core: photodisintegration of nuclei by high-energy gamma rays and electron capture processes. In the first, the energy is used to unbind the nuclei, while in the second, energy is converted into the kinetic energy of neutrinos, which stream out of the star largely unhindered. Let’s consider each of these two processes in more detail.

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