ROLLIN': Rotating globular cluster simulations II. The complex morphology of globular clusters driven by multi-scale dynamics
Globular clusters (GCs) are inherently non-spherical systems that in many cases show internal rotation. Typically, rotation is considered the main driver of GC morphology; however, the relationship between ellipticity and rotational support is not a simple one-to-one mapping, and other multi-scale dynamical processes may contribute. We investigate how morphology evolves in realistic models of rotating GCs, and how it correlates with key physical ingredients, including mass loss, stellar evolution, external tidal fields, and two-body relaxation. Using the \texttt{ROLLIN'} suite of direct N-body simulations, we measure the intrinsic ellipticity and triaxiality of our models using the second-moment tensor method, and explore their evolution and the physical mechanisms driving them. We find that early GC evolution can be dominated by dynamical instabilities driven by internal rotation and velocity anisotropy, leading to bar-like structures that rapidly erode due to collisional effects around the time of the first core collapse. These bars are stronger and longer-lived ($\lesssim 800,\mathrm{Myr}$) in strongly rotating clusters with longer relaxation times and subject to stellar evolution. In the long term, clusters evolve toward less flattened and gradually triaxial configurations, particularly when they experience stronger mass loss, are more tidally filling and isotropic, and have lower rotational support. Our models provide a physical explanation for the observational $V/\sigma$--ellipticity relation and demonstrate that morphology can serve as a reliable tracer of the dynamical state of GCs. Initially retrograde, dense, and inclined rotating models deviate from this relation, providing a physical explanation for observational outliers. This framework will aid the interpretation of GC evolution in upcoming large-scale photometric surveys.