16-07 The Hubble Law

• The Hubble law
   
  • In 1929, Edwin Hubble published his discovery of the relation between red shifts and distances of galaxies within 2 Mpc, later in 1931 extended to 32 Mpc
    
    
    
    
    
     
  • The red shift is "interpreted" as a receding velocity (can it be something else?)
     
    z = (l₁-l)₀/l ₀= (1+b_r)/(1-b²)^1/2 - 1
     
    b = [(z+1)²-1]/[(z+1)²+1]    for b=b_r
    
    [b(z)]
     
    b ~ z    for b=b_r << 1
     
  • The Hubble law

    v(=cz) = Hd (only valid for z << 1; for larger z, the relation between z (the redshift) and d (the distance) is an important issue)
     

• H, the Hubble constant (better called the Hubble parameter), is difficult to determine.
  Its value ranges from 50 km/sec/Mpc ~ 100 km/sec/Mpc.
  A recently often quoted value is 70 km/sec/Mpc.
  
  
  
  (check Hubble's original value ~560 km/sec/Mpc)
  [Hubble 1931 paper]
  
   
• With a Hubble constant, the Hubble law can be used to determine the distance, given an observation-determined redshift.
  The distance is very often expressed like d = 90 Mpc h^-1, where h=H/100 km/sec/Mpc
   
• An expanding universe! However, we do not think we are at the center of the universe.
   
• Not all galaxies are moving away from us.
  Galaxies have their own local, intrinsic motion.
  M31 is actually approaching us, blue-shifted.
  At larger distance, the 'Hubble flow velocity' dominates
   
• The Hubble law does not hold any more for very large distance
  
  [the SN Type-Ia d-Z diagram; the "calibrated apparent magnitude" in the ordinate (y-axis) corresponds to the (luminosity) distance. ]