What is the distance between solar system and a distant galaxy

When we say a galaxy is 300 million light-years away, is that its distance now or 300 million years ago?

• People use cosmological distances differently, so you can't really be sure. Some use the current distance, while some use the light travel time, multiplied by the speed of light. But this doesn't really have anything to do with dark matter halos, so you probably need to clarify why you think the two are connected.
– pela
Jul 26, 2021 at 7:42

When you consider an expanding universe, the meaning of "distance" becomes difficult, and different reporters use different definitions.

In many newspapers the distance used is the "light travel time distance". This is the time that light has been travelling from the galaxy multiplied by the speed of light. So a galaxy that is 300 million light-years away means that light from the galaxy left the galaxy 300 million years ago.

But a better measure is the "co-moving distance". A galaxy that is 300 million light-years away in the co-moving distance would mean that you could fit 300 million 1-lightyear rulers between you and the galaxy.

Locally these two definitions give the same value, but for galaxies they give slightly different values. A galaxy that has a light travel distance of 300 million light years would have a co-moving distance of 304 million light years. So for a galaxy that is nearby (!!) the difference isn't very significant, it is less than the uncertainty in measurement. For more distant galaxies it becomes greater. A 7.8 billion ly light-travel-time galaxy has a co-moving distance of 10.9 billion light-years.

There are other measures of distance: The redshift (not a distance, but it can be used to infer distance), the luminosity distance and the angular scale distance. Again, these are all equal for nearby galaxies, but diverge for distant ones. In a carefully written report you would expect the type of distance to be mentioned, if it is significant. But sometimes you just have to guess.

• +1, but I'd argue that the interesting quantity is the physical distance (which is what you'd measure if you froze the Universe and started laying out meter sticks). By definition this corresponds to the comoving distance today, but not tomorrow…
– pela
Jul 27, 2021 at 6:59