Why Stars Explode: Examining the Physics Behind Supernovas

[jaydnul]

All of my internet research comes up with the same answer which is that when the core fuses all of its fuel, there is no more outward pressure, so the gravitational attraction takes over. What isn't explained is WHY it will explode outwards. I realize that the temperature will increase, but wouldn't conservation of energy say that the star would bounce back out to its original size, almost like a harmonic oscillator? There has to be another source of energy other than the Coulombic and gravitational repulsion/attraction of the atoms?

My only guess would be that the gravitation potential energy is converted into such a high temperature when compressing that the nuclei fuse into heavier elements than iron. But that wouldn't give off energy, it would remove it.

 

[SteamKing]

All of my internet research comes up with the same answer which is that when the core fuses all of its fuel, there is no more outward pressure, so the gravitational attraction takes over. What isn't explained is WHY it will explode outwards. I realize that the temperature will increase, but wouldn't conservation of energy say that the star would bounce back out to its original size, almost like a harmonic oscillator? There has to be another source of energy other than the Coulombic and gravitational repulsion/attraction of the atoms?

My only guess would be that the gravitation potential energy is converted into such a high temperature when compressing that the nuclei fuse into heavier elements than iron. But that wouldn't give off energy, it would remove it.

There's plenty happening when a core collapse event occurs, and it's all over in less than a second:

http://en.wikipedia.org/wiki/Type_II_supernova

Read this article, especially the section on 'Core collapse'.

 

[jaydnul]

I see, so the energy becomes great enough for electron capture, then a small portion of the neutrinos are absorbed by the outer layers, causing explosion. Thanks

edit: among other things

 

[SteamKing]

I see, so the energy becomes great enough for electron capture, then a small portion of the neutrinos are absorbed by the outer layers, causing explosion. Thanks

edit: among other things

You've overlooked the best part: When the core collapses, the rebound sets up this tremendous shock wave which blows off the outer envelope of the star. Because of the compression and heating which take place, additional nuclear reactions are created which generate the heavy elements not created by the normal stellar fusion process, and of course, all the fireworks which we see on Earth years later.

 

[snorkack]

All of my internet research comes up with the same answer which is that when the core fuses all of its fuel, there is no more outward pressure, so the gravitational attraction takes over. What isn't explained is WHY it will explode outwards. I realize that the temperature will increase, but wouldn't conservation of energy say that the star would bounce back out to its original size, almost like a harmonic oscillator?

Energy has to be conserved between the core and outside of the star, but this does not require the whole star to bounce to its original structure and size because energy can be and is transferred from core to outer parts. The result is that it is not the whole star that bounces (to original size) - the core is left behind in bounce (and remains as neutron star or black hole), the outer parts bounce with a greater speed (and thus explodes past its original size, escaping to infinity).

 

[Matterwave]

All of my internet research comes up with the same answer which is that when the core fuses all of its fuel, there is no more outward pressure, so the gravitational attraction takes over. What isn't explained is WHY it will explode outwards. I realize that the temperature will increase, but wouldn't conservation of energy say that the star would bounce back out to its original size, almost like a harmonic oscillator? There has to be another source of energy other than the Coulombic and gravitational repulsion/attraction of the atoms?

My only guess would be that the gravitation potential energy is converted into such a high temperature when compressing that the nuclei fuse into heavier elements than iron. But that wouldn't give off energy, it would remove it.

It's good that you are thinking about conservation of energy. However, the 99% of the gravitational potential energy of the core which is released (it collapses from 6000km to 20-30km, you can calculate how much energy that is, given the mass is ~1.5 solar masses) is enough to blow up the rest of the star, as snorkack mentions. This is about 10% the rest mass of the core. The problem in supernova simulations is that actually most of this energy (~90%) is carried away by neutrinos and not by the shock wave itself. The shock wave stalls about 500km from the center (not very far) due to losing energy to nuclear dissociation reactions. This is why you need the neutrino heating to revive and reheat the shock wave in order for the supernova explosion to occur. Whether this reheating is enough depends on details from the neutrino transport. It might not be totally enough. In fact, in 1-D simulations, it is never enough. But that is why people are exploring other mechanisms for reheating the shock wave, including looking at the rotation of the star, looking at magnetic fields present, and the newest development which is the SASI (standing accretion shock instability) which is basically the turbulence leading to non-symmetric explosions - allowing a large amount of material to remain at the "gain radius" where the neutrino heating is most efficient for a long enough time to revive the shock (hence the "standing accretion").

I should mention that the supernova physics is horribly complicated and is at the vertex of many different kinds of physics. Not all simulations give a robust explosion as of yet. The development of supernova explosion simulations has mostly been "oh, there's an explosion, so that's how it's done", "oh wait, we forgot to add this effect, dang it, no explosion", "oh, but what about this? Yes! Explosion!", etc...

 

[Ken G]

All of my internet research comes up with the same answer which is that when the core fuses all of its fuel, there is no more outward pressure, so the gravitational attraction takes over.

This isn't really the part you are asking about, but it is unfortunate that it is easy to find such a completely wrong description in a lot of places. It's actually just an absurd version of what is happening there, fomenting a number of misconceptions in the process. The pressure that exists in the core of a star is there by virtue of the kinetic energy in that gas. When fusion stops, nothing happens to that kinetic energy, it is still there and so is the pressure. But gradually, and over a long time, that energy leaks out and is not replaced by fusion, so the gas gradually, and nearly in force balance, contracts. None of that represents a "collapse", and this is not what causes core-collapse supernovae. Instead, what happens is, if there is no other fuel that can fuse, the contraction just continues gradually, but something else happens-- gravitational energy is gradually released, and the gas heats up. It's a kind of irony that heat leaking out causes the gas to heat up, but that's due to the gravitational energy release. Still, this is all happening slowly-- it's not a supernova. The supernova only happens when the particles responsible for the pressure go relativistic, and that creates a gravitational instability that allows the contraction to go into a state of free fall. That's the collapse, and it happens well after fusion has stopped, because it relies on relativistic behavior, in addition to fusion-free behavior.

 

[jaydnul]

The supernova only happens when the particles responsible for the pressure go relativistic, and that creates a gravitational instability that allows the contraction to go into a state of free fall. That's the collapse, and it happens well after fusion has stopped, because it relies on relativistic behavior, in addition to fusion-free behavior.

Interesting. Could you go into more detail about how/what relativistic effects create a gravitational instability? I have taken special relativity (no general yet), so I think I'll be able to understand.

 

[Ken G]

It all has to do with the connection between momentum flux and kinetic energy density. These two quantities have the same units, and are deeply related, but the first one is what we call pressure, and the second one is what is actually tracked as a star goes through energy-conserving processes. So this means, we should track what is happening to the kinetic energy density, and then ask what this means for the pressure. If the pressure comes from nonrelativistic particles, then the pressure is 2/3 the kinetic energy density. If the pressure comes from relativistic particles, then the pressure is 1/3 the kinetic energy density (that comes from applying special relativity to the momentum flux density, just make a ratio of that to the kinetic energy density and note that momentum flux density acts like a scalar if the particle distribution function is isotropic, because even though momentum is a vector, its flux involves a dot product between the momentum and the velocity that is carrying that momentum across some imaginary surface). This falling of that ratio from 2/3 to 1/3 is the reason we have core collapse supernova. That's the part that requires some further explanation.

When a gravitationally self-bound gas contracts, considerable gravitational energy is released, which raises the kinetic energy of the gas. Also, the volume drops, which raises the kinetic energy density, and therefore the pressure (that's where the 2/3 or 1/3 comes in). But the gravitational force also increases, so it is not immediately obvious which effect "wins." If the ratio of pressure to kinetic energy density is 2/3, then the rise in kinetic energy density wins-- the adiabatic compression of a nonrelativistic self-gravitating gas bounces back because the positive kinetic pressure goes up more than the negative "gravitational pressure", if you will. But if the ratio is only 1/3, both go up the same-- the gas is very easy to compress, you could do it with a breath. This is the basic cause of the instability, if you add onto this any process which removes heat (like photodisintegration of nuclei, or like neutrino escape as in the URCA process), you get a runaway contraction which is a free fall-- that's the "collapse" of a core-collapse supernova. So it's completely false to say that the absence of fusion causes pressure to be lost and the core to collapse, indeed in a universe that did not have relavitivity and no speed limit at c, nothing would ever gravitationally collapse and there would be no core-collapse supernovae, even if there was also no such thing as fusion.

 

[snorkack]

Interesting. Could you go into more detail about how/what relativistic effects create a gravitational instability? I have taken special relativity (no general yet), so I think I'll be able to understand.

Look at it this way:
If you decrease the linear size of a box where a nonrelativistic particle is, two times, then its momentum doubles... and thus its kinetic energy quadruples. Whereas its gravitational potential energy just doubles.
If you decrease the size of the box two times, but the particle is relativistic, then its momentum still doubles... but since it is relativistic then its kinetic energy just doubles, like its potential energy.