Short-term periodicities of the sun's 'mean' and differential rotation

We have looked for periodicities in solar differential rotation on time scales shorter than the Ii-year solar cycle through the power-spectrum analysis of the differential rotation parameters determined from Mt. Wilson velocity data (1969-1994) and Greewich sunspot group data (1879-1976). We represent the differential rotation by a set of Gegenbauer polynomials (omega(phi) = (A) over bar + (B) over bar(5 sin(2) phi - 1) + (C) over bar(21 sin(4) phi + 14 sin(2) phi + 1)). For the Mt. Wilson data, we focus on observations obtained after 1981 due to the reduced instrumental noise and have binned the data into intervals of 19 days. We calculated annual averages for the sunspot data to reduce the uncertainty and corrected for outliers occurring during solar cycle minima. The power spectrum of the photospheric 'mean rotation' (A) over bar; determined from the velocity data during 1982-1994, shows peaks at the periods of 6.7-4.4 yr, 2.2 +/- 0.4 yr, 1.2 +/- 0.2 yr, and 243 +/- 10 day with greater than or equal to 99.9% confidence level, which are similar to periods found in other indicators of solar activity suggesting that they are of solar origin. However, this result has to be confirmed with other techniques and longer data sets. The 11-yr periodicity is insignificant or absent in (A) over bar. The power spectra of the differential rotation parameters (B) over bar and (C) over bar, determined from the same subset, show only the solar cycle period with a > 99.9% confidence level. The time series of (A) over bar determined from the yearly sunspot group data obtained during 1879-1976 is very similar to the corresponding time series of (B) over bar. After correcting for data with large error bars (occurring during cycle minima), we find periods, which are most likely harmonics of the solar cycle, such as 18.3 +/- 3.0 yr and 7.5 +/- 0.5 yr in (A) over bar and confirmed these and the 3.0 +/- 0.1 yr period in (B) over bar. The original time series show in addition some shorter periods, absent in the corrected data, representing temporal variations during cycle minimum. Given their large error bars, it is uncertain whether they represent a solar variation or not. The results presented here show considerable differences in the periodicities of (A) over bar and (B) over bar determined from the velocity data and the spot group data. These differences may be explained by assuming that the rotation rates determined from velocity and sunspot data represent the rotation rates of the Sun's surface layers and of somewhat deeper layers.