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We model the projected b/a-log a distributions of CANDELS main sequencestar-forming galaxies, where a (b) is the semi-major (semi-minor) axis of thegalaxy images. We find that smaller-a galaxies are rounder at all stellarmasses M and redshifts, so we include a when analyzing b/a distributions.Approximating intrinsic shapes of the galaxies as triaxial ellipsoids andassuming a multivariate normal distribution of galaxy size and two shapeparameters, we construct their intrinsic shape and size distributions to obtainthe fractions of prolate, oblate and spheroidal galaxies in each redshift andmass bin. We find that galaxies tend to be prolate at low m and high redshifts,and oblate at high M and low redshifts, qualitatively consistent with van derWel et al. (2014), implying that galaxies tend to evolve from prolate tooblate. These results are consistent with the predictions from simulations(Ceverino et al. 2015, Tomassetti et al. 2016) that the transition from prolateto oblate is caused by a compaction event at a characteristic mass range,making the galaxy center baryon dominated. We give probabilities of a galaxy'sbeing prolate, oblate or spheroidal as a function of its M, redshift, projectedb/a and a, which can facilitate target selections of galaxies with specificshapes at hight redshifts. We also give predicted optical depths of galaxies,which are qualitatively consistent with the expected correlation that AV shouldbe higher for edge-on disk galaxies in each log a slice at low redshift andhigh mass bins.

The evolution of galaxy shapes in CANDELS: from prolate to oblate