Lecture 22: Extreme Stars: White Dwarfs & Neutron Stars

Readings: 22-2, 22-4, 23-1, 23-3, 23-4, 23-5, 23-8, 23-9


Key Ideas


White Dwarf

         Remnant of a low-mass star

         Supported by Electron Degeneracy Pressure

         Maximum Mass ~1.4 MSun (Chandrasekhar Mass)


Neutron Star

         Remnant of a massive star

         Supported by Neutron Degeneracy Pressure

         Pulsar=rapidly spinning neutron star

         Maximum Mass ~2-3 MSun


The Stellar Graveyard


What happens to the cores of dead stars?



They continue to collapse until either:

A new pressure law halts further collapse & they settled into hydrostatic equilibrium

If too massive, they collapse to zero radius and become a black hole.


Degenerate Gas Law

At high density, a new gas law takes over:

         Pack many electrons into a tiny volume

         These electrons fill all low-energy states

         Only high-energy=high-pressure states left

Result is a degenerate gas

         Pressure is independent of temperature

         Compression does not lead to heating

         Compression does give higher density=greater pressure

Allows cold objects to exist in hydrostatic equilibrium


White Dwarfs

Remnant cores of stars with M < 8 MSun

         Held up by Electron Degeneracy Pressure

         M < 4MSun: C-O white dwarfs

         M between 4-8 MSun: O-Ne-Mg white dwarfs


Mass < 1.4 MSun (reflects large amount of mass loss in planetary nebula phase)

Radius ~ Rearth (<0.02 RSun)

Density~105-8 g/cc

Escape Speed: 0.02 c (2% speed of light)

Shine by residual heat: no fusion or contraction


Example: Sirius B

M=1.0 MSun

R=5800 km



Chandrasekhar Mass

Mass-Radius Relation for White Dwarfs

         Larger Mass=Smaller Radius

         Different than Normal Matter, such as Chocolate Cake

Larger Mass=Higher Gravitational Force=Larger Pressure=Higher Density=Smaller Volume

Chandrasekhar Mass

         Maximum Mass for White Dwarf

                  MSun=1.4 MSun

                  Calculated by S. Chandrasekhar in the 1930s

         Above this mass, electron degeneracy fails and the star collapses


Evolution of White Dwarfs

White dwarfs shine by leftover heat

         No sources of new energy (no fusion)

         Cool off and fade away slowly

Ultimate State: A Black Dwarf

         Old, cold white dwarf

         Takes ~10 Trillion years to cool off


Age of Universe ~ 13.7 billion years < 10 trillion years, so

Galaxy is not old enough for Black Dwarfs


Not to be confused with “Black Holes”

         Black dwarfs are black=do not shine because they are the same temperature as their surroundings

         Black holes do not shine because light cannot escape.


Path of White Dwarfs on H-R Diagram: Cool quickly at first , then gradually approach the temperature of empty space


The Other Supernova

What happens mass is added to the white dwarf and M > 1.4MSun

         Electron degeneracy falls, star collapses

         Ignites C-O fusion at high density

Generates heat, but no pressure because degeneracy pressure is independent of temperature

         Greater heat=greater fusion=greater heat…..


Runaway nuclear explosion:

         Fusion of light elements into Iron & Nickel

         White Dwarf detonates as a Type Ia Supernova


Leaves behind no remnant (total disruption)


Mass Transfer in a Binary

See Figure 21-18b


A white dwarf can exceed the Chandrasekhar mass by getting mass from a companion. If the mass transferred (mostly hydrogen & helium) is less than the Chandrasekhar mass, a runaway nuclear reaction can happen, but it will be much less energetic and not disrupt the star. This is a nova.








Type I and Type II Supernovae


Type I                          Type II

White dwarf binary                 High Mass Star

Runaway fusion of light           Core bounce/neutrino

elements                                 emission

Peak L~1010 LSun                                        Peak L ~108-109 LSun

Standard Candle                      Not standard


Neutron Stars


Remnant cores of massive stars:

         8 < M <  18 MSun

         Leftover core of core-bounce supernova


Held up by Neutron Degeneracy Pressure:


         Mass: ~1.2 – 2 MSun, Radius: ~ 10 km

         Density 1014 g/cc

         Escape Speed ~0.7c (70% speed of light)

Shine by residual heat: no fusion or contraction



         Very hot at beginning, but very small

         Low luminosity

         Emit in X-rays

~6 isolated neutron stars seen. Otherwise we see them with their supernova remnants.


Structure of a Neutron Star


At densities > 2x1014 g/cc

         Nuclei melt into a sea of subatomic particles (protons & neutrons)

         Protons & electrons combine into neutrons


Surface is cooler

         Solid crystalline crust


Inside is exotic matter

         Superfluid of neutrons, superconducting protons, and weirder stuff.

         Subject of much current research


Accidental Discovery of Pulsars



Jocelyn Bell (Cambridge grad student) & Anthony Hewish (her advisor) discover pulsating radio sources while looking for something else

Pulsars=Pulsating Radio Sources

         Emit sharp millisecond-long pulses every second

         Cannot be normal stars or white dwarfs. Strong evidence for neutron stars.




Rapidly spinning, magnetized neutron stars

Lighthouse Model:

         Spinning magnetic field generates a strong electric field.

         Electric field rips electrons off the surface

         Magnetic field accelerates them along the poles.


Result: twin beams of intense radiation



Example: Crab Nebula Pulsar


Pulsar Evolution

Pulsars spin slower as they age

Radiating energy, so that energy must be coming from somewhere (not fusion!)

Lose rotational energy

Young neutron stars

         Fast spinning pulsars

         Found in supernova remnants (e.g. Crab Pulsar, Vela Pulsar)

Old neutron stars:

         Cold and hard to find


Over the top?

What if the remnant core is very massive?

         Mcore > 2-3 MSun (original star had M > 18 MSun)

         First forms neutron star, but material keeps falling on it

         Neutron degeneracy pressure fails

         Nothing can stop gravitational collapse

         Collapse to a singularity: zero radius and infinite density


Becomes a BLACK HOLE, Gravity’s final victory.