The Expanding Universe: Evidence for Acceleration

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The Expanding UniverseEvidence for Acceleration

• Review of Hubbles Law
• Excel Activity Hubbles Law with recent data
• Modern interpretation of a Hubble diagram
• Brainstorm Activity Hubble diagrams that account
  for a changing rate of expansion
• Excel Activity Hubble diagrams with very distant
  galaxies

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Part 1 What is Hubbles Law?

• In 1929 Edwin Hubble plotted the velocities of
  various galaxies vs. their distances
• Interpretation all galaxies are moving away from
  each other

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Measuring Velocity by Doppler Effect

• Light waves and sound waves spread outward in
  circles.
• If the source of waves is moving, then observer A
  will see these waves far apart (low frequency)
  while observer B sees them close together (high
  frequency).
• For sound waves, different frequencies are heard
  as different pitches. For light waves, different
  frequencies are seen as different colors in the
  rainbow.
• This change in frequency (Doppler Effect) can be
  used to measure the velocity of the source.

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Redshift as a measure of velocity
Definition of Redshift
z

• At low velocities

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Measuring DistanceBrightness of a Standard
Candle

• Hubble used Cepheid variables and typical
  galaxies
• Newest standard is Type Ia supernovae
• As bright as an entire galaxy

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Measuring brightnessand finding distance

• Stellar brightness is quantified using visual
  magnitude scale
• Hipparchus ranked stars from 1 to 6 1 being the
  brightest in the sky, 6 the dimmest (with unaided
  eye)
• Now we quantify magnitude
• where m is apparent magnitude, d is distance,
  and M is the absolute magnitude--the brightness
  of the object from a distance of 10 parsecs (pc)
• For Type Ia supernova,

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Part II Hubbles Law with recent Data

• Open Expanding Universe Data
• Create a column of distances in megaparsecs.
  (Calculate these from visual magnitudes.)
• Create a column of velocities in km/s (calculated
  from redshifts.)
• Make a Hubble diagram. (Graph velocity vs.
  distance.)

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Part 3 Interpretation of a Hubble Diagram

• Slope of graph is called the Hubble constant it
  represents the rate of expansion
• from our graph
• Work backwards and calculate the time since the
  Big Bang if a galaxy were 1 Mpc away, how long
  would it take to reach Earth moving at a speed of
  56 km/s? Hint

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Modern Interpretation of Hubble Diagram

• Re-interpreting redshift Wavelengths are
  stretched by expansion of space (not Doppler
  shifted by velocity). So the y-axis shows the
  percent by which the universe expanded during the
  time that light traveled a distance, d.
• Example from our data SN1990O
• z 0.030 distance 129 Mpc 4.13 x 108 ly
• So the universe expanded by 3.0 during the 413
  million years that light traveled to us from this
  supernova.

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So how do we interpret the graph?

• Amount the universe has expanded as a function of
  time during which it has expanded.
• Careful Large values of time represent times
  long ago (from galaxies far, far away), not times
  in the future.

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Part 4 Brainstorm

• Before 1998, most people assumed that gravity
  was causing the expansion of the universe to slow
  down. If this assumption were correct, and the
  universe used to be expanding at a faster rate,
  what would our graph look like when we include
  galaxies that are very far away? Would it be
  straight or curved? If it curves, would it curve
  up or down?

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Part 5 Including Data for Distant
Galaxies

• Within the Expanding Universe Data there is a
  worksheet called Distant Supernovae. Copy this
  data and paste it immediately below the Nearby
  data.
• Fill Down the formula for distance.
• Make a graph of redshift vs. distance using both
  Nearby and Distant supernova data
• Is the graph linear or does it curve?
• How should we interpret this?

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Measuring Velocity from Redshift

• Doppler shift from receding source of light
• Redshift (z) is defined by
• Combining these

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Approximating

• At low velocities