The key to finding the answer seems to involve processing data from astronomical databases, which I'm not sure how to do in this case. I'd prefer to limit the answer to the original list of approximately 1500 stars, but answers that rely on a list that contains stars with more recently acquired designations could be interesting to consider as well.
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1 Answer
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See important caveat to this answer below
At a distance of 2992 light years, Tau Canis Major is the furthest of the 1513 stars that have a Bayer designation, with several others almost equally distant. I computed the full list of Bayer-Sun distances: https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-bayer-distance.csv
Important Caveat
I used the HYG catalog at https://github.com/astronexus/HYG-Database but it may be inaccurate. In particular, Wikipedia gives Tau Canis Major's distance as 5,000 light years, although I couldn't find this number in the source provided (https://doi.org/10.1088/0067-0049/199/1/8), although I only skimmed.
The far from canonical https://www.universeguide.com/star/taucanismajoris notes that 2992.32 is a revised figure, down from 3197.68, but, of course, the figure may have been revised again.
Methodology
After downloading the HYG database file, this one liner creates bc-bayer-distance.csv:
zcat hygdata_v3.csv.gz | perl -F, -anle 'if ($F[9] < 100000 && length($F[27])>0) {$F[9] *= 3.26156; print "$F[9], $F[27] $F[29]"}' | sort -nr | tee bc-bayer-distance.csv
A brief explanation:
The 9th field (starting our count with 0 as Perl does) is the distance, but there's a note on the HYG git page: "A value >= 10000000 indicates missing or dubious (e.g., negative) parallax data in Hipparcos". It turns out the actual number is 100,000 (I've submitted a correction), so we ignore distances greater than 100,000.
The distance is in parsecs, so I multiply by 3.26156 to convert to light years.
The 27th field is the stars Bayer letter designation without the constellation. If it's empty, we ignore the star.
The 29th field is the stars constellation name, which, combined with 27th field, yields the Bayer designation.
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$\begingroup$ Surely any answer should be based on Gaia DR2. There is also the issue of uncertainty on the parallax. The object with the smallest parallax is not necessarily even the most likely most distant source. $\endgroup$– ProfRobSep 11, 2018 at 22:36
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$\begingroup$ @RobJeffries, the OP asked only for stars with a Bayer designation, not all known stars (another similar question has been edited a few times, but I think this one's been fairly constant) $\endgroup$– user21Sep 12, 2018 at 0:06
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1$\begingroup$ The point is that you are not using accurate parallaxes, so though it is interesting methodology, I doubt the answer is correct. According to the revised Hipparcos catalogue the parallax of Tau CMa is $1.09 \pm 0.59$ mas, so its distance is essentially unconstrained at the upper end. Unfortunately, it appears to be absent in DR2 and this might be the case for many other bright stars. $\endgroup$– ProfRobSep 12, 2018 at 7:16
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$\begingroup$ @RobJeffries So you are saying github.com/astronexus/HYG-Database isn't a reliable source because the technique it uses to compute distance is flawed? Would you agree this the best possible answer given what we know, or do you feel there's a better answer? heasarc.gsfc.nasa.gov/w3browse/all/hipparcos.html states "Parallax: The trigonometric parallax pi in units of milliarcseconds: thus to calculate the distance D in parsecs, D = 1000/pi". Of course, that doesn't mean the distance is accurate, but at least NASA notes it CAN be used for distance calculations. $\endgroup$– user21Sep 12, 2018 at 17:11