Neutron Stars and Black Holes

Neutron Stars and Black Holes Please press “1” to test your transmitter.

The Death of a Massive Star

Neutron Stars A supernova explosion of a M > 8 Msun star blows away its outer layers. The central core will collapse into acompact object of ~ a few Msun.

The Chandrasekhar Limit Can such a remnant of a few Msun 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 Msun, beyond which white dwarfs can not exist: Chandrasekhar Limit.

0 Formation of Neutron Stars Compact objects more massive than the Chandrasekhar Limit (1.4 Msun) 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 + ne → Neutron Star

Properties of Neutron Stars Typical size: R ~ 10 km Mass: M ~ 1.4 – 3 Msun Density: r ~ 1014 g/cm3 → Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!!

Pulsars / Neutron stars Neutron star surface has a temperature of ~ 1 million K. Cassiopeia A

Considering the typical surface temperature of a neutron star, they should be observable preferentially in which wavelength range? • radio • infrared • optical • ultraviolet • X-ray

0 Pulsars Angular momentum conservation => Collapsing stellar core spins up to periods of ~ a few milliseconds. Magnetic fields are amplified up to B ~ 109 – 1015 G. (up to 1012 times the average magnetic field of the sun) => Rapidly pulsed (optical and radio) emission from some objects interpreted as spin period of neutron stars

0 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.

0 Images of Pulsars and other Neutron Stars The vela Pulsar moving through interstellar space The Crab nebula and pulsar

0 The Crab Pulsar Pulsar wind + jets Remnant of a supernova observed in A.D. 1054

0 The Crab Pulsar X-rays Visible light

Which one of the following is a phenomenon through which white dwarfs could be (indirectly) observed? • Supernova remnants • Globules • Pulsars. • X-ray binaries. • Solar eclipses.

Neutron Stars in Binary Systems: X-ray binaries 0 Accretion disk material heats to several million K => X-ray emission

Black Holes Just like white dwarfs (Chandrasekhar limit: 1.4 Msun), there is amass limit for neutron stars: Neutron stars can not exist with masses > 3 Msun We know of no mechanism to halt the collapse of a compact object with > 3 Msun. It will collapse into a single point – asingularity: => A Black Hole!

The Concept of Black HolesEscape Velocity vesc Velocity needed to escape Earth’s gravity from the surface: vesc≈ 11.6 km/s. Ggravitational force decreases with distance (~ 1/d2) => lower escape velocity when starting at larger distance. vesc Compress Earth to a smaller radius => higher escape velocity from the surface. vesc

The Concept of Black HolesSchwarzschild Radius => limiting radius where the escape velocity reaches the speed of light: The Schwarzschild Radius, Rs (Event Horizon) Vesc = c 2GM ____ Rs = c2 G = Universal const. of gravity M = Mass

0 Schwarzschild Radius and Event Horizon Nothing (not even light) can escape from inside theSchwarzschild radius • We have no way of finding out what’s happening inside the Schwarzschild radius • “Event horizon”

0 Take a guess: How large is the Schwarzschild radius of the Earth?(The actual radius of the Earth is 6380 km) • 1.35 million km • 6380 km • 250 m • 0.9 cm • 12 nm

0 “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)

0 General Relativity Effects Near Black Holes Time dilation Clocks closer to the BH run more slowly. Time dilation becomes infinite at the event horizon. Event Horizon

0 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. a) No time at all. b) More than 0, but less than 1 hr c) 1 hr d) Several hours e) Forever Event Horizon

0 Falling into the Black Hole => You will never actually see something “falling into the Black Hole” (i.e., crossing the Event Horizon)! The Distant Observer’s View Event Horizon

0 Falling into the Black Hole The Falling Observer’s View “Spaghettification” Event Horizon

0 General Relativity Effects Near Black Holes Spatial distortion of light → gravitational lensing

Deflection of Light by the Sun

Einstein Cross

0 General Relativity Effects Near Black Holes Gravitational Red Shift Wavelengths of light emitted from near the event horizon are stretched (red shifted). Event Horizon

0 What would happen to the Earth if the sun suddenly turned into a black hole (of the same mass as the sun has now) • It would be sucked into the black hole. • Its orbit around the black hole would be exactly the same as around the sun now. • 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 Rs = Schwarzschild Radius 3 Rs Rs There is no stable orbit within 3 Schwarzschild radii from the black hole.

0 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 Msun => Black hole!

0 Black Hole X-Ray Binaries Accretion disks around black holes Strong X-ray sources Rapidly, erratically variable (with flickering on time scales of less than a second) Sometimes: Radio-emitting jets

Neutron Stars and Black Holes