Talk:Degenerate matter

I suggest a re-write of the https://en.wikipedia.org/wiki/Degenerate_matter#Neutron_degeneracy section.
The first sentence ('Neutron degeneracy is analogous to electron degeneracy and is demonstrated in neutron stars, which are partially supported by the pressure from a degenerate neutron gas') is fine, but the whole rest of the paragraph is talking about electron degeneracy and the formation of neutron stars, which is talked about in the previous section on electron degeneracy.

The second sentence of the second paragraph sounds like it was written by primitive AI: 'In the case of neutron stars and white dwarfs, this phenomenon is compounded by the fact that the pressures within neutron stars are much higher than those in white dwarfs'. I think what it should say is: 'In the case of neutron stars, this phenomenon is compounded by the fact that the pressures within neutron stars are much higher than those in white dwarfs', and even then, it should come with a citation.

The first sentence of the last paragraph states: 'There is an upper limit to the mass of a neutron-degenerate object, the Tolman–Oppenheimer–Volkoff limit, which is analogous to the Chandrasekhar limit for electron-degenerate objects.' I don't see why you would say 'neutron-degenerate object' when I think what you mean is 'neutron star' - keep it simple & readable.

The section then finishes with these words: 'The theoretical limit for non-relativistic objects supported by ideal neutron degeneracy pressure is only 0.75 solar masses; however, with more realistic models including baryon interaction, the precise limit is unknown, as it depends on the equations of state of nuclear matter, for which a highly accurate model is not yet available. Above this limit, a neutron star may collapse into a black hole or into other possible dense forms of degenerate matter'

I think the Tolman–Oppenheimer–Volkoff limit article gives it a better treatment. It states: 'Theoretical work in 1996 placed the limit at approximately 1.5 to 3.0 solar masses, corresponding to an original stellar mass of 15 to 20 solar masses; additional work in the same year gave a more precise range of 2.2 to 2.9 solar masses... In the case of a rigidly spinning neutron star, the mass limit is thought to increase by up to 18–20%.' I think it's also OK to mention the unrealistic 0.75 solar mass limit for historical purposes too though. I also wonder if thermal pressure caused by friction between different layers and latitudes rotating at different rates would be significant. I don't know if there's any evidence of this in neutron stars, but there is in ordinary stars: https://www.space.com/does-the-sun-rotate

MathewMunro (talk) 08:59, 1 January 2024 (UTC)


 * The section has only two references. If you disagree with sentences with references please explain. Otherwise I would just encourage you to make your edits in logical chunks with edit summaries and have at it. Johnjbarton (talk) 16:37, 1 January 2024 (UTC)

neither heat nor rotation are cited
@MathewMunro The recently added paragraph that ends with a sentence including "neither heat nor rotation are cited" makes no sense to me. If this subject is not notable, why is the paragraph included? Johnjbarton (talk) 00:10, 5 January 2024 (UTC)


 * Fair point. I'll delete anything that's speculative and unreferenced, post a question to the Wikipedia Science Reference Desk as to whether or not heat & rotation have any significant effect (say a tenth of a solar mass or more) on the maximum mass of neutron stars, and if anyone comes back with some references, I'll re-edit the last paragraph of the 'Neutron degeneracy' section accordingly.
 * I wrote 'yet it has been estimated that temperatures can reach up to 5x109 during formation of a neutron star'. You added the [citation needed] tag. It's actually lifted straight from the 'Neutron star' wiki. Unfortunately they didn't include a freely available reference that quotes that figure. I found a free article (https://academic.oup.com/mnras/article/442/4/3484/1357581) by A. D. Kaminker, A. A. Kaurov, A. Y. Potekhin and D. G. Yakovlev published by the Royal Astronomical Society titled 'Thermal emission of neutron stars with internal heaters' that quotes a figure of >~10^9 K though (fully two orders of magnitude above the temperature considered by Oppenheimer and Volkoff).
 * I wrote: 'Other potential heat sources include friction between different layers of the neutron star, known as nuclear pasta, or between the neutron star and its accretion disk if it has one, Starquakes, and Gamma-ray bursts'
 * The Kaminker et al. article supports the accretion disk as a heat source (in binaries) but seems to consider things like gamma-ray bursts as cooling or heat emission rather than heating, so that definitely needs to be corrected. They also mention neutron mergers as a heat source:
 * 'Internal heat sources operate also in transiently accreting neutron stars in low-mass X-ray binaries (LMXBs; see, e.g. Turlione, Aguilera & Pons 2013; Wijnands, Degenaar & Page 2013, and references therein).'
 * 'Quiescent thermal emission of transiently accreting neutron stars in LMXBs is currently explained (Brown et al. 1998) by the deep crustal heating of these stars (Haensel & Zdunik 1990, 2008).'
 * 'SGRs/AXPs exhibit large persistent thermal and non-thermal high-energy emission, X-ray and gamma-ray bursts and flares (losing more energy than their magnetic braking). This indicates wild processes of energy release in their interiors and/or magnetospheres.'
 * 'Before neutron stars merge, they are likely heated by hydrodynamical motions due to tidal interactions and associated phenomena'.
 * The Kaminker et al. article also mention 'heating due to viscous friction in the presence of differential rotation (e.g. Chirenti et al. 2013)'. I'll be happy to substitute those words for my less precise "nuclear pasta" inter-layer friction statement.
 * I still think it's worth mentioning though that the temperature and therefore the temperature-related pressure assumptions upon which Oppenheimer and Volkoff calculated the mass limit of neutron stars was off by up to multiple orders of magnitude, as the temperature-pressure relation in ordinary matter is well established, and it has been found that neutron stars have been found to be up to two, and possibly more, orders of magnitude hotter (at least in formation, merger or binary accretion).
 * I'm sure there would be a reference on spin and its relation to neutron maximum mass, it's just a matter of finding it and/or joining the dots. The mass at which a neutron star becomes a black hole is a factor in the maximum mass of a neutron star*, and rotation is known to produce different solutions to the black hole radius (Schwarzchild vs Kerr), so there's bound to be an analogous reference to neutron spin vs maximum mass.
 * See https://articles.adsabs.harvard.edu//full/1991BASI...19..105A/0000105.000.html 'Classical equation of state for a nonrelativistically degenerate gas containing free fermions gives an upper limit to the radius of a neutron star while the Schwarzschild radius gives the lower limit. The lower mass limit for a neutron star is given by the Oppenheimer-Volkoff solution. These three curves define a triangular region in the mass-radius plane which is available for a real neutron star.' MathewMunro (talk) 05:28, 5 January 2024 (UTC)

Proposal to move four paragraphs
The four paragraphs starting with "There is an upper limit to the mass of a neutron star,..." are not really about degenerate matter, but about issues related to neutron star dynamics and advances since the original Tolman–Oppenheimer–Volkoff work. I think these paragraphs should be move to Tolman–Oppenheimer–Volkoff limit. Johnjbarton (talk) 16:46, 5 January 2024 (UTC)


 * @MathewMunro a suggestion. Johnjbarton (talk) 16:46, 5 January 2024 (UTC)
 * If you move them, can you please preserve all the references I've gathered, thanks. MathewMunro (talk) 17:21, 5 January 2024 (UTC)
 * Done, please review. Johnjbarton (talk) 18:01, 5 January 2024 (UTC)
 * Thanks. It may now be a little too brief. How about at least changing the sentence: 'The properties of neutron matter set an upper limit to the mass of a neutron star, the Tolman–Oppenheimer–Volkoff limit, which is analogous to the Chandrasekhar limit for white dwarf stars.' to read 'The properties of neutron matter set an upper limit to the mass of a neutron star, the Tolman–Oppenheimer–Volkoff limit, which is now estimated to be [?] to [?] M☉ [reference, reference], which is analogous to the Chandrasekhar limit for white dwarf stars.' MathewMunro (talk) 01:12, 6 January 2024 (UTC)
 * Sure go ahead. BTW the Talk:Tolman–Oppenheimer–Volkoff limit has some discussion that the TOV can not be used in context of a mass limit (because it explicitly rules out rotation I gather). Johnjbarton (talk) 01:45, 6 January 2024 (UTC)
 * Regarding whether or not the term 'TOV' is strictly applicable only to models/estimates of the mass at which *non-rotating* neutron stars collapse:
 * The Oppenheimer & Volkoff paper 'On Massive Neutron Cores' says just after heading II, 'If the matter... has no mass motion, then its energy momentum tensor is given by...'.
 * I can't fully follow the paper, as I'm not even a physics major, but I gather that's the simplifying assumption they proceed upon - and if the particles have 'no mass motion', then the star isn't rotating.
 * Amusingly, one paper I just stumbled on (https://web.mit.edu/8.322/Spring%202007/notes/DFSCropped.pdf) called it 'a mere “cartoon” of a neutron star'.
 * The second paragraph of the neutron star Wiki mentions the Bhatia - Hazarika Limit, and that article says: '[The] Bhatia Hazarika limit  is astronomical event that occurs on forming Black hole after the Gravitational collapse of a Neutron star attaining the size of 2.8 Solar mass, theoretically, for rotating neutron star or Pulsar unlike Tolman–Oppenheimer–Volkoff limit which is for non-rotational neutron stars.'
 * But that article is nominated for deletion, and there's hardly any reference to it on Google outside of those two Wikipedia pages.
 * If the source of the assertion that the TOV limit only applies to non-rotating bodies is basing their assertion on the 'Bhatia - Hazarika Limit' article then I'd call it dubious because it seems to me that the term 'Bhatia - Hazarika Limit' distinguishing rotating neutron star models never really took off, and that the term 'TOV' is used more broadly.MathewMunro (talk) 08:52, 6 January 2024 (UTC)

potential typo
The phrase "he also pointed out that ordinary atoms broadly similar in regards to the filling of energy levels by fermions" in the fourth paragraph seems to be missing an "are" in between "atoms" and "broadly". 155.190.0.9 (talk) 15:34, 26 April 2024 (UTC)
 * Fixed. Next time do not hesitate to edit it yourself :-) --ReyHahn (talk) 16:00, 26 April 2024 (UTC)