\textit{Ab initio} calculated $M1$ observables: The role of symmetry, structure and selection rules*

Electromagnetic observables provide probes for nuclear structure. In particular, $M1$ observables provide information on angular momentum structure. We explore $M1$ observables in \textit{ab initio} no-core shell model (NCSM) predictions for light nuclei ($p$-shell). In order to understand how the predicted $M1$ moments and transition strengths relate to underlying structure of the nucleus, we study the contributions of the different components of the $M1$ operator (orbital and spin, broken into isoscalar and isovector parts). Each of these components is subject to different selection rules on angular momentum (orbital and spin), isospin and $\mathrm{SU}(3)$ quantum numbers. We use the Lanczos decomposition method to determine the dominant $LS$ and $\mathrm{SU}(3)$ contributions to the calculated wave functions and thus understand the relevant selection rules for each transition. We also study the convergence properties of NCSM calculations for $M1$ observables, including the role of symmetry, structure and selection rules.