The M4 Transition: Toward a comprehensive understanding of the transition into the fully convective regime

The difference in stellar structure above and below spectral type ~M4 is expected to be a very important one, connected directly or indirectly to a variety of observational phenomena in cool stars---such as rotation, activity, magnetic field generation and topology, timescales for evolution of these, and even the basic mass-radius relationship. In this Cool Stars XVI Splinter Session, we aimed to use the M4 transition as an opportunity for discussion about the interiors of low-mass stars and the mechanisms which determine their fundamental properties. By the conclusion of the session, several key points were elucidated. Although M dwarfs exhibit significant changes across the fully convective boundary, this "M4 transition" is not observationally sharp or discrete. Instead, the properties of M dwarfs (i.e. radius, effective temperature, rotation, activity lifetime, magnetic field strength and topology) show smooth changes across M3--M6 spectral types. In addition, a wide range of stellar masses share similar spectral types around the fully convective transition. There appears to be a second transition at M6--M8 spectral types, below which there exists a clear dichotomy of magnetic field topologies. Finally, we used the information and ideas presented in the session to construct a framework for how the structure of an M dwarf star, born with specific mass and chemical composition, responds to the presence of its magnetic field, itself driven by a feedback process that links the star's rotation, interior structure, and field topology.