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Pulsars. A pulsar is a neutron star that beams radiation along a magnetic axis that is not aligned with the rotation axis. Pulsars. The radiation beams sweep through space like lighthouse beams as the neutron star rotates. Why Pulsars must be Neutron Stars.
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Pulsars • A pulsar is a neutron star that beams radiation along a magnetic axis that is not aligned with the rotation axis
Pulsars • The radiation beams sweep through space like lighthouse beams as the neutron star rotates
Why Pulsars must be Neutron Stars Circumference of NS = 2π (radius) ~ 60 km Spin Rate of Fast Pulsars ~ 1000 cycles per second Surface Rotation Velocity ~ 60,000 km/s ~ 20% speed of light ~ escape velocity from NS Anything else would be torn to pieces!
Matter falling toward a neutron star forms an accretion disk, just as in a white-dwarf binary
Accreting matter adds angular momentum to a neutron star, increasing its spin Episodes of fusion on the surface lead to X-ray bursts
A black hole is an object whose gravity is so powerful that not even light can escape it.
Supernovae/Supernova Remnants • Massive stars fuse heavier elements, up to Iron (Fe) • Core is billions of Kelvin and greater than Chandrasekhar Limit (1.4 Msun) • Rapid collapse to neutron star • Rebound of core results in expulsion of outer layers Supernova Remnant
A black hole is an object whose gravity is so powerful that not even light can escape it.
Thought Question What happens to the escape velocity from an object if you shrink it? A. It increases B. It decreases C. It stays the same Hint:
Escape Velocity Initial Kinetic Energy Final Gravitational Potential Energy = (escape velocity)2 G x (mass) = 2 (radius)
Eluding Gravity’s Grasp Escape Velocity Escape Velocity Speed Needed To Escape An Object’s Gravitational Pull Mass M Radius R Earth: Vesc = 27,000 miles/hour (11 km/s) Sun: Vesc = 1.4 million miles/hour (600 km/s)
“Dark Stars”Rev. John Michell (1783) & Pierre-Simon Laplace (1796) Speed of light 1 billion miles/hour (3x105 km/s) • What if a star were so small, escape speed > speed of light? A star we couldn’t see! Earth mass: R 1 inch Solar mass: R 2 miles Vesc = speed of light
“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 event horizon is known as the Schwarzschild radius.
Neutron star 3 MSun Black Hole The event horizon of a 3 MSun black hole is also about as big as a small city
No Escape • Nothing can escape from within the event horizon because nothing can go faster than light. • No escape means there is no more contact with something that falls in.
Mass versus radius for a neutron star Objects too heavy to be neutron stars collapse to black holes
Neutron Star Limit • Neutron pressure can no longer support a neutron star against gravity if its mass exceeds about 3 Msun • Some massive star supernovae can make black hole if enough mass falls onto core
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 a singularity.
Singularity • The shrunken star too small to be measured but with indefinite density
If the Sun shrank into a black hole, its gravity would be different only near the event horizon Black holes don’t suck!
Einstein’s theory of gravity is built on the principle that • The speed of light is constant. • As an object speeds up its clock runs faster. • The effects of gravity cannot be distinguished from the effects of acceleration. • Motion is a relative state.
Our conceptions of space and time has to be changed. • Facts: • Regardless of speed or direction, observers always measure the speed of light to be the same value. • Speed of light is maximum possible speed. • Consequences: • The length of an object decreases as its speed increases • Clocks passing by you run more slowly than do clocks at rest (example: solar wind particles)
Light waves are stretched out leading to a gravitational redshift
Tidal forces near the event horizon of a 3 MSun black hole would be lethal to humans Tidal forces would be gentler near a supermassive black hole because its radius is much bigger
Falling into a black hole Falling into a black hole gravitational tidal forces pull spacetime in such a way that time becomes infinitely long (as viewed by distant observer). The falling observer sees ordinary free fall in a finite time.
Falling into a black holes • With a sufficiently large black hole, a freely falling observer would pass right through the event horizon in a finite time, would be not feel the event horizon. • A distant observer watching the freely falling observer would never see her fall through the event horizon (takes an infinite time). • Falling into smaller black hole, the freely falling observer would be ripped apart by tidal effects.
Falling into a black hole • Signals sent from the freely falling observer would be time dilated and redshifted. • Once inside the event horizon, no communication with the universe outside the event horizon is possible. • But incoming signals from external world can enter. • Time travel and other fairy tales…
How do we know it’s a BH? • Nature is tricky: couldn’t it be another “small star” like a neutron star or a white dwarf? • Measure mass of “X-ray star” by motion of its companion (a star like the sun) Mass > 3 solar masses BH! • Roughly a dozen BHs found this way (tip of the iceberg) Chandrasekhar
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)
One famous X-ray binary with a likely black hole is in the constellation Cygnus
