Q: Volume of the largest ellipsoid in space which contains no stars?

[Buzz Bloom]

TL;DR Summary

It seems plausible that astronomers must have found somewhere is space a largest volume which contains no stars. To make this question better defined, I suggest visualizing this volume to have the shape of an ellipsoid. I am interested in learning about this volume, primarily its size, and out of curiosity how far away from Earth it is. My reason for wanting to know the answer to the primary question is explained in the body of this post.

The answer to the primary question in the summary is the first step in seeking an answer to a more complicated question I plan to post in a separate thread later. This more complicated question is a consequence of the thread:

https://www.physicsforums.com/threads/qs-re-the-behavior-of-atoms-after-decoupling-completed.994581/ .​

An answering post which I received from @kimbyd pointed out that reionization would make the temperature of the H atom gas larger than the value I calculated for the current time: 0.002959 K.
Wikipedia gives a good explanation of the phenomenon, but no numerical values.

https://en.wikipedia.org/wiki/Ionization​

That is the more complicated question I want to pursue after I can get some help with respect to this thread.
How much would reionization increase the temperature of isolated H atom gas (or maybe H2 gas)?

 

[phyzguy]

We cannot see individual red dwarfs, which are the most common stars in the universe, at very great distances. A typical red dwarf has an absolute magnitude of +10, and the best telescopes can see objects down to about magnitude +28. If you work it out, we can see these stars out to a distance of about 40,000 parsecs, which is just outside our galaxy. So beyond that, these stars are invisible to us. So I think the answer to your question is that we don't know. Even the most empty voids that we see, which appear to be devoid of large galaxies, could have a sprinkling of small stars in them and we wouldn't be able to see them.

 

[jim mcnamara]

https://en.wikipedia.org/wiki/Stellar_kinematics - hypervelocity stars appear to have sufficient velocity to exit a galaxy.

Assume these stars were sling shot (slung shot?) out of their home galaxy 12 billion years ago - and they are still in the main sequence.

So, following up on @phyzguy nice point, it is not implausible to further assume these stars can penetrate into voids for some distance, adding a very sparse stellar cloud out a distance into the void. But we cannot detect them.

Checkout filaments and voids:
https://www.space.com/13336-universe-history-structure-evolution-infographic.html
Do a search on publications by Margaret Geller or maybe 'Sloan Great Wall'.

The primary point is that there is a limit to our understanding of these voids and filaments. When you look at graphics it seems clear that voids are not discrete simple structures, they squiggle and wiggle. And interconnect.

Voids seem to occupy a large percent of the observable universe. Which means we probably will not ever be able to see the full extent of a given void, if such a thing even makes sense.

Opinion --
Sometimes trying to describe or document the '-est' ( as in large-est, small-est ) of something is not very informative or maybe even not really sensible. Consider that your void size quest could possibly fall into this category.