White Dwarfs and Neutron StarsWhite dwarfsDegenerate gasesMass versus radius relationNeutron starsMass versus radius relationPulsars, magnetars, X-ray pulsars, X-ray bursters
White dwarf Core of solar mass star Degenerate gas of oxygen and carbon No energy from fusion or gravitational contraction
Mass versus radius relationFor objects made of normal matter, radius tends to increase with mass
Mass/radius relation for degenerate starStar mass = M, radius = RGravitational potential energy = Heisenberg uncertainty:Electron density
Mass/radius relation for degenerate starTotal energyFind R by minimizing E
Radius decreases as mass increases
Mass versus radius relation
Maximum white dwarf massAs mass increases, electron speed c, kinetic energy equation E=pc Electron degeneracy cannot support a white dwarf heavier than 1.4 solar masses, the Chandrasekhar limit.
What happens to a star more massive than 1.4 solar masses?There arent anyThey shrink to zero sizeThey explodeThey become something else
Neutron StarsDegenerate stars heavier than 1.4 solar masses collapse to become neutron starsFormed in supernova explosionsElectrons are not separateCombine with nuclei to form neutronsNeutron stars are degenerate gas of neutrons
Neutron energy levels Only two neutrons (one up, one down) can go into each energy level. In a degenerate gas, all low energy levels are filled. Neutrons have energy, and therefore are in motion and exert pressure even if temperature is zero. Neutron star are supported by neutron degeneracy.
Mass v Radius1015205
Neutron StarsVery compact about 10 km radiusVery dense one teaspoon of neutron star material weighs as much as all the buildings in ManhattanSpin rapidly as fast as 600 times per secondHigh magnetic fields compressed from magnetic field of progenitor star
Spin up of neutron starCollapse of star increases both spin and magnetic field
Angular momentumFor single particle, angular momentum L = mvrWrite in terms of rotation rate , v = 2r , L = 2mr2 = I 2 I = moment of inertiaIn general, I = #MR2 M = mass of object R = length of object
Spin up of neutron starAngular momentum of sphere:Where M is mass, R is radius, is spin rateIf the Sun (spin rate 1/25 days, radius 7108 m) were to collapse to a neutron star with a radius of 12 km, how fast would it be spinning?
Spin up of neutron starVery high rotation rates can be reached simply via conservation of angular momentum.This is faster than any known (or possible) neutron star. Mass and angular momentum are lost during the collapse.
PulsarsDiscovered by Jocelyn Bell in 1967. Her advisor, Anthony Hewish, won the Nobel Prize in Physics for the discovery in 1974.
PulsarsEnergy source is spin down of neutron star.Must lie along pulsar beam to see pulsed signals.
Spin down of a pulsarFor Crab pulsar: = 30/s, M = 1.4 solar masses, R = 12 km, and d /dt = 3.910-10 s-2. Therefore, P = 7 1031 W = 200,000 solar luminosities.Over a year, the spin rate changes by only 0.04%.
MagnetarsMagnetic fields so strong that they produce starquakes on the neutron star surface.These quakes produce huge flashes of X-rays and Gamma-rays.Energy source is magnetic field.
X-Ray PulsarsNeutron star in binary system with a normal star
X-Ray PulsarsHigh magnetic field neutron stars make regular pulsations. Energy source is gravitational energy of infalling matter.
X-ray BurstLow magnetic field neutron stars make X-ray bursts.Source of energy is nuclear burning.
Review QuestionsWhat is the exclusion principle?Does a more massive white dwarf have a larger or smaller radius than a less massive one?What is the maximum mass of a white dwarf?What are some of the properties of neutron stars?Why do many neutron stars spin rapidly?In what different forms does one find neutron stars?