Context. Standing transverse oscillations of coronal loops are observed to operate in two regimes: rapidly decaying, large amplitude oscillations and undamped small amplitude oscillations. In the latter regime the damping should be compensated by energy supply, which allows the loop to perform almost monochromatic oscillations with almost constant amplitude and phase. Different loops oscillate with different periods. The oscillation amplitude does not show dependence on the loop length or the oscillation period. Aims. We aim to develop a low-dimensional model explaining the undamped kink oscillations as a self-oscillatory process caused by the effect of negative friction. The source of energy is an external quasi-steady flow, for example, supergranulation motions near the loop footpoints or external flows in the corona. Methods. We demonstrate that the interaction of a quasi-steady flow with a loop can be described by a Rayleigh oscillator equation that is a non-linear ordinary differential equation, with the damping and resonant terms determined empirically. Results. Small-amplitude self-oscillatory solutions to the Rayleigh oscillator equation are harmonic signals of constant amplitude, which is consistent with the observed properties of undamped kink oscillations. The period of self-oscillations is determined by the frequency of the kink mode. The damping by dissipation and mode conversion is compensated by the continuous energy deposition at the frequency of the natural oscillation. Conclusions. We propose that undamped kink oscillations of coronal loops may be caused by the interaction of the loops with quasi-steady flows, and hence are self-oscillations, which is analogous to producing a tune by moving a bow across a violin string.
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