What Determines the Height of Spicules? I. Alfven‐Wave Model and Slow‐Wave Model

We perform numerical simulations for torsional Alfvén waves and slow waves propagating along an open magnetic flux tube in the solar atmosphere to elucidate the mechanisms of spicule formation and coronal heating. We introduce random motions of about 1 km s -1 in the photosphere as the source of Alfvén and slow waves, and solve the 1.5-dimensional magnetohydrodynamic equations. The waves generated by the random motions propagate upward and lift up the transition region. The chromospheric plasma just below the transition region is thought to be observed as a spicule. We investigate the effect of the initial height of the transition region, or transition-region pressure, on spicule formation. Our results agree well with the observational fact that spicules are absent over plages, where the transition-region pressure is high, and tall under coronal holes, where the transition-region pressure is low. We also show that the dependence of spicule height on the initial transition-region height (or pressure) is well described by the theoretical relation, which is for the slow-wave acceleration of spicules even though we input only Alfvén waves in the photosphere. Although both fast and slow waves are excited by the nonlinear coupling of Alfvén waves, our results suggest that the slow waves play a more fundamental role in the generation of spicules. How much energy flux is transported to the corona is also estimated. A part of the energy flux carried by the waves that generate spicules propagates into the corona and contributes to the heating of the corona. Alfvén waves can transport enough energy flux to heat the quiet corona, but slow waves cannot.