# Comoving vs. proper RE: TC08

in TC08 – the gas radius is Rg=80 comoving h^-1 kpc

but we need to make sure this is a proper radius.

a SMALL comoving distance \delta D_c is the distance between two nearby objects in the Universe that is time invariant (moving with the hubble flow). i.e it is the distance between them which would be measured with rulers at the time they are being observed (proper motion,D_p) divided by the ratio of the scale factor of the Universe

i.e. \dektaD_c = D_p *(1+z) where z is the redshift at which these two nearby objects are located.

this works because we’re talking SMALL comoving distances, if you look at large comoving distances you must integrate over all the contributions between the each.

I argue that since our 80 kpc is a very SMALL comoving distance with respect to the distances at which we’re observing (z mostly >0.4), then we can simply apply the formula above, DIVIDE by the scaling (1+z_abs).

this is backed up also by the fact that we treat any absorption through the gaseous cloud to be all at one redshift, even though it is most likely happening at all peculiar velocities during its path through gaseous cloud.

(see Hogg 2000, arXiv:9905116v4)