How far away is that ancient galaxy?

Credit: NASA, ESA and P. Oesch (Yale University)
The news has been full of the remarkable discovery of galaxy GN-z11, which appears to have formed just 400 million years after the origins of the universe. Definitely 'A long time ago, in a galaxy far, far away.' But exactly how far? Unfortunately some of those reporting the news have been a little confused on the distance to the galaxy.

What do we actually know? We are seeing GN-z11 as it was around 400 million years after the Big Bang - so the light has taken 13.4 billion years to reach us. And it was discovered with a redshift of around z=11.1. (You can read the actual paper here.) That 'z' value represents the difference between the observed wavelength and the emitted wavelength divided by the emitted wavelength, so z=0 would mean there was no red shift at all.

Unfortunately, some of those reporting this went a step too far with headlines like this:

Here's a few more iffy remarks:
  • 'GN-z11 is a record-breaking 13.4 billion light years away...'
  • 'Located a record 13.4 billion light years from Earth...'
  • 'NASA's Hubble Space Telescope has discovered the most remote galaxy ever seen from Earth - 13.4 billion light years away.'
  • 'A galaxy 13.4 billion light years away has been spotted by the Hubble Space Telecope.'
It seems a reasonable idea. We've heard that the light has taken 13.4 billion years to reach us - so surely the galaxy is 13.4 billion light years away? Unfortunately, no - because the universe has not been sitting around doing nothing for the last 13.4 billion years. The point of that 11.1 value for z is that this galaxy is seriously red shifted, which means it is moving away from us at a heck of pace. While the light has been on its way, the universe has expanded massively, so this ancient galaxy is now far more than 13.4 billion light years away.

How far away? We don't know for certain. The calculation is messy. Luckily Edward Wright of UCLA has produced a calculator that will give us a feel for just how far away the galaxy is. The bad news is that there are several factors that have to be entered into the calculator, including an assumption about the nature of the curvature of the universe, Hubble's constant, which relates the redshift to the distance, and the proportion of matter and dark energy - the more dark energy, the faster the acceleration of the expansion. (I slightly over-simplify the model, but that's a fair picture.)

Plugging in what seem to be the best accepted current values into the calculator comes up with an approximate 'comoving radial distance', the most meaningful measure to call the distance to the galaxy, of around 31.8 billion light years - rather more than 13.4. Far, far away indeed.