13.1 White Dwarfs
What is a white dwarf?
- White Dwarf
- White dwarfs are the remaining cores of dead stars.
- Electron degeneracy pressure supports them against gravity (quantum mechanical phenomena).
- White dwarfs cool off and grow dimmer with time.
- Size of a White Dwarf
- White dwarfs with the same mass as the Sun are about the same size as Earth.
- Higher-mass white dwarfs are smaller.
- The White Dwarf Limit
- Quantum mechanics says that electrons must move faster as they are squeezed into a very small space.
- As a white dwarf's mass approaches 1.4 MSun, its electrons must move at nearly the speed of light.
- Because nothing can move faster than light, a white dwarf cannot be more massive than 1.4 MSun, the white dwarf limit.
- Accretion Disks
- A star that stars with less mass gains mass from its companion.
- Mass falling toward a white dwarf from its close binary companion has the same angular momentum.
- The matter orbits the white dwarf in an accretion disk.
- Friction between orbiting rings of matter in the disk transforms angular momentum.
- Nova
- The temperature of accreted matter eventually becomes not enough for hydrogen fusion.
- Fusion begins suddenly and explosively, causing a nova.
- The nova star system temporarily appears much brighter.
- The explosion drives accreted matter out into space.
- The temperature of accreted matter eventually becomes not enough for hydrogen fusion.
- Two Types of Supernova
- Massive Star Supernova
- Iron core of massive star reaches white dwarf limit and collapses into a neutron star, causing an explosion.
- White Dwarf Supernova
- Carbon fusion suddenly begins as white dwarf in close binary system reaches white dwarf limit, causing a total explosion.
- One way to tell supernova types apart is with a light curve showing how luminosity changes with time.
- Massive Star Supernova
- Nova or Supernova?
- Supernovae are much more luminous than novae (10 million times).
- Nova: H to He fusion of a layer f accreted matter, white dwarf left intact.
- Massive Star or White Dwarf?
- Light curves differ.
- Spectra differ (exploding white dwarfs don't have hydrogen absorption lines).
What is a neutron star?
- A neutron star is a ball of neutrons left behind by a massive star supernova.
- The degeneracy pressure of neutrons support a neutron star against gravity.
- Electron degeneracy pressure goes away because electrons combine with protons, making neutrons and neutrinos.
- Neutrons collapse to the center, forming a neutron star.
- A neutron star is about the same size as a small city.
How were neutron stars discovered?
- Discovery of Neutron Stars
- Using a radio telescope in 1967, Jocelyn Bell noticed a regular pulse.
- Pulsars
- The pulsar at the center of the Crab nebula pulses 30 times per second.
- A pulsar is a neutron star that beams radiation along a magnetic axis that is not aligned with the rotation axis.
- The radiation beams sweep as the neutron star rotates.
- Matter falling toward a neutron star forms an accretion disk.
- Accreting matter adds angular momentum to a neutron star, increasing spinning.
- X-Ray Bursts
- Matter accreting onto a neutron star can eventually become hot enough for helium to fuse.
- Neutron Star Limit
- Neutrons in the same place cannot be in the same state (quantum mechanics).
- Neutron degeneracy pressure can no longer support a neutron star against gravity if its mass exceeds about 300 MSun.
13.3 Black Holes: Gravity's Ultimate Victory
What is a black hole?
- A black hole is an object whose gravity is so powerful that not even light can escape it.
- Escape Velocity
- Initial Kinetic Energy = Final Gravitational Potential Energy
- (escape velocity) ^2 / 2 = 6 X (mass) / (radius)
- Light would not be able to escape Earth's surface if you could shrink it to < 1 cm.
- Surface of a Black Hole
- The 'surface' of a black hole is the radius at which the escape velocity equals the speed of light.
- This spherical surface is known as the event horizon.
- The radius of the even horizon is known as the Schwarzschild radius.
- A black hole's mass strongly wraps space and time in the velocity of the event horizon.
- No Escape
- Nothing can escape from within the event horizon because nothing can go faster than the speed of light.
- No escape means there is no more contact with something that falls in.
- It increases the hole's mass, changes its spin, or charge, but otherwise loses its identity.
- Singularity
- Beyond the neutron star limit, no known force can resist the crush of gravity.
- As far as we know, gravity crushes all the matter into a single point known as singularity.
- Black holes don't suck.
- If the Sun shrank into a black hole, its gravity would be different only near the event horizon.
- Light waves take extra time to climb out of a deep hole in space-time, leading to gravitational redshift.
- Time passes more slowly near the event horizon.
- Tidal forces near the event horizon of a 3MSun lack hole would be lethal to humans.
- Tidal forces would be gentler near the super massive black hole because its radius is much bigger.
- Black Hole Verification
- Need to measure mass
- Use orbital properties of companion
- Measure velocity and distance of orbiting gas
- It's a black hole if it's not a star and its mass exceeds the neutron star limit (~3 MSun)
- Need to measure mass
- Some X-Ray binaries contain compact objects of mass exceeding 3 MSun (too massive to be a neutron star).
What causes gamma ray bursts?
- Gamma Ray Bursts
- Gamma ray bursts signify the birth of black holes.
- Brief bursts of gamma rays coming from space were first detected in the 1960's (announced in 1973).
- Observations in the 1990's showed that many gamma ray bursts were coming from very distant galaxies.
- Most powerful explosions in the universe formation of the black hole
- Supernovae and Gamma Ray Bursts
- Observations show that at least some gamma ray bursts are produced by supernova explosions.
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