I was checking the definition of 'galaxy flatennes' given in the catalogue of the axis ratios and defined in item c) of the data specifications as the ratio between M1/SQRT(M2*M3). Where does this definition come from? Is there any reference that supports it? For me it sounds a bit odd as in most cases is more common to use the ellipticity and the mass tensor in 2D projection, instead of the 3D mass tensor to quantify the flatenning of a galaxy.
Thanks in advance,
for this catalog we consider the 3D axis ratio rather than a 2D-based definition because any 2D axis ratio definition will depend on the viewing angle, so will not be unique for any given object. Here, since M1 is the smallest eigenvalue in 3D, the proposed definition is similar to the standard definition of "thickness", which is M1/M3. The M1/sqrt(M2M3) definition was used in Genel et al. (2015), and it serves to make triaxial or prolate systems less "flat" than perfectly round ones, or in other words: for a given thickness M1/M3, the smaller M2 is, the less "flat" the system will be considered. Except for very prolate systems where M1~M2<<M3, the two quantities M1/M3 and M1/sqrt(M2M3) are not very different from one another.
I see, now it is crystal clear. Thanks very much for the clarification.