I have a galaxy 'A', say at redshift 1. Let's suppose this galaxy has no peculiar velocity. What would be the redshift of another galaxy 'B', that has a radial velocity of 500 km/s, relative to A?

All this in the standard (Planck) model.

Any tools to do get this easily (an python code, astropy?)


1 Answer 1


From eq. 10 in Hogg's classic paper, assuming that the peculiar velocity $v_\mathrm{pec} \ll c$: $$v_\mathrm{pec} = c \frac{z_\mathrm{obs} - z_\mathrm{cos}}{1 + z_\mathrm{cos}},$$ where $z_\mathrm{obs}$ is the observed redshift, and $z_\mathrm{cos}$ is the redshift from cosmological expansion only.

Let me invert that and wrap it up in Python for ya:

def zobs(vpec,zcos):
  c = 3e5
  return (1+zcos) * vpec/c + zcos
  • $\begingroup$ Thanks for the ref and the very complete answer! (and I corrected my typo thanks to you). $\endgroup$ Commented May 18, 2015 at 18:36
  • $\begingroup$ You very welcome @cbienpourtoi. I'll remove my first comment, then. $\endgroup$
    – pela
    Commented May 18, 2015 at 20:39

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