How full of galaxies is the sky?

kw: references, galaxies, astronomy

This is just a quick reference note, to bring together a few useful quantities. I began to wonder just how many galaxies there might be in each square arc-minute or arc-second of the sky. I was surprised at the result.

First, the entire sky contains 4 x pi x (180/pi)² = 41,252.96 square degrees. This comes to 148.51 million square arc-minutes or 534.62 billion square arc-seconds.  The best resolution under "good seeing" with a ground-based telescope, and not enhanced with wavefront correction technology, is about one arc second. Thus, just recording and managing those half a trillion "sky pixels" is a big job already. The Hubble Space Telescope has a resolution in blue light of 0.05 arc-sec, so its potential number of "sky pixels" is 400 times greater.

How well populated is the sky? The Atlas of the Universe contains these figures:

• Number of large galaxies in the visible universe: 350 billion.
• Number of dwarf galaxies (ditto): 7 trillion.

Thus, an average set of three one-square-second bits of sky must contain two large galaxies. Each square second must contain about 13 dwarf galaxies. It takes a long time to gather enough light to see them all, clear out to just over 13 billion light years, but there is a lot going on in every square arc-second!

How big will they appear? A typical dwarf galaxy of 1,000-light-year size, 13.4 billion light years away (right after the universe cleared up enough to see that far), has an angular diameter of 0.015 arc second. So even Hubble won't be able to do more than register its existence in a particular pixel. Back up to 13 billion light years, when larger galaxies were forming up, and a 100,000 light-year-sized galaxy would subtend 1.5 arc seconds. Hubble can see a little detail in such an object. We can expect, as wavefront correction improves for large, and multiple-instrument, ground-based telescopes, that clearer images of such faraway objects will be obtained.

It is going to take a while, however, for a multi-exabyte database of the sky to be gathered and curated. Astronomers have a never-ending subject to explore!