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The smallest observed spiral galaxies I can find are NGC 2976 and NGC 4605, both with a diameter of 20 kly, but I don't have anything like an exhaustive source to search. I've also found a mention that the Small Magellanic Cloud (7 kly diameter) might have had more spiral structure before it was distorted by the Milky Way.

From looking at these galaxies, spiral structure seems to be less clear the smaller the galaxy is, which makes me think there might not be a clear lower limit. Still, I'm curious how small a galaxy with recognizable spiral structure could be, either based on observations or theory.

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    $\begingroup$ NGC 6503 is only ~15 klyr across… $\endgroup$
    – pela
    Commented Mar 10, 2020 at 9:57
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    $\begingroup$ memeguy.com/photos/images/… $\endgroup$
    – userLTK
    Commented Mar 10, 2020 at 12:11
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    $\begingroup$ en.wikipedia.org/wiki/Dwarf_spiral_galaxy 5kly, think this is what you were looking for. $\endgroup$
    – Dkcash413
    Commented Apr 11, 2020 at 22:35
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    $\begingroup$ Dkcash413 - The size mentioned in that article is 5 kpc, not 5 "kly". $\endgroup$
    – Peter Erwin
    Commented Apr 12, 2020 at 9:56
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    $\begingroup$ @adrianmcmenamin Am I right in guessing the answer might be that we don't know because models are lacking and small galaxies are hard enough to image that we maybe just wouldn't find tiny spirals if they existed? $\endgroup$
    – Elukka
    Commented Apr 28, 2020 at 19:14

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The first Google-hits suggest that Segue 2 is the smallest spiral galaxy, but that is actually incorrect since it is the smallest spherical galaxy yet discovered. It has a radius of roughly 34 parsec or 110 light years. The original publication on that topic dates back to 2013, but it was again in the news in April 2020.

Then, there are lecture notes on a course Astronomy 626 Galaxies which shows the following diagram:

Radius vs. mass for galaxies

Also, the lecture notes claim:

Typical values for the scale length [of spiral glaxies] are: $1 {\rm kpc} < h_R < 10 {\rm kpc}$

I agree that this does not answer your question fully, but I got the impression that the lower bound should be around $1 {\rm kpc}$.

References

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    $\begingroup$ @ConnorGarcia I did not manage to figure out how to deduce a lower bound for the size of a spiral galaxy using the TFR, but I updated my question so that it hopefully deserves less downvotes. $\endgroup$
    – B--rian
    Commented Feb 10, 2021 at 10:57
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    $\begingroup$ The (baryonic) T-F relation applies to spiral and irregular galaxies; since the latter tend to be smaller than spirals, the T-F relation cannot reliably be used to estimate lower limits for spiral galaxies. $\endgroup$
    – Peter Erwin
    Commented Feb 10, 2021 at 11:48

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