Measured Red Shifts
Measured Doppler red shifts give the recession velocity of stars or galaxies, presuming that the Hubble law is valid. It is common practice to express this velocity as a fraction of the speed of light and to use a parameter z defined by:
where λ is understood to be λemitted = λrest, in the rest frame of the emitter.
|Calculating v/c from this expression gives:|
The largest red shifts measured are those of the quasars. Measurements of >100 quasars have given a range of 0.16 to 3.53, corresponding to recession speeds of 0.15c to 0.91c.
Another application of the z parameter is to imply the scale factor R of the universe at the time that light was emitted from a given observed object. The z parameter is related to R by the expression
where the scale is taken as R0 =1 at the present time. For example, if the redshift of an object is found to correspond to z=3, then R=1/4 and we imply that the universe has expanded by a factor of four since light left that object. The wavelength of the received radiation has expanded by a factor of four because space has expanded by a factor of four during its transit from the emitting object. At such large values of z, the redshift is mainly the cosmological redshift, and not a valid measure of the actual recessional velocity of the object with respect to us.
The z parameter can also be used to assess the mass density compared to the mass density ρ0 at the present time.
With z=3, the density is 64 times that of the present density.
Reference:Carroll & Ostlie