Separating Peculiar Motion

In the previous lecture we already noted that the interpretation of redshift determined from line spectra depends on the distance range at which we are observing. Galaxies move through space and at shorter distances this motion will be dominant in the redshift. At the largest distances this “peculiar motion” through space will be unnoticeable among the more dominant expansion of space itself. This scale at which we observe determines how we are measuring distance.




Nearby
Hubble’s law describes the expansion of space itself but it ignores any local relative motion between the source and us as observers. Such motion is often dubbed “peculiar” motion. If we are really “close” (let’s say nearby galaxies) we can largely ignore the expansion of space and only observe peculiar motion. An example is the blue shift of the Andromeda galaxy. That shift in wavelength, using the Doppler method, gives us the radial velocity of about 300 km/s. To measure distance, e.g. to the Andromeda galaxy, we must use one of the standard candle techniques we discussed before. In the case of the Andromeda galaxy its distance is obtained from the Cepheid method to be 2.5 Mly.

Mid-range
At larger distances redshift due to peculiar motion of a galaxy becomes mixed with redshift due to the expansion of space. The latter is often called “Hubble flow”. This is a particularly difficult distance scale in which we must try to separate these two distinctly different effects. Most often a general model for the expansion of space is used to subtract the Hubble flow from the measurements, to obtain the peculiar motion.

Far away
At very large distances we only see the expansion that is described by Hubble’s law as any peculiar motion is so much less. At this range we interpret redshift from the spectra as cosmological redshift. This can give us a measure of distance within the framework of a cosmological model, which includes the Hubble parameter.




For the determination of the important current value of the Hubble parameter, which is called the Hubble constant denoted by H₀, we must accurately determine the distance to faraway objects, using any of the Standard Candles of the Cosmic Distance Ladder or alternative methods (see below).