1446 Introductory Astronomy II

1. 1446 Introductory Astronomy II Chapter 14 General Relativity and Black Holes R. S. Rubins Fall 2011

2. Special Relativity: Einstein (1905) • The Special Theory of Relativityis based on the postulate of the constancy of the speed of light, regardless of the motion of the source or observer. • Some consequences of special relativity (all verified) are i.a moving object appears shorter (see figure); ii. time passes slower on a moving object; iii. no signal or material object can travel faster than c; iv. the equation, E = mc2, shows that mass is a form of energy.

3. General Relativity: Einstein (1915) • According to thePrinciple of Equivalence, a gravitational force in a small region of space can be duplicated by an acceleration of the observer. • Some consequences of general relativity are i. the bending of a light beam by a strong gravitational field, such as in the apparent change in a star’s position as it passes close to the Sun; ii. the precession of Mercury’s perihelion predicted correctly; iii. gravitational redshifts in the spectra of dense stars, such as white dwarfs; iv. gravitational lensing; v. gravitational waves.

4. Principle of Equivalence 1 Accelerating frame (left) versus Gravitational field (right)

5. Principle of Equivalence 2 Bending of a light beam in a Gravitational field (right)

6. Deflection of Light by a Gravitational Field • On May 29, 1919, just 4 years after Einstein predicted that light passing near the Sun would be deflected by the Sun’s gravity, Eddington, Dyson and Davidson confirmed the prediction by measurements during a total solar eclipse observed in Brazil and West Africa.

7. The Precession of Mercury’s Perihelion A planet’s perihelion is its point in its orbit of closest approach to the Sun. Mercury’s perihelion rotates once around the Sun in about 20,000 years. Most of this effect is produced by the other planets, but a residual effect was explained to within ½ percent by General Relativity. perihelion Mercury 

8. Time Dilation: Effect of Gravity on Clocks • The General Theory of Relativity shows that time passes slower in a larger gravitational field. • If two clocks are placed in a building on the Earth’s surface, one 75 feet above the other, the lower clock would lose about 1 second in ten million years, a result verified to within 2% in 1954 with gamma ray sources placed at the top and bottom of a tower in Harvard University • Aswillbe discussed in detail later, the succesful operation of the Global Positioning Satellite (GPS) system, that provides location information anywhere on the Earth, depends crucially on the correctness of General Relativity.

9. Search for Gravititational Waves: LIGO • LIGO (the Laser Interferometer Gravitational Wave Observatory), which became operational in 2003,has detectors in Hanford, WA (shown below) and Livingston, LA, situated in opposite parts of the US.

10. Gravitational Waves • Optical interference of the laser beams passing through the two 4 km arms detects changes of less than one thousandth of the diameter of an atomic nucleus. • Having two similar detectors far apart allows local signals to be distinguished from those coming from space, and also should allow scientists to determine the direction of an incoming wave. • Planned for launch in 2015 is LISA (Laser Interference Space Antenna), a space-based system, in which three detectors form an equilatoral triangle of side 5 million km. • A promising source of gravitational waves for detection by LIGO, and the proposed LISA, are the anticipated waves emitted during the collision of two black holes.

11. Curvature of Spacetime by Gravity 1 In the flat spacetime analogy, an object moves with constant velocity; i.e. with constant speed in a straight line. A large mass, such as the Sun, curves spacetime, so that a much less massive object, such as the Earth, is constrained to move with constant speed in a circle. Flat spacetime analogy Curvedspacetime analogy

12. Earth’s Surface: an Example of Curved Space • The shortest distance between two points at the same latitude, such as Philadelphia and Beijing is not on that obtained by following the line of latitude, but by following a great circle. • This is found by following the intersection of the Earth’s surface with a plane through the two cities that passes through the center of the Earth. 0 miles Great Circle Ph Be Constant latitude 25,000 miles

13. Comparison of Newton and Einstein • Newton’s description of gravity between Sun and Earth • The Earth is pulled towards the Sun by gravity, which stops the Earth flying into space, and causes it to circle around the Sun. • Einstein’s description The Sun is a massive object which distorts spacetime in its vicinity. The Earth moves freely through spacetime, but the distortion of spacetime by the Sun causes the Earth to move in a circle. Note that Einstein’s description of 1915 removes the concept of action-at-a-distance, which bothered Newton over 200 years earlier.

14. A pulsar is a neutron star with the Sun’s mass and a city’s size. In 2004, a double pulsar system - two pulsarscircling each other - was found about 2000 ly (10 million billion miles) away. The two pulsars are separated from each other by roughly 3 times the Earth-Moon separation, which is about 700,000 miles. The radio beams emitted by each pulsar periodically pass very close to the curved spacetime around the other pulsar, which delays its transit to the Earth. In one of the greatest achievements in experimental physics, the largest radio telescopes in Australia, England and the US, were used to determine that the two pulsars were spiraling inwards towards each other at the rate of 7mm per day, a result which was in agreement with the predictions of GR. Double Pulsar System: Test of GR 1

15. Double Pulsar System: Test of GR 2 • “The achievement is breathtaking. These are spinning neutron stars orbiting around each other at a distance of a million kilometers and located 2000 light years from Earth. Their behavior was predicted to millimeter precision using a theory developed in 1915 by a man who wanted to understand why two lumps of stuff dropped off a leaning tower in Pisa three centuries previously hit the ground at the same time.” Cox and Forshaw in “Why Does E = mc2 ?“. • Another feature of the double pulsar system is that they should produce ripples in spacetime, or gravitational waves, which we hope to find with a future gravitational detector.

16. Relativity: Practical Examples 1. Giant particle accelerators, such as the LHC in CERN, Switzerland, which cost billions of dollars to build, work only because they are designed to relativistic specifications. 2. The functioning of the GPS satellite system, which uses 24 satellites circling the Earth at an altitude of about 12,000 miles, depends crucially on the correctness of Einstein’s theories, especially, the General Theory of Relativity. • According to GR, the weaker gravitational field of the Earth at that altitude causes the satellite clocks to gain 45 μs each day. (roughly 1 second in 60 years), while SR indicates that the satellite clocks should lose 7 μs each day, because the satellites are traveling at about 9000 mph. • If the net correction of 38μs each day were not made, there would be a total failure of the GPS system within a few hours.

17. Trapping of Light by a Black Hole The curvature of space by matter causes the bending of light rays by the gravitational field of the star, which is so large for a black hole that no light escapes from it.

18. X Rays Generated by Black-Hole Accretion

19. Artist’s Impression: Black hole and Companion

20. Stellar Black Holes • A black hole has a mass so concentrated that neither EM radiation nor matter can escape from it. • Stellar black holes are formed from neutron stars of more than 3MSun, in which gravitational forces have overcome even the neutron degeneracy pressure, crushing the star into a far denser form of matter, not describable by present-day physics. • The best experimental evidence for stellar black holes has come from binary star systems, in which one star is a black hole. • While stellar black holes typically contain between 5 and 15 solar masses, supermassive black holes with millions to billions of solar massesare found at the centers of spiral galaxies.

21. Flicker Time and Star Size • An instantaneous change in brightness of a star would be observed for the time light took to traverse the star’s radius. • For the sun, this time would be 2 seconds. • Measurements of the “flicker time”, enable us to obtain an upper limit for the radius of an astronomical object.

22. Cygnus X-1: a Black Hole • Cygnus X-1, a variable X-ray emitter, which belongs to a binary pair, is the best black hole candidate so far observed. • Its companion star, a B0 supergiant, has a mass of about 30 MSun, and from its orbit, Cygnus X-1 was deduced to have a mass of about 10 MSun. • Because of the rapidity in the variation of the X-ray emissions (the flicker time), the diameter of Cygnus X-1 was deduced to be less than 3000 km – smaller than that of the Earth. • The combination of very large mass and very small radius, shows Cygnus X-1 to be a black hole.

23. Black Hole Properties • The creation of black holes is both an important requirement for life, and a most dangerous hazard to life. • Without the Tape II supernovae explosions, which produce the elements beyond iron in the periodic table and are necessary for life, we could not exist. • But, the supernova explosion of a nearby star would produce such enormous amounts of dangerous radiation, that life would be destroyed on our planet.