A year ago, I taught a 3D Computer Modelling and Animation class. Most of the class was focused on the students working on projects in groups of 1-3. During that time, I did a small project myself as well. I posted a still image from the project a year ago, and promised to post the movie. I’m only now getting around to doing that….
Here is a direct link to the movie. The text in this blog post, and the movie, are also available on the web here. The movie is currently in Ogg Theora format. At some point, I may also put online on that web page a file in another format.
A thermonuclear supernova, also called a Type Ia supernova, occurs when a white dwarf star passes a critical mass (the Chandrasekhar mass). Too massive to support itself under the influence of gravity it starts to compress. This compression triggers runaway nuclear fusion, and the entire star blows itself away in a massive thermonuclear explosion.
White dwarf stars are whats left over when a moderate mass star (less than about 8 times the mass of the Sun) ends its life. Towards the end of its life, such a star will slough off its outer layers, which briefly (for a few ten thousand years) glow as a planetary nebula. The core of the star, which is probably somewhere between 0.4 and 1.4 times the mass of the Sun but only about the size of the Earth, is left behind. It’s made of Carbon and Oxygen, but given its mass and size is incredibly dense. It is supported by “Fermi degeneracy pressure”. To those who know some Quantum Mechanics, the electrons in the white dwarf are in a degenerate fermi gas. If you don’t know what that means, suffice to say that the electrons (and thus the nuclei that go along with them) are packed together absolutely as close together as the fundamental laws of physics (the same basic things that give us the Heisenberg Uncertainty Principle) will allow them to be.
Such a configuration in a star is only stable up to 1.4 times the mass of the Sun (which is the aforementioned Chandrasekhar mass). If it starts smaller than that, how does it get to the necessary size? It must have a source of mass somewhere. There are two possible ways for a white dwarf to reach the Chandrasekhar mass. First, if the white dwarf star has another regular star as a companion, and if it’s orbiting that star closely enough, it’s possible that the gravity of the white dwarf will be able to slowly pull some of the gas off of the surface of the other star and accete it on to itself. If the mass builds up to the critical mass, the white dwarf starts to collapse, and, boom, thermonuclear bomb 1.4 times the mass of the Sun. This is called the “single degenerate” scenario, beacuse there is only one white dwarf (the degenerate object).
The second possibility is called the “double degenerate” scenario. In this case, two white dwarfs, both of them less than the Chandrasekhar mass, come together. Neither one by itself has enough mass to explode. But, if the two come together and merge, the result can be a degnerate object that’s above the Chandrasekhar mass, and boom, supernova.
This movie depicts the single-degenerate scenario, where a white dwarf has a regular star (or perhaps a subgiant or giant star) as a companion. The mass pulled off of the companion builds up in an swirling accretion disk around the white dwarf. Mass from the inner part of the disk falls in on to the white dwarf until it reaches the critical mass and explodes.
Stages and Timescales
So that the movie can complete in a reasonable period of time, I play a little fast and loose with timescales. I’m going to describe the major steps of the movie, and talk about how everything evolves too fast in the movie as compared to in real life.
A star that is several times the mass of the Sun will live a few hundred million years before it becomes a white dwarf. If it’s close enough to its companion (which will be of lower mass than the star that left behind the white dwarf started as), it might start accreting matter from it right away. If it’s farther, it might not start accreting matter until the companion star approaches the end of its life and starts to swell. This can mean a delay of anywhere from millions to hundreds of millions of years after the first star becomes a white dwarf before it has accreted enough mass of its companion to reach the very final stages depicted in the movie here. It’s possible while this is happening that there might be sub-supernova explosions, as some of the hydrogen gas collected on to the white dwarf undergoes a (smaller, but still huge) fusion explosion; we might observe such an event as a nova.
You might object that the camera is moving through the system faster than the speed of light, and you would be right. But, what the heck, it’s an animation! I’m showing you what’s there, not what it would look like if you were really flying through the system.
The explosion itself is instantaenous on astronomical timescales. There is some debate amongst theorists who model the explosions exactly how it happens, but even those arguing for a slower explosion still calculate that the explosion itself is over in about a second (e.g. Ciaraldi-Schoolman, Seitenzhal, and Röpke, 2013). The movie doesn’t really depict the thermonuclear fusion itself; it depictes the expanding blast wave of material blasted away and expanding as a result of the explosion. (Pictures of nuclear explosions we’ve created with our bombs on Earth are the same; the actual nuclear event is over instantly, and then the “explosion” is the expanding blast wave.) Watching the movie, you may think that the expanding blast wave is awfully sedate for such an extreme explosion. In fact, if anything it’s expanding too fast compared to how long it should take to expand in reality! If the star depicted in the video is a subgiant star, it probably has a radius that is at least several times the radius of the Sun. The white dwarf is a similar distance away from the surface of the companion star. If the white dwarf is 10 Solar Radii away from the surface of the star, that’s a distance of about 6,000,000 km. The blast from a supernova expands fast, but not at the speed of light. From memory (and I should really check this), we expect the blast wave to expand out at something like a third the speed of light. At that speed, it would take the blast wave a full minute to reach the nearby star! Things are far apart in astronomy. The 4-5 seconds it takes the blast wave to reach the companion star in the movie is almost certainly too fast.
The movie starts outside the explosion, but eventually the blast wave overtakes the camera and we see it from the inside… at about the same time that the blast wave is overtaking the companion star. What happens to the companion star? You might think it would suck to be next to a thermonuclear bomb one and a half times the mass of the Sun. And, it would. You might think you would be completely blown away. And, you would be. But a star wouldn’t. The gravitational force holding together the companion star is strong enough to allow it to survive despite the tremendous amount of energy deposited into it by being next to an exploding white dwarf. That being said, it is a lot of energy, and so we expect some fraction of the outer layers of the star to be stripped away. That indeed happens in this movie.
Finally, the movie zooms out, so that you can see the supernova in the context of its host galaxy. This supernova in the movie is really on the outskirts of the galaxy. It’s true that you find thermonuclear supernova more often in the outskirts of the galaxy than you do core-collapse supernovae (the other type), so it’s not unreasonable for the supernovae to be where I’ve shown it. I have made it rather optimistically far out, however. It’s also true that when it reaches maximum brightness, a supernova can be as bright as its whole host galaxy, which is qualitatively what you see in the movie. However, here is perhaps the greatest acceleration of time. It takes about 20 days for a supernova to reach maximum light after it explodes… not the mere handful of seconds that you see in the movie. However, the movie would be really boring if you had to sit and watch it for 20 days for the supernova to get as bright as the galaxy!
(You might be surprised by how long it takes for the supernova to reach maximum light; why isn’t it brightest right at the explosion? Parts of the exploding gas cloud are opauqe. Not all of it, and indeed as it expands, more and more of the outer layers become transparent. However, because the inner parts are opaque, the energy is effectively trapped inside the expanding cloud, and the rate at which it can be radiated away is limited by the surface area of the opaque part. So, as the supernovae gets bigger, it has more and more surface area, and so can get brighter. However, that’s only part of the story. The profile of rising and falling on the lightcurve is also driven by the detailed physics of what’s going on in the supernova. Some of the energy of the explosion goes into creating unstable nuclei that aren’t entirely stable, which then decay over time, releasing their energy into the expanding gasses.)
After maximum light, a supernova fades. Depending on how far away it is and how sensitive a telescope you use, it will be visible for weeks or months, or perhaps even years. In fact, if it’s close enough, it will be visible for thousands of years. At that point, though, we no longer call it a supernova explosion, but rather call it a “supernova remnant”. As an example, the X-ray and radio source Cassiopeiae A is the left over remnant of a thermonuclear supernova in our Galaxy that exploded in 1572.
Galaxy Image: NGC 1309, imaged by the Hubble Space Telescope. Hubble Legacy Archive, ESA, NASA; processing by Martin Pugh.
Music: Symphony No. 5 in C Minor by Ludwig van Beethoven, performers unknown; from the public-domain music site musopen.org