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Neutron Stars and Black Holes Chapter 14
Guidepost The preceding chapters have traced the story of stars from their birth as clouds of gas in the interstellar medium to their final collapse. This chapter finishes the story by discussing the kinds of objects that remain after a massive star dies. How strange and wonderful that we humans can talk about places in the universe where gravity is so strong it bends space, slows time, and curves light back on itself! To carry on these discussions, astronomers have learned to use the language of relativity. Throughout this chapter, remember that our generalized discussions are made possible by astronomers studying general relativity in all its mathematical sophistication. That is, our understanding rests on a rich foundation of theory. This chapter ends the story of individual stars. The next three chapters, however, extend that story to include the giant communities in which stars live— the galaxies.
Outline I. Neutron Stars A. Theoretical Prediction of Neutron Stars B. The Discovery of Pulsars C. A Model Pulsar D. The Evolution of Pulsars E. Binary Pulsars F. The Fastest Pulsars G. Pulsar Planets II. Black Holes A. Escape Velocity B. Schwarzschild Black Holes C. Black Holes Have No Hair D. A Leap into a Black Hole E. The Search for Black Holes
Outline (continued) III. Compact Objects with Disks and Jets A. X-Ray Bursters B. Accretion Disk Observations C. Jets of Energy from Compact Objects D. Gamma-Ray Bursts
Neutron Stars A supernova explosion of a M > 8 Msun star blows away its outer layers. The central core will collapse into a compact object of ~ a few Msun.
Formation of Neutron Stars Compact objects more massive than the Chandrasekhar Limit (1.4 Msun) collapse further. 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!!!
Discovery of 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
Pulsars / Neutron Stars Neutron star surface has a temperature of~ 1 million K. Cas A in X-rays Wien’s displacement law, lmax = 3,000,000 nm / T[K] gives a maximum wavelength of lmax = 3 nm, which corresponds to X-rays.
Pulsar Periods Over time, pulsars lose energy and angular momentum => Pulsar rotation is gradually slowing down.
Lighthouse Model of Pulsars A Pulsar’s magnetic field has a dipole structure, just like Earth. Radiation is emitted mostly along the magnetic poles.
Neutron Star (SLIDESHOW MODE ONLY)
Images of Pulsars and Other Neutron Stars The vela Pulsar moving through interstellar space The Crab nebula and pulsar
The Crab Pulsar Pulsar wind + jets Remnant of a supernova observed in A.D. 1054
The Crab Pulsar (2) Visual image X-ray image
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
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.
Neutron Stars in Binary Systems: X-ray Binaries Example: Her X-1 Star eclipses neutron star and accretion disk periodically 2 Msun (F-type) star Neutron star Orbital period = 1.7 days Accretion disk material heats to several million K => X-ray emission
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.
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!
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.
The Schwarzschild Radius => There is a limiting radius where the escape velocity reaches the speed of light, c: 2GM ____ Rs = Vesc = c c2 G = Universal const. of gravity M = Mass Rs is called the Schwarzschild Radius.
Schwarzschild Radius and Event Horizon No object can travel faster than the speed of light => 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”
Schwarzschild Radius of Black Hole (SLIDESHOW MODE ONLY)
Black Holes in Supernova Remnants Some supernova remnants with no pulsar / neutron star in the center may contain black holes.
“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 An astronaut descending down towards the event horizon of the BH will be stretched vertically (tidal effects) and squeezed laterally.
General Relativity Effects Near Black Holes (2) Time dilation Clocks starting at 12:00 at each point. After 3 hours (for an observer far away from the BH): Clocks closer to the BH run more slowly. Time dilation becomes infinite at the event horizon. Event Horizon
General Relativity Effects Near Black Holes (3) Gravitational Red Shift All wavelengths of emissions from near the event horizon are stretched (red shifted). Frequencies are lowered. Event Horizon
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!
End States of Stars (SLIDESHOW MODE ONLY)
Candidates for Black Hole Compact object with > 3 Msun must be a black hole!
Compact Objects with Disks and Jets Black holes and neutron stars can be part of a binary system. Matter gets pulled off from the companion star, forming an accretion disk. => Strong X-ray source! Heats up to a few million K.
X-Ray Bursters Several bursting X-ray sources have been observed: Rapid outburst followed by gradual decay Repeated outbursts: The longer the interval, the stronger the burst
The X-Ray Burster 4U 1820-30 In the cluster NGC 6624 Ultraviolet Optical
Black-Hole vs. Neutron-Star Binaries Black Holes: Accreted matter disappears beyond the event horizon without a trace. Neutron Stars: Accreted matter produces an X-ray flash as it impacts on the neutron star surface.
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: Quasi-periodic oscillations (QPOs) Sometimes: Radio-emitting jets
Radio Jet Signatures The radio jets of the Galactic black-hole candidate GRS 1915+105
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
Gamma-Ray Bursts (GRBs) Short (~ a few s), bright bursts of gamma-rays GRB of May 10, 1999: 1 day after the GRB 2 days after the GRB Later discovered with X-ray and optical afterglows lasting several hours – a few days Many have now been associated with host galaxies at large (cosmological) distances. Probably related to the deaths of very massive (> 25 Msun) stars.
New Terms neutron star pulsar lighthouse model pulsar wind glitch magnetar gravitational radiation millisecond pulsar singularity black hole event horizon Schwarzschild radius (RS) Kerr black hole ergosphere time dilation gravitational red shift X-ray burster quasi-periodic oscillations (QPOs) gamma-ray burster soft gamma-ray repeater (SGR) hypernova collapsar
Discussion Questions 1. Has the existence of neutron stars been sufficiently tested to be called a theory, or should it be called a hypothesis? What about the existence of black holes? 2. Why would you expect an accretion disk around a star the size of the sun to be cooler than an accretion disk around a compact object? 3. In this chapter, we imagined what would happen if we jumped into a Schwarzschild black hole. From what you have read, what do you think would happen to you if you jumped into a Kerr black hole?
Quiz Questions 1. What is the lower limit for the mass of neutron stars? a. About 0.08 solar masses. b. About 0.4 solar masses c. Exactly 1 solar mass. d. About 1.4 solar masses. e. Between 2 and 3 solar masses.
Quiz Questions 2. White dwarfs and neutron stars are both end products of stellar evolution. White dwarfs are composed of mostly carbon, oxygen, and electrons, whereas neutron stars are composed of mostly neutrons. What happens to the protons in the atomic nuclei and the degenerate electrons that were inside the star that creates a neutron star? a. The protons and electrons, being charged particles, are all ejected during the supernova event by the strong magnetic field. b. The electrons and protons combine to form neutrons and neutrinos. c. Protons decay into neutrons and positrons and neutrinos. The positrons combine with the electrons and form pairs of gamma rays. d. The protons remain in the neutron star and the electrons are ejected by the magnetic field. e. Our understanding of atomic nuclei is not yet good enough to determine what happens to them.
Quiz Questions 3. Why don't we use visible-wavelength telescopes to locate neutron stars? a. Neutron stars have wavelengths of maximum intensity in the X-ray band of the electromagnetic spectrum. b. Neutron stars are too cold to emit visible light. c. Neutron stars have strong magnetic fields. d. Neutron stars pulse too rapidly. e. Neutron stars are very small.
Quiz Questions 4. What prevents neutron stars from contracting to a smaller size? a. Gas pressure fueled by hydrogen fusion. b. Gas pressure fueled by helium fusion. c. Gas pressure fueled by carbon fusion. d. Degenerate neutrons. e. Degenerate electrons.
Quiz Questions 5. Why do we expect that neutron stars spin rapidly? a. The law of conservation of energy. b. The law of conservation of angular momentum. c. Equatorial jets spin them up. d. Both a and b above. e. All of the above.