HURST ANALYSIS OF MT-WILSON ROTATION MEASUREMENTS

I study the temporal variation of the solar rotation on time scales sh orter than the 11-year cycle by analyzing the daily Mt. Wilson Doppler measurements from 1967 to 1992. The differential rotation is represen ted by the three coefficients, A, B, and C, of the following expansion : omega = A + B sin2(theta) + C sin4(theta). The A, B, and C time seri es show clearly the 11-year solar cycle and they also show high-freque ncy fluctuations. The Hurst analysis of these time series shows that a Gaussian random process such as observational noise can only account for fluctuations on time scales shorter than 20 days. For time scales from 20 days to 11 years, the variations of A give rise to a Hurst exp onent of H = 0.83, i.e., the variations of A are 'persistent'. The tem poral variations of B show the same behavior as C, which is different from A. From one to 11 years, the B and C variations are dominated by the 11-year cycle, while for time lags shorter than about 250 days, th e B and C fluctuations give rise to a Hurst exponent of H = 0.66, whic h lies between H = 1/2, of a Gaussian random process, and the exponent of the persistent process shown by A. An analysis of the equivalent c oefficients of the first three even Legendre polynomials, computed usi ng A, B, and C, provides additional information. For time scales betwe en 100 and 1000 days, the ranges, R/S, of Legendre polynomial coeffici ents decrease with increasing order of the polynomials which suggests that the persistent process operates mainly on large spatial scales. T he Hurst exponent of H = 0.83 for variations in A is the same as H for monthly sunspot numbers with time scales between 6 months and 200 yea rs and for C-14 radiocarbon data with time scales between 120 years an d 3000 years, previously analyzed by other authors. The combined resul ts imply that the underlying solar process shows the same persistent b ehavior for time scales as short as about 20 days up to time scales of a few thousand years.