Published on October 7, 2007
Black Holes, Etc.: Black Holes, Etc. Escape Velocity and Black Holes: Escape Velocity and Black Holes No physical object can travel faster than light. The speed of light, according to special relativity, is an absolute upper limit. M in solar masses and Rs in km What is the radius of an object of given mass that has an escape velocity equal to the speed of light? The Event Horizon of a Non-rotating (Schwartzschilde)Black Hole: The Event Horizon of a Non-rotating (Schwartzschilde)Black Hole According to general relativity, the singularity is enclosed by a spherical surface called the event horizon. The radius of the event horizon, Rs, is called the Schwartzschilde radius. Nothing can cross the event horizon in the outward direction. Since this includes light, we can’t observe anything inside the event horizon. RS Summary of Schwartzschilde Black Hole Properties: Summary of Schwartzschilde Black Hole Properties Nothing that enters the event horizon can escape from the black hole. No force can stop collapse to zero volume. The radius of the event horizon is called the “Schwartzschilde radius”. Time slows down and light is red-shifted as the event horizon is approached. Tidal forces squeeze, stretch, tear apart, and ionize material before it reaches the event horizon. Animation: http://oposite.stsci.edu/pubinfo/pr/2001/03/content/CygnusXR-1.mpg Kerr (Rotating) Black Holes: Kerr (Rotating) Black Holes A black hole can have only three properties: mass, angular momentum, and charge. Stellar black holes are electrically neutral. A neutral rotating black hole is called a Kerr black hole. Outside its event horizon, a Kerr black hole has a region, called the ergosphere, in which spacetime is dragged along with the rotating black hole. In principle, energy can be extracted from the ergosphere. An object dropped into the ergosphere can break into two parts. One of them drops through the event horizon. The other leaves the ergosphere with more energy than the original object had, and the mass of the black hole decreases. Searching for Black Holes: Searching for Black Holes Isolated black holes are virtually impossible for us to see from Earth, because they’re small and emit no light. A black hole is more likely to be recognized if it has a visible companion that isn’t a black hole. A black hole with a visible companion will be a source of x-rays. The x-ray emission intensity should exhibit rapid fluctuations because of the chaotic nature of the processes that cause the x-ray emission. So, we search for binary systems in which (a) one of the objects is visible, (b) the other is invisible and (c) there are x-ray sources that have short time scale fluctuations We deduce the mass of the visible companion from its spectrum. Having the mass of the visible companion and some information about the orbit, we can find a lower limit to the mass of the invisible companion. If it’s greater than about 3 times the mass of the Sun, it’s probably a black hole. Otherwise, it’s likely to be a neutron star. Behavior of a Blob of Matter Falling Toward a Black Hole Event Horizon or Onto a Neutron Star: Behavior of a Blob of Matter Falling Toward a Black Hole Event Horizon or Onto a Neutron Star Neutron star – Blob of matter spirals inward, hits the hard surface, and explodes, producing a powerful burst of high energy radiation. Black hole – Blob of matter spirals inward, reddens, and gradually disappears. Very little radiation escapes from the blob. http://science.nasa.gov/headlines/y2001/ast12jan_1.htm Some Black Hole Candidates: Some Black Hole Candidates X-Ray Bursters, Gamma Ray Bursters, QPO’s, and SS433: X-Ray Bursters, Gamma Ray Bursters, QPO’s, and SS433 X-Ray Bursters: X-Ray Bursters Powerful bursts of energy at irregular intervals. The longer the period between bursts, the stronger the burst. Explanation: Neutron star with a normal star companion. Close enough for normal star material to pass through the inner Lagrangian point, form a disk around the neutron star, and accrete onto it. As the mixture of hydrogen and helium accumulates on the surface of the neutron star, the hydrogen fuses steadily and a layer of helium builds up. When the layer of helium becames dense enough and hot enough, it fuses to form carbon and emits a burst of x-rays. The burst lasts just a few seconds, but emits ~1037 Joules of energy. The helium layer can then build up until another burst occurs. How long would it take the Sun to produce the amount of energy in a typical x-ray burst? Quasi-periodic Oscillations: Quasi-periodic Oscillations Observation: X-ray pulses from accretion disks around neutron stars and black holes. Pulses have very short periods – as short as 0.00075 s. Pulse periods decrease rapidly before the pulse vanishes completely. Because of the changing pulse period, these are called QPO’s (quasi-periodic oscillations). Explanation: Blobs of material near the surface of a neutron star or black hole emit x-rays while orbiting in the accretion disk. The period decreases because the blob moves faster as it spirals into the compact object. http://science.nasa.gov/headlines/images/blackhole/cygxr1w.jpg Slide12: Calculate the orbital period for a blob of material 20 km from the center of a neutron star of mass 2.0 times the mass of the Sun. SS433: SS433 One set of spectral lines is blue-shifted and another is red-shifted. Model: neutron star or black hole with a normal star companion. Accretion disk and bipolar jets. Disk and jet precess with a 164-day period. Jet velocity ~ ¼ the speed of light. Gamma Ray Bursters: Gamma Ray Bursters Short (seconds or minutes) bursts of high energy gamma rays. Seen in all directions → originate outside our galaxy. Measured red shifts indicate that they are billions of light years away. What are they? Binary neutron star systems? They emit energy in the form of gravitational waves and eventually merge. This results in a black hole + a short burst of high energy gamma rays. Hypernovae (collapsars)? High mass star collapses, but supernova is suppressed by infalling mass from the star’s envelope.→ Star collapses to form a black hole. → Bursts of high energy gamma rays along the polar axes.