Caption: A redshift illustrated.

Features:

1. The redshift (with symbol z) for electromagnetic radiation (EMR) is defined in general by the formula:

         z=(λ_observed-λ_rest)/λ_rest ,

   where λ_observed is the observed wavelength and λ_rest is the wavelength in the rest frame of emission. Note z is dimensionless number (i.e., it has no units).

2. There are three well known redshifting processes:
   1. The Doppler shift (AKA Doppler effect).

      The Doppler shift is due to the (line-of-sight) relative velocity between two observers one of whom may be a source.

      It is an effect of special relativity and the physical velocities of the two observers. Physical velocities are velocities relative to inertial frames in spacetime that is or can be approximated as Minkowski space (which is a spacetime NOT affected by the effects of general relativity). They are what we ordinarily just call velocities.

      The Doppler shift can be a negative redshift in which case it is called a blueshift.

   2. The cosmological redshift.

      The cosmological redshift is caused by a increase in wavelength of EMR due to the literal growth of space through which the EMR is propagating. It is an effect of general relativity in expanding universe models.

      We usually think of the redshift from source to observer. In the expanding universe there are only positive redshifts due to the cosmological redshift.

      Unfortunately, many people conflate the Doppler shift and cosmological redshift.

      They are DIFFERENT effects and their formulae are DIFFERENT in general.

   3. The gravitational redshift. This is a general relativity effect on EMR moving in a gravitational field.

3. All EMR from extragalactic sources will possess both a Doppler shift and cosmological redshift. In general, it's difficult to separate the two effects into two components z_Doppler and z_cosmological.

   However, z_Doppler ≤ ∼ 0.003 almost always at least for large objects like galaxies and quasars.

   On the other hand, z_cosmological grows rapidly with distance from us, and we can usually neglect the Doppler shift z for high-z extragalactic sources: i.e., we can usually neglect the Doppler shift except for very nearby objects.

4. What is called the redshift velocity is defined by the formula:

         v_redshift = zc ,

   where c is the vacuum light speed c = 2.99792458*10**5 km/s ≅ 3*10**5 km/s . We use units of kilometer per second since they are the natural units in many astrophysical contexts.

5. The redshift velocity for a Doppler shift is the 1st-order-in-small-z relative velocity between two observers.

   1st-order in small z means that the relative velocity obtained from the formula is accurate for |z| << 1. In this case, the formula is very inaccurte for |z| approaching or exceeding 1. The relative error in the formula for relative velocity grows as z for z << 1.

6. The redshift velocity for the cosmological redshift is the 1st-order-in-small-z recession velocity between observer and source.

   1st-order in small z means that the recession velocity obtained from the formula is accurate for |z| << 1 and ceases to be accurate for z approaching 1. The relative error in the formula for recession velocity grows as z for z << 1.

7. Note a recession velocity is NOT a physical velocity. It is literally the rate of growth of space between observer and source.

   Recession velocities exceeding the vacuum light speed occur for the cosmologically remote observable universe.

8. Redshift is a direct observable.

   We can usually measure the emission line and absorption line wavelengths in good quality spectra to high accuracy and precision.

   We recognized the pattern of the emission lines and/or absorption lines and so know what atoms or molecules they came from.

   Laboratory measurements give us very high accuracy and precision rest frame wavelengths.

   Thus, we can calculate z to high accuracy and precision very often.

9. Separating z_Doppler and z_cosmological can be hard.

   However, for high z, the Doppler shift is usually negligible as discussed above.

   For objects within the Local Group of galaxies, there is no cosmological redshift since this nearby region of space is gravitationally bound together and does NOT participate in the expansion of the universe.