WHITE DWARFS AND NEUTRON STARS

White Dwarfs are about the size of the Earth; their sizes have a mass dependence- as the mass increases their sizes get smaller.

Neutron Stars are about the size of a small city; their sizes are fairly constant; that is, the size does not depend upon the mass.

White Dwarfs (WDs)

WDs are the hot core remnant of a low mass star (those with masses less than about 8 times the sun's mass). They are composed of the the carbon and oxygen, the products of helium fusion. WDs are found in the centers of Planetary Nebulae.

Equation of State (EOS)

The EOS is a mathematical relationship between the size of a stellar remnant and its density. The typical density of a WD is about 10⁶ grams per cubic centimeter (about 1 million time that of water; water has a density of 1 gram per cubic centimeter [g/cc], that is 10⁶ = 1 million.) Chandrashekar discovered that the size of a WD gets smaller as the mass increases.

Chandrashekaer Limit

Usually, the larger the original star's mass, the larger the mass of its left over core (i.e. WD). Chandrashekar also discovered that there is an upper limit to the mass of WDs. When the star's core exceeds 1.4 times the solar masses, the WD must collapse under its own weight. This upper mass limit for the WD is called the Chandrashekar Limit.

For WDs with larger mass, the density is higher and the size smaller. But, when the density of a WD would exceed a few million g/cc, the compressed oxygen and carbon nuclei and free electrons cannot withstand the pressure. The physics (electrical repulsion of particles) that supports the WD from its own weight breaks down. The WD must collapse.

The EOS has no solution in the density range above a few million g/cc! Not until all the density of matter becomes equal to the density of an atomic nucleus, does the EOS have a solution again. The meaning of the EOS having no solution is basically a way of saying that there is no physics that exists for a given density range.

Neutron Stars (and Pulsars)

A NS is really just a big ball of neutrons. The density of a NS is about 10¹⁴ g/cc (100 trillions time that of water!). At this density the EOS again has a solution; NS have a size given by the crushing compression of all the matter now in the form of neutrons.

NS usually are formed in the center of supernovae explosions. That is, stars that originally had masses greater than about 8 times that of the sun explode and their left over cores are compressed into a NS.

Many NS can be found because they emit beams of light. When the star collapses, its magentic field gets highly compressed and the star rotation becomes very very rapid (like when an ice skater pulls in her arms during a spin). The magnetic fields channel charged particles out the poles of the NS in a powerful beam. Because the NS is rapidly rotating, this beam of light spins around and each time is passes our line of vision we see a pulse of light. You can think of this as a light house beam that sweeps the sky, but very very rapidly. If NS pole is aligned such that the beam sweeps Earth, then we see the pulses (like a ship on the sea sees the light house beam, but an airplane in the sky would not). These NS are called Pulsars. We do not see all NS as pulsars.

In the Crab Nebula, which is a supernova remnant, we see a Pulsar in the center. This NS rotates 30 times per second(!) and we see its pulse every 0.033 times per second (1/30).