Foundations of Astronomy 13e Seeds Phys1403 Introductory Astronomy Instructor: Dr. Goderya Chapter 14 Neutron Stars and Black Holes Cengage Learning 2016 Topics for Today s Class Neutron Stars What is a Neutron Star Pulsars Model of a Pulsar Binary Pulsars Black Holes What is a Black Hole Escape Velocity Schwarzcschild Radius Black Holes and Weird Physics Compact Objects with Disks and Jets X-Ray Bursters Gamma-Ray Bursts Neutron Stars The central core will collapse into a compact object of ~ a few M sun. A supernova explosion of a M > 8 M sun star blows away its outer layers. Formation of Neutron Stars Compact objects more massive than the Chandrasekhar Limit (1.4 M sun ) collapse further. 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!!! 1
Proper Motion of Neutron Stars Some neutron stars are moving rapidly through interstellar space. Discovery of Pulsars Angular momentum conservation => Collapsing stellar core spins up to periods of ~ a few milliseconds. Magnetic fields are amplified up to B ~ 10 9 10 15 G. (up to 10 12 times the average magnetic field of the sun) This might be a result of anisotropies during the supernova explosion forming the neutron star => 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 Lighthouse Model of Pulsars A Pulsar s magnetic field has a dipole structure, just like Earth. Wien s displacement law, max = 3,000,000 nm / T[K] gives a maximum wavelength of max = 3 nm, which corresponds to X-rays. Radiation is emitted mostly along the magnetic poles. Pulsar Periods The Crab Pulsar Over time, pulsars lose energy and angular momentum => Pulsar rotation is gradually slowing down. Pulsar wind + jets Remnant of a supernova observed in A.D. 1054 2
The Crab Pulsar (2) Light Curves of the Crab Pulsar Visual image X-ray image Binary Pulsars Some pulsars form binaries with other neutron stars (or black holes). Neutron Stars in Binary Systems: X-ray Binaries Example: Her X-1 2 M sun (F-type) star Star eclipses neutron star and accretion disk periodically 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 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. 3
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! Escape Velocity Velocity needed to escape Earth s gravity from the surface: v esc 11.6 km/s. Now, gravitational force decreases with distance (~ 1/d 2 ) => Starting out high above the surface => lower escape velocity. If you could compress Earth to a smaller radius => higher escape velocity from the surface. v esc v esc v esc The Schwarzschild Radius Schwarzschild Radius and Event Horizon => There is a limiting radius where the escape velocity reaches the speed of light, c: R s = 2GM c 2 G = Universal const. of gravity M = Mass R s is called the Schwarzschild Radius. V esc = c 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 Black Holes in Supernova Remnants Schwarzschild Radii Some supernova remnants with no pulsar / neutron star in the center may contain black holes. 4
Black Holes Have No Hair Candidates for Black Hole 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) Compact object with > 3 M sun must be a black hole! 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) Clocks starting at 12:00 at each point. After 3 hours (for an observer far away from the BH): Time dilation 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. 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. Event Horizon Mass > 3 M sun => Black hole! 5
Compact Objects with Disks and Jets X-Ray Bursters Black holes and neutron stars can be part of a binary system. => Strong X-ray source! Heats up to a few million K. Matter gets pulled off from the companion star, forming an accretion disk. 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 Black Hole X-Ray Binaries Accretion disks around black holes Optical Ultraviolet 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 Model of the X-Ray Binary SS 433 Gamma-Ray Bursts (GRBs) 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 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 M sun ) stars. Short (~ a few s), bright bursts of gamma-rays 6
Black-Hole vs. Neutron-Star Binaries Black Holes: Accreted matter disappears beyond the event horizon without a trace. Common Misconception Misconception: Black holes are giant vacuums that will suck in everything in the Universe Truth: a black hole is just a gravitational field Neutron Stars: Accreted matter produces an X-ray flash as it impacts on the neutron star surface. If you fell into the gravitational field of a star, you would hit the star s surface before you fell very far. Because a black hole is so small, you could fall much deeper into its gravitational field and eventually cross the event horizon. At a distance, the two gravitational fields are the same. Acknowledgment The slides in this lecture is for Tarleton: PHYS1411/PHYS1403 class use only Images and text material have been borrowed from various sources with appropriate citations in the slides, including PowerPoint slides from Seeds/Backman text that has been adopted for class. 7