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Runaway instability operates in fluid tori around black holes. It affectssystems close to the critical (cusp overflowing) configuration. The runawayeffect depends on the radial profile l(R) of the angular momentum distributionof the fluid, on the dimension-less spin a of the central black hole, and otherfactors, such as self-gravity. Previously it was demonstrated that, for thepower-law dependence of the radial angular momentum profile, non-magnetizedtori always become runaway stable for a sufficiently high positive value of q.Here we discuss the role of runaway instability within a framework of anaxially symmetric model of perfect fluid endowed with a purely toroidalmagnetic field. The gradual accretion of material over the cusp transfers themass and angular momentum into the black hole, thereby changing the intrinsicparameters of the Kerr metric. We studied the effect of the ratio of gas tomagnetic pressure and other parameters of the model on the evolution ofcritical configurations that are just on the verge of cusp overflow. We showthat the toroidal magnetic component inside an accretion torus does not changethe frequency of its oscillations significantly. We identify these oscillationsas the radial epicyclic mode. These weak effects can trigger the runawayinstability even in situations when the purely hydrodynamical regime of thetorus is stable. On the other hand, in most cases the stable configurationremains unaffected, and the initial deviations gradually decay after severalorbital periods. We show examples of the torus evolution depending on theinitial magnetization beta, the slope q, and the spin a. The toroidal magneticfield plays a more important role in the early phases of the accretion processuntil the perturbed configuration finds a new equilibrium or disappears becauseof the runaway instability.

Effect of the toroidal magnetic field on the runaway instability of relativistic tori