# Can the Sun contain degenerate matter?

Degenerate matter (neutronium) is hypothesized to be very dense and, at a certain amount, unstable - in the sense of collapsing on itself and causing fusion. The result would be a massive fusion detonation. Such a detonation could cause the Sun to lose its photosphere and cook the inner Solar System with a wave of radiation. This event is described enjoyably in Robert Sawyer’s book, "The Oppenheimer Alternative". The discovery of the neutron core, however, is made by identifying a transient rise in products of the CNO fusion cycle which is hypothesized to require 20 million Kelvin, whereas the Sun’s core temperature is ‘only’ 15 million Kelvin. These fusion products are detected by solar spectroscopy.

Can such a neutron core exist? If it did exist, how could the by products of the CNO cycle be identified before the actual explosion? I mean, if the neutronium degenerates, fuses, and raises the Sun's temperature to allow CNO fusion, then isn't the explosion going to happen before any of the photons from the explosion have time to heat the Sun up enough to make CNO products detectable in the spectra?

EDIT: Fortunately there are many people here who are smarter than me and still kind enough to show it nicely. I will try to clarify the facts of the novel without spoilers (Rather like describing the phenomena of Red Matter in Star Trek (2009) without spoiling the plot)

1. Edward Teller presents three spectra of the sun taken in 1929,1938 and 1945 at a colloquium in Los Alamos
2. Fermi remarks that the second spectrum is not of our sun but of an F class star because of the strong carbon absorption lines
3. Teller infers that something happened to our sun around 1938 to heat it up a little to spark off C-N-O fusion
4. Oppenheimer relates von Neumann's weather data that the Earth was indeed statistically warmer during that 'period'. He goes on to say that the problem is not with the spectrograph plates from Bethe nor the math done by Teller. Rather, Oppenheimer says that the sun is indeed having a 'problem'
5. Oppenheimer recalls publications from Zwicky and Landau that hypothesized a neutron core to our sun.
6. Oppenheimer recalls a paper he wrote with Robert Serber that refuted Landau's work with calculations that a neutron core greater than 0.1 solar masses would be unstable.
7. Neutron core instability would manifest as a hotter sun
8. Oppenheimer starts to say that such instability is transient and Teller interrupts him to blurt out that the unstable neutronium would be ejected from the sun
9. Teller goes on to say that a neutron core would be formed by an implosion, then compares it to the process that happens in the atomic bomb,FatMan, where an explosive array is used to implode a plutonium core. The inevitable result he states is an explosion (It is unclear if he means fission or perhaps his own demon, fusion)
10. Hans Bethe then calculates that based on the expected size of a neutron core, the known size of the sun, and the opacity of the sun that the outwardly exploding degenerate matter would hit the photosphere in 90 years.

At this point, I will let the other really knowledgeable people here comment on these points and their veracity. However, I am still haunted by the idea that a small really heavy object (microscopic black hole, white dwarf, etc) could be captured by our sun and then precipitate instability.

• There are two kinds of degenerate matter (at least). Matter supported by electron degeneracy which makes up most of the mass of white dwarf stars, and neutronium, supported by neutron degeneracy which makes up a large part of the mass of neutron stars. I'm fairly sure neither is found in the sun at present, but in any event, could you clarify in your question which you mean? – Steve Linton Jun 16 '20 at 18:11
• "The Oppenheimer alternative", A nail-biting new science fiction thriller... – James K Jun 16 '20 at 18:30
• neutronium. thank you for fixing it. – aquagremlin Jun 16 '20 at 18:36
• apparently, c-n-o cycle does occur in the sun. en.wikipedia.org/wiki/CNO_cycle The premise of the novel is that degenerate matter causes a temp rise (through fusion of neutronium) to accelerate the c-n-o cycle. My question is whether ANY event that acclerates the c-n-o cycle could be detected before the inevitable coronal mass ejection occurs? – aquagremlin Jun 16 '20 at 18:42
• The CNO cycle does not produce neutrons. Neutronium doesn't collapse unless you have more than 2 solar masses of it. The collapse doesn't cause fusion; it disappears into a black hole. None of this scenario makes any sense. – ProfRob Jun 17 '20 at 20:16

The answer to whether a normal star can contain a core of degenerate neutrons is a yes. Thorne & Zytkow 1977 produced numerically models where a neutron star becomes embedded in the center of a massive giant or supergiant star, surrounded by a large gaseous envelope. In this scenario, the main source of energy becomes not nuclear fusion but instead gravitational contraction from matter flowing from the inner envelope onto the outer core. The energy production ratios are $$L_{\text{nuc}}/L\approx0.04,\quad L_{\text{grav}}/L=0.96$$ for stars with $$M_{\text{tot}}\leq10M_{\odot}$$, as above this, convective envelopes form. The models, regardless of mass, predict some degree of shell burning, with hydrogen-, helium-, and carbon- burning layers outside the core. In the inner regions, temperatures are orders of magnitude higher than that required for the CNO cycle, which sets in at around 15 million Kelvin, actually (not 20 million K) and dominates over the p-p chain at about 17 million K.

Thorne & Zytkow did find that for $$M_{\text{tot}}<2M_{\odot}$$, the envelopes were unstable against radial adiabatic pulsations, implying that it's likely not possible to extend the analysis to the case of the Sun - at that mass, the object is quite vulnerable to instabilities. That said, I am fairly confident that we would be able to tell if there was a degenerate object in the solar core; unlike the red giant or supergiant case, there is no large envelope to hide it, and the mass of the neutron star would at least be comparable to or (much more likely) exceed the mass of the Sun itself.

Some points on the stability of neutron degenerate matter: The problem is actually with small quantities, not large quantities. Small amounts are incapable of remaining bound by their own gravity; the pressures involved are simply too high, and the solar core is nowhere near high-pressure enough to maintain stability. Optimistically, you'd need somewhere in the $$0.1M_{\odot}\text{-}0.2M_{\odot}$$ range at minimum for stability, though I would be surprised if a mass of degenerate matter this low was produced naturally - a neutron star of a more typical mass would likely have to lose mass somehow.

• Given that typical neutron stars exceed the mass of the Sun, an embedded neutron star in the Sun should be fairly noticeable! – user24157 Jun 16 '20 at 18:41
• @antispinwards I suppose I'm guilty of the understatement of the year, yeah. – HDE 226868 Jun 16 '20 at 18:42
• @ HDE 226868 Thank you and I marked your answer. But a teaspoon of neutronium would only weigh 5 tons. How much neutronium is needed before it becomes unstable? Would such a small amount even be noticeable? – aquagremlin Jun 16 '20 at 18:59
• @aquagremlin It goes the other way -- small quantities of neutronium are unstable, you need a bit more than a solar mass before its own gravity supplies enough pressure to keep it stable. Also a teaspoonfull of neutronium masses about 500 million tons! – Steve Linton Jun 16 '20 at 19:23
• 5 tons/teaspoonfull is the density of a white dwarf, the other kind of degenerate matter – Steve Linton Jun 16 '20 at 19:24

There are problems with the scenario outlined above.

Firstly, if the CNO cycle were to operate, it would have to operate for millions/billions of years to noticeably affect the relative abundances of CNO in the solar photsophere. That is because the core is embedded within a radiative zone where only comparatively slow mixing processes operate.

A much more obvious signature of an increase in the solar core temperature would be a dramatic increase in the rate at which neutrinos were detected from the pp-chain. Given that it isn't clear when the story is set, I suppose it could be that it is pre-neutrino detectors which would have immediatey confirmed or otherwise whether the Sun's core was hotter than it should be.

Secondly, in the usual CNO cycle, the net effect is to transform the core's carbon into nitrogen. So contrary to point #2, the photospheric signature of CNO burning (and mixing upward) would be an excess of nitrogen and a depletion of carbon.

Thirdly, the Oppenheimer/Serber idea of a degenerate neutron core requires the neutron core to be more massive than $$0.1-0.2 M_{\odot}$$. It is neutron-core masses lower than that which could not form and could not be stable.

Given the creation (somehow) of a neutron core with $$M>0.1 M_{\odot}$$ , the Sun would very rapidly become a red supergiant. How rapidly? It would basically be the Kelvin-Helmholtz timescale of the envelope. The luminosity of the core would rise rapidly to around $$10,000 L_{\odot}$$ (due to accretion onto the core, not CNO burning, e.g. see Cannon et al. 1992), which given the gravitational potential energy, gives a KH timescale of around 100-1000 years for the envelope.

The "outward explosion" would not really be an explosion, so much as an expansion and rarefaction of the Sun's outer layers, such that it engulfed the Earth.

The timescale for seeing evidence of this from CNO burning would be much longer than the expansion timescale I would have thought. The CNO cycle doesn't even run to completion on timescales of less than about a million years at typical burning temperatures.

Probably I shouldn't read the book...

• The book is well written and I hope Sawyer doesn’t see my ‘calling attention to questionable facts’. A gratifying conclusion to the plot is how the physicists redeem themselves. Though that achievement is hand-wavy. After all, it is they, in their desire to achieve technological victory over Hitler, who conceived of atomic weapons. The fabrication and dissemination of this technology has burdened our earth with low level fallout from testing as well as from failed fission reactors. Additionally, the anxiety of mutually assured destruction has led to unsustainable political posturing. – aquagremlin Jun 18 '20 at 21:25
• And of course there is always a love story. In this case it involves Oppenheimer and another woman. Somewhat reminiscent of Feynman and Arline, there is a poignant and tragic twist. – aquagremlin Jun 18 '20 at 21:29