Converting Redshift to distance
I was trying to work out the relationship of Z to distance in light years, and if my rough calculation is right with a value of z=0.866 this galaxy is something like 7.25 Billion light years away.
Am I in the ballpark?
Ah, distances in the real universe! 😃
Our current, best, models of the universe have it ruled by General Relativity (GR). And the geometry of such a universe is strange indeed.
For example, there is no longer a single 'distance', as there is in the Euclidean geometry we were taught at school, but many different ones.
Ned Wright has an excellent tutorial on this topic, as well as a very useful online calculator (CosmoCalc; there are links to his tutorial on the CosmoCalc page). You can plug whatever parameters of a GR-based cosmological model you want into the calculator (and the default values are, helpfully, the ones currently accepted as 'the best'). Doing so gives me:
- a light travel time of 7.233 Gpc (giga-parsecs; a parsec is ~3.26 light-years)
- a 'comoving radial distance' of 3.0 Gpc (9.8 Gly)
- an 'angular size distance' of 1.61 Gpc (5.25 Gly)
- a 'luminosity distance' of 5.6 Gpc (18.28 Gly)
The last one is, as far as I can see, the one usually meant, when you see 'distance' in the popular press. However, for estimating the distance between the lobes of a doublelobe source, you need to use the 'angular size distance'. And for that, CosmoCalc helpfully gives a "scale", 7.806 kpc per arcsec in this case.
Hope this helps (ain't astronomy fascinating!).