We use the low surface brightness galaxy (LSBG) samples created from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP, 781 galaxies), the Dark Energy Survey (DES, 20977 galaxies), and the Legacy Survey (selected via HI detection in the Arecibo Legacy Fast ALFA Survey, 188 galaxies) to infer the intrinsic shape distribution of the low surface brightness galaxy population. To take into account the effect of the surface brightness cuts employed when constructing LSBG samples, we simultaneously model both the projected ellipticity and the apparent surface brightness in our shape inference. We find that the LSBG samples are well-characterized by oblate spheroids, with no significant difference between red and blue LSBGs. This inferred shape distribution is in good agreement with similar inferences made for ultra-diffuse cluster galaxy samples, indicating that environment does not play a key role in determining the intrinsic shape of low surface brightness galaxies. We also find some evidence that LSBGs are more thickened than similarly massive high surface brightness dwarfs. We compare our results to intrinsic shape measures from contemporary cosmological simulations, and find that the observed LSBG intrinsic shapes place considerable constraints on the formation path of such galaxies. In particular, LSBG production via the migration of star formation to large radii produces intrinsic shapes in good agreement with our observational findings.
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