What is "velocity distance" in astrophysics?

Question

I was reading some papers on astrophysics, and in several of them, I've encountered velocity being used as distance. Or more precisely, distance being in dimensions of distance over time. For example, a paper referred to a group of galaxies at "roughly $2000\:\mathrm{km\:s^{-1}}$ in distance." Another used the specific phrase "velocity distance." It said there was a super-cluster "an observed concentration of galaxies at a velocity distance of ${\sim}2500$ to $4000\:\mathrm{km\:s^{-1}}$." I searched for what this could mean for quite a bit, and couldn't find it. If anyone has any idea what this means, some insight would be greatly appreciated.

Answer 1

It is used because of uncertainty in the Hubble constant. The relationship between recession velocity and distance is given by

$v=H_{0}d$

Where $H_{0}$ is the Hubble constant. Since that isn't known precisely, distances aren't known precisely, so talking about distances doesn't necessarily make sense.

Taking about the distance velocity on the other hand is using something they can be measured pretty precisely from the redshift. And you know that if object B had twice the velocity of object A then it is twice as far away even if you don't know the actual distances.

Since distances depend on the Hubble parameter then, especially back when it was only known to be in the range 50-100 km/s/Mpc there wasn't a great deal of point in reporting distances: to compare distances between two papers you'd have to convert them to velocities using whatever value of the Hubble parameter each paper used, since there is no guarantee they'd use the same value.

Answer 2

Hubble's law will convert the velocity to a proper (as opposed to co-moving) distance for you; indeed Wikipedia states one form of Hubble's law as:

"... the observation ... that ... Objects observed in deep space (extragalactic space, 10 megaparsecs (Mpc) or more) are found to have a Doppler shift interpretable as relative velocity away from Earth"

This law comes from the FLRW metric in the special case when the the standard $\Lambda{\rm CDM}$ cosmological equation of state prevails, and is also, of course, confirmed by observations first made by Edwin Hubble (but formerly theoretically predicted by Georges Lemâitre and contemporary theoreticians).