cosmology - How far away must a galaxy be for its light never to reach us due to the expansion of the universe?

My understanding is that at the present rate of expansion of the universe some galaxies are growing more distant from us at such a rate that light from them will never reach us. My question is how far away a galaxy must be for this to be true of it.

Answer

In this paper by Gott et al., on p. 466 they define the "future visibility limit", saying in the published version that "No matter how long we wait, we will not be able to see farther than this", and on p. 7 of the arxiv preprint they similarly say "If we wait until the infinite future we will eventually be able to see the Big Bang at the co-moving future visibility limit. Stars and galaxies that lie beyond this co-moving future visibility limit are forever hidden from our view." The text under Fig. 1 on p. 467 of the paper (p. 43 of the arxiv preprint) gives the future visibility limit as 4.5 times the Hubble radius, mentioned on p. 465 (p. 7 or the preprint) to be 4220 Mpc, which is 13.76 billion light years. So if the future visibility limit is 4.5 times that, it should be about 62 billion light years, which matches with where the cosmological "event horizon" cone hits the "comoving distance" axis in the third diagram in fig. 1 in this paper by Davis and Lineweaver (the text underneath says that "Our event horizon is our past light cone at the end of time, $t = \infty$ in this case", so evidently this is the same as the future visibility limit).

Note that this may actually not be exactly what you're asking, because the diagram in the second paper indicates that the event horizon they're talking about is the comoving distance such that we will never see light emitted from that location at any point in time, even arbitrarily close to the Big Bang. (If you're not familiar with the term, comoving distance is defined so that an average pair of galaxies will have a fixed comoving distance, basically leaving out the expansion of space, and it's also defined so that the comoving distance to a galaxy at present is identical to its present proper distance, i.e. the distance that would be measured by a series of small rulers laid end-to-end at the present cosmological time.) You may have been asking instead about the comoving distance such that if light was emitted from that location now, it would never reach us. I don't have a paper that gives a precise number for this distance, but looking at where the event horizon (the past light cone of our location at $t=\infty$) intersects the "now" axis in the third diagram in Fig. 1 of Davis/Lineweaver paper, along with the pretty much identical diagram created by Pulsar that appears in Christoph's answer, if you use a drawing program to draw a straight line between the intersection point and the "comoving distance" axis, it appears the answer is very close to 16 billion light years.