  The Tayler-Spruit dynamo mechanism has been proposed two decades ago as a
plausible mechanism to transport angular momentum in radiative stellar layers.
Direct numerical simulations are still needed to understand its trigger
conditions and the saturation mechanisms. The present study follows up on
(Petitdemange et al. 2023), where we reported the first numerical simulations
of a Tayler-Spruit dynamo cycle. Here we extend the explored parameter space to
assess in particular the influence of stratification on the dynamo solutions.
We also present numerical verification of theoretical assumptions made in
(Spruit 2002), which are instrumental in deriving the classical prescription
for angular momentum transport implemented in stellar evolution codes. A
simplified radiative layer is modeled numerically by considering the dynamics
of a stably-stratified, differentially rotating, magnetized fluid in a
spherical shell. Our simulations display a diversity of magnetic field
topologies and amplitudes depending on the flow parameters, including
hemispherical solutions. The Tayler-Spruit dynamos reported here are found to
satisfy magnetostrophic equilibrium and achieve efficient turbulent transport
of angular momentum, following Spruit's heuristic prediction.
