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Exam Study Guide

# Exam Study Guide - Endpoints of Stellar Evolution White...

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Endpoints of Stellar Evolution: White Dwarf Stars: White dwarfs are the endpoints of evolution of stars like the Sun (near one solar mass). In fact, the mass limit for a white dwarf is the Chandresekhar Limit, 1.4 solar masses. The radius of a white dwarf is about 10 4 km, that is, planet-sized (the radius of the earth is about 6000 km). If a star were to shrink from about the size of the sun, 10 6 km, down to 10,000 (a factor of 100), its volume (V=4/3 л r 3 ) would shrink by 100 3 =10 6 . If little or no mass is lost and the volume shrinks by this factor, the density, ρ = M/V, would increase by a factor of 10 6 . So the density of a white dwarf star is on the order of one million grams per cubic centimeter (since the Sun’s density is about 1 g/cm 3 ). The weight of one teaspoon of wd star material, at the earth’s surface, would be about one ton. What halts the collapse of a white dwarf star? A white dwarf can be thought of as a gas of electrons (plus nuclei that we won’t worry about right now). Electrons are “fermions” which obey the Pauli Exclusion principle, which says that only one fermion can be in a given state. When the electrons fill all the lowest energy states, none can lose any energy (since all lower states are filled), so the electrons are at T (temperature)=0. They are called “degenerate.” It is also true that two fermions cannot be in the same place, so they resist being pressed closer and closer together, which results in “electron degeneracy pressure.” The collapse of a white dwarf star is halted by electron degeneracy pressure. The more massive a wd star is, the smaller it is. Also, if a star contracts by a factor of 100, it should spin 100 2 = 10,000 times faster, by conservation of angular momentum. The sun rotates with a period of

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about 10 6 seconds, so a wd star should rotated with a period of about 100 seconds. Its magnetic field should be stronger by the same factor. The best known white dwarf star is Sirius B; the only one we have looked at is 40 Eridani B. Neutron Stars and Black Holes: In a supernova collapse and explosion, when an aging star runs out of nuclear fuel and collapses catastrophically, a “squeezed-down” remnant is left, which could be a neutron star or black hole. Essentially what happens is that the electron degeneracy pressure is overwhelmed, and the stellar remnant collapses until that collapse is halted by “neutron degeneracy pressure,” neutrons also being fermions. This happens because the electrons are used up in converting protons to neutrons: e + p à n + ν . With no electron degeneracy pressure, the stars collapses to a radius of about 10 km, where neutron degeneracy pressure halts the collapse. The star is a ball of neutrons, neutron-rich nuclei, and other exotic particles. It has collapsed from something like 10 6 km to 10, a f actor of 10 5 . The volume decreases by (10 5 ) 3 = 10 15 , so the density increases by a factor of 10 15 . Because some mass is lost and converted to energy, we say that its density is about 10 14 g/cm 3 . As was the case with the wd star, the neutron star should rotate very rapidly,
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Exam Study Guide - Endpoints of Stellar Evolution White...

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