• White Dwarfs, Neutron Stars, Black Holes,



• Are the remains of stars no longer energized due to nuclear reactions
• May be very hot, and may emit EM radiation - but not due to nuclear reactions
• Usually very compact
White Dwarfs
• Hot (25000 K) from residual heat.
• Strong magnetic fields (rapid spin)
• Approximately the mass of the sun but about the size of the earth (or smaller)
• Exposed core of the dead star
• Mainly carbon and oxygen with a thin layer of hydrogen and helium on the surface
• Cool to about 20000 K in about 10 million years.
• Density about 106 g/cm3 (about 16 tons per square inch!)
• Atoms are packed very tightly together
• Eventually become Black Dwarfs (long time)




• Increasing the mass of a white dwarf makes it shrink. How?
• The Pauli Exclusion Principle limits the number of electrons that may inhabit a give
volume of space.
• Degeneracy Pressure – created by the P.E.P. Depends only upon density and not
temperature.
• In ordinary gasses pressure and temperature are directly related.
• When degenerate gasses are compressed they heat up but the pressure in the gas
is not increased by the increasing temperature.
• As mass is added to a white dwarf the increased gravity between particles, which
are already very close together, causes the star to compress.
• Pressure does rise but because the star is degenerate and less “springy” the
increase in pressure is minimal.
• If a white dwarf acquires more mass (from a variety of sources) it may collapse into
a further state of degeneracy.
• This further state of degeneracy occurs at the Chandrasekhar Limit when a white
dwarf acquires about 1.4 solar masses
• A white dwarf beyond the Chandrasekhar Limit will collapse to a Neutron Star.
Gravitational Redshift
• Light loses energy, but not speed, as it escapes the gravity well from any massive
object.
• This loss of energy results in a redshift of the escaping light.
• The greater the redshift the greater the mass of the object at the center of the
well.








• Useful for measuring the masses of all massive objects.





White Dwarf Stars, Novae and Type I Supernovae
• White Dwarfs in binary systems may accrete material from a companion


• By accumulating hydrogen from a companion a white dwarf star may briefly reignite.
• Ignition in the presence of degeneracy causes an explosion. (Nova)














• A Type I supernova occurs if the White Dwarf accumulates enough material to




 exceed 1.4 Ms. This occurs if the white dwarf accumulates material from it’s




 companion very rapidly.




 • Type I supernovae spray radioactive 56Ni into space (increasing the energy of the




 explosion) which decays into → 56N which decays into 56Fe which is stable.






 • Type I supernovas leave no remnant, only a cloud rich in carbon, oxygen, silicon and






 iron.




 • Type II supernovae occur in more massive stars.






 • The steel in your car and the iron in your blood may have been made from iron




 created in a Type I or Type II supernova.










































• Rapid spin due to conservation of angular momentum 








• Strong changes in magnetic flux create strong electric 




fields which ionize all particles in the region of the 






star.







































• The charged particles are accelerated due to the rapid spin of the star.






















• Synchrotron radiation or nonthermal radiation is produced by the rapid acceleration












of charged particles.

















• Most pulsars radiate in the low energy (radio) portion of the EM spectrum.















• Pulsars emit some thermal radiation but it is very small





























• Neutron stars have three layers: a 1 mil thick gaseous atmosphere, an iron crust 


















about 1 meter thick and a superfluid core about 10 km in radius.





























• Glitch – a brief increase in the rotation of a pulsar












caused by differential rotation between the 






























superfluid core and the crust



























• Pulsars are not often found in binary systems.













































• Those pulsars that are found in binary systems










































































may form X-ray binaries .










































• Consider escape velocity. Recall:










v Gm esc












= 2 , G = 6.67 × 10-11










• vearth = 11 km/sec, vsun = 600 km/sec










• Note that for a given value of m a decreasing r yields a greater escape velocity










• For a white dwarf with the mass of the sun and the radius of the earth the escape










velocity is about 6000 km/sec










• For a neutron star with the mass of the sun and the radius of a few kilometers the










escape velocity is about 180,000 km/sec (about half the speed of light)










• What happens if an object is massive enough and small enough that escape velocity










equals or exceeds the speed of light?










• If vesc = c , then the radius of the object must be 2










2










c










r = Gm










• For 1 solar mass this calculation yields a radius of about 3 km.










• If the sun could be compressed into a volume with a radius of 3 km or less it would










become a black hole.










• Inside the event horizion (Rs ) no light escapes. All phenomena within the event










horizion are unobservable except gravity, charge, and angular momentum.










• A black hole with the mass of the sun has the same gravity as the sun. If the sun










were to collapse into a black hole the earth would continue to orbit it unaffected by











the change.