Beyond the Tayler instability: A new global instability of toroidal magnetic fields in stars
Stellar toroidal magnetic fields are known to be unstable to the Tayler instability. Here we demonstrate the existence of a complementary current-driven instability of essentially arbitrary toroidal-field configurations in stably stratified nonrotating stars with the following properties: (i) in ideal magneto-hydrodynamics, it grows on the Alfvén timescale $τ_{\rm A}$; (ii) under certain conditions, it may reveal itself by driving shellular differential rotation about an arbitrary axis perpendicular to the magnetic-field symmetry axis; (iii) it is large-scale in the angular directions $θ$ and $φ$, and develops at radial wave-numbers $k \lesssim \mathcal{N}τ_{\rm A}/R$, where $\mathcal{N}$ is the Brunt-Väisälä frequency and $R$ is the stellar radius. Thus, unlike the Tayler instability, the proposed instability is intrinsically global. Consequently, it may be less susceptible to dissipative suppression than the Tayler instability and can prevail over it in some regimes. This instability may have broad implications for magnetic field generation in stars and could modify scenarios of magnetic field amplification within the Tayler-Spruit dynamo, contributing to models of efficient angular-momentum transport and chemical mixing in stellar interiors.