# Temperature of a neutron star

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Matter in a neutron star is made only of neutron packed together. There is no space between the neutrons so they can not move. Temperature is the mesure of the kinetic energy of the particle that constitute matter. Then if the neutron can not move the temperature of a neutron star should be 0 K

Does that make sense or am I missing something ?

Thanks

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I really like the logical analytical way you follow thru

what you are doing (finding apparent contradictions) is a good way to come up with questions that are useful to discuss

In fact there are a number of papers about the INTERNAL STRUCTURE

of neutron stars

Interestingly enough, the astrophysics experts who model the structure of NS do not assume that they are simply a compact bunch of neutrons.

They are just CALLED neutron stars. that is the customary term. but the models have other species of particle assembled in various ways.

I will see if I can easily find some recent stuff on that. Did you try Wikipedia? I could search arxiv with keyword "neutron star structure"

or "quark star" or other stuff like that. You could too.

About temperature: the outer layer of neutron stars start out very hot, and they radiate off their heat gradually, and gradually cool down. I suspect the core is even hotter than the outerlayer because of usual way heat behaves.

I dont know how temperature would be defined at the core of a neutron star but there is stuff happening there. It is not some dead static crystal of pure neutrons

(at least according to recent papers about NS that I've seen). Swansont might know how one defines temperature in these extreme conditions. I feel fairly sure it would not turn out to be zero kelvin though

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for sure jaques can look up the Wikipedia, but in case other casual readers are interested, I will paste a bit of it.

Remember that Wikipedia is unreliable and sometimes has bad information, but you can use it to get a start and find out the main keywords to use, and do a search elsewhere if you suspect Wiki is wrong. And often it is excellent too.

==exerpt from Wik article on "neutron star"==

Structure

[diagram here]

Current understanding of the structure of neutron stars is defined by existing mathematical models. A neutron star is so dense that one teaspoon would weigh 100 million metric tons. On the basis of current models, the matter at the surface of a neutron star is composed of ordinary atomic nuclei as well as electrons. The "atmosphere" of the star is roughly one meter thick, below which one encounters a solid "crust". Proceeding inward, one encounters nuclei with ever increasing numbers of neutrons; such nuclei would quickly decay on Earth, but are kept stable by tremendous pressures. Proceeding deeper, one comes to a point called neutron drip where free neutrons leak out of nuclei. In this region, there are nuclei, free electrons, and free neutrons. The nuclei become smaller and smaller until the core is reached, by definition the point where they disappear altogether. The exact nature of the superdense matter in the core is still not well understood. While this theoretical substance is referred to as neutronium in science fiction and popular literature, the term "neutronium" is rarely used in scientific publications, due to ambiguity over its meaning. The term neutron-degenerate matter is sometimes used, though not universally as the term incorporates assumptions about the nature of neutron star core material. Neutron star core material could be a superfluid mixture of neutrons with a few protons and electrons, or it could incorporate high-energy particles like pions and kaons in addition to neutrons, or it could be composed of strange matter incorporating quarks heavier than up and down quarks, or it could be quark matter not bound into hadrons. (A compact star composed entirely of strange matter would be called a strange star.) However so far observations have neither indicated nor ruled out such exotic states of matter.

==endquote==

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Thanks Martin

So the neutron star are not completly made out of neutron.

With time as the neutron star cool down, all neutron will lose there kinetic energy and nothing will replace it except for the microwave background radiation. I guess that it would take a lot of time to dissipate that heat since the radiative surface is so small compare to the mass...

I can conclude that the neutron are not toutching each other if they can move.

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I can conclude that the neutron are not toutching each other if they can move.

I really like this train of thought!

You should make some effort to contact Atheist or Swansont for broader perspective.

remember they aren't marbles!

what does a multineutron superfluid state actually look like?

how does one imagine a superfluid?

remember what Wiki article said "a superfluid mixture of neutrons..."

and that was just one possibility

what if there are vortexes, whirlpools

what if there are neutrons changing back and forth into kaons and other werewolves, constantly releasing and absorbing energy

I am trying to picture various kinds of ACTION going on in heart of neutronstar.

how fast can a proton move thru a superfluid neutron state? remember there might be a few odd exceptional particles like protons added to the mix.

my mental image of a superfluid is that it has no viscosity

don't know if that is right or if it applies here

any kind of random action that is possible can absorb energy and participate in heat.

If Atheist does not notice this thread, then write him PM and ask him directly what form thermal energy would take at core of NS. It's a reasonable question. I just cant answer it.

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Well, the main problem I see is that I think the classical picture (neutrons as little hard balls with definite momentum and position) breaks down in the case of a neutron star. A remarkable property of a neutron star is that the gravitational force that tries to collapse the star to a single point in space is not countered by electromagnetic interaction (the repulsion of the electron clouds around different molecules) but by a mixture of a Quantum Mechanical principle called "Pauli exclusion principle" and the energy-dependence of the different QM states of the star's radius (the boundary condition). In other words: I think you need QM at least for understanding why the whole thing is even stable.

The model you use for describing a system often also depends on what you actually want to know about that system - you can almost never model a realistic system completely. For the question why a neutron star is stable (i.e. the countering of gravitational interaction and "QM repulsion") there is a relatively simple model giving reasonable results. I could probably put down the maths of that either here or on the sfn-wiki if you´re interested in that. But I´m not sure to what extend that covers your original question.

Some points in short:

- I don´t think a classical model is appropriate for neutron stars.

- Temperature is not necessarily a measure for the kinetic energy of the particles in the sample. You can apply temperature to systems like a set of spins and their orientation in a magnetic field that don´t even have any kinetic energy at all.

- By pure intuition I would assume that realistically, a neutron star won´t have T=0K. It would probably not even have a uniform temperature - but that´s both just guesses.

-- Some properties, like the stable radius, can be approximated reasonably well with models that use T=0K, I think.

@Martin: Sry, but for any information on the topic that is beyond the simple model in which the pressure of the compressed fermion gas counters the gravitational attraction, I´d have to look it up somewhere, too (and you´d possibly know the better sources, though).

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As has been mentioned, you cannot view a neutron star like a regular star. You may or may not know that a neutron on its own is not stable; it will decay in ~11 minutes (off the top of my head). Yet, neutron stars apparently do not decay, at least according to our limited understanding of them. This can draw parallels between a neutron star and an atomic nucleus- which is where most neutrons exist and where they can remain stable.

So, basically, you need quantum mechanics to be able to understand such a system. This doesn't look so good, because even something like the neucleus of say a uranium atom is rather complicated. And instead having a few tens of particles, a neutron star would have... yikes, something like 10^57 neutrons***!? Thats a fair amount. Treating a neutron star like one incredibly massive atomic neucleus is a very appealing idea to me, although I doubt this works beyond being an analogy.

*** calculation

Wiki says neutron stars are 1.3-2.1 solar masses, so on the same order of magnitude as our sun which has a mass of 2x10^30 kg. A neutron has a mass of 1.6x10^-27 kg. 57 orders of magnitude of difference. Assuming that all or at least the vast majority of a neutron star is in fact neutrons.

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I can conclude that the neutron are not toutching each other if they can move.

As Martin said, they are not marbles. They are also not a collection of atoms in a solid. You have to account for the wave nature and that there has to be spatial separation from the degeneracy pressure; the neutrons are fermions and have to have some difference in their state from the Pauli exclusion principle, and you have to account for the things Atheist pointed out about temperature in this kind of system. It's not center-of-mass KE as in a collection of atoms or molecules.

If you have a bunch of fermions, they fill up their energy states, and only two to a customer (spin up and down). So unlike a Bose-Einstein Condensate, where you have most of the particles at the lowest energy level — and where cold is synonymous with little KE — in a fermion collection many of the particles have lots of KE, even if the system is "cold," i.e. few vacancies in lowest energy states, below the Fermi level. (it's also harder to get there through simple scattering, making a Fermi degenerate gas is more difficult than making a BEC)

So you have the apparent conundrum of neutrons moving about — quite a lot — even if the star is cold.

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Thanks all for your answers. Can we say that a neutron star is a macroscopic QM object ?

Isn't it QM that keep electron from falling on the proton of the nucleus ?

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Thanks all for your answers. Can we say that a neutron star is a macroscopic QM object ?

Isn't it QM that keep electron from falling on the proton of the nucleus ?

"Macroscopic QM object" works for me and my very basic understanding of the situation. "Degeneracy pressure" is the term used in this context to describe the dynamics of the Pauli exclusion principle. But yes, it's a QM effect.

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I read up that some people think a neutron star has a QGP core or builds one up, can this core be in a superfluid state?

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I'm not sure if Quark gluon plasma (QGP) can be a superfluid, although it will become quark-gluon liquid which does have very low viscosity, but im not sure if its quite zero.

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A note on the temperature things. Yes, this is an axiomatic claim, but I would definitely say no system whatsoever in this universe may be of 0 K (apart from one thing, follows). Temperature is a boundary condition of existence of energy like c is (vacuum wave propagation). i.e. no matter how much energy or heat you would add to a [closed] system of 0 K, the system would never increase its temperature from 0. Thus this infers only black holes may have 0 K, not a neutron star. Don't take this as a fact, (I'm more a metaphysicist in research), but this property came out as an 'seemingly' axiomatic property of the universe when I was working on these things. Going a little further would be to claim that this axiom would state that vacuum energy density > 0 as any [open] system of space having energy added with be reactive to it (virtual particles bla bla).

Please note, this is not a scientific explanation but thought I would mention an axiom postulate I worked with which I think is worth mentioning when one talks about 0 K (metaphysics).

ok, so on the neutron star....ye I also think QM (as Pauli's principle is of importance) is the best way forward to predict stability. Martin mentioned the way 'heat normally works' would make it hotter as one radially went inwards.

Hmm, I am not so sure about that intuitively, but ya we unfortunately don't have a lot of these lovely celestial strangeities we could fly out n pick up a sample of and chuck into the good ol' testtube

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I asked this some months back and got the answer, "asymptotically cooling" until you consider possible shell structure, and of course influx, so ???

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I asked this some months back and got the answer, "asymptotically cooling" until you consider possible shell structure, and of course influx, so ???

hehe, not an answer... typically something when people know the concepts involved in the problem but have on real insight of what might be the case....

if one did, the topic would of been far more discussed than just that

But ye, on this topic I am ignorant. I am not sure if degenerate matter should be in the spectrum of extreme heat due tothe massive internal forces/pressures involved or if it is extreme cold and if a neutron star would be more isotropic or having a proportionality relation as one traverses radially, temperature-wise. I suspect they are extremely cold but damn if I'd know

As I mentioned in a different post, I suspected neutron stars to have an angular momentum so great they would be spinning with ~ > 0.6c but nah, not at all :/

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just saw that, to double-check something for me, could you(Alber? anyone?) tell me what you would say (if that data were to hold, for arguments sake) the rotatory velocity of that object is:

diameter (seems to be assumed ) ~ 10 km

frequency : 1122 Hz

maybe one needs to predict a mass here (I used to use the relativistic equations for momentum for these things; however they were from SR so...)

(Many years ago, the velocities of neutron stars just was too low to hold for where I was heading, so I kinda gave up on everything )

PS. Have also asked the same group which observed this object, to what angular velocity they attribute to the object....

I really need to see a ~ 0.6c

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Multiply the circumference by that frequency and you're looking at about one-tenth of the speed of light, still a low-gamma state but a good boogey. For some reference, figure the Schwarzschild radius of a solar mass: $GM/c^2$. I get roughly 1.5 kilometers.

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ya , thats right (for the sun, although thats according to the Schwarz. radius, dont trust it, so a black hole could easily have in reality half of that, 0.75km), but nvm. For the neutron star however, I get this Alber according to the trivial 2piR/t:

assumed radius : 5 km ,

freq : 1122 so I get v = 1122 x 10000x pi m/s , dont you?

In which case would be problematic and not ~ 0.1c

oh sigh, what is the matter with me( I managed to mix up km/m so a order of magnitude of 3...thats what happens when you work with other things then pplug in the simplest ratios in the world :/), ye sure it is, just forget the whole thing and yup, 0.1 c is still far too low.... I guess the possibility of non rotating black holes exists. I just can't seem to convince myself of it.... mathematically sure thing, they are both valid but I just can not see how a black hole comes about without angular momentum sigh.

Guess I will never live to see an object reported to be spinning at ~0.6 c...

This would require a frequency of almost 5 kHz for a celestial object (in this case a 10 km neutron star) . I just got reminded why I abandoned GR several years ago...

lak

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I am not up on the Kerr rotating solution but that's the basis of discussion here. Remember that in the formation of these objects there was much mass ejected and transfer of angular momentum.

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Ye, good point.

Tell me Alber.The way you work with things. How would an idea of a black hole (no wait), take away the black hole and generalize the celestial object to be rotating at c? (of course if anything , it would have to be(come) a black hole)

What obvious limitations would you put on that idea and still , do you think that could be so?

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Oh and I strongly recommend the more general Kerr solution than Schw. The S.R. is so popular cos it brings around the concept of the black hole itself in simpler terms. Although I do not thing black holes exist which are not Kerr holes.

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