Rick's Critique of the Cosmic Coincidences: Appendix I

A star initiates a Type II supernova when the sequence of fusion reactions, ending in iron, is exhausted. The event begins with the gravitational collapse of the star. This occurs when the nuclear fusion reactions are depleted to the extent that they can no longer sustain the temperatures, and hence pressures, required to support the star against gravity. During the ensuing collapse, the intense gamma ray production photodisintegrates the iron into alphas, neutrons and protons. Neutronisation takes place within the core, in which electrons and protons combine to form neutrons and neutrinos. This is an endothermic reaction. It leads to further loss of pressure support and exacerbates the ongoing collapse. The central core collapses to nuclear densities, and transiently even higher, followed by a ‘bounce’ which creates a shock wave. This shock wave is the root cause of the Type II supernova explosion, but the exact mechanism by which its energy is transferred to the stellar mantle to create the explosion is not universally agreed or quantified. The generally favoured model involves stalling of the shock wave and extremely high temperatures generating thermal neutrinos. The neutrinos transfer a small fraction (~1%) of their energy to the mantle material, causing the explosion, but the majority of the energy is carried away by the neutrinos themselves.

One of the unresolved problems in Type II supernova theory is elucidation of the mechanism for transferring the neutrino energy to the mantle. Neutrinos, of course, interact extremely weakly. There are two reasons why their interactions are rather stronger than usual in Type II supernovae, sufficient to make them credible candidates as the cause of the explosion. The first is that the star is very dense just prior to the explosion. The second is that the neutrino energies are very high, and weak interactions increase in strength at higher energies (cross sections are proportional to energy squared). Some authors have claimed that fine tuning of the Fermi constant is required to allow Type II supernovae to occur. The argument is that the interaction strength must be delicately balanced to allow the neutrinos to escape the core and yet be able to transfer significant energy to the mantle.

In moving through a dense star, neutrinos can react with the nucleons, either free nucleons or those within nuclei, via weak nuclear processes. If a Type II supernova is in progress then we can imagine the material of the mantle expanding rapidly outwards. This expansion will have some characteristic timescale, called the dynamical timescale, defined by the initial speed and the resisting pull against gravity. Carr and Rees argued that the neutrino reaction time must be of the same order as the dynamical timescale. The reasoning is that, firstly, the neutrinos mostly escape the star’s core, rather than being trapped within it. Consequently, the reaction time cannot be too short compared with the dynamical timescale. On the other hand, if the explosion is caused by the neutrinos, then it is necessary that some interactions occur before they escape. So the reaction time cannot be too long compared with the dynamical timescale either. Hence, the two timescales must be of the same order.

In this Appendix we attempt rough estimates each of these timescales. The accuracy of these estimates is too poor to conclude whether the claimed 'coincidence' is, or is not, particularly remarkable.

Stonehenge at the summer solstice sunrise