Neutron Stars 

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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 M_sun, 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:

• A 1.4 M_sun neutron star has a radius of 10-15 km (city-sized!).
• So a neutron star has an average density of ~ 6x10¹⁴ gm/cm³, similar to the density of atomic nuclei.
• Also, we are now entering the regime of strong relativity: V_escape ~ 0.6c! (What does it look like if we travel around a neutron star? Look here!)

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

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 P_NS ~ 5x10^-3 seconds!

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, B_NS ~ 10¹⁴ Gauss! Compare to the Sun, which has a magnetic field strength of 2 Gauss.

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: Lambda_Max = 0.29/T ~ 29 Angstroms -- X-rays!