Let us remind you that, although it may seem that the information we provide you is enough to make a classification of elliptical and spiral galaxies by observing only their spectra, the reality is that this problem is part of a very broad reserch field with many unknowns still unsolved today. Although we have approximations and descriptions that are close to the general case, let us not forget that there are always exceptions, which, many times, turn out to be the most interesting cases to study.
There’s still a long way to go, but the view from where we are is already beginning to take shape. Would you like to help forge this path?