| Abstract: | A periodic long-term modulation of the solar surface rotation with a time scale on the order of 100 years is found in the sunspot data from 1874 to 1992 obtained by combinig the Greenwich Photoheliographic Results from cycle 11 to cycle 20 analysed by Balthasar, Vázquez, and Wöhl and the Mitaka sunspot sketch data from cycle 18 to 22 of the National Astronomical Observatory of Japan which was the Tokyo Astronomical Observatory of the University of Tokyo until 1988. A new index of the solar rotation M defined by integrating the angular momentum density over the whole surface, which we call the angular momentum surface layer density, reached a maximum at solar cycle 14, decreased to a minimum at cycle 17, and then increased to reach another maximum at cycle 21. The increase of M means acceleration of the surface layer as a whole by transport of angular momentum from the deeper layer. This implies an decrease (increase) of the radial gradient of the differential rotation if the basic radial gradient of the differential rotation increases (decreaes) inward. The decrease of M means deceleration of the surface layer and implies an increase (decrease) of the radial gradient. The degree of the equatorial acceleration of the surface differential rotation is also found to have undergone the same 100 year periodic modulation during the same interval, reaching a minimum at cycle 14, a maximum at cycle 17, and a minimum at cycle 21 in antiphase with the modulation of M. Thus both radial and latitudinal gradients of the differential rotation increased and decreased in phase (in anti-phase) if the basic radial gradient increases (decreases) inward. |
