Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics

First results from a high-resolution three-dimensional nonlinear numerical study of the kink oscillation are presented. We show in detail the development of a shear instability in an untwisted line-tied magnetic flux tube. The instability produces significant deformations of the tube boundary. An extended transition layer may naturally evolve as a result of the shear instability at a sharp transition between the flux tube and the external medium. We also discuss the possible effects of the instability on the process of resonant absorption when an inhomogeneous layer is included in the model. One of the implications of these results is that the azimuthal component of the magnetic field of a stable flux tube in the solar corona, needed to prevent the shear instability, is probably constrained to be in a very specific range

The temporal behaviour of solar activity (as manifested in sunspots) has long been debated. The 11-year periodicity in the total number of sunspots is well established observationally, as is a periodicity of 152–158 days in the occurrence of high-energy solar flares that was seen during cycle 21 (1,​ 2,​ 3,​ 4,​ 5,​ 6,​ 7). The cause of the latter periodicity is not clear, although several mechanisms have been proposed^8,9,10. Here we report a time–frequency analysis, using the wavelet technique, of sunspot areas between 1874 and 1993, which reveals a 158-day periodicity coincident with that of energetic solar flares. The signature of this periodicity is strongest in cycle 19, which was the most intense cycle of the century. The periodicity disappears after cycle 21. The analysis shows that the 158-day periodicity in both high-energy solar flares and sunspots is related to a periodic emergence of magnetic flux which only appears near the maxima of some solar cycles.