The Expanding Universe

Sources:

•  Cosmos in a Computer
•  Strobel Notes
•  Cosmic Horizons  (a Stanford Class)

Outline

• Doppler Effect & expansion evidence
• redshift example
• Hubble Diagrams
• Expansion Interpretation

Doppler Effect

• Relative motion between a source of radiation and an observer causes a wavelength shift:


• blueshift when source is approaching
• redshift when source is receding
• For Small  =  - ₀, the equation is
• /₀ = z = 
• where 
• The Doppler Effect can be measured accurately with spectra showing
• emission or
• absorption lines

Doppler Effect Example

• Here's galaxy NGC 2276 which exhibits strong emission lines in its spectrum:


• 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.)
• Here's its full optical spectrum:


• Note the strong emission lines and the weak absorption lines near 4000 Angstroms.
• (1 Angstrom = 0.1 nm = 10^-10 m)
• Here's a blowup of the spectrum near the Hydrogen "alpha" line:


• The black line indicates the rest wavelength of the Hydrogen "alpha"  line, so
• ₀ = 656.3 nm
• = 661.7 nm
• using z =  , we find
• - ₀= 5.4 nm
• z = 0.0082 = v/c
• v = 2,500 km/sec (since c = 300,000 km/sec)
• Now, what wavelength should we expect for the Hydrogen "beta" line?
• ₀ = 486.1 nm
• z = 0.0082, as in the H-alpha case, so
• - ₀= z ₀= 4.0 nm, or
• = 490.0 nm
• Here's the Hydrogen "beta" part of the spectrum:

Hubble's Law

• How does the redshift depend on distance?
• we need a distance indicator
•  Cepheids could only be seen in the nearest galaxies
• the galaxy's size? (crude, but it sort of works)
• the brightest stars in a galaxy
• Hubble's method
• ok, theoretically
• Hubble's plot of distance vs. velocity
• now, called a Hubble diagram

• v = H₀ d
• v = velocity of galaxy
• d = distance to galaxy
• H₀ = Hubble constant
• H₀ = 70 ± 10 km/sec
• very difficult to measure due to distance errors
• type I vs. type II Cepheids
• "brightest" star can be several nearby stars
• see BWS pp 228 and 229
• also LBBB p. 64
• Here's another one using clusters of Galaxies:


• Note: Hubble's law takes a different form for large z
• z > 1 is ok.

Interpretation of Hubble's Law

• The Universe is Expanding
• there is no center:
•  A Toy Universe
•  A little later
•  Expansion Comparison
•  Expansion from red elliptical point of view
• Big Bang Theory Assumptions:
• Homogeneous - the same everywhere
• Isotropic - no special direction

• an assumption which is now supported by observations
• The Universe has no Edge - another assumption
• can be flat
• or curved:

• Finite or infinite

Olber's Paradox

• If the Universe is
• infinite in extent
• infinite in age
• like our local region everywhere
• Why is the sky dark at night?
• Every line of sight will lead to a star eventually