The Expanding Universe
Sources:
Outline
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Doppler Effect & expansion evidence
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redshift example
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Hubble Diagrams
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Expansion Interpretation
Doppler Effect
Doppler Effect Example
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Here's galaxy NGC 2276 which exhibits strong emission lines
in its spectrum:
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NGC 2276 is the one in the center; the smooth galaxy to the
lower left is a companion galaxy. (Many galaxies are found to come in pairs
or groups.)
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Here's its full optical spectrum:
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Note the strong emission lines and the weak absorption lines
near 4000 Angstroms.
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(1 Angstrom = 0.1 nm = 10-10 m)
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Here's a blowup of the spectrum near the Hydrogen "alpha"
line:
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The black line indicates the rest wavelength of the Hydrogen
"alpha" line, so
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0 =
656.3 nm
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=
661.7 nm
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using z =
, we find
-
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0=
5.4 nm
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z = 0.0082 = v/c
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v = 2,500 km/sec (since c
= 300,000 km/sec)
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Now, what wavelength should we expect for the Hydrogen "beta"
line?
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0 =
486.1 nm
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z = 0.0082, as in the H-alpha
case, so
-
-
0=
z
0=
4.0 nm, or
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=
490.0 nm
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Here's the Hydrogen "beta" part of the spectrum:

Hubble's Law
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How does the redshift depend on distance?
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we need a distance indicator
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Cepheids
could only be seen in the nearest galaxies
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the galaxy's size? (crude, but it sort of works)
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the brightest stars in a galaxy
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Hubble's method
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ok, theoretically
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Hubble's plot of distance vs. velocity
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now, called a Hubble diagram
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v = H0 d
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v = velocity of galaxy
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d = distance to galaxy
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H0 = Hubble constant
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H0 = 70 ± 10 km/sec
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very difficult to measure due to distance errors
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type I vs. type II Cepheids
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"brightest" star can be several nearby stars
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see BWS pp 228 and 229
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also LBBB p. 64
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Here's another one using clusters of Galaxies:
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Note: Hubble's law takes a different form for large z

Interpretation of Hubble's Law
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The Universe is Expanding
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Big Bang Theory Assumptions:
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Homogeneous - the same everywhere
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Isotropic - no special direction
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an assumption which is now supported by observations
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The Universe has no Edge - another assumption
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Finite or infinite
Olber's Paradox
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If the Universe is
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infinite in extent
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infinite in age
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like our local region everywhere
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Why is the sky dark at night?
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Every line of sight will lead to a star eventually
