Starship Asterisk*

Intense pressure can force neutrons into cubes rather than spheres, say physicists

As pressure and density in a neutron star go up, normally sphere-like neutrons might take on an increasingly cubic shape. (F.J. Llanes-Estrada and G.M. Navarro/arXiv:1108.1859)

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Inside atomic nuclei, protons and neutrons fill space with a packing density of 0.74, meaning that only 26 percent of the volume of the nucleus in is empty.

That's pretty efficient packing. Neutrons achieve a similar density inside neutron stars, where the force holding neutrons together is the only thing that prevents gravity from crushing the star into a black hole.

Today, Felipe Llanes-Estrada at the Technical University of Munich in Germany and Gaspar Moreno Navarro at Complutense University in Madrid, Spain, say neutrons can do even better.

These guys have calculated that under intense pressure, neutrons can switch from a spherical symmetry to a cubic one. And when that happens, neutrons pack like cubes into crystals with a packing density that approaches 100%.

Anyone wondering where such a form of matter might exist would naturally think if the centre of neutron stars. But there's a problem.

On the one hand, most neutron stars have a mass about 1.4 times that of the Sun, which is too small to generate the required pressures for cubic neutrons. On the other, stars much bigger than two solar masses collapse to form black holes.

That doesn't leave much of a mass range in which cubic neutrons can form.

As luck would have it, however, last year astronomers discovered in the constellation of Scorpius the most massive neutron star ever seen. This object, called PSR J1614-2230, has a mass 1.97 times that of the Sun.

That's about as large as theory allows (in fact its mere existence rules out various theories about the behaviour of mass at high densities). But PSR J1614-2230 is massive enough to allow the existence of cubic neutrons.

Astrophysicists will be rubbing their hands at the prospect. The change from spherical to cubic neutrons should have a big influence on the behaviour a neutron star. It would change the star's density, it's stiffness and its rate of rotation, among other things.

So astronomers will be getting their lens cloths out and polishing furiously in the hope of observing this entirely new form of matter in the distant reaches of the galaxy.

[i]Illustration of a neutron star. (NASA/JPL-Caltech)[/i]

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Deep inside the super-dense hearts of exploding stars, gravity may squash neutron particles from spheres into cubes.

The idea could mean that neutron stars, as researchers call the stellar corpses, are denser than anyone expected. It could also question what stops them from collapsing into black holes and out of existence.

“If you take this result purely at face value, it means neutron stars are in trouble. They should collapse into black holes at lower masses,” said theoretical physicist Felipe Jose Llanes-Estrada of Complutense University of Madrid, co-author of a study published Aug. 9 on the prepublication server arXiv.

“But that’s not what we observe. It’s possible there’s an additional repulsive interaction [between neutrons] to counter a collapse that we just haven’t thought of yet.”

A star between nine and 20 times the sun’s mass detonates as a supernova toward the end of its life. At that weight, a star isn’t heavy enough to create a critical, ultra-dense state and shrink into a black hole. Instead, it collapses into a sphere no bigger than 15 miles wide and so dense that a single teaspoon of it weighs as much as everyone on Earth, multiplied by 18.

Late last year, astronomers discovered the biggest-ever neutron star, called J1614-2230, that weighed in at 1.97 times the sun’s mass. Prior to its discovery, the most massive neutron weighed 1.67 solar masses.

The find left more than a few astrophysicists scratching their heads. Its existence ruled out some models of neutron stars that relied on exotic forms of matter to explain why they didn’t collapse farther, and instead supported models of neutron stars as containing only neutrons and protons.

When Llanes-Estrad and his university colleague Gaspar Moreno Navarro heard of J1614-2230, they wanted to know what might be happening inside of it.

The duo knew of a model from the 1970s suggesting pure neutrons could form a crystal lattice under incredible pressure (similar to how carbon forms diamonds in the bowels of the Earth). When they tweaked a familiar computer model to incorporate the idea, they discovered that — at the pressures anticipated deep in neutron stars — neutrons deformed from spheres into cubes.

“There’s an optimum packing density with spheres, including neutrons. It’s about 74 percent. No matter how efficiently you arrange them, like oranges on display at a supermarket, there’s always space in between,” Llanes-Estrada said. “If you want to be most efficient, you distort the oranges. Pack them a mile high and squish the ones on the bottom.”

Gravity shapes aggregate particles of matter into the simplest, most efficiently-packed object possible, normally a sphere like the Earth. The particles themselves, though, remain individually unaffected; gravity is too weak to overcome the strong interactions that hold neutrons and other particles together. But if gravity becomes intense enough, it might overpower the interactions.

So deep within a neutron star, a neutron’s most efficient shape may be a cube. “They’ll be flattened on all sides, like dice,” Llanes-Estrada said.

So far, the response to their study has proven lukewarm.

Particle physicist Richard Hill of the University of Chicago, for example, noted the study looks at a neutron in isolation, not in aggregate.

“It’s an interesting idea, but what happens among the neutrons isn’t clear,” said Hill, who wasn’t involved in the study. At the densities in neutron stars, he noted, the “identities of individual neutrons may be blurred out.”

Llanes-Estrada acknowledged the criticism, which a second physicist who wished to remain anonymous also shared. But Llanes-Estrada said that pushing boundaries was, in part, the point.

“I think there is a large uncertainty of what happens to neutrons at very high compressions,” he said. “I think we should keep studying all of the possibilities.”

• arXiv.org > nucl-th > arXiv:1108.1859 > 09 Aug 2011

bystander wrote:Neutrons Become Cubes Inside Neutron Stars
Technology Review | The Physics arXiv Blog | kfc | 2011 Aug 11

Intense pressure can force neutrons into cubes rather than spheres, say physicists

last year astronomers discovered in the constellation of Scorpius the most massive neutron star ever seen. This object, called PSR J1614-2230, has a mass 1.97 times that of the Sun.

That's about as large as theory allows (in fact its mere existence rules out various theories about the behaviour of mass at high densities). But PSR J1614-2230 is massive enough to allow the existence of cubic neutrons.

Super-Dense Stars May Squash Neutrons Into Cubes
Wired Science | Dave Mosher | 2011 Aug 16

Late last year, astronomers discovered the biggest-ever neutron star, called J1614-2230, that weighed in at 1.97 times the sun’s mass. Prior to its discovery, the most massive neutron weighed 1.67 solar masses.

The find left more than a few astrophysicists scratching their heads. Its existence ruled out some models of neutron stars that relied on exotic forms of matter to explain why they didn’t collapse farther, and instead supported models of neutron stars as containing only neutrons and protons.

http://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_limit wrote:
<<The Tolman–Oppenheimer–Volkoff limit (or TOV limit) is an upper bound to the mass of stars composed of neutron-degenerate matter (i.e. neutron stars). The TOV limit is analogous to the Chandrasekhar limit for white dwarf stars.

The limit was computed by J. Robert Oppenheimer and George Volkoff in 1939, using the work of Richard Chace Tolman. Oppenheimer and Volkoff assumed that the neutrons in a neutron star formed a cold, degenerate Fermi gas. This leads to a limiting mass of approximately 0.7 solar masses. Modern estimates range from approximately 1.5 to 3.0 solar masses. The uncertainty in the value reflects the fact that the equations of state for extremely dense matter are not well-known.

In a neutron star less massive than the limit, the weight of the star is balanced by short-range repulsive neutron-neutron interactions mediated by the strong force and also by the quantum degeneracy pressure of neutrons, preventing collapse. If its mass is above the limit, the star will collapse to some denser form. It could form a black hole, or change composition and be supported in some other way (for example, by quark degeneracy pressure if it becomes a quark star). Because the properties of hypothetical more exotic forms of degenerate matter are even more poorly known than those of neutron-degenerate matter, most astrophysicists assume, in the absence of evidence to the contrary, that a neutron star above the limit collapses directly into a black hole.

A black hole formed by the collapse of an individual star must have mass exceeding the Tolman–Oppenheimer–Volkoff limit. Theory predicts that because of mass loss during stellar evolution, a black hole formed from an isolated star of solar metallicity can have mass no more than approximately 10 solar masses.:Fig. 21 Observationally, because of their large mass, relative faintness, and X-ray spectra, a number of massive objects in X-ray binaries are thought to be stellar black holes. These black hole candidates are estimated to have masses between 3 and 20 solar masses.>>

For these eclipsing binary systems it is possible to measure the mass of the neutron star! For the 11 masses so far measured, the mass is 1.4MSun in 10 cases and 1.8MSun in the 11th.

This is good! Neutron stars are supposed to be greater than 1.4MSun and there is even reason to think that they should all be pretty close to the Chandrasekar Limit since that is what initiates the core collapse in a SNII.

[i]The currently popular analogy to describe the density of matter within a neutron star is that it's like compressing the entire human population into a sugar cube. And speaking of cubes... (Credit: E. Galactica)[/i]

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The nature of the highly compressed matter that makes up neutron stars has been the subject of much speculation. For example, it’s been suggested that under extreme gravitational compression the neutrons may collapse into quark matter composed of just strange quarks – which suggests that you should start calling a particularly massive neutron star, a strange star.

However, an alternate model suggests that within massive neutron stars - rather than the neutrons collapsing into more fundamental particles, they might just be packed more tightly together by adopting a cubic shape. This might allow such cubic neutrons to be packed into about 75% of the volume that spherical neutrons would normally occupy.

Some rethinking about the internal structure of neutron stars has been driven by the 2010 discovery that the neutron star PSR J1614–2230, has a mass of nearly two solar masses – which is a lot for a neutron star that probably has a diameter of less than 20 kilometres.

PSR J1614–2230, described by some as a ‘superheavy’ neutron star, might seem an ideal candidate for the formation of quark matter – or some other exotic transformation – resulting from the extreme compression of neutron star material. However, calculations suggest that such a significant rearrangement of matter would shrink the star’s volume down to less than the Schwarzschild radius for two solar masses - meaning that PSR J1614–2230 should immediately form a black hole.

But nope, PSR J1614–2230 is there for all to observe, a superheavy neutron star, which is hence almost certainly composed of nothing more exotic that neutrons throughout, as well as a surface layer of more conventional atomic matter.

[i]Modelling the quantum field waveforms of neutrons under increasing densities suggests a cubic, rather than a spherical, geometry is more likely. Credit: Llanes-Estrada and Navarro.[/i]

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Nonetheless, stellar-sized black holes can and do form from neutron stars. For example, if a neutron star in a binary system continues drawing mass of its companion star it will eventually reach the Tolman–Oppenheimer–Volkoff limit. This is the ultimate mass limit for neutron stars – similar in concept to the Chandrasekhar limit for white dwarf stars. Once a white dwarf reaches the Chandrasekhar limit of 1.4 solar masses it detonates as a Type 1a supernova. Once, a neutron star reaches the Tolman–Oppenheimer–Volkoff mass limit, it becomes a black hole.

Due to our current limited understanding of neutron star physics, no-one is quite sure what the Tolman–Oppenheimer–Volkoff mass limit is, but it is thought to lie somewhere between 1.5 – 3.0 solar masses.

So, PSR J1614–2230 seems likely to be close to this neutron star mass limit, even though it is still composed of neutrons. But there must be some method whereby a neutron star’s mass can be compressed into a smaller volume, otherwise it could never form a black hole. So, there should be some intermediary state whereby a neutron star’s neutrons become progressively compressed into a smaller volume until the Schwarzschild radius for its mass is reached.

Llanes-Estrada and Navarro propose that this problem could be solved if, under extreme gravitational pressure, the neutrons’ geometry became deformed into smaller cubic shapes to allow tighter packing, although the particles still remain as neutrons.

So if it turns out that the universe does not contain strange stars after all, having cubic neutron stars instead would still be agreeably unusual.