By inverting the distributions of galaxies ’ apparent ellipticities and misalignment angles ( measured around the projected half-light radius R _ { e } ) between their photometric and kinematic axes , we study the intrinsic shape distribution of 189 slow rotator early-type galaxies with stellar masses 2 \times 10 ^ { 11 } M _ { \odot } < M _ { \ast } < 2 \times 10 ^ { 12 } M _ { \odot } , extracted from a sample of about 2200 galaxies with integral-field stellar kinematics from the DR14 of the SDSS-IV MaNGA IFU survey .
Thanks to the large sample of slow rotators , Graham+18 showed that there is clear structure in the misalignment angle distribution , with two peaks at both 0 ^ { \circ } and 90 ^ { \circ } misalignment ( characteristic of oblate and prolate rotation respectively ) .
Here we invert the observed distribution from Graham+18 .
The large sample allows us to go beyond the known fact that slow rotators are weakly triaxial and to place useful constraints on their intrinsic triaxiality distribution ( around 1 R _ { e } ) for the first time .
The shape inversion is generally non-unique .
However , we find that , for a wide set of model assumptions , the observed distribution clearly requires a dominant triaxial-oblate population .
For some of our models , the data suggest a hint for a minor triaxial-prolate population , but a dominant prolate population is ruled out .