  In addition to buoyancy- and magnetic tension-driven instabilities, magnetic
flux rings are also susceptible to an instability induced by the hydrodynamic
drag force. We investigate the influence of the toroidal shape and equilibrium
condition on the thresholds of the friction-induced instability and on their
relevance for emerging magnetic flux in solar-like stars. Analytical
instability criteria are derived for axial symmetric perturbations and for flux
rings in the equatorial plane by analysing the sequence of principal minors of
the coefficient matrices of dispersion polynomials. The general case of
non-equatorial flux rings is investigated numerically by considering flux tubes
in the solar overshoot region. The friction-induced instability occurs when an
eigenmode reverses its direction of propagation due to advection, typically
from the retrograde to the prograde direction. Since the reversal requires a
certain relative velocity difference between plasma inside the flux tube and
the environment, the instability criterion depends on the location and field
strength of the flux ring. The friction-induced instability sets in at lower
field strengths than buoyancy- and tension-driven instabilities. Its threshold
is independent of the strength of friction, but the growth rates depend on the
strength of the frictional coupling between flux tube and environment. The
friction-induced instability lowers the critical magnetic field strength beyond
which flux tubes are subject to growing perturbations. Whereas buoyancy- and
tension-driven instabilities depend on the magnetic field strength alone, the
dependence of hydrodynamic drag on the tube diameter gives rise to an
additional dependence of growth times on the magnetic flux.
