High Redshift

Light travel time distance is simply the time it took the light to travel from the object to us. It is easily determined from the object’s redshift and applying a few assumptions such as the value of Hubble’s constant (rate the universe is expanding), the Omega value, the age of the universe and if the universe is flat or not. I’m assuming the values determined by the 5-year WMAP data as that was the latest available when I started annotating images. Since then Hubble, Plank and others have come up with later values. These have more effect at high redshift values (z). Because of this I later started adding z to the annotated images for high redshift objects, mostly quasars. That way those interested can use any of several online calculators to determine the distance using their favorite values for these factors.

During this time the light has traveled to us universe has expanded. The light had to travel through this expanding universe to reach us. For “nearby” galaxies this added distance isn’t significant, usually less than the error bar of the light travel time itself. But for more distant objects this can become significant, especially with distant galaxy clusters and quasars. Because of this I now include the actual redshift value, “z”. Redshift look back time is rather meaningless at these distances but the z value isn’t bothered by the issues that hinder look back time distances.

For instance, a quasar with a light travel time distance of 7.785 billion light-years would have a z value of 1 using 5-year WMAP factors. During the nearly 8 billion years the light was traveling to us the expansion of the universe has been at work. When you do the math the quasar was 5.45 billion light-years distant when the light left it. It had to travel over 2 billion light-years more than the true distance to reach us but we see it as it was when 5.45 billion light-years away. Of course, thanks to this expansion the galaxy is now further away than even the light-travel time. The further you are from us the faster the expansion. Thus, the universe between us and the quasar expanded slower than the quasar itself moved from us as that speed kept increasing while the part of the universe the light passed through slower the closer it got to us. The math gets a bit complicated but that quasar would “now” be 10.9 billion light-years distant. Though in a relativistic universe there is no “now”. This just assumes you could freeze the universe and time then lay out a tape measure to find its distance.

Things get even more interesting with larger values of z. At z=2 the quasar was 5.74 billion light-years distant and the light travel time was 10.4 billion years. The light needed nearly 5 billion years longer than its “distance” to travel through the expanding universe yet the distance to either when the light left it was rather similar. The reason is, in the second case the universe was only 3.37 billion years old whereas the z=1 quasar is seen in a much older universe, one just under 6 billion years old. The universe was much smaller when the light left the z=2 object than when it left the z=1 object.

Things get really strange when you consider the z=2 quasar’s “current” distance. That turns out to be over 17.2 billion light-years. Yes, it is beyond the observable edge of the universe. During the 10.4 billion years the light took to reach us the quasar (if it still exists) moved from a distance of 5.74 billion light-years to 17.2. So it covered 11.46 billion light-years in 10.4 billion years. That means, on average, the distance increased faster than the speed of light. This does NOT violate Einstein’s rule that you can’t travel through the universe faster than the speed of light. This because it’s the universe itself that’s expanding, nothing is moving through the universe faster than the speed of light. “Through” is the key here. We didn’t move through the universe we were carried along by its expansion. A very different thing that Einstein understood well but often gets lost in simple texts.

Things get even stranger when imaging something at a z of 3. Then the light travel time is 11.6 billion light-years though the quasar was only 5.3 billion light-years distant. Yes, closer than either z=1 or z=2 objects. This is due to imaging an even younger and smaller universe. When the light left the z=3 quasar the universe was only 2.2 billion years old so much smaller than today, at least the part we could see. At Z=4 (I’m yet to image an object this distant as my camera has little IR sensitivity needed for this distance) the light travel time is 12.2 billion years and the object only 4.8 billion light-years distant when the light left it. The James Webb telescope hopes to reach z=12. Such an object would need 13.4 billion years for the light to reach us when the universe was only 2.5 billion years old. Such an object would “now” be 33 billion light-years distant.

All this non-intuitive math is why the pros use z rather than light travel time for anything but the very nearby universe.