Announcements

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Announcements

• Monday, March 26 Midterm II
• Thursday, March 22, 6-8 pm review session
• Friday, April 6 Project outline due

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Lecture 26The expanding universe II How does it
expand?
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History

• 1916 Einsteins theory of general relativity
• 1920-25 spiral nebulae are galaxies like the
  Milky Way
• 1920-25 Extragalactic distance scale
• 1929 Hubble redshift-distance relation. Meeting
  with Einstein and Lemaître ? Big Bang model

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Edwin Hubble (1889-1953)

• Four major accomplishments
• in extragalactic astronomy
• The establishment of the Hubble classification
  scheme of galaxies
• The convincing proof that galaxies are island
  universes
• The distribution of galaxies in space
• The discovery that the universe is expanding

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Redshift
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The redshift-distance relation
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The redshift-distance relation
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Key results

• Most galaxies are moving away from us
• The recession speed v is larger for more distant
  galaxies. The relation between recess velocity v
  and distance d fulfills a linear relation
  v H0 ? d
• Hubbles measurement of the constant H0
  H0 500 km/s/Mpc
• todays best fit value of the constant
  H0 65 km/s/Mpc

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So why was Hubbles original measurement so far
off ?

• Distance measurement based on the
  period-luminosity relation of Cepheid stars
• What are Cepheids? They are variable pulsating
  stars

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So why was Hubbles original measurement so far
off ?

• There exists a luminosity-period relation for
  Cepheid stars

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So why was Hubbles original measurement so far
off ?

• there are two populations of Cepheids (but Hubble
  was not aware of that)
• type I metal rich stars (disk of galaxies)
• type II metal poor stars (halo of galaxies)
• type II Cepheids are less luminous than type I
  Cepheids

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Consequence

• Distance scale was calibrated based on type II
  Cepheids
• Distances to other galaxies were measured using
  type I Cepheids
• yard stick was systematically to small

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initial distance 1 length unit final
distance 2 length units recess velocity
1 length unit per time unit
initial distance 2 length units final
distance 4 length units recess velocity
2 length units per time unit
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Question

• If all galaxies are moving away from us,
• does this imply that we are at the center?

Answer
Not necessarily, it also can indicate that the
universe is expanding and that we are at no
special place.
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Lets go back 15 years ...
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Lets apply Einsteins equation to the Universe

• What is the solution of Einsteins equation for a
  homogeneous, isotropic mass distribution?
• As in Newtonian dynamics, gravity is always
  attractive
• a homogeneous, isotropic and initially static
  universe is going to collapse under its own
  gravity
• Alternative expanding universe (Friedmann)

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A toy universe

• The model Universe is going to collapse under its
  own gravity

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Einsteins proposal cosmological constant ?

• There is a repulsive force in the universe
• vacuum exerts a pressure
• empty space is curved rather than flat
• The repulsive force compensates the attractive
  gravity ? static universe is possible
• but such a universe turns out to be unstable
  one can set up a static universe, but it simply
  does not remain static
• Einstein greatest blunder of his life, but is
  it really ?

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The great synthesis (1930)

• Meeting by Einstein, Hubble and Lemaître
• Einstein theory of general relativity
• Friedmann and Lemaître expanding universe as a
  solution to Einsteins equation
• Hubble observational evidence that the universe
  is indeed expanding
• Consequence
• Universe started from a point? The Big Bang
  Model

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Announcements

• Monday, March 26 Midterm II
• Thursday, March 22, 6-8 pm review session
• Friday, April 6 Project outline due