Inverse cascade of hybrid helicity in $B\mathrm{\Omega }$-MHD turbulence

We investigate the impact of a solid-body rotation ${\mathrm{\Omega }}_0$ on the large-scale dynamics of an incompressible magnetohydrodynamic turbulent flow in presence of a background magnetic field ${\mathbf{B}}_{\mathbf{0}}$ and at low Rossby number. Three-dimensional direct numerical simulations are performed in a periodic box, at unit magnetic Prandtl number and with a forcing at intermediate wavenumber $k_f=20$. When ${\mathrm{\Omega }}_0$ is aligned with ${\mathbf{B}}_{\mathbf{0}}$ (i.e. $\theta \equiv \widehat{\left(\Omega_{0}, \bf B_0 \right)} = 0$), inverse transfer is found for the magnetic spectrum at $k<k_f$. This transfer is stronger when the forcing excites preferentially right-handed (rather than left-handed) fluctuations; it is smaller when $\theta >0$ and becomes weak when $\theta \ge 35^o$. These properties are understood as the consequence of an inverse cascade of hybrid helicity which is an inviscid/ideal invariant of this system when $\theta =0$. Hybrid helicity emerges, therefore, as a key element for understanding rotating dynamos. Implication of these findings on the origin of the alignment of the magnetic dipole with the rotation axis in planets and stars is discussed.