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(Abridged) We investigate the intrinsic shapes of low-luminosity galaxies inthe central 300 kpc of the Virgo cluster using deep imaging obtained as part ofthe NGVS. We build a sample of nearly 300 red-sequence cluster members in theyet unexplored $-14 < M_{g} < -8$ magnitude range. The observed distribution ofapparent axis ratios is then fit by families of triaxial models withnormally-distributed intrinsic ellipticities and triaxialities. We develop aBayesian framework to explore the posterior distribution of the modelparameters, which allows us to work directly on discrete data, and to accountfor individual, surface brightness-dependent axis ratio uncertainties. For thispopulation we infer a mean intrinsic ellipticity E=0.43, and a mean triaxialityT=0.16. This implies that faint Virgo galaxies are best described as a familyof thick, nearly oblate spheroids with mean intrinsic axis ratios 1:0.94:0.57.We additionally attempt a study of the intrinsic shapes of Local Groupsatellites of similar luminosities. For the LG population we infer a slightlylarger mean intrinsic ellipticity E=0.51, and the paucity of objects with roundapparent shapes translates into more triaxial mean shapes, 1:0.76:0.49. Wefinally compare the intrinsic shapes of NGVS low-mass galaxies with samples ofmore massive quiescent systems, and with field, star-forming galaxies ofsimilar luminosities. We find that the intrinsic flattening in thislow-luminosity regime is almost independent of the environment in which thegalaxy resides--but there is a hint that objects may be slightly rounder indenser environments. The comparable flattening distributions of low-luminositygalaxies that have experienced very different degrees of environmental effectssuggests that internal processes are the main drivers of galaxy structure atlow masses--with external mechanisms playing a secondary role.

astrophysical journal/the astrophysical journal

The Next Generation Virgo Cluster Survey. VII. The intrinsic shapes of  low-luminosity galaxies in the core of the Virgo cluster, and a comparison  with the Local Group