Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Lecture 19: Extreme Stars
White Dwarfs & Neutron Stars

Readings: Readings: Ch 22, section 22-4; Ch 23, sections 22-1 thru 5

Key Ideas

White Dwarfs:: Remnants of low-mass stars; Supported by Electron Degeneracy Pressure; Maximum Mass ~1.4 M_sun (Chandrasekhar Mass)
Neutron Stars:: Remnants of some post-supernova massive stars; Supported by Neutron Degeneracy Pressure; Pulsar = rapidly spinning magnetized neutron star

The Stellar Graveyard

Question:

What happens to the cores of dead stars?

Answer:

They continue to collapse until either:

A new pressure law takes hold to halt further collapse & they settle into a new hydrostatic equilibrium.
If too massive they collapse to zero radius and become a Black Hole.

All of these are seen as the remnants of stellar evolution.

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.

This means that the objects could, in principle, be very cold but still have enough pressure to maintain a state of Hydrostatic Equilibrium.

Can such objects exist?

White Dwarfs

These are the remnant cores of stars with M < 8 M_sun.

Supported against gravity by Electron Degeneracy Pressure
M<4 M_sun: C-O White Dwarfs
M = 4-8 M_sun: O-Ne-Mg White Dwarfs

Properties:

Mass < 1.4 M_sun
Radius ~ R_earth (<0.02 R_sun)
Density ~ 10^5-6 g/cc
Escape Speed: 0.02 c (2% speed of light)

No nuclear fusion or gravitational contraction. It shines by residual heat.

Comparison of a White Dwarf Star and the Earth.

Chandrasekhar Mass

Mass-Radius Relation for White Dwarfs:

Larger Mass = Smaller Radius

Chadrasekhar Mass:

Maximum Mass for White Dwarf: M_ch = 1.4 M_sun
First calculated by Subrahmanyan Chandrasekhar in the 1930s.
Above this mass, electron degeneracy pressure fails & the star collapses.

This prediction of a maximum white dwarf mass is upheld by observations. So far, all white dwarfs we have seen in binary stars have masses below the Chandrasekhar Mass.

Evolution of White Dwarfs

White dwarfs shine by leftover heat.

No energy source (no fusion, nothing)
Cools off and fades away slowly.
Forms a White Dwarf Cooling Sequence on the H-R diagram

Ultimate State: A "Black Dwarf":

Old, cold white dwarf
Takes ~10 Tyr to cool off
Galaxy is not old enough for there to be any Black Dwarfs yet.

Note: Be careful not to confuse Black Dwarfs (old, cold remnant cores of low-mass stars) with "Black Holes" (the extremely collapsed cores of very massive stars).

White Dwarfs: The Other Supernovae

Question:: What would happen if you added enough matter to a White Dwarf to exceed its Chandrasekhar Mass?

Above the Chandrasekhar Mass, the internal electron degeneracy pressure is no longer able to balance Gravity, and it will begin to collapse...

As the density rises, the temperature does not increase
Eventually ignites carbon-oxygen burning at high enough density
This begins to generate heat, but no additional pressure to slow the collapse
The extra heat leads to greater fusion, which leads to greater heat...

The effect is a runaway nuclear explosion:

Fusion of the light elements into Iron and Nickel
The white dwarf detonates and disrupts completely as a Type Ia Supernova.

Type Ia Supernovae leave no remnant behind, and may be responsible for the production of much of the Iron in the Universe.

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
Escape Speed: 0.70 c (70% speed of light)

No nuclear fusion or gravitational contraction. It shines by residual heat.

Comparison of a Neutron Star and the Island of Manhattan.

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, forming a solid crystalline crust!

Inside is exotic matter: superfluid neutrons, superconducting protons, and stranger subatomic particle matter:

Inside a Neutron Star

Accidental Discovery

1967:: Jocelyn Bell (Cambridge grad student) & Anthony Hewish (her adviser) discover rapidly pulsating radio sources while looking for something else.

They called these new, otherwise unknown objects

"Pulsars" = Pulsating Radio Sources

Pulsars emitted sharp, 1 millisecond-long pulses every second at an extremely repeatable rate (most accurate clocks known at the time).

Anthony Hewish shared the 1974 Nobel Prize for Physics for his role in the discovery of pulsars. Jocelyn Bell, however, did not.

Pulsars

Rapidly spinning, magnetized neutron stars.

Lighthouse Model:

Spinning magnetic field generates a strong electric field.
Electric field rips electrons of the surface and accelerates them along the magnetic poles.

Result:

Twin beams of radiation shining out of the magnetic poles:

Schematic of a Pulsar

If the magentic axis is mis-aligned with the rotation axis of the neutron star (as shown), the star's rotation sweeps the beams over us as it rotates, and we will see regular, sharp pulses of light (optical, radio, X-ray, etc.)

Pulsar Evolution

Pulsars spin slower as they age.

lose rotational energy

Young neutron stars:

fast spinning pulsars.
found in supernova remnants (e.g., Crab pulsar)

Old neutron stars: cold and hard to find.

[But some neutron stars that are not also pulsars have been finally seen. Hubble Space Telescope detection of a lone neutron star.]

Over the Top?

What if the remnant core is very massive?

"Very Massive" = M_core > 2-3 M_sun

(original star would have had a mass M > 18 M_sun)

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

The core becomes a Black Hole.

We will meet these exotic objects in the next lecture.

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Lecture 19: Extreme Stars White Dwarfs & Neutron Stars