Neutron Stars A supernova explosion of a M > 8 M sun star blows away its outer layers. The central core will collapse into a compact object of ~ a few M sun.
The Chandrasekhar Limit Can such a remnant of a few M sun be a white dwarf? The more massive a white dwarf is, the smaller it is (radius decreases as mass increases)! There is a limit of 1.4 M sun, beyond which white dwarfs can not exist: Chandrasekhar Limit.
Formation of Neutron Stars Compact objects more massive than the Chandrasekhar Limit (1.4 M sun ) collapse beyond the degenerate (white dwarf) state. → Pressure becomes so high that electrons and protons combine to form stable neutrons throughout the object: p + e - → n + e → Neutron Star
Properties of Neutron Stars Typical size: R ~ 10 km Mass: M ~ 1.4 – 3 M sun Density: ~ 10 14 g/cm 3 → Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!!
Pulsars / Neutron stars Cassiopeia A Neutron star surface has a temperature of ~ 1 million K.
Considering the typical surface temperature of a neutron star, they should be observable preferentially in which wavelength range? 1.radio 2.infrared 3.optical 4.ultraviolet 5.X-ray
Pulsars => Collapsing stellar core spins up to periods of ~ a few milliseconds. Angular momentum conservation => Rapidly pulsed (optical and radio) emission from some objects interpreted as spin period of neutron stars Magnetic fields are amplified up to B ~ 10 9 – 10 15 G. (up to 10 12 times the average magnetic field of the sun)
The Lighthouse Model of Pulsars A Pulsar’s magnetic field has a dipole structure, just like Earth. Radiation is emitted mostly along the magnetic poles.
Images of Pulsars and other Neutron Stars The vela Pulsar moving through interstellar space The Crab nebula and pulsar
The Crab Pulsar Remnant of a supernova observed in A.D. 1054 Pulsar wind + jets
Which one of the following is a phenomenon through which white dwarfs could be (indirectly) observed? 1.Supernova remnants 2.Globules 3.Pulsars. 4.X-ray binaries. 5.Solar eclipses.
Neutron Stars in Binary Systems: X-ray binaries Accretion disk material heats to several million K => X-ray emission
Black Holes Just like white dwarfs (Chandrasekhar limit: 1.4 M sun ), there is a mass limit for neutron stars: Neutron stars can not exist with masses > 3 M sun We know of no mechanism to halt the collapse of a compact object with > 3 M sun. It will collapse into a single point – a singularity: => A Black Hole!
The Concept of Black Holes Escape Velocity Velocity needed to escape Earth’s gravity from the surface: v esc ≈ 11.6 km/s. v esc Ggravitational force decreases with distance (~ 1/d 2 ) => lower escape velocity when starting at larger distance. v esc Compress Earth to a smaller radius => higher escape velocity from the surface.
The Concept of Black Holes Schwarzschild Radius => limiting radius where the escape velocity reaches the speed of light: V esc = c The Schwarzschild Radius, R s (Event Horizon) R s = 2GM____ c2c2 G = Universal const. of gravity M = Mass
Schwarzschild Radius and Event Horizon Nothing (not even light) can escape from inside the Schwarzschild radius We have no way of finding out what’s happening inside the Schwarzschild radius “Event horizon”
Take a guess: How large is the Schwarzschild radius of the Earth? (The actual radius of the Earth is 6380 km) 1.1.35 million km 2.6380 km 3.250 m 4.0.9 cm 5.12 nm
“Black Holes Have No Hair” Matter forming a black hole is losing almost all of its properties. Black Holes are completely determined by 3 quantities: Mass Angular Momentum (Electric Charge)
General Relativity Effects Near Black Holes Time dilation Event Horizon Clocks closer to the BH run more slowly. Time dilation becomes infinite at the event horizon.
For how long would we – in principle – receive signals from a space probe that we are sending into a black hole (if there were no limit to how faint the signals are that it is sending back to us)? Assume that the free-fall time to reach the event horizon (without GR effects) is 1 hr. Event Horizon c) 1 hr b) More than 0, but less than 1 hr d) Several hours e) Forever a) No time at all.
Falling into the Black Hole Event Horizon => You will never actually see something “falling into the Black Hole” (i.e., crossing the Event Horizon)! The Distant Observer’s View
Falling into the Black Hole Event Horizon The Falling Observer’s View “Spaghettification”
General Relativity Effects Near Black Holes Spatial distortion of light → gravitational lensing
General Relativity Effects Near Black Holes Gravitational Red Shift Event Horizon Wavelengths of light emitted from near the event horizon are stretched (red shifted).
What would happen to the Earth if the sun suddenly turned into a black hole (of the same mass as the sun has now) 1.It would be sucked into the black hole. 2.Its orbit around the black hole would be exactly the same as around the sun now. 3.It would be ejected from the solar system.
A Myth about Black Holes Far away from the black hole, gravity is exactly the same as for the uncollapsed mass!
Getting Too Close to a Black Hole RsRs 3 R s There is no stable orbit within 3 Schwarzschild radii from the black hole. R s = Schwarzschild Radius
Observing Black Holes No light can escape a black hole => Black holes can not be observed directly. Black hole or Neutron Star in a binary system Wobbling motion Mass estimate Mass > 3 M sun => Black hole!
Black Hole X-Ray Binaries Strong X-ray sources Rapidly, erratically variable (with flickering on time scales of less than a second) Sometimes: Radio-emitting jets Accretion disks around black holes