# Role of Strong Force in Neutron Stars

1. Oct 21, 2012

### Drakkith

Staff Emeritus
Does the strong force have any major role in neutrons stars other than obviously holding individual nuclei together? Would low energy neutrons tend to "clump" together in the core?

2. Oct 21, 2012

### mathman

3. Oct 22, 2012

### ImaLooser

I've read a lot about neutron stars and no one seems to mention the strong force. So I'm baffled too.

The core is superfluid, so all the neutrons have the same wave function and are at the same energy. Superfluids are extremely conductive of heat, it moves at c/2 or something like that.

4. Oct 22, 2012

### ImaLooser

The quark-gluon plasma theory lost popularity when a star with mass of 1.96 AU was discovered.

5. Oct 23, 2012

Staff Emeritus
What you are looking for is something called the Equation of State or EOS of a neutron star. The simplest model are what are called polytropes, where the pressure goes as the density to some power (often 5/3 for relativistic fermions and 4/3 for nonrelativistic fermions).

6. Oct 28, 2012

### lpetrich

It's actually:

Nonrelativistic: 5/3
Partially relativistic: 4/3
Completely relativistic: 1

In general, electron number density n ~ p3
where p is the Fermi momentum, the maximum momentum an electron has in the system.

Mass density = den
Pressure ~ kinetic-energy density

Nonrelativistic (p << m):
den ~ n * (M + m)
P ~ n * (p2/(2m))
where m is the mass of an electron and M is the mass of the nuclei per electron

den ~ p3
P ~ p5
P ~ den5/3

Partially relativistic (p >> m, p << M):
den ~ n * (M + p)
P ~ n * p

den ~ p3
P ~ p4
P ~ den4/3

Completely relativistic (p >> M)
den ~ n * p
P ~ n * p

den ~ p3
P ~ p3
P ~ den1

7. Oct 28, 2012

### lpetrich

I'll now do some simple stability calculations. I'll work in the Newtonian limit for simplicity.

Kinetic energy ~ (pressure)*R3

Potential energy ~ - G*M2/R
for mass M and grav. const. G

GR creates effects with relative size (G*M)/(R*c2), so it makes a small effect for any condensed object less massive or larger than than a neutron star.

Take a polytropic equation of state: pressure = K*(density)g -- a power law

Density ~ M/R3
so the kinetic energy varies as
K*Mg*R3(1-g)

To be stable, an object must have its kinetic energy decreasing faster for increasing radius than the absolute value of the potential energy. This gives the condition

g > 4/3

meaning that if an object has too little resistance to compression, it will collapse.

One can get a good approximation of the Chandrasekhar mass of a white dwarf from this simple argument.

This result also means that a neutron star can only be stable if its particles have a sufficiently strong repulsive interaction. That is indeed what happens, though how strong has been a VERY difficult subject.

8. Jan 7, 2013

### Astrofan

Could you give a link to this finding? Seems interesting to get some exact details of why that causes problems with the quark-gluon theory.