Undergrad Core collapse of a supernova: the "void" left by the collapsed core?

[nikkkom]

Because of decades of supernova research, not done by me, but I am aware of it.

So am I aware of it too.

The simulations have computing power restrictions. The simulated volume can't be too big; the time the simulation runs can't be too long.

Researchers make sensible decisions based on the availability of CPU power.

If simulating a (400km)^3 cube for 1 second takes 2 days, then simulating (4000km)^3 cube for 10 seconds on the same hardware would take 5000 days (~15 years). It makes sense to _not_ try that as the first (or second, or tenth) attempt to figure out why simulation does not match expectations. "Maybe we overlooked something. Maybe it's magnetic fields?" etc. Completely sensible. I'd do the same. I don't want to wait 15 years for one test run! And I'm not ready to give up on my codes simply because they didn't work in the first few tries. Bugs are a fact of life.

However, maybe the simulations _were_ mostly correct. Maybe they do show what really happens in (400km)^3 cube for 1 first second. Maybe star's explosion is not generated in this volume.

I'd be happy to hear this was looked at, and shown not to be the case, by people who did work on it.

 

[Ken G]

So am I aware of it too.

The simulations have computing power restrictions. The simulated volume can't be too big; the time the simulation runs can't be too long.

Of course, but none of that justifies an expectation that a region where there is no material and no energy has anything to do with getting an explosion. Also, none of that justifies thinking that radiation is important, when simulations include radiation and find that it is not important.

 

[JMz]

Fusion weapons designers would most certainly disagree.

Yes, but they have no neutrinos to make use of, right?

 

[alantheastronomer]

Yes, but they have no neutrinos to make use of, right?

Of course they do...p+p->d+e*+v, but the neutrinos aren't dense enough to make a difference in fusion weapons, while they are thought to be critical in creating supernovae explosions.

 

[stefan r]

Of course they do...p+p->d+e*+v, but the neutrinos aren't dense enough to make a difference in fusion weapons, while they are thought to be critical in creating supernovae explosions.

There is no p+p in any fusion weapons created by humans.

 

[alantheastronomer]

There is no p+p in any fusion weapons created by humans.

So what reaction is used in fusion weapons?

 

[alantheastronomer]

Of course, but none of that justifies an expectation that a region where there is no material and no energy has anything to do with getting an explosion. Also, none of that justifies thinking that radiation is important, when simulations include radiation and find that it is not important.

It doesn't have anything to do with getting an explosion, that's the whole point...the failure of the core bounce mechanism to produce an outward going shockwave means there's a void left behind between the newly formed neutron star and the stellar envelope. The outer layers do not fall onto the neutron star immediately; they fall on a free fall timescale. This means there's only a few moments for some mechanism to produce an explosion. Gamma radiation from the formation of the neutron star sounds like a viable possibility.

All researchers who've done computer simulations have NOT included radiation in their calculations. Not Bethe, not Wilson at Los Alamos, not Stirling Colgate, not Stan Woosley at Santa Cruz, not Arnett, not Rood, not Adam Burrows. Instead, they all assume, without any proof, that 99% of the energy is carried away by neutrinos and they ignore radiation completely.

There's also another problem with the core collapse scenario - If the inner core collapses and the outer core is blown away by the shock wave, then only a fraction of the 1.4 solar mass iron core is left as a neutron star. Observations of neutron star masses compiled by Lattimer find they vary only from 1.2 to 1.4 solar masses, so the theory doesn't agree with observations.

Also, if the explosion is going to be powered by the gravitational potential of the neutron star, then the outer lying material has to first access that potential - it needs to fall down the potential well of the neutron star in order to extract that energy.

Fortunately, that doesn't need to happen. Using a very crude approximation, by the mass-luminosity relation, a 15 solar mass star has a luminosity of 2x10^38 erg/sec. While the diffusion timescale for photons is very roughly 300,000 years. This means there's roughly 10^51 ergs stored in the star's interior that could be released all at once in a supernova explosion without having to access the gravitational potential well. This is also the amount of energy that is observed in supernovae explosions.

 

[andrew s 1905]

So what reaction is used in fusion weapons?

Dutirium and or tritrium

 

[anorlunda]

This article is from the 70s, so it may be dated, but it is a wonderful description of the time evolution by Hans Bethe and Gerald Brown.
http://www.cenbg.in2p3.fr/heberge/EcoleJoliotCurie/coursannee/transparents/SN%20-%20Bethe%20e%20Brown.pdf

A couple of interesting points from that article.

• The time to maximum density in the collapse is not several seconds, it is on the order of 5 ms.
• Densities are so great that the infalling materials are opaque to neutrinos. Even thermonuclear explosions do not duplicate that condition.

 

[alantheastronomer]

This article is from the 70s, so it may be dated, but it is a wonderful description of the time evolution by Hans Bethe and Gerald Brown.
http://www.cenbg.in2p3.fr/heberge/EcoleJoliotCurie/coursannee/transparents/SN%20-%20Bethe%20e%20Brown.pdf

A couple of interesting points from that article.

• The time to maximum density in the collapse is not several seconds, it is on the order of 5 ms.
• Densities are so great that the infalling materials are opaque to neutrinos. Even thermonuclear explosions do not duplicate that condition.

The article you're referencing is referring to the time for the core to collapse to neutron star densities, NOT the time for the rest of the stellar envelope to freefall onto the newly formed neutron star. That timescale, for a neutron star of 1.5 solar masses and a distance to the envelope of 400,000 km. is given by the formula t=(d^3/(2GM))^1/2 ignoring general relativistic effects, turns out to be about 400 sec.
While the infalling nuclear material is opaque to neutrinos, all computational simulations thus far have failed to produce an explosion due to neutrino pressure. Thermonuclear explosions don't need to resort to that condition in order to produce an explosion; nikkkom's whole point is that if a thermonuclear explosion can be achieved at temperatures of millions of degrees due to gamma ray heating and photon pressure, why aren't temperatures of billions of degrees relevant for supernova explosions?
Computer simulations that model the formation of the neutron star from the stellar core occur at timescales of nanoseconds, any modelling of the physics in the stellar envelope would occur on a hydrodynamic timescale of milliseconds. Thus for anyone timestep of the envelope, a thousand timesteps of the core would have to be calculated. For a fully three dimensional model that would be increased to a billion, not to mention the increased spatial resolution...
So out of the many papers modeling the supernova problem, I've only found two that look at the physics in the stellar envelope;
One, by Stirling Colgate, that found that energies from neutrinos produced a high pressure, low density region in the envelope that might be susceptible to Rayleigh-Taylor overturn instability producing an outward flow, and
Second, a paper by Stan Woosley which found that a combination of angular momentum conservation and nuclear reactions in the oxygen layer produced an outward motion. This study was done in the early eighties and I thought it was an extremely promising avenue for further investigation, and I thought that with the increase in computing power coming, that he would pursue it further, but for some reason he never did...

 

[nikkkom]

The article you're referencing is referring to the time for the core to collapse to neutron star densities, NOT the time for the rest of the stellar envelope to freefall onto the newly formed neutron star. That timescale, for a neutron star of 1.5 solar masses and a distance to the envelope of 400,000 km. is given by the formula t=(d^3/(2GM))^1/2 ignoring general relativistic effects, turns out to be about 400 sec.

Thanks for the support/understanding my point. However, the inner part of envelope should be much closer to the newly formed NS - on the order of 10000 km instead of 400000 km - since only the core of the star is collapsing.

 

[alantheastronomer]

Thanks for the support/understanding my point. However, the inner part of envelope should be much closer to the newly formed NS - on the order of 10000 km instead of 400000 km - since only the core of the star is collapsing.

For a 15 solar mass star it's radius is roughly 20 solar radii, from Arnett - "Supernovae and Nucleosynthesis" table 7.3 - the radius of a stellar core of 1.5 solar masses is actually 700,000 km, about 1/20 the stellar radius, or one solar radius, so I underestimated... :)

 

[nikkkom]

For a 15 solar mass star it's radius is roughly 20 solar radii

Radius of the entire star is not what you need. Outer parts of the envelope are mere bystanders of the event.
You need the radius of the *core* - only core is initially collapsing.
It is about white-dwarf-sized - ~10000km radius.

 

[nikkkom]

the radius of a stellar core of 1.5 solar masses is actually 700,000 km

A stellar core of 1.5 solar mass star is larger that the Sun (not the core - the entire Sun)? I very much doubt it.

 

[alantheastronomer]

A stellar core of 1.5 solar mass star is larger that the Sun (not the core - the entire Sun)? I very much doubt it.

You misunderstand - the core is 1.5 solar masses; the star is 15 solar masses in total. The size of the core is that of one before reaching iron peak not of one after reaching white dwarf degeneracy size - that's why it seems so large to you, and yes, I agree that a stellar core the size of our entire sun seems unusually large; that's why I prefaced my statement with the information that the radius of a 15 solar mass star is about 20 solar radii, so that you can see the core radius is only 1/20th that of the entire star...

 

[alantheastronomer]

You need the radius of the core...it is about white dwarf sized - 10000km radius.

No, wait - you're right! My mistake, I was using the size of the hydrogen burning core by mistake, sorry! So the freefall time is only about a couple of seconds - still large compared to the time for core collapse to a neutron star of a few milliseconds...so too long for an outward moving shockwave to have bridged the gap, but plenty of time for gamma ray radiation pressure to affect the stellar envelope.