## 3. Angular rotation rate## 3.1. Global rotationThe differential rotation rate is calculated for each
latitude bin and is plotted in Fig. 1,
along with the 1- deviation from the mean. These
deviations are of the order of /day. The
rotation appears rigid over a broad range of latitudes. This rigidity
may be due to a deep anchoring of young sunspots, if we may indeed
assume such is the case, because our tracking procedure preferentially
selects these young sunspots. To compare with other data, we began by
performing a fourth-degree Legendre polynomial fit, using a
least-squares minimization of the observed data, averaged over
latitude bins. Since we observed no strong
north-south asymmetry in rotation rates, we kept only the even
Legendre coefficients, which are then converted to where is the latitude. Fig. 2 compares the polynomial fit performed on cycle 19 and 21 sunspots. The rotation during cycle 21 seems to be a little more rigid than that of cycle 19, and exhibits a slightly smaller equatorial rotation rate, though the differences are not significant. This rigidity has also been observed by Antonucci et al. (1990) on large-scale photospheric features.
## 3.2. Cycle variabilityWe now investigate the variability of the rotation rate throughout the cycle. Table 2 shows the expansion (1) coefficients during cycle 19. The period ranging from 1957 to 1959 is one of intense activity, while the minimum occurred in 1963. Errors at the 1- confidence level are computed using a Monte Carlo simulation.
The errors in the Legendre polynomial coefficients are usually determined by computing the covariance matrix (see Press et al. 1986, p521ff). However, this method assumes that when the fit parameters are displaced from their optimum values by a deviation then the resulting deviation in is quadratic: When higher order terms are significant, the covariance matrix becomes unreliable, and we turn to Monte Carlo simulations to estimate realistic errors (Press et al. 1986, p529ff). We found that errors computed with the two methods are different, so we adopted the Monte Carlo method to determine them. Based on these errors, we conclude that the variations of the
coefficients ## 3.3. North-south asymmetryTo investigate the north-south asymmetry of sunspot rotation rates, we now consider the odd coefficients of the polynomial expansion where , , and
are the coefficients
## 3.4. Age and magnetic polarity dependenceWe then examined the variability of the rotation rates with sunspot
age. For this purpose, two classes of sunspots were considered: those
four days old or less (759 sunspots) and those more than eight days
old (194 sunspots). We also considered "complex sunspot" rotation
rates. Complex sunspots belong to groups in which it is not possible
to determine their age. Fig. 3.2 shows the rotation rates for the
three classes and compares their respective polynomial fits. Young
sunspots show a slightly more rigid rotation than old ones. The
uncertainty on the coefficients
A bipolar group consists of a pair of sunspots of opposite polarity, with one leading and one following. The rotation rates of leaders (432 points) and followers (175 points) is studied separately (Fig. 3.4). However, the error bars are too large to detect any significant differences between these two sunspot classes, as the one observed by Gilman & Howard (1985) and in Paper II (faster rotation of leaders). © European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |