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Thread: Neutrons are unstable; how come neutron stars are stable?

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    Neutrons are unstable; how come neutron stars are stable?

    "[...] presumably based on the chemistry/physics which shows that free neutrons are unstable with a half life of about 15 minutes, and atomic nuclei are unstable when there are more than about 150 neutrons present"

    This is an extract from a recent BAUT post, intended (I think) to show that neutron stars are inconsistent with modern physics.

    So, without math, how to explain the stability of neutron stars?

    Of the material that one could find googling, which would you say provides a (very) good explanation?

    Is it possible to write an explanation without introducing the concept of 'degeneracy pressure'? (I very much doubt it!)
    Last edited by Nereid; 2006-Dec-29 at 12:15 AM. Reason: typo (missing word "good")

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    I would think that gravity holds them in an inescapeable grip.

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    Quote Originally Posted by max8166 View Post
    Quote Originally Posted by Nereid
    Is it possible to write an explanation without introducing the concept of 'degeneracy pressure'? (I very much doubt it!)
    I would think that gravity holds them in an inescapeable grip.
    That's what Nereid meant by degeneracy pressure.

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    Yes but I didn't want to say that

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    Since a neutron star consists of neither free neutrons nor atomic nuclei, where is the problem?

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    Quote Originally Posted by Jason Thompson View Post
    Since a neutron star consists of neither free neutrons nor atomic nuclei, where is the problem?
    If all you have to work with are free neutrons and atomic nuclei, generalising from an N of 2, you could conclude that all neutrons are unstable, except in certain atomic nuclei.

    Or you could say: a priori, I see no reason for neutron stars to be stable or unstable, so why not unstable?

    I presume you have some familiarity with the relevant physics (i.e. you know about 'degeneracy pressure')?

    As an OT note, I must say that I was awe-struck when I first learned why electron degeneracy cannot provide infinite pressure - it's such a cool thing! (and the numbers work out pretty nicely too).

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    The decay of a neutron into proton + electron in an earthly laboratory is a transition from high-energy state to low-energy. However, in the crushing gravitational field of a neutron star, the proton + electron are in a higher energy state than the neutron.

    So the energy situation--with respect to free neutrons--is reversed, which is why neutrons in neutron stars do not decay.

  8. #8
    So, without math, how to explain the stability of neutron stars?
    I see no reason why we should be required to explain an astronomical phenomenon without math. Atoms, protons, neutrons, stars, forces, masses, lentgth, depth, height, time... It's all quantitative. In what universe do you think you're living in where math should not be used to assist in (and be necessary for) quantitative phenomenon?

    Oh well. It's still this simple: There's enough mass in the neutron star that it's held together by it's own gravity and the same weak nuclear force that allows neutrons to stick protons together in normal atoms. There's a glib explanation, but without math you can't really understand it.

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    Quote Originally Posted by Aerik View Post
    It's still this simple: There's enough mass in the neutron star that it's held together by it's own gravity and the same weak nuclear force that allows neutrons to stick protons together in normal atoms. There's a glib explanation, but without math you can't really understand it.
    I'm no expert on neutron stars, but there should indeed be a fairly straightforward explanation, and none of the other explanations have hit the nail on the head (though Peter Wilson's seems the closest). The fact is, the neutrons in a neutron star do want to decay, but the problem is, there has to be somewhere for the proton and electron to go to complete the decay process. In the high density environment (caused by the gravity, yes, but it's not the gravity that's the issue) of a neutron star, the electron states are nearly full (from other decayed neutrons)-- there's nowhere for the electron to go unless it had a higher energy than it has access to. It's analogous to why you get neutral hydrogen atoms even at very high temperature when the density is high enough. Thus I actually think it's much easier to understand why they are stable in neutron stars than why they are stable in normal nuclei, which I don't know at all.

    Edited for accuracy: I'm murky on the internal weak forces, but they are not why the neutrons don't decay, so far as I know.
    Last edited by Ken G; 2006-Dec-29 at 05:30 AM.

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    Perhaps slightly off topic, but a related question: does it happen that the neutrons in a neutron star do, in fact, decay with some non-trivial frequency, but the external pressure simply causes rapid recombination into neutrons? If so, one could describe it as analogous to a chemical equilibrium, where the rate coefficient is very small, so the products are essentially non-existent.

    Since degeneracy pressure is the correct answer, it seems reasonable to assume that you can't answer your question without the concept. You could, however, simplify it a bit.

    Anyway, I disagree with part of the original premise, that nuclei are unstable with more than 150 neutrons. There's something called the Island of Stability, which for some reason always makes me think of the Island of Dr. Moreau.... The basic idea is that there exist stable configurations for nuclei, in much the same way that there are stable configurations of electrons around a nucleus. There will always be such islands as atomic number is increased (though further and further apart).

    Of course, there's the problem that we don't know what happens when more than 138 protons get together... but it could happen, especially if the answer to the question at the start of this post is "yes."

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    Quote Originally Posted by snarkophilus View Post
    Perhaps slightly off topic, but a related question: does it happen that the neutrons in a neutron star do, in fact, decay with some non-trivial frequency, but the external pressure simply causes rapid recombination into neutrons?
    Yes, that's my understanding, along with preventing the decay from happening in the first place if the final decay states are occupied with electrons already. The idea of a chemical reaction equilibrium is very appropriate, as all physical processes that proceed one way can also proceed in the opposite direction, including beta decay. But I'd like someone to explain to me why neutrons are stable in a helium nucleus (and I don't mean the stability of the nucleus as a whole and isospin attraction), which seems harder to understand than in neutron stars.
    Since degeneracy pressure is the correct answer, it seems reasonable to assume that you can't answer your question without the concept.
    I don't think neutron degeneracy pressure is relevant to the decay question, it is relevant to the force balance.

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    Degeneracy and stability

    If we consider first electron degeneracy, where the stability of the electron(s) is not an issue, we may get a handle on neutron degeneracy (and neutron stability).

    In a degenerate electron gas, the electrons are not localised to atoms (or molecules), yet matter in this state is neither a metal nor a (classical) plasma - in the former, only the valence electrons form the electron 'gas'*; in the latter the fermionic nature of the electrons is irrelevant.

    So what's the difference? It's necessary to go through the concept of energy levels and energy states (in a 'gas' - and deal with the conceptual barriers imposed by one's intuitive sense of what a gas is) and the Pauli exclusion principle.

    Fast forward to neutron degeneracy - we need to know that neutrons are fermions (so the analogy can be applied) ... and in this view of a neutron star, the neutrons form a (Fermi) gas - they are not localised!

    So far, so good ... particularly the part about why you need gravity, to get a degenerate electron gas and a degenerate neutron gas - if you view these as (perfect) gases, with a requirement that they need a certain minimum pressure to exist, you need something more than a diamond anvil.

    Now we can turn on the weak force (responsible for the decay of the neutron) ... and things get tricky, or murky (if you prefer). For example, is neutron decay, for neutrons in a degenerate neutron gas, suppressed because it is no longer energetically favourable? Or is it, as snarkophilus suggests, happening all the time, and that the equilibrium state is 99.999% neutrons? Neither? both? something else (as well)??

    *And in all metals there are (other) electrons in the inner shells ... except for metalic hydrogen.

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    Quote Originally Posted by Ken G View Post
    Yes, that's my understanding, along with preventing the decay from happening in the first place if the final decay states are occupied with electrons already. The idea of a chemical reaction equilibrium is very appropriate, as all physical processes that proceed one way can also proceed in the opposite direction, including beta decay. But I'd like someone to explain to me why neutrons are stable in a helium nucleus (and I don't mean the stability of the nucleus as a whole and isospin attraction), which seems harder to understand than in neutron stars.I don't think neutron degeneracy pressure is relevant to the decay question, it is relevant to the force balance.

    My intuition too , if neutron stars do exist . It means pressure , a mechnical force caused by gravity can override the weak and the strong nuclear force. And fuse protons and electrons giving neutrons. These neutrons can live in great numbers and fuse into a giant nucleus.

    May be we can say weak nuclear forces and strong nuclear forces are dummy forces because they are equivalent to a pressure ?

    Or Can we conclude it is possible to change the nucleus by changing its environment ? that There is a bridge between the nuclear domain and the external electrons.

    Galacsi (In full qualitative mode )
    Last edited by galacsi; 2006-Dec-29 at 02:58 PM.

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    [I was ready to post this, but it seems too remedial after seeing a couple of new, quality posts. But then again, this may also serve as an analgoy of lower level degeneracy. What level of pedagogary do you want to be at? ]

    It sounds to me like y'all are saying the gravitational force becomes so strong that it squeezes the atoms so much that, first, electrons get smashed into the nucleus and merge with the proton, creating all neutrons. Then, as the star shrinks further, and the gravity becomes more impressive (sorry), the neutrons don't really have any place to go, so they take their place, though, I suspect, they are pounding each other more than a little. Even, at times, when some neutrons break apart into protons and electrons, they will quickly recombine back into neutrons. [Is this close?]

    Would two opposing magnets being forced mercilessly into each other with enough impact to neutralize their magnetic behavior be a useable analgoy?

    Pauli with his Exclusion Principle, as per Nereid, is very helpful and intuitive concept.

    It may be important to get a small handle on the degree of [gravitational] force on a neutron star. For instance, it is proposed that a neutron star may have an outer crystalline mantle. Mountains might exist on this solid structure lunging outward, possibly as high as several centimeters. So, how much more energy would be required to climb these mountains as opposed to, say, Mt. Everest (using a simplistic E=gh potential energy equation)? The answer gives some umph to the forces involved, at least for me.

    [Added: Per NASA page..."a neutron star possesses a surface gravitational field about 2 x 10^11 times that of Earth"]
    Last edited by George; 2006-Dec-29 at 04:01 PM.
    We know time flies, we just can't see its wings.

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    Wink neutron instability

    Although the neutron has a high degree of stability in the isotope island of the periodic table, when it comes to strong magnetic fields, it does not. Neutrons will shed their seemingly high stability when field strengths approach 1011-1013 Gauss....just the strength range of known pulsars.
    There is a rapid drop in half-life, hence neutrons near the poles of pulsars can and will decay. This can contribute to the polar emissions seen in pulsars with "tails", and the evaporation of the neutron star to the point of minimal mass instability....around ~ 0.1 solar mass. Pete.

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    My astrophysics book says Ken is right. According to the book, degenerate neutron material is a mix of nuclei and electrons with an 8 neutron to 1 proton and 1 electron ratio. This fills all the possible electron states in the material, so when a neutron wants to decay, there is nowhere for the electron to go, due to the exclusion principle.

    I would imagine that at the top of the neutron degenerate zone, neutrons do decay, but that electron capture also occurs, and that both processes occur at the same rate.

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    That was a very useful link Ilya, thank you, and thanks for your points as well korjik. Grey's explanation of nuclei reaching their lowest energy state with a mix of protons and neutrons is very illuminating. However, I don't buy his explanation that gravity stabilizes neutrons against decay in neutron stars, it just explains why the neutron star doesn't fall apart. So there are really too competing views that are emerging here-- one says that the more particles you have, the higher will be the fraction of neutrons vs. protons, because the more important is the energy increase associated with electrostatic repulsion between protons. In that view, neutronization of a neutron star is the natural end in the progression we see in the neutron content in the periodic table. The other view is the balanced reaction approach, which says that proton density is what counts, because if a neutron decays its daughter electron can then undergo the inverse process and re-establish a new neutron somewhere else. Furthermore, the electrons in the neutron star might already form a Fermi sea, so to create a new electron may require very large energy and that is the real issue. I'm frankly not sure which is the correct explanation, but I tend to favor the latter approach simply in analogy to all types of reactions in equilibrium, and that seems to be supported by korjik's textbook.

    It's possible that both views are valid, in the sense that one talks about the global energy minimum, while the other considers the details of the reaction rates involved in achieving that global minimum.

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    They is a little something I dont undestand : What about the neutrinoes ?

    When a neutron split , in a proton and an electron , a neutrino is emitted. This a ghost particle which fly away.

    Then , Is it not a problem for gravity to build back a neutron from proton and electron ?

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    Quote Originally Posted by Nereid View Post
    ...For example, is neutron decay, for neutrons in a degenerate neutron gas, suppressed because it is no longer energetically favourable? Or is it, as snarkophilus suggests, happening all the time, and that the equilibrium state is 99.999% neutrons? Neither? both? ...
    According to Thermodynamics , there will be some equalibrium distribution. Since neutron stars are hot--"billions and billions of degrees"--some non-zero quantity of neutrons will always be in the elevated energy state (proton + electron).

    Neutron stars are also known to harbor intense magnetic fields, so they must have some conductors free to circulate. This, too, tells us neutron stars are not 100% pure neutrons.

  21. #21
    My astrophysics textbooks vouch for Peter Wilson's explanations, and that protons and electrons aren't terribly numerous except in the NS exteriors (in statistical equilibrium with neutrons, as mentioned previously). As for whether gravity has anything to do with the stabilization of the neutrons - well, maybe one could argue that indirectly it does. Hydrostatic equilibrium demands the enormous densities found within the NS interiors which then set up the conditions that stabilize the free neutrons.

    Deep inside NS interiors the neutrons probably have enough energy to produce pions and hyperons, and who knows what else.

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    Yes, no doubt gravity is a key player overall, but that's in determining the high density. To understand why the neutrons don't decay, we need to understand what the high density is doing, not what gravity is doing. Also note that you don't need very many electrons to fill the Fermi sea when the volume is that small. As for the neutrinos, I don't know the ramifications of neutrino escape, it certainly seems like an important energy loss channel. However, I don't think energy is very important in neutron stars. Since they are supported by degeneracy pressure, they don't need kinetic energy, and don't care if they are radiating energy, they just readjust slightly. The basic answer as to why the neutrons don't decay seems to still be that the resulting electrons cannot find an available state, and the few that do are easily balanced by the inverse reaction. There is a different question, which is what sets the neutron/proton ratio, and that probably has to do with the energy available to the electrons as they fill their Fermi sea. I'll bet the proton fraction falls as the star ages and loses energy.

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    So are neutron stars copious emitters of neutrinos, or not?

    If the mean free path in neutronium is ~km, then a vigourous equilibrium between neutrons, protons, and electrons would suggest rapid cooling via neutrino loss (whatever cooling means for a degenerate neutron gas).

    The transition region - the thin (?) skin between neutronium and the vacuum of space above the surface, including any (normal) gaseous atmosphere - must be a fascinating realm, for a physicist!

    But back to neutron decay ... as the neutron, like the proton, is a three-quark trick, weak decay means some kind of Feyman diagram involving Zs and Ws, doesn't it?

  24. #24
    Quote Originally Posted by Ken G View Post
    Yes, no doubt gravity is a key player overall, but that's in determining the high density. To understand why the neutrons don't decay, we need to understand what the high density is doing, not what gravity is doing. Also note that you don't need very many electrons to fill the Fermi sea when the volume is that small.
    Yes, fair enough - I understand the distinction. However, I was merely recalling how it was these neutrons (and protons and electrons) found themselves in such a high density environment.

    Quote Originally Posted by Ken G View Post
    As for the neutrinos, I don't know the ramifications of neutrino escape, it certainly seems like an important energy loss channel. However, I don't think energy is very important in neutron stars. Since they are supported by degeneracy pressure, they don't need kinetic energy, and don't care if they are radiating energy, they just readjust slightly.
    Yep. The neutrinos are responsible for most of the rapid cooling the occurs in the first days and ~ century of a neutron star's existence, and as I understand it don't play an important role in the equation of state.

    Quote Originally Posted by Ken G View Post
    The basic answer as to why the neutrons don't decay seems to still be that the resulting electrons cannot find an available state, and the few that do are easily balanced by the inverse reaction.
    Yep. that's the way I read it as well.

    Quote Originally Posted by Ken G View Post
    There is a different question, which is what sets the neutron/proton ratio, and that probably has to do with the energy available to the electrons as they fill their Fermi sea. I'll bet the proton fraction falls as the star ages and loses energy.
    Good questions.

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    And then your point about pions and other particles in the interior is probably why the internal structure is not even known all that well. The role of the weak force may also be poorly understood, I don't know. Basically, I think Nereid has opened up a real Pandora's box here at the edge of what anyone knows about matter, and I'm certain it surpasses what I know about it!

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    Quote Originally Posted by Ken G View Post
    Basically, I think Nereid has opened up a real Pandora's box here at the edge of what anyone knows about matter, and I'm certain it surpasses what I know about it!
    It may be a pandora's box, but it's damned interesting and some good questions are coming out of it.

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    What goes in the interior of neutron stars is indeed a many-splendored thing. I was trying to find some article I read about some of the bizarre stuff -- apparently some recent observations during thermonuclear "flaring" events have put some constraints on things. IIRC, some guy was having a field day with the data.

    Anyway, IIRC, 90% of the mass is in the form of neutrons. The other 10% is doing all sorts of interesting things. There are apparently all sorts of exotic matter phases and transitions between phases going on. There's little clumps of various exotic phases.

    Now, there is the quark business, where the pressure and density get so high, that you have a quark soup of sorts. If a neutron star is a "giant nucleus", then a quark matter phase would be a giant *nucleon*.

    But all of that is still highly speculative. There was a something about spin down -- as the thing spins down, and the centrifugal component decreases, the pressure goes even higher, and some theorize that things could go from mostly neutrons to mostly quark phase here.

    -Richard

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    strange answer

    My guess is that the heavier strange quarks beginning to dominate the interior of neutrons within the NS coupled with their ability to produce charge and associated fields contributes the existence of the magnetic field associated with the NS and not the protons and electrons still in existence. It has been shown in experiments that the strange sea is the major contributor to the proton's charge and not the up quark.

    Like the example above, the strong magnetic field will induce energy into the components of the star,likely stirring up the strange fields and making their virtual particle/antiparticle pairs become real for extended periods . As the field expands, gluons will be stretched and new mesons appear possibly with strangeness attached. As it contracts, the gluons will be compressed and the quarks will tend to have more degrees of freedom. The contraction also has cooling asssociated with it. An equilibrium likely results between the amount of strangeness and nonstrangeness that is contained in the overall structure of the star.

    http://qd.typepad.com/33/2005/06/strangeness_in_.html


    http://www.economist.com/science/dis...ory_id=4342393

    http://flux.aps.org/meetings/YR97/BA.../S1400006.html
    Last edited by blueshift; 2007-Jan-02 at 07:30 PM. Reason: clarity

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    That's the beauty of astronomy-- there are always more things in heaven, Horatio, than dreampt of in your accelerators.

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    Wink neutron decay....

    Quote Originally Posted by Nereid View Post
    So are neutron stars copious emitters of neutrinos, or not?

    If the mean free path in neutronium is ~km, then a vigourous equilibrium between neutrons, protons, and electrons would suggest rapid cooling via neutrino loss (whatever cooling means for a degenerate neutron gas).

    The transition region - the thin (?) skin between neutronium and the vacuum of space above the surface, including any (normal) gaseous atmosphere - must be a fascinating realm, for a physicist!

    But back to neutron decay ... as the neutron, like the proton, is a three-quark trick, weak decay means some kind of Feyman diagram involving Zs and Ws, doesn't it?
    Nereid. The neutron is two downs and an up, the proton two ups and a down quark. So in neutron decay, essentially a down quark converts to an up. This is exothermic. The down quark emits a W-, and converts to an up as it does, giving a proton with plus 1 charge. The W- converts to an electron, and an electron-type antineutrino. The electron is free to stay with the proton, giving conserved charge, and the anti-neutrino escapes promptly.
    In the reverse scenario, the simultaneous coalescing of electron, proton, and electron-type anti-neutrino is statistically very unlikely, though not forbidden. In the formation of a neutronized core to a pulsar, the compression raises the temperature to such a point that the endothermic can occur.....a neutron can also be formed if a proton emits a positron, and a neutrino. This occurs when an up converts to a down, thereby forming the neutral neutron, and emits a W+. The W+ decays to the positron and neutrino. The positron so formed annihilates the former proton's electron in a pair or trio of gamma rays, (1.022 Mev total), and this time neutrinos escape promptly. (Core collapse supernovae, accompanied by beamed directional gamma ray burst).... Bhodan Paczynski, Physics Colloquia, MIT.
    Pete.

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