Neutron Stars 

So what do we get if the mass of the stellar core exceeds the Chandrasekhar limit?

The core cannot be supported by electron degeneracy, and collapse down until neutron degeneracy takes over. Neutrons are fermions, and subject to the Pauli exclusion principle just like electrons were.

How massive are neutron stars? Typically, about 1.4 Msun, the Chandrasekhar mass. Why??

Because they are supported by (neutron) degeneracy, they also follow a mass-radius relationship similar in behavior to that of white dwarfs (R~M-1/3), but at much smaller sizes:

Also like white dwarfs, as a neutron star becomes more and more massive, the neutrons become relativistic, and the equation of state becomes that of a relativistic degenerate gas (of neutrons). So there is a maximum mass of a neutron star (analagous to the Chandrasekhar limit for white dwarfs) of about 3 Msun.

Past this? Black holes....


Structure of a neutron star

 
  • Outer crust: Iron and neutron rich nuclei, mixed with relativistic degenerate electrons
  • Inner crust: Neutron rich nuclei, free superfluid neutrons (from neutron drip), and relativistic degenerate electrons
  • Interior: full of superfluid neutrons
  • Core: who knows? Pions?
      A strange world, indeed!
       

Properties of neutron stars

They spin - fast!
Conservation of angular momentum as the core collapses:

Or, for a sphere of constant structure,

So the final spin frequency is

or the final spin period is

What is the initial rotation period? Not certain, but for an example, let's use the rotation period of a nearby white dwarf: 1350 seconds. Then the rotation period of the neutron star will be PNS ~ 5x10-3 seconds!

They have very strong magnetic fields!
Magnetic flux (B times area) through the surface of the core is also conserved in collapse. So

Which means that

Again,  using the magnetic field strength of an extreme white dwarf, B=5x108 Gauss, BNS ~ 1014 Gauss! Compare to the Sun, which has a magnetic field strength of 2 Gauss.

They are hot!
The temperature of their creation (in a supernova) is 1011 K. They rapidly cool by neutrino emission down to a temperature of 106 K (in a thousand years or so).

Stefan-Boltzmann: L = 4piR2sigmaT4 = 7x1032 erg/s. Like the Sun.

Easy to see? Nope: LambdaMax = 0.29/T ~ 29 Angstroms -- X-rays!
 

Hmm, tiny, X-ray emitting neutron stars. Could we ever see them?