But I'm not sure if I actually understand why the galaxy mass "rotate as a whole" instead of "swirling" like the disc of a forming planetary system.
Trying to understand it I imagined a given object in the border of the visible portion of a disc galaxy, the 2nd part of the shell theorem cancels the gravitational effect of the DM further from the center, but the extra inner mass increases the speed of rotation of this object. Then a closer object, with higher rotation speed due to visible matter mass, again by the shell theorem ignore some of the DM affecting the first object. Thus the inner DM mass increases its speed a bit less. And so subsequently with objects closer to the center.
Is this idea correct?
Excuse the plainness of my question and thanks for your help in advance. Best regards!