Researchers theorize that neutrons may be squished into cubes in neutron stars

Aug 18, 2011 by Bob Yirka report
Trial wavefunction that interpolates between sphere, and cube. Image: arXiv:1108.1859v1 [nucl-th]

(PhysOrg.com) -- Neutrons, those particles that reside here on Earth inside the nucleus of atoms, along with protons, collectively called nucleons, are thought to exist in the far reaches of the universe inside of so-named neutron stars, which are the remnants of stars that have exploded. In a paper published on the preprint server arXiv, Spanish physicists Felipe Llanes-Estrada, and Gaspar Moreno Navarro, suggest that the densities in the cores of certain sizes of such neutron stars might be so great as to squash the neutrons down from their normal spherical shape, into cubes.

The key is in the size of the neutron star, the researchers say; too big and they’d collapse down to black holes. Too small and they'd simply exist as run of the mill . Since the tipping point is believed to be such stars that are of twice the density as the sun, the discovery of a neutron star last year, PSR J1614-2230 (the largest ever found) with a solar masses of 1.97 seems to fit the bill as it’s about as dense as a neutron star can get without collapsing. The researchers speculate that in order to achieve such a density, the neutrons at its core would have to facilitate a means of having the same number of neutrons in a smaller space. And because cubes are more efficient, they theorize that those neutrons closet to the core, would be the ones squished down to cube shapes.

Llanes-Estrada likens it to a stack of oranges sitting on a grocer’s shelf. Normally spherical they begin to flatten as more and more are piled on top. If the same amount of weight (gravity) were applied in all directions, the oranges would flatten from both above and below, but also on all sides as well.

In their natural state, as spheres, neutrons have a packing density of about 74%; collapsing them down to cubes, creating a sort of crystal lattice such as happens when diamonds from carbon in the Earth, could possibly bring that number up to nearly 100%.
Not everyone agrees with the results of the duo’s paper, some even suggesting that the huge density numbers could come about as the result of the blurring of lines between individual ; but the two researchers seem undaunted, suggesting that pushing boundaries, is all a part of science.

Explore further: Cold Atom Laboratory creates atomic dance

More information: Cubic neutrons, arXiv:1108.1859v1 [nucl-th] arxiv.org/abs/1108.1859

Abstract
The neutron is largely spherical and incompressible in atomic nuclei. These two properties are however challenged in the extreme pressure environment of a neutron star. Our variational computation within the Cornell model of Coulomb gauge QCD shows that the neutron (and also the Delta-3/2 baryon) can adopt cubic symmetry at an energy cost of about 150 MeV. Balancing this with the free energy gained by tighter neutron packing, we expose the possible softening of the equation of state of neutron matter.

via Arxiv Blog

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User comments : 33

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rawa1
3.7 / 5 (3) Aug 18, 2011
Actually, the free electrons are behaving in the same way like the neutrons - just at much lower energy density. In three dimensions the sufficiently cooled electrons forming bulk-centered cubic lattice, which is known as Wigner crystal. A pretty well like the apples or oranges stacked in the pyramidal pile.

http://en.wikiped..._crystal

It means, when the neutrons are squeezed enough, their short distance repulsive lepton charge applies in similar way, like at the case of long distance electromagnetic charge of free electrons. It's not rocket science, despite it appears so at the first look.
Gawad
4.4 / 5 (7) Aug 18, 2011
the tipping point is believed to be such stars that are of twice the density as the sun
Mass, Bob, mass.
rawa1
3.2 / 5 (5) Aug 18, 2011
A much more interesting situation would emerge, when the repulsing particles are compressed even more. Due the asymptotic freedom of free quarks the neutrons would literally dissolve into superfluous quark-gluon condensate, the inner properties of which would appear quite similar to our vacuum. I presume, many intermediate semi crystalline states may appear during this, which would enable the formation of primitive molecules inside the core of neutron stars. The pieces of condensed neutrons would revolve mutually like planetary systems inside of molten quark gluon fluid and they should appear quite transparent for energy waves spreading through this fantastic system.

I presume, we could study such a geometry experimentally with electrons or tiny charged nanoparticles, attracted to surface of insulators with strong external electrostatic field.
shockr
5 / 5 (1) Aug 18, 2011
So... gravity only works in 6 directions? Or we get a cube because gravity decides not to work normally?

Likening this to the 'orange pile' is no good. That pile only has one direction of gravitational force..
physpuppy
4.7 / 5 (3) Aug 18, 2011
:-)
For some reason, this story reminded me of something here on Earth:

http://www.snopes...elon.asp

(square watermelons)
rawa1
3 / 5 (2) Aug 18, 2011
..or we get a cube because gravity decides not to work normally..
The gravitational force is strongest in just three dimensions. The surface/volume ratio is minimized just for 3D hyperspheres.

http://arxiv.org/abs/1106.4548
http://xxx.lanl.g.../0506053
http://mathworld....ing.html
that_guy
4.3 / 5 (9) Aug 18, 2011
the tipping point is believed to be such stars that are of twice the density as the sun
Mass, Bob, mass.

Gawad, I'm surprised you missed "Too small and they'd simply exist as run of the mill neutron stars."
Correction - too small and they would exist as run of the mill white dwarfs.

What happened to Oliver. This paper has relevant information on the sun's neutron core.

@shockr - the orange pile metaphor is perfectly fine. the neutrons pack in like a pyramid made of oranges. In fact, I think they over explained it. Let me lay it out simply for your reading comprehension skills. They are basically saying that the neutrons crystallize into a cubic type crystal.
RacinReaver
5 / 5 (2) Aug 18, 2011
There are tons of things that pack more efficiently than spheres. I remember seeing a paper with how M&Ms pack more efficiently than gumballs (both in random and ordered packing). Haven't read this paper, but I can't really see why they'd make the shift to cubes before slightly modifying their spherical shape.
Gawad
4.2 / 5 (5) Aug 18, 2011
Gawad, I'm surprised you missed "Too small and they'd simply exist as run of the mill neutron stars."
Good point, Guy. In my defence that "x2 the density" bit was just burning out my retina. :)

Also, I couldn't really make out if Bob was trying to situate these special case "squaring the neutrons" neutron stars between black holes and white dwarfs or between black holes (supposedly JUST above the mass limit for these special neutron stars) and "regular" neutron stars with round neutrons. It seems to me that Mr. Yirka usually manages to be a little more clear!
Gawad
4.5 / 5 (8) Aug 18, 2011
What happened to Oliver. This paper has relevant information on the sun's neutron core.
And geeze! Come on! The Spirit of Neutron Revulsion really doesn't need any encouragement!
that_guy
not rated yet Aug 18, 2011
Gawad, I'm surprised you missed "Too small and they'd simply exist as run of the mill neutron stars."
Good point, Guy. In my defence that "x2 the density" bit was just burning out my retina. :)

Also, I couldn't really make out if Bob was trying to situate these special case "squaring the neutrons" neutron stars between black holes and white dwarfs or between black holes (supposedly JUST above the mass limit for these special neutron stars) and "regular" neutron stars with round neutrons. It seems to me that Mr. Yirka usually manages to be a little more clear!


You're right, I didn't think about that. Maybe it was unclear instead of incorrect.
Gawad
1 / 5 (1) Aug 18, 2011
Maybe it was unclear instead of incorrect.
And a little frustratingly incomplete: what I would really like to know is whether neutrons would really deform under such pressures or dissolve into a quark-gluon strange matter plasma. He kind of hints at the alternate possibility when he writes "the blurring of lines between individual neutrons" but doesn't go any further.
Shootist
1 / 5 (1) Aug 18, 2011
Gawad, I'm surprised you missed "Too small and they'd simply exist as run of the mill neutron stars."
Good point, Guy. In my defence that "x2 the density" bit was just burning out my retina. :)


You're both wrong.

The author is saying that a NS of 1.4sols isn't massive, or dense, enough to pack its neutrons in the manner described.

Just sayin'
that_guy
5 / 5 (3) Aug 18, 2011
Gawad, I'm surprised you missed "Too small and they'd simply exist as run of the mill neutron stars."
Good point, Guy. In my defence that "x2 the density" bit was just burning out my retina. :)


You're both wrong.

The author is saying that a NS of 1.4sols isn't massive, or dense, enough to pack its neutrons in the manner described.

Just sayin'

Isn't that what Gawad is saying in the statement you quoted??
hemitite
5 / 5 (3) Aug 18, 2011
Maybe they turn into legos - That would be some kit!
that_guy
not rated yet Aug 18, 2011
addendum to my last comment - the part you omitted from your quote shootist.
Gawad
3 / 5 (2) Aug 18, 2011
Gawad, I'm surprised you missed "Too small and they'd simply exist as run of the mill neutron stars."
Good point, Guy. In my defence that "x2 the density" bit was just burning out my retina. :)


You're both wrong.

The author is saying that a NS of 1.4sols isn't massive, or dense, enough to pack its neutrons in the manner described.

Just sayin'

Isn't that what Gawad is saying in the statement you quoted??

It's OK, Guy, he's just being Shootist. Shootin' from the hip, BANG, BANG!

Some day he'll figure out either that twice the density of the Sun doesn't quiiiite match the density of any neutron star, or that doubling the Sun's *density* won't do Jack S*it as far as its mass. Or better yet, he'll pull those two ideas together and conclude that "twice the density as the sun" and "need to be twice the mass of the sun to be dense enough" aren't equivalent statements. And, yes, we all figured out what Bob was trying to say there anyway.
Graeme
5 / 5 (2) Aug 18, 2011
cubes does sounds a pretty unlikely packing arrangement. If this is happening then the normally fluid neutrons are basically crystallizing. They are likely to form the more close packed crystal latices. you can read about the packing arrangements in https://secure.wi...spheres. It looks to be much more likely that it would pack into dodecahedron 12 side shapes. This would reduce those low density regions on the vertices of cubes.
sender
5 / 5 (1) Aug 18, 2011
I imagine a bowtie to be a more likely configuration however in 3D so a cube surrounded by a "semi-soft" sphere.
sender
5 / 5 (1) Aug 18, 2011
I wonder if this model would yield a better picture of quadrupole magnetic reconnection events.
DarkHorse66
5 / 5 (1) Aug 19, 2011
@shockr
So... gravity only works in 6 directions? Or we get a cube because gravity decides not to work normally?


Yes, such an object would have high gravity, but it's not actually about the gravity. It's about the pressure being generated by all the many particles being closely packed around each other in a VERY confined space and pushing against each other (density). This density being high enough to here generate this famous cube. The gravity field being generated will still be omnidirectional, but the shape of the field will follow the shape of the object as long as it is still separate. However, as all these objects and fields are in such close proximity, we get a collective field that is by extension, the field of gravity of the (collective) entity we call a neutron star.
Husky
5 / 5 (2) Aug 19, 2011
honeycomb structure seems more likely
Kinedryl
3 / 5 (2) Aug 19, 2011
honeycomb structure seems more likely

At 2D, not 3D...
shockr
5 / 5 (1) Aug 19, 2011
@DarkHorse66

I can appreciate that under pressure the neutrons may crystallise into such a lattice form. But surely there are still neutrons on the periphery that are not under such pressure and thus still mould around to form the sphere I'd expect from the gravity well. Is this still the case? I can't image anything having naturally flat sides. Surely some particles would adhere to the flat sides and make it non-uniform in that respect?
Moebius
1 / 5 (1) Aug 19, 2011
honeycomb structure seems more likely


I think he means 3D. Wouldn't that be a Octadecagon with 18 sides? I think that shape packs perfectly.
DavidMcC
5 / 5 (1) Aug 22, 2011
honeycomb structure seems more likely


I think he means 3D. Wouldn't that be a Octadecagon with 18 sides? I think that shape packs perfectly.

Aren't the apical angles wrong for that? Octadecagons are too like a sphere for close packing.
ubavontuba
3 / 5 (2) Aug 22, 2011
honeycomb structure seems more likely
Right, but the article is essentially defining a cubic honeycomb structure.

http://en.wikiped...oneycomb

The cubic honeycomb is the most space efficient because it's externally smooth (no outer layer graininess), when packed into a box.

But, I don't know if it's any more efficient than several other polyhedron shapes, when packed into a sphere.

http://en.wikiped...eometry)

But I suppose the outer layers might exhibit "smoothing" (to conform to the sphere's 2D boundary). Therefore, a variety of shapes seem just as likely.

DavidMcC
3 / 5 (1) Aug 22, 2011
Ubavontuba, even though Wikipedia uses the term "honeycomb" to desribe a cubic lattice, I think it is an unfortunate word, as it conjures up the hexagonal cells that bees make.
Vlasev
not rated yet Aug 22, 2011
It looks to be much more likely that it would pack into dodecahedron 12 side shapes. This would reduce those low density regions on the vertices of cubes.


Exactly what I first thought. It seams logical that spheres would deform easier (read more likely) into something closer to spherical shape while utilizing the gaps.
If there is a reason for the neutrons to be aligned into cubical crystal lattice before they start to change their shape, yet the author has omitted to point this out.
ubavontuba
1 / 5 (1) Aug 22, 2011
@DavidMcC
...even though Wikipedia uses the term "honeycomb" to describe a cubic lattice, I think it is an unfortunate word, as it conjures up the hexagonal cells that bees make.
I generally agree, but the word simplifies the principle. I doubt the lay audience would easily understand the principle of "tessellation." I think the references I provided clear up any subsequent misunderstandings.

What I wonder is how much resistance to compression the neutrons may have. I definitely think it's likely harder to squeeze a sphere into a cube than a truncated octahedra, or some other semi-spherical polyhedron, as the corners of the cube are significantly extruded away from the center of mass/energy.

DarkHorse66
1 / 5 (1) Aug 23, 2011
@Shockr:
You have deduced correctly, the outer particles would be under less pressure, therefore there would be correspondingly less 'deformity'. This is because the direction of the pressure is inwards, towards the centre and is greatest there. So, the further out from the centre the particle, the less it is being deformed. It is NOT a case of a couple of rounder ones sticking to a group of square ones. We are talking about a VERY large collection of VERY small (but uniform-sized) particles and that each deform gradually less and less, as we travel towards the outer parts. If you want a kind of a lineal analogy, maybe think of stacking a whole pile of loose fluffy cushions on top of each other. The top layer will still be loose and fluffy. As you go down the layers, each will be a little more flattened by the pressure being generated by the ones above. The direction of force is straight down, at a right angle to the floor. To take this to a 2D picture representative of a sphere..cont
DarkHorse66
1 / 5 (1) Aug 23, 2011
...cont
cut down the middle, take your floor and roll it into a tight circle. The cushions are stuck together above and below, so that they don't fall off. The lines of force STILL point at right angles to the tangent of the corresponding point on the floor. And the operation of the force has not changed. The only difference is that the lines now meet at a central point. I tend to be somewhat pictorial (to be as clear as possible) when I try to explain things and I rather suspect that the picture I have painted is somewhat simplistic for you. I'm not trying to imply anything nasty, but I daresay that there are some on this site for whom this is what it takes. I prefer to hope that at least somebody has actually gained some genuine insight from this, however minor. As I would hope that others would do for me, when I don't get it right.

Cheers.
DavidMcC
not rated yet Aug 23, 2011
I think the most important issue in neutronium is "How is the degeneracy pressure that keeps a neutron star from collapsing to a black hole overcome?" The standard model posits that neutronium becomes "quark soup". However, this material would also have degeneracy pressure, because quarks aren't bosons. Particle physics eventually has to allow for the mass of a star to be converted to massive bosons, so that it loses its degeneracy pressure, and collapses to a black hole.