Question

Explain white dwarfs, neutron stars, and black holes using statistical mechanics.

Answer 1

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1) White Dwarfs :

Remnant cores of stars with M  < 8 M(sun)

Held up by Electron Degeneracy Pressure.

Properties:

• Mass < 1.4 M(sun)
• Radius ~ R_earth (<0.02 R_sun)
• Density ~ 10^5-6 g/cc
• No nuclear fusion or gravitational contraction

Evolution of White Dwarfs

   White dwarfs only shine by leftover heat.

• No energy source (no fusion, nothing)
• Cools off and fades away slowly.

Ultimate State: A "Black Dwarf":

• Old, cold white dwarf
• Takes ~ 10 Tyr to cool off
• Galaxy is not old enough to see Black Dwarfs.

2) Neutron Stars :

Remnant cores of massive stars:

• 8 < M* <18 M_sun (??)
• Leftover core of a core-bounce supernova

Held up by Neutron Degeneracy Pressure:

• Mass ~ 1.2 - 2 M_sun
• Radius ~ 10 km
• Density ~ 10¹⁴ g/cc

Structure of a Neutron Star

At densities > 2x10¹⁴ g/cc:

• nuclei melt into a sea of subatomic particles.
• protons & electrons combine into neutrons.

Surface is cooler: Solid, crystalline crust.

Inside is exotic matter: superfluid neutrons, superconducting protons.

Surface of a Neutron Star

* Surface gravity ~10¹¹ g's

• Escape velocity ~0.5 c
• Temperature ~ 1 Million K
• Magnetic Field Strength ~ 10¹² Gauss (Earth is ~0.5 Gauss)
• Rotation Rate: 6000 rpm (100 rotations/second)

3) BLACK HALL :

  

M_core > 2-3 M_sun

(original star had M > 18 M_sun)

• Neutron degeneracy pressure fails.
• Nothing can stop gravitational collapse.
• Collapses to zero radius and infinite density.

The core becomes a Black Hole.