B What is the Hoyle State of Carbon and How Does it Contribute to Star Fusion?

[lavinia]

A popular video I just watched described Fred Hoyle's discovery that the elements of the universe are created in stars. Key to his theorizing was the prediction that fusion would produce of a new state of carbon that had never been observed and which theory predicted would be unstable. Hoyle believed that under the physical conditions present in stars this form of carbon could exist. Once detected Hoyle's theory was verified.

What was this new type of carbon? Why was it considered unstable? Why can it exist on stars? If this form of carbon is what is created, where does regular everyday carbon come from? Are there other elements which are fusion products but which would not exist only in stars?

 

[rootone]

I didn't know about this theory of Fred Hoyle, but Carbon is a very versatile element both in it's physical forms and it's chemistry.
All the carbon now in the Universe in various forms will have been produced by stars.
Hydrogen, Helium, and probably some Lithium are the only elements thought to have been generated after the big bang.
All the other elements were produced later by fusion within stars.

 

[Bandersnatch]

A popular video I just watched described Fred Hoyle's discovery that the elements of the universe are created in stars. Key to his theorizing was the prediction that fusion would produce of a new state of carbon that had never been observed and which theory predicted would be unstable. Hoyle believed that under the physical conditions present in stars this form of carbon could exist. Once detected Hoyle's theory was verified.

Hmmm, this doesn't look like anything to me. The landmark papers on nucleosynthesis by Hoyle (et al. in the second case) are these two:
http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1954ApJS...1..121H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

SYNTHESIS[/PLAIN] OF THE ELEMENTS IN STARS; E. Margaret Burbidge, G. R. Burbidge, William A. Fowler, F. Hoyle


Skimming the relevant sections of both, I can't find anything about a 'new form of carbon'. What I can see are predicted equilibrium abundances of C¹² and C¹³ isotopes w/r to other elements, in different types of stars. The abundances are based on the calculable ratio of production vs destruction of these isotopes given the specific conditions in stellar interiors.
This would be sufficient as a predicted observable.

Perhaps you could give us a more precise reference to the claim made in the program.
Let me also cast a bat-signal calling @e.bar.goum - she might know something more about it.

 

[CapnGranite]

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501
Structure and Rotations of the Hoyle State
"The excited state of the C12 nucleus known as the “Hoyle state” constitutes one of the most interesting, difficult, and timely challenges in nuclear physics, as it plays a key role in the production of carbon via fusion of three alpha particles in red giant stars. "

http://physicsworld.com/cws/article/news/2013/jan/03/carbons-hoyle-state-calculated-at-long-last
"By calculating the behaviour of protons and neutrons inside carbon nuclei from first principles, physicists in Germany and the US have identified the shape of carbon's Hoyle state – which is an important step in the production of heavy elements inside stars."

Lawrence Berkeley Lab's NERSC was involved in some work on the Hoyle state of carbon. I think some of that work has been published.

 

[e.bar.goum]

A popular video I just watched described Fred Hoyle's discovery that the elements of the universe are created in stars. Key to his theorizing was the prediction that fusion would produce of a new state of carbon that had never been observed and which theory predicted would be unstable. Hoyle believed that under the physical conditions present in stars this form of carbon could exist. Once detected Hoyle's theory was verified.

What was this new type of carbon? Why was it considered unstable? Why can it exist on stars? If this form of carbon is what is created, where does regular everyday carbon come from? Are there other elements which are fusion products but which would not exist only in stars?

What the video was referring to is a particular "nuclear state" of carbon. This isn't the same as a "new type" of carbon, or a different form, it's just a way of re-arranging the protons and neutrons in the carbon nucleus. Let me explain.

Like electrons in atoms, nuclei have a shell structure. This shell structure is a result of quantum mechanics, and basically says that nuclei (like atoms) can only have certain amounts of internal energy. If you add extra energy to a nucleus, you can excite the nucleus from its normal, "ground" state, to a higher energy excited state or "energy level". Then, like an atom, the nucleus will de-excite to its ground state by emission of a photon (a gamma ray) or by kicking out an electron. If you give a nucleus enough energy, the nucleus can also shed energy by particle emission, and turn into another nucleus. The analogue in atomic physics is ionisation, sort of.

Now, in the case of carbon-12, there is a special energy level located 7.65 MeV above it's ground state. This is the famous Hoyle state. It just so happens that the energy required to pull out an alpha particle from carbon-12 is 7.37 MeV. So, then, a carbon-12 nucleus in its Hoyle state will, the vast majority of the time, de-excite by spitting out an alpha particle, giving you 8Be (which decays into two alpha particles) and an alpha. This is why it's unstable. But, sometimes, it decay back to its ground state, via the emission of pairs of pairs of electrons and positrons and gammas. This is where regular everyday carbon comes from.

The reason it can exist in stars is related to the energy difference between the hoyle state and the 8Be + alpha energy. The energy difference is small enough that in a hot star, the 8Be + alpha -> 12C nuclear reaction has enough energy to produce carbon-12 in the Hoyle state. Nuclear like the Hoyle state are important because they live for a reasonably long time (about 10^-16 seconds!), long enough for the carbon 12 to have a chance to decay back to the ground state (which takes waaay longer than just 8Be + alpha -> 12C -> 8Be + alpha, which will happen in about 10^-21 seconds without the hoyle state). It's thanks to the Hoyle state that we can exist at all.

Let me also cast a bat-signal calling @e.bar.goum - she might know something more about it.

Thanks for the earburn Bandernatch! The Hoyle state is a really neat piece of nuclear physics, and astonishingly, even some sixty years after Hoyle predicted it, we're still working on fully understanding this really important nuclear state.

 

[lavinia]

What the video was referring to is a particular "nuclear state" of carbon. This isn't the same as a "new type" of carbon, or a different form, it's just a way of re-arranging the protons and neutrons in the carbon nucleus. Let me explain. ...

Lovely explanation.

How is this state detected experimentally?
Are there any other unusual atomic states of elements that play a similar role in creating heavier elements in stars?

 

[e.bar.goum]

Lovely explanation.

Thank you!

How is this state detected experimentally?

You can detect nuclear states like this a few different ways. One thing you can do is have a nuclear reaction that produces 12C. Because of the Hoyle state, there will be a huge increase of the probability of producing 12C with an excitation energy of 7.65 MeV. This is called a resonance. You can measure the excitation energy of nuclei because this internal energy removes kinetic energy from the system -- energy conservation tells you that there is a state. This is way the Hoyle state was originally discovered - through a reaction of 14N + d -> alpha + 12C by Dunbar, an Australian physicist.

The other thing you can do is look at the gammas that result from the decay of the hoyle state into the ground state. For technical reasons (to do with angular momentum), you can't have a gamma decay from the Hoyle state into the ground state, but you can have a cascade of two gammas, one of 3.26 MeV to a different state and one of 4.40 MeV. If you add up those two gammas, you will discover the state. The Hoyle state can be detected that way too.

Finally, sometimes, (0.1% of the time) the Hoyle state decays via electron-positron pairs directly to the ground state ("pair conversion"), which is allowed. You can also detect the Hoyle state that way. All three of these methods are used in general in nuclear physics, and they each can tell you something different about the properties of nuclei.

Are there any other unusual atomic states of elements that play a similar role in creating heavier elements in stars?

Plenty! The Hoyle state is definitely the most important, but particularly in light nuclei and at low stellar temperatures, the fact that you get this "boost" in probability associated with resonances will vastly change the amount of an element that is produced in a reaction at a particular energy. A lot of people study these structures to try to more firmly predict the way elements are made in stars.

For heavier nuclei, there are some very big accelerators either being made or recently finished (FRIB in the US, RIBF in Japan, FAIR in Germany) that will try to understand the properties of nuclei with very large numbers of neutrons. We need to understand these nuclei so we can fully understand the way that elements heavier than iron were made.

 

[ShayanJ]

It's thanks to the Hoyle state that we can exist at all.

What about other Carbon isotopes? Why is it that the Carbon that initiated life, has to come from the de-excitation of the Carbon-12 in the Hoyle state? Isn't there any other way?

 

[Ken G]

But why would you need an excited state that can sometimes decay into destroying the carbon? Why not simply fuse carbon into a different state, or even its ground state? I guess the point is, when you fuse carbon, you have to do something with the fusion energy. If there aren't good pathways to emit particles, such that you end up in the ground state right after fusion, then you have to create an excited nuclear state. So it's important that there be a resonant nuclear state there, ready to take up that energy. Of course that state will be subject to the reverse process, destroying the carbon, so in addition to that resonant state, you also need a decay pathway that is better at emitting particles (other than an alpha particle) than the original fusion was.

 

[e.bar.goum]

What about other Carbon isotopes? Why is it that the Carbon that initiated life, has to come from the de-excitation of the Carbon-12 in the Hoyle state? Isn't there any other way?

The only other relevant carbon isotopes are 13C and 14C. 13C is made by proton capture from 12C in AGB stars forming 13N which subsequently decays to 13C. 14C is produced in cosmic ray reactions in the atmosphere with n + 14N -> 14C +p. 14N, in turn, is produced from 12C in stars. It all comes back to 12C!

You can make 12C directly in other states (the ground or first 2+ state), but you can't make much of it (not enough for cabon based life). The amazing thing about the Hoyle state is that it's in exactly the right position to be populated at the temperature of hot stars. The 8Be + 4He reaction will net you an energy of 7.37 MeV, and the kinetic energy of the nuclei in a stellar environment gets you the extra 280 keV, and bam, you're in the Hoyle state. One thing I've not mentioned is that the structure of the Hoyle state is a strong alpha cluster shape structure - it basically looks like three alpha clusters close together (in triangular or boomerang shape, it's not quite clear which, yet) not a sphere. The shape also enhances the probability of populating this resonance.

As far as I know, Hoyles prediction of this state is the only successful prediction based on anthropic grounds - I exist, therefore it must exist.

 

[e.bar.goum]

But why would you need an excited state that can sometimes decay into destroying the carbon? Why not simply fuse carbon into a different state, or even its ground state? I guess the point is, when you fuse carbon, you have to do something with the fusion energy. If there aren't good pathways to emit particles, such that you end up in the ground state right after fusion, then you have to create an excited nuclear state. So it's important that there be a resonant nuclear state there, ready to take up that energy. Of course that state will be subject to the reverse process, destroying the carbon, so in addition to that resonant state, you also need a decay pathway that is better at emitting particles (other than an alpha particle) than the original fusion was.

Pretty much. The existence of the state means that 8Be + a has a larger chance of becoming a compound nucleus of 12C. It just so happens that it's also in exactly the right spot to be populated in stars.

 

[lavinia]

@e.bar.goum

Just to make sure I understand the idea of the explanation.

When three alpha particles are fused with 7.37 MeV of energy the resulting nucleus is unstable and will collapse back into alpha particles. But in a star there is extra energy - coming from the heat of the star - that pushes the three fused alpha particles into the Hoyle state of carbon 12 at 7.65 MeV. This higher energy state has a "high" probability of collapsing into stable good old carbon 12. This is how carbon 12 is created in stars.

Yes?

 

[Ken G]

I think it would be more accurate to say that fusing 3 alpha particles always releases energy, but there is not a good pathway for that energy to be emitted from the system, such that you could end up with a carbon nucleus in its ground state. So if you want to create carbon, you have two problems that stem from the fusion energy. The first is that you need someplace to put it so the reaction can occur, and the second is if you cannot radiate that energy away, it is still available to undo the fusion. The first problem is resolved by the Hoyle state itself, because it's a nuclear resonance that gives you a place to put the fusion energy, making the fusion much more likely to occur. But the existence of that state by itself would not solve the second problem, you also need a way to de-excite that nuclear state so you can get rid of the fusion energy before it undoes the fusion. The de-excitation is just how the Hoyle state makes transitions to the ground state of carbon, probably by gamma-ray emission I would imagine. So the Hoyle state gives you a high probability of forming because it is a resonant state, and it gives you a way to get rid of the excess energy because it can make transitions to the ground state.