1446 Introductory Astronomy II

1
1446 Introductory Astronomy II

• Chapter 14
• General Relativity and Black Holes
• R. S. Rubins
  Fall, 2009

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Special Relativity Einstein (1905)

• The Special Theory of Relativity is 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.

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General Relativity Einstein (1915)

• According to the Principle 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 stars
  position as it
• passes close to the Sun
• ii. the precession of Mercurys perihelion
  predicted correctly
• iii. gravitational redshifts in the spectra of
  dense stars, such as
• white dwarfs
• iv. gravitational lensing
• v. gravitational waves.

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Principle of Equivalence 1
Accelerating frame (left) versus Gravitational
field (right)
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Principle of Equivalence 2
Bending of a light beam in a Gravitational field
(right)
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Deflection of Light by a Gravitational Field
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The Precession of Mercurys Perihelion
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Search for Gravititational Waves LIGO

• LIGO (Laser Interferometer Gravitational Wave
  Observatory) has detectors in Hanford, WA (below)
  and Livingston, LA.
• 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.

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Trapping of Light by a Black Hole
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X Rays Generated by Black-Hole Accretion
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Artists Impression Black hole and Companion
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Stellar Black Holes

• A black hole has a mass so concentrated that
  neither EM radiation nor matter can escape from
  it.
• A black hole is formed from a neutron star of
  mass more than three solar masses (3MSun).
• In a black hole, 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 black holes
  has been come from binary star systems, in which
  one star is a black hole.
• Stellar black holes typically contain about 10
  solar masses.
• However, black holes of about 16 and 30 solar
  masses were observed in 2007, both from the X
  rays emitted when matter from a companion star
  falls into the black hole.

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Flicker Time and Star Size

• An instantaneous change in brightness of a star
  would be observed for the time light took to
  traverse the stars 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.

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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.