Magnetic inhibition of centrifugal instability

Recently, it was shown that the centrifugal instability may be important in the dynamics of astrophysical jets undergoing reconfinement by external pressure. However, these studies were limited to the case of unmagnetized flows. Here, we explore the role of the magnetic field within both the Newtonian and relativistic frameworks. Since the jet problem is rather complicated, we focus instead on the simpler problem of cylindrical rotation and axial magnetic field, which shares significant similarity with the jet problem, and consider only axisymmetric perturbations. The studied equilibrium configurations involve a cylindrical interface and they are stable to non-magnetic centrifugal and magnetorotational instabilities everywhere except this interface. We use a heuristic approach to derive the local stability criterion for the interface in the magnetic case and numerical simulations to verify the role of the magnetic field. The theory and simulations agree quite well for Newtonian models but indicate a potential discrepancy for the relativistic models in the limit of high Lorentz factor of the rotational motion at the interface. In general, the magnetic field sets a critical wavelength below which the centrifugal modes are stabilized. We discuss the implication of our findings for the astrophysical jets, which suggest that the centrifugal instability develops only in jets with relatively low magnetization. Namely, the magnetic pressure has to be below the thermal one and for the relativistic case the jets have to be kinetic-energy dominated.