Neutron Stars and Black Holes Chapter 13: 0 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!!! A supernova explosion of an M > 8 Msun star blows away its outer layers. The central core will collapse into a compact object of ~ a few Msun. Pressure becomes so high that electrons and protons combine to form stable neutrons throughout the object. 0 Discovery of 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 ~ 109 ? 1015 G. (up to 1012 times the average magnetic field of the sun) 0 The Crab Pulsar Remnant of a supernova observed in A.D. 1054 Pulsar wind + jets 0 The Crab Pulsar Visual image X-ray image 0 Light curves of the Crab Pulsar 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 Effects of Pulsar Winds Pulsars blow off a constant stream (wind) of high-energy particles: pulsar winds 0 Proper Motion of Neutron Stars Some neutron stars are moving rapidly through interstellar space. This might be a result of anisotropies during the supernova explosion forming the neutron star. 0 Binary Pulsars Some pulsars form binaries with other neutron stars (or black holes) Radial velocities resulting from the orbital motion lengthen the pulsar period when the pulsar is moving away from Earth ? and shorten the pulsar period when it is approaching Earth. 0 Neutron Stars in Binary Systems: X-ray binaries Example: Her X-1 2 Msun (F-type) star Neutron star Accretion disk material heats to several million K => X-ray emission Star eclipses neutron star and accretion disk periodically Orbital period = 1.7 days 0 Compact Objects with Disks and Jets Black holes and neutron stars can be part of a binary system. => Strong X-ray source! Matter gets pulled off from the companion star, forming an accretion disk. Heats up to a few million K. 0 The X-Ray Burster 4U 1820-30 Optical Ultraviolet Several bursting X-ray sources have been observed: Rapid outburst followed by gradual decay 0 Pulsar Planets Some pulsars have planets orbiting around them. Just like in binary pulsars, this can be discovered through variations of the pulsar period. As the planets orbit around the pulsar, they cause it to wobble around, resulting in slight changes of the observed pulsar period. 0 Black Holes Just like white dwarfs (Chandrasekhar limit: 1.4 Msun), there is a mass 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 ? a singularity: => A black hole! 0 Escape Velocity Velocity needed to escape Earth?s gravity from the surface: vesc ? 11.6 km/s. vesc Now, gravitational force decreases with distance (~ 1/d2) => Starting out high above the surface => lower escape velocity. vesc vesc If you could compress Earth to a smaller radius => higher escape velocity from the surface. 0 The Schwarzschild Radius => There is a limiting radius where the escape velocity reaches the speed of light, c: Vesc = c Rs = 2GM ____ c2 Rs is called the Schwarzschild radius. G = gravitational constant M = mass 0 Schwarzschild Radius and Event Horizon No object can travel faster than the speed of light We have no way of finding out what?s happening inside the Schwarzschild radius. => nothing (not even light) can escape from inside the Schwarzschild radius ?Event horizon? 0 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 The Gravitational Field of a Black Hole Distance from central mass Gravitational Potential The gravitational potential (and gravitational attraction force) at the Schwarzschild radius of a black hole becomes infinite. 0 General Relativity Effects Near Black Holes An astronaut descending down towards the event horizon of the black hole will be stretched vertically (tidal effects) and squeezed laterally. 0 General Relativity Effects Near Black Holes (II) Time dilation Event horizon Clocks starting at 12:00 at each point. After 3 hours (for an observer far away from the black hole): Clocks closer to the black hole run more slowly. Time dilation becomes infinite at the event horizon. 0 General Relativity Effects Near Black Holes (III) gravitational redshift Event horizon All wavelengths of emissions from near the event horizon are stretched (redshifted). ? Frequencies are lowered. 0 Observing Black Holes No light can escape a black hole => Black holes can not be observed directly. If an invisible compact object is part of a binary, we can estimate its mass from the orbital period and radial velocity. Mass > 3 Msun => Black hole! 0 Compact object with > 3 Msun must be a black hole! 0 Jets of Energy from Compact Objects Some X-ray binaries show jets perpendicular to the accretion disk 0 Model of the X-Ray Binary SS 433 Optical spectrum shows spectral lines from material in the jet. Two sets of lines: one blue-shifted, one red-shifted Line systems shift back and forth across each other due to jet precession 0 Gamma-Ray Bursts (GRBs) Short (~ a few s), bright bursts of gamma-rays Later discovered with X-ray and optical afterglows lasting several hours ? a few days GRB of May 10, 1999: 1 day after the GRB 2 days after the GRB Many have now been associated with host galaxies at large (cosmological) distances. Probably related to the deaths of very massive (> 25 Msun) stars. 0 Black hole animation http://www.pbs.org/wgbh/nova/blackhole/program.html
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