Caltech Fireworks day 2: Mostly Core-Collapse

The second day of the Fireworks Meeting was devoted to core-collapse supernovae (CC SNe). Observationally, this has meant “any SN that isn’t a type Ia”, leaving SNe which show evidence for hydrogen (SNe II) or helium (SNe Ib), or neither (SNe Ic) but without much of the silicon that characterizes SNe Ia. This nomenclature may not last long since the number of new observational types of SN is expanding rapidly in this golden age of robotic telescopes. But from a theoretical standpoint, we call them core-collapse SNe because we think that instead of nuclear fusion, the dominant energy source for the supernova explosion comes from gravitational potential energy, released when the core of the progenitor star collapses upon itself.

A brief reminder about potential energy

Let me unpack what I mean by that a little bit, using an an analogy closer to our own everyday experience. Let’s say you’re climbing the stairs of a tall building carrying a bag of tomatoes. In the process you’re increasing the gravitational potential energy of those tomatoes. The energy is “potential” because the tomatoes don’t look very different, but it’s stored and available to be released when you drop a tomato off the roof of the building. By the time the tomato hits the pavement, nearly all that potential energy has been converted to the “kinetic” energy of the tomato’s motion, which is subsequently deposited into the tomato itself in its abrupt interaction with the pavement and serves to, um, “unbind” it. (SPLAT)

This is not entirely unlike the process that goes on in the core of a massive star. Gas pressure supports the star against its own gravity (like your hand holding the tomato above the ground). The pressure is generated by the heat from ongoing nuclear reactions in the star’s center. If the star is massive enough (at least 8 times the mass of our Sun), those nuclear reactions go through several stages, converting material into progressively heavier elements until the star’s core is made mostly of iron — and it turns out you use up energy by fusing iron, rather than liberating it. At this point the pressure drops abruptly (like your hand being removed from beneath an ill-fated tomato) and the star’s core begins to contract under its own gravity, becoming denser and denser (like the tomato falling). Soon the iron core becomes so dense that it is transmuted into a neutron star, an object made entirely of neutrons so closely packed that a tablespoon of the stuff is as massive as a mountain. This material strongly resists further compression — it’s at this point that the tomato hits the pavement.

We know a lot about core collapse progenitors

We’re fortunate in that, unlike SNe Ia, we know a lot about CC SNe. There are many known examples of neutron stars in our Galaxy; perhaps the most famous is the one in the center of the Crab Nebula in the constellation of Taurus, the remnant of SN 1054 (recorded by the Chinese). The most two convincing pieces of evidence, however, are more contemporary observations.

First of all, the first SN that went off in 1987 (SN 1987A) went off in a very nearby small galaxy orbiting the Milky Way, called the Large Magellanic Cloud (LMC). This was a once-in-a-century event, and we were ready for it: a detector in the Kamioka mine in Japan registered a handful of neutrinos coming from the direction of the supernova at the time it went off. Neutrinos are produced in the final collapse of the progenitor’s iron core to a neutron star, and as very light particles able to go straight through the Earth without hitting anything, most of them are very conveniently allowed to escape the collapse and live to tell the tale. In fact, more than 99% of the gravitational potential energy released in the supernova must be converted into neutrinos and escape. So we know that the nuclear processes leading to the formation of a neutron star must occur in CC SNe.

The second is that we’ve actually watched CC SNe explode. People had used the Hubble Space Telescope to take pictures of the region in which SN 1987A went off before it happened. Turns out there was a very bright blue star there. This was lucky, but not absurdly so, since the LMC is nearby and an interesting object; in fact, by searching through the HST’s archives we’ve been able to find many more pre-explosion images of CC SN progenitors. They are “giant” or “supergiant” stars thousands of times more luminous than our Sun, and many times more massive. So we know that massive stars are the progenitors of CC SNe; they’re so bright we can even see them in other galaxies. In contrast, white dwarfs are so many millions of times fainter that in order to repeat this feat for SNe Ia, we’ll have to wait until the next one goes off in the Milky Way.

Image of the LMC field surrounding SN 1987A, shown in the inset. Courtesy of NASA.

Core collapse explosion mechanisms are highly uncertain

Despite knowing all this, nobody has yet been able to figure out how the energy from the collapsing core is transferred to the rest of the star to make it blow up. When the core “hits the pavement”, it rebounds, slamming into the inner layers of the star’s atmosphere and causing a shock wave which propagates outwards like a sonic boom. However, most existing simulations use an outdated model for neutron star material which makes it more compressible than real neutron star material is now (as of a few months ago) known to be. This means that real neutron stars are stiffer and don’t bounce back as much, so that the initial rebound shock is weaker than expected — it’s like trying to jump on a trampoline that’s made of wood (or concrete!) instead of elastic. What’s worse, in any simulation where the interactions of neutrinos with atomic nuclei are treated realistically, even an unrealistically strong shock wave peters out and the star fails to explode.

As with SN Ia progenitors, there are plenty of ideas:

  • Neutrino-driven: Probably the most popular (and venerable) option, in which neutrinos released by the formation of the neutron star don’t all escape. Some of them interact with the star’s atmosphere and heat it up, reviving the shock wave and blowing up the star. These models have been around since the 1960s and still don’t quite work right.

  • MHD-driven: Some neutron stars are known to have very strong magnetic fields — the entire magnetic field of the star’s original core is squeezed into a space the size of Manhattan, and is amplified a trillionfold in the process. When the core collapses, the dense inner regions of the star suddenly experience a much stronger magnetic field, and the resulting pressure could drive a SN explosion.

  • Acoustic mechanism: The collapse of the core sucks the rest of the star’s inner layers inward, setting up oscillations in the star’s interior which are unstable and grow with time, eventually blowing the star apart.

  • Phase-transition-induced explosion: When the core collapses, its inner regions are squeezed such that the neutrons within are further transmuted into even more exotic nuclear material. Depending on how compressible this stuff is, it may provide a second bounce-back which drives a new shock into the star’s inner layers and gets the star to blow up.

Dimensionality, resolution and approximations all matter

And as with SN Ia explosion simulations, the efficacy of all of these mechanisms depend strongly on approximations of uncertain physics and on numerical effects which arise only in simulations, not in nature.

As one example, early computers only had enough memory and CPU power to run SN simulations which were forced to be spherically symmetric (“1-D”). In one dimension, blobs of SN matter can only crash into each other and can’t slip past each other, form loops or plumes, or many other things that real fluids are seen to do in nature. Axially symmetric (“2-D”) models allow more freedom but require much more computing brawn to calculate. Full 3-D models are the most expensive in terms of time and resources, and also the most complex and hardest to get right, but promise qualitatively different and more realistic results than artificially symmetrized models. In fact many aspects of SN explosions are inherently asymmetric (e.g., relativistic jets) and can’t be represented at all in one dimension.

A 2-D CC SN simulation from a group at MPA-Garching, demonstrating the acoustic mechanism.

Similarly, the resolution of the simulations also makes a big difference. The simulations have to take a star much larger than our Sun and simulate processes which depend on interactions happening on human-sized scales or smaller. Unless you’ve got enough particles, cells, finite elements, or whatever in your simulation to explicitly represent what’s going on, you need to use some kind of averaged, approximate description. The “MHD-driven” scenario is an example; the kinds of processes involved in that explosion model all happen on much smaller scales than can be represented in the simulation. Various different simulation techniques exist which are more or less clever in getting around these limitations, but it’s always a problem at some level.

A full 3-D simulation of the gravitationally confined delayed detonation of a SN Ia, courtesy of the ASCI Flash Center at the University of Chicago. This movie was shown by Alan Calder during the SN Ia progenitor review session on Tuesday.

There’s more actual physical diversity than we thought

Another recurring theme was that the more we learn about massive stars, the more we realize that rather similar beginning states can lead to very different final appearances. Similarly, the same end state can map to many different initial states. This is part of why it’s so hard to figure out what exploded in the first place, and why we’re lucky for CC SNe to have been able to detect the actual progenitor star in pre-existing images for many explosions.

Examples: “Electron-capture” SNe, the explosions of stars 7-8 times as massive as our Sun, were usually thought to be very faint, could be significantly brighter depending on how much of their outer layers the progenitor stars have lost before they explode. “Pair-instability” SNe, explosions of stars 150-250 times as massive as our Sun, have always been thought to be bright, but could be very faint, for similar reasons. “Stripped-envelope” SNe, believed to result from the same kinds of explosions that power gamma-ray bursts, may have a variety of appearances and may or may not have a lot of heavy elements mixed into the progenitor star at the time it blows up. “Fallback” SNe, in which the inner layers fall back onto the central neutron star and trigger its further collapse into a black hole, may happen in different ways and leave either no black hole or black holes of different masses depending on the explosion mechanism.

I’m not completely convinced I even understood the debate at the level at which I just tried to summarize it above. I might further point out the obvious, that to those of you who like the elegance of theoretical physics, with sleek and simple equations giving rise to beautiful, profound, symmetric or crazy and intricate things, this field is not necessarily for you. It’s very much in the messy stages of trying to conceptually unify a crazy zoo of incredibly complicated events about which we have very limited information — kind of like particle physics in the 1950s, before the Standard Model was fully formulated. I definitely needed to pass out by the end of the proceedings today.


About Richard

I'm an American scientist who is building a new life in Australia. This space will contain words about science and math, but also philosophy, policy, literature, my travels, occasional rants, all sorts of things I find strange and awesome. The views expressed in this blog do not necessarily reflect the opinions of my employer at the time (currently University of Sydney), though personally, I think they should.
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