So I am not totally sure if they are hawks, eagles or falcons

Krugger said:

So I am not totally sure if they are hawks, eagles or falcons

Biggest difference has to do with their flying habits, though I do see a "toothed" part of the beak on Kaga's which is typically characteristic of falcons. (Still a damn big falcon though.)

Eh since the job is typically "falconer" and we can't expect all artists to be bird-of-prey experts I believe "falcon" will suffice.

I can't help but be concerned for Akagi's shoulder. That'll end up in hours in the bath if she's not careful around those talons.

[almost] hilarious in hindsight considering the result Taiyou....