Neutron Stars and Black HolesToday’s Lecture:Neutron Stars (Chapter 13, pages 312-323)• General properties• Pulsars• Test beds of general relativityBlack Holes (Chapter 14, pages 324-343) • What’s a black hole? • Are there really black holes? • Gamma-ray burstsType II Supernova: massive star• Massive stars (> 10 Msun)continue to burn fuel until iron (Fe)forms in the core. Fe is the mostbound atomic nuclei. No morereactions in the Fe.• The Fe core continues to grow.• When the Fe core reaches1.4Msun the core collapses.p + e- --> n + ν The core is converted into neutrons• The outer layers bounce off the core creating an explosion!(neutrinos also very important for driving the envelope away)• A neutron star is formed.Neutron Stars• The core left over by a Type II supernova• Held up from gravity by neutron degeneracy pressure• First predicted in the 1930s, and confirmed with thediscovery of pulsars in 1967 by Jocelyn Bell (her advisor gotthe Nobel Prize for the discovery).• We think the maximum mass (like the Chandra limit forWDs) is 2-3Msun and 10 km radius. This is 1011 kg/cm3!!!• We now know about hundreds of neutron stars doing manyexciting things (pulsing, surface explosions, highlymagnetized).• Neutron stars are important for testing Einstein’s GeneralTheory of Relativity and testing our understanding ofsubatomic particles.• If one star is a white dwarf and the other star fills itsRoche lobe (like a growing red giant), material canaccrete onto the white dwarf.Pulsars• The first discovered neutron star was a pulsing radiosource with a period of 1.3373011 seconds (1967)• Initially thought to be extra terrestrial life• Soon other sources were seen in all different directions,and it was realized that these are actually neutron stars• The regular period is due to the spin of a neutron staremitting radio waves like a lighthouse.• A pulsar was also discovered within the Crab Nebula,with a period of 0.033 sec. This confirmed pulsars areneutron stars!• In 1982, a pulsar was found rotating around 642 timesper second! A millisecond pulsar.Albert Einstein’sGeneral Theory of Relativity (1916)• A theory of gravity more general than Newton’s.• Matter (and energy) warp space and time, causingpaths of objects (including light) to curve.Two early test of general relativity:1.) Precession of Mercury’s orbit. 43 seconds of arcper century!2.) Bending of starlight in the vicinity of the Sun,seen during an eclipse (1919)Fig. 14-2, p. 326Binary Pulsars• In 1974, a pulsar (17 times per sec) was found that wasorbiting another neutron star (the other is not a pulsar)• By measuring the shifts in the arrival time of pulses(like the Doppler effect) small changes in the orbits can bemeasured• Joseph Taylor and Russell Hulse used thesemeasurements to show that gravitational waves must beleaving the orbiting neutrons stars, removing energy andcausing them to spiral together (got Nobel Prize for this).• In 2003, the first double pulsar binary was found. Twoneutron stars orbiting each other every 2.4 hours!Incredible laboratory for testing Einstein’s theory ofgeneral relativity.Neutron Star “Equation of State”• The relation betweenpressure and density in aNS is not yet know. Thematerial is just too weird!• No experiments can bedone on Earth to help.• By measuring the massand radius, we canconstrain which relationswork best.• Mass is easy (binaries),but radius is more difficultto study.Black holesform hereSpectral Line from NS surface explosions• Absorption line is redshifted from coming out of theneutron star’s very strong gravitational field --> R ~ 12 kmBlack Holes (BH)• Neutron degeneracy pressure cannot support a neutronstar having M > 2-3Msun. So if more mass than this collapses(as may be the case for 20-100 Msun stars) it will form ablack hole.• Gravity is so strong that nothing can escape, not evenlight!Consider Newton’ s Law of Gravity:Halve d --> quadruple F --> escape velocity increases(actually Vescape ∝ d-1/2)M1M2dBlack hole conditions• If matter is compressed so much that escape velocityequals the speed of light, then we have a black hole.(“escape velocity” is the minimum initial speed an objectsneeds to escape to “infinity”)For a given M, a BH forms ifExample: for the Sun, RS = 3 kmSince RS ∝ M, you should be able to use this to calculate theSchwarzchild radius of any mass object.This is also called the EVENT HORIZON of a black hole.Once you’re inside, there’s no way out.Some properties of black holes• Far from the event horizon, space-time is normal. If theSun turned into a BH, the orbit of Earth would not be affected(BHs don’t suck!) Only close to the BH do amazing thingshappen.• Matter inside the BH has collapsed to a mathematical pointcalled a singularity (at least according to Einstein’s theory,we expect quantum effects will come into play here).• A black hole has no hair-- the “no hair theorem”A BH is completelydescribed by 3 properties:Mass, electric charge, andspin (angular momentum)BHPhotons (light) near a black hole• Light is trapped inside a blackhole due to the effects of generalrelativity: space-time is severelywarped within the event horizon.Other consequences:• Light coming from a region closeto (but outside) a BH is bent (ifnot radial) and redshifted.• The photon sphere: Light canorbit a BH at a radius of 3GM/c2(this is 1.5 times the Schwarzchildradius, RS)Tidal forces near a black hole• Near a low-mass black hole, the differential (or tidal)forces can become huge!• So you don’t want to gettoo close to a low-massBH, or you’d be torn apart(spagh etification)• It’s actually safer to gonear a massive BHbecause the tidal forcesnear the event horizon aremuch less.Suppose you (far from a BH)watch a friend fall toward a BH1) You would see his clock slow down.2) It would appear that he never falls in.3) From his perspective, he does fall in!4) If he escapes before crossing the eventhorizon, he will have aged less than you. This isa method for jumping into the future while aginglittle! (actual life span is unaffected)5) Light signals from horizon are redshifted tozero energy: can’t see them!Detecting a Black Hole• Light doesn’t escape, so you can’t “see” a BH.• We detect BHs by their gravitational influence.• In some binary systems, we find an invisiblecompanion and infer a minimum mass greater than 3solar masses --->
View Full Document
Unlocking...