Prograde and Retrograde Waves in Sunspot Eruption Patterns with Longitudinal Velocities of ∼30 – 75 m s−1

Sunspots are discrete objects in the background magnetic activity on the Sun. Their individual proper motions are partially influenced by both the differential rotation of the Sun’s outer envelope and the meridional flows toward the equator and poles, but their collective behavior is more complex, suggesting other forces at work. Previous examinations of long-term sunspot patterns revealed longitudinal clusters (nests) with apparent stability over a few Carrington rotations (CRs) but with drifts, 180° shifts, and apparent standing-wave patterns over longer periods. Evidence is presented in this report that slowly moving prograde and retrograde waves characterize the eruption patterns of sunspot groups over a several-year period in the middle of each 11-year sunspot cycle. Making use of modified stackplots with the dimensions of longitude and time, the sunspot eruptions that occur in both hemispheres within the same windows of latitude, longitude, and CR are selected for examination. A convolution method, based on an adaptive function, is developed to enhance and display the trajectories occurring through space and time. Examples are provided from different solar cycles to demonstrate the general nature of the phenomenon. A linear relationship is observed between wave velocity and maximum magnitude of the sunspot index of the past 12 solar cycles. Overall, the trajectories suggest longitudinal traveling waves that appear to interact in a manner similar to solitons, suggesting that they originate from nonlinear dynamics affecting the appearance of flux tubes at the solar surface. These bidirectional traveling waves, and their collisions, also explain the recently described evidence for standing waves observed in surface spherical harmonic analysis of sunspot patterns.