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Based on this answer, I should be able to figure out this question, if I know the distance between Betelgeuse and its nearest neighbor. So what is Betelgeuse's nearest neighbor?

I do mean the nearest neighbor in 3D space, not in the plane of the sky. Since Betelgeuse is fairly close to the Sun, I'm guessing we should know its neighborhood with a pretty good precision.

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    $\begingroup$ On the other hand, Betelgeuse is very bright which might hide faint stars in the glare. I'd suggest doing a query on the Gaia archive for stars located nearby in the sky then use RA/Dec/parallax to calculate the 3D positions. I wouldn't be surprised if Betelgeuse itself is missing because it's too bright for Gaia to measure so you may need to resort to Hipparcos2 for that. $\endgroup$ – antispinwards Feb 27 at 8:44
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    $\begingroup$ The star closest was of course Michael Keaton $\endgroup$ – uhoh Feb 27 at 8:58
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    $\begingroup$ Note that the margin of error for star distances (including Betelgeuse) is quite large. Wikipedia's page discusses several estimates, but a recent value is 720 lyr with an error range of about $\pm$120 lyr. So distances to the nearest star to Betelgeuse are probably meaningless calculations as the margins of error will be huge. $\endgroup$ – StephenG Feb 27 at 12:14
  • $\begingroup$ I'd suggest using GAIA DR 2 instead of a smaller catalog. The answer will still be inaccurate, but it'll be inaccurate from a larger selection of stars. $\endgroup$ – user21 Feb 27 at 15:34
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    $\begingroup$ Betelgeuse is too bright for Gaia. However if you can get coordinates for Betelguese is should be possible to search the area around it for stars in the Gaia catalogue. $\endgroup$ – Steve Linton Feb 27 at 18:30
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$$ \begin{array}{|c|c|c|} \hline \textbf{Star} & \textbf{Magnitude} & \textbf{Distance (ly)} \\ \hline \text{Betelgeuse} & \text{0.45} & \text{0.00} \\ \hline \text{HIP27648} & \text{8.24} & \text{17.82} \\ \hline \text{HIP28478} & \text{8.42} & \text{19.03} \\ \hline \text{HIP27573} & \text{7.41} & \text{24.27} \\ \hline \text{HIP28175} & \text{9.1} & \text{39.34} \\ \hline \text{HIP26887} & \text{7.28} & \text{39.34} \\ \hline \text{HIP29261} & \text{7.66} & \text{41.42} \\ \hline \text{HIP26914} & \text{9.6} & \text{41.87} \\ \hline \text{HIP27513} & \text{8.28} & \text{42.65} \\ \hline \text{HIP27386} & \text{5.26} & \text{44.20} \\ \hline \text{HIP28261} & \text{8.45} & \text{46.08} \\ \hline \text{HIP28686} & \text{6.09} & \text{46.73} \\ \hline \text{HIP27004} & \text{7.89} & \text{47.16} \\ \hline \text{HIP29537} & \text{7.82} & \text{49.28} \\ \hline \text{HIP27324} & \text{9.22} & \text{49.88} \\ \hline \text{HIP27932} & \text{8.26} & \text{50.41} \\ \hline \text{HIP29868} & \text{8.92} & \text{50.69} \\ \hline \text{HIP28397} & \text{8.24} & \text{50.95} \\ \hline \text{HIP29236} & \text{6.57} & \text{52.93} \\ \hline \text{HIP27902} & \text{6.3} & \text{52.98} \\ \hline \text{HIP28232} & \text{6.22} & \text{54.81} \\ \hline \text{HIP27315} & \text{7.14} & \text{55.28} \\ \hline \text{HIP27751} & \text{6.9} & \text{55.37} \\ \hline \text{HIP30124} & \text{9.75} & \text{56.46} \\ \hline \text{HIP29685} & \text{7.69} & \text{56.79} \\ \hline \text{HIP27412} & \text{9.31} & \text{58.80} \\ \hline \text{HIP27153} & \text{7.46} & \text{60.13} \\ \hline \text{HIP28202} & \text{7.97} & \text{60.42} \\ \hline \text{HIP27919} & \text{7.15} & \text{60.85} \\ \hline \text{HIP28056} & \text{7.17} & \text{60.89} \\ \hline \text{HIP29381} & \text{8.88} & \text{61.26} \\ \hline \text{HIP26986} & \text{9.17} & \text{61.26} \\ \hline \text{HIP29630} & \text{8.15} & \text{62.56} \\ \hline \text{HIP29590} & \text{7.82} & \text{64.37} \\ \hline \text{HIP30120} & \text{6.76} & \text{64.57} \\ \hline \text{HIP26795} & \text{6.82} & \text{66.03} \\ \hline \text{HIP26655} & \text{7.09} & \text{66.99} \\ \hline \text{HIP26615} & \text{9.13} & \text{67.50} \\ \hline \text{HIP27895} & \text{7.04} & \text{68.80} \\ \hline \text{HIP27309} & \text{9.7} & \text{69.04} \\ \hline \text{HIP28323} & \text{8.16} & \text{69.12} \\ \hline \text{HIP28171} & \text{8.68} & \text{69.91} \\ \hline \text{HIP25767} & \text{8.93} & \text{70.26} \\ \hline \text{HIP25698} & \text{8.74} & \text{70.31} \\ \hline \text{HIP26107} & \text{7.83} & \text{71.05} \\ \hline \text{NuOri} & \text{4.42} & \text{72.70} \\ \hline \text{HIP27284} & \text{8.72} & \text{73.29} \\ \hline \text{HIP27968} & \text{8.42} & \text{73.36} \\ \hline \text{HIP29599} & \text{7.96} & \text{73.41} \\ \hline \text{HIP25424} & \text{8.63} & \text{73.44} \\ \hline \end{array} $$

Subject to important caveats below, the table above lists the 50 stars closest to Betelguese including Betelguese itself:

I'm hoping to get a "better" list by using GAIA DR2 data, and will amend this answer when I do. Of course, while GAIA DR2 lists more stars, the distance measurements can be even further off.

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    $\begingroup$ As you say - no error bars. The biggest caveat is it appears to only include stars down to about V=10; given the distance to Betelgeuse then this means it only includes the most luminous ~10% of stars in that volume. Nice though. $\endgroup$ – Rob Jeffries Mar 4 at 22:16
  • $\begingroup$ @RobJeffries To be fair, I did disclaim that I'm using the HYG catalog and so all the limits for that catalog apply. And I agree using HYG is not ideal, working on a "better" solution, but distance estimates are always an issue at that range. $\endgroup$ – user21 Mar 5 at 17:25
  • $\begingroup$ Beetlejice has a bacon number of 2! Please call your webapp six degrees of Betelguese. $\endgroup$ – uhoh Mar 6 at 3:54
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Barry Carter's nice piece of work contains 50 stars within $\sim 74$ light years of Betelegeuse.

Leaving aside the question marks over exactly where Betelegeuse is (in terms of distance) and the parallax uncertainties of the 50 stars listed, there is also the problem that the faintest stars in the HYG catalogue are based on the Hipparcos catalogue, which is only complete to something like 8th magnitude, though it does contain some stars down to about 10th mag. If we assume that Betelgeuse is at around 700 light years (214 pc), then a magnitude of 10, corresponds to an absolute magnitude of about 3.3. These stars are very luminous indeed, about 3 times as luminous as the Sun or more, so either upper main sequence stars are giants.

Upper main sequence stars and giants form a tiny fraction of the local stellar population (and one presumes the locale around Betelgeuse since it is only 30 pc below the Galactic plane) - see for example this plot from Jeffries & Elliott (2003), which shows an absolute magnitude vs colour (HR) diagram for 1000 stars within $\sim 15$ pc of the Sun. As you can see, objects with $M_V<3.3$ are rare, perhaps $\sim 2$% of the population.

Local HRD

So the point of this is, that assuming Betelegeuse isn't sitting in a void, or in a cluster (which as far as we know, it isn't) then the stellar density around it is at least (and I say at least, because there is no way that the catalogue I used to produce the picture above is complete beyond spectral type M3-M4) is at least 0.07 stars per cubic parsec, or 0.002 stars per cubic light year.

If that is the case, then there should be at least 3400 stars within 74 light years of Betelgeuse and finally (the whole point of this "answer"), the nearest star to Betelgeuse is likely to be separated from it by $1/(0.002)^{1/3} = 7.9$ light years.

Unfortunately, it is an "answer" because we are no closer to knowing which star that is! Gaia DR2 (and DR3 later in 2020) would help in completing the census, since it has (or will have) parallaxes for stars down to about $V\sim 19$ (absolute magnitude of about 12.3 at the distance of Betelgeuse) and should then include about 60-70% of stars in its vicinity. However, Gaia will not (I think) yield an accurate parallax for Betelgeuse because it is too bright(!), so we will be no further forward in answering the question.

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  • $\begingroup$ And for all we know there's some star sitting a few light years directly behind Betelgeuse so we can't (currently) see it. $\endgroup$ – PM 2Ring Mar 5 at 20:13
  • $\begingroup$ I've actually done some work on this that I haven't published here yet: youtube.com/watch?v=jAHUaQKkcy4 (but I go way off topic many times, so this isn't really great-- I hope to publish a clean answer from it soon) $\endgroup$ – user21 Mar 7 at 4:38

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