We investigate the role of Alfvén waves in a core-collapse supernova (SN) explosion. We assume that Alfvén waves are generated by convections inside a proto-neutron star (PNS) and emitted from its surface. These waves then propagate outward, dissipate via nonlinear processes, and heat up matter around a stalled prompt shock. To quantitatively assess the importance of this process for the revival of the stalled shock, we perform one-dimensional time-dependent hydrodynamical simulations, taking into account the heating via the dissipation of Alfvén waves that propagate radially outward along open flux tubes. We show that shock revival occurs if the surface field strength is larger than ∼2 × 1015 G and if the amplitude of the velocity fluctuation at the PNS surface is larger than ~20% of the local sound speed. Interestingly, the Alfvén wave mechanism is self-regulating in the sense that the explosion energy is not very sensitive to the surface field strength or initial amplitude of Alfvén waves, as long as they are larger than the threshold values given above.
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