# How to calculate radial velocity from redshift? [duplicate]

Ok, I know the question sounds silly, but please hear me out (at the very end it will probably still be silly though, albeit maybe differently).

I'm trying to create a visualization of the galactic web on different distances measured in v. In 2d and 3d. I'm using Hyperleda datatabase as the source of data - there are over 2.8 million galaxies with data on redshift. HyperLeda doesn't provide redshift per se, but it provides v, which is cz, so getting redshift is just a question of dividing it by the speed of light. This seems correct, highest one in the database is 7.019723.

The problem I encountered was when I tried to show distances on the visualizations - the radius of my universe was at over 2 times bigger then current estimations of the radius of the Observable Universe (30.3 billion parsecs compared to estimated.14.3 billion parsecs).

The problem seem to lie with the "v" (Mean Heliocentric radial velocity, in km/s) from Hyperleda, which I tried to use to estimate the distance in parsecs:

df['d_v_pc'] = (df['v'] / cosmo.H(0)) * 1000000


where cosmo.H(0)) is Hubble Constant, 69.32 km/Mpc s.

I noticed that the higest v in the data is 2,104,460.

At the same time, GN z11, galaxy with the higest redshift observed, has estimated helio radial velocity of 295,050 ± 119,917 km/s.

So some of the galaxies seem to be moving away over 7 times faster then GN-z11, which doesn't look very correct.

The question is, how can I (can I?) convert the current HyperLeda 'v' (cz) to actual helio radial velocity, that would be in the same order as the one of GN z11, and which I could in turn use to calculate distance? And why is there such a difference in those numbers?

• If you look it up in the NASA Extragalactic Database, you will find that GN-z11 has a "V (heliocentric)" of 3,324,699 km/s, which corresponds to z = 11.09. The "295,050" value you're quoting is simply wrong. Jan 2, 2022 at 9:27
• I realize that the Wiki article on GN-z11 has "295,050", with a link to a Simbad entry, so the error is in the Simbad entry; nonetheless, it's an error. Jan 2, 2022 at 9:31
• @PeterErwin I think the NED value is just $cz$, which isn't the recession velocity. I think $z=11$ should be around $2.5c$. Jan 2, 2022 at 10:13
• @ProfRob The question is about $cz$ values, not “recession velocities”. The point I was making is that GN-z11 does not have a “helio[centric] radial velocity” (i.e., $cz$) of “290,050 km/s”, despite what its Simbad entry says. Jan 2, 2022 at 14:17
• @PeterErwin I've checked other very distant objects, and you ar right, it must be a mistake. To compare: MACS1149-JD1: 2878008±59958 km/s EGSY8p7: 2,603,098 km/s EGS-zs8-1: 2,098,548 km/s GN-z11 has an invalid entry on Wikipedia. Jan 3, 2022 at 12:35