Men have known of the existence of supernovae for centuries; the Chinese recorded the observation of a very bright object in the sky that appeared suddenly and faded slowly over the course of a hundred days or so in 1054. Not until relatively recently, however, have scientists managed to agree on the cause of these suddenly bright objects; the idea that they were caused by exploding stars was not suggested until 1934 (Mayle 267). While most astronomers will now agree that supernovae are caused by exploding stars, they are still debating the specifics of how and why stars explode.
One of the first questions one must ask when considering supernovae is: Why would a star that has been essentially stable for billions of years become unstable enough to explode in less than a second? To answer this, we must determine what it is that kept the star stable during its lifetime. Obviously, gravity pulls in on the star constantly; what holds the star up against the force of gravity? The answer to this involves the way in which the star generates its energy. As gravity pulls the matter closer to the center of the star, the center becomes very dense and hot. Eventually, the center of the star reaches temperatures and densities such that fusion is possible; hydrogen atoms are fused together into helium, energy is released, and a star is born. The energetic photons which are then released must random-walk their way out of the center of the star. This whole process creates a pressure which is given by
where rho is the density, k is Boltzmann's constant, T is the temperature, mu is the average mass of each atom or nucleus in units of mH, and mH is the mass of a hydrogen atom.
Eventually, there is no longer any hydrogen in the center of the star; all of it has been turned into helium. At this point, the star must contract further until it reaches a higher temperature and pressure at which helium can fuse. This process continues, leading to successively heavier elements in the center of the star. Each step in this process takes less time to complete than the last one; in the final step, the star burns silicon to create iron for only two days.
At this point, the entire process grinds to a screeching halt. This is due to the nature of the material involved. We know from nuclear physics that the binding energy of a nucleus is given by
where A is the number of nucleons, Z is the number of protons, a = 0.01691u, b = 0.01911u, c = 0.000763u, d = 0.1075u, and e = 0.012u. This function reaches a maximum at iron. In other words, fusing iron produces no energy; instead the process requires energy. Since no energy is being released, the internal pressure no longer balances the force of gravity, and the star collapses in on itself.
As the star collapses, the amount of gravitational potential energy that the star has decreases; this energy must go somewhere. In fact, there is so much gravitational potential energy released that astrophysicists have developed a new unit of energy to deal with this: the foe. One foe equals 1051 ergs. This energy largely goes into dissociating the iron nuclei into alpha particles and free neutrons and protons. Some of the free electrons present in the core combine with free or bound protons to create more neutrons in the reaction
The neutrinos created in this reaction carry a significant fraction of the energy of the star out, since they have such a small cross-section for interaction with other particles that they can escape from the star quite easily.
How far the star collapses is determined by something known as the equation of state. A hard equation of state is one which causes the star to bounce earlier; a soft equation of state allows the star to collapse farther before bouncing. An example of a typical equation of state that one might use is:
where K1 = 255 MeV, gamma1 = 4/3, K0 = 140 MeV, and u is the fraction of electrons which are inside the nuclear volume (Cooperstein 246). Much of the uncertainty that exists as to whether the equation of state is hard or soft has to do with the fact that no one is really sure what happens in nuclear physics at the incredibly high pressures and temperatures that exist in the center of a star. Many astrophysicists have their own pet equations of state, and very few astrophysicists can actually agree about what terms belong in the equation of state. However, the basic idea relates back to the Fermi energy. Just as a system has a characteristic maximum energy that is finite even at 0 K; confining the particles to a smaller volume necessarily raises their energy and therefore their momentum. This creates a pressure that eventually stops the collapsing star and starts the matter of the star on a path back out of the center.
We have now made a great deal of progress towards explaining why stars explode and create supernovae; we at least have the matter in the star moving in the right direction. However, we now run into the cause of the largest debate involving supernovae mechanisms. The difficulty arises because the matter that has fallen in must now overcome gravity in order to escape from the star and create an explosion. Two possible solutions have been suggested; both will be discussed here.
The first solution is to use a very soft equation of state, as this allows the matter to fall in farther and to thus pick up more energy. Simulations done with a soft equation of state have been successful in creating an explosion. This would seem to be an acceptable solution, and it may well be the correct mechanism for some supernovae, but it does have three slight bugs. The first is quite simple: no one really knows what the equation of state is, since the physics behind it is not yet fully understood; a more complete understanding of the underlying physics could eliminate the possibility of a sufficiently soft equation of state. The second problem is that most simulations take into account only electron neutrinos; those taking into account the presence of other types of neutrinos produce weaker shock waves, due to increased energy leakage via neutrinos; this leads to longer times for explosions and requires an even softer equation of state in order for the explosion to occur. The third, and largest, problem is that this solution only works for stars with iron cores that weigh less than approximately 1.33 times the mass of the sun, while neutron stars (the remnants of supernovae) with larger masses than this have been observed.
The second solution is for the neutrinos generated in the core of the star to interact with the surrounding material, so that they deliver energy to this material. The amount of energy generated in a supernova is on the order of 100 foe; however, only about 1 foe of this usually gets imparted to the envelope of material surrounding the core. (Most of the 1 foe of energy that the envelope does get goes into kinetic energy; only about 0.01 foe go into producing the bright flash of light we see.) This mechanism of imparting additional energy to the envelope via neutrinos is known as late-time neutrino heating supernovae, due to the fact that this is thought to occur approximately 1 second after the beginning of the explosion. (Note that the time from bounce to the stalling of the shock wave is approximately 20 milliseconds.) This is possible because of the dissociation of the iron in the outer part of the core into free protons and neutrons. The structure of a nucleus causes it to have a very small cross-section for interaction with neutrinos; if the same nucleus is dissociated into its component particles, it has a much higher cross-section for interaction with neutrinos.
Thus, because iron has the largest binding energy per nucleon, the star becomes unstable when it runs out of silicon to turn into iron. It then collapses; the incompressibility of nuclear matter turns this motion around, and a shock wave is formed which moves out from the center of the star. It may be that this is enough to cause a supernova; however, it is more likely that, at least in the case of larger stars, neutrino interactions with the material of the shock wave are necessary to give the shock wave enough energy to escape the gravity of the star and cause an explosion. This explosion drives material from the star out into the surrounding regions, creating beautiful nebulae such as the well-known Crab and Horsehead nebulae and leaving behind a neutron star.
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