3 Coronal rotation rate

Figure 3 shows the power spectrum of the 10.7 cm flux over the whole data for period intervals from 16.5 to 50 d. We see an large group of frequencies spread around the Carrington Rotation period of 27.27 d. It shows that coronal rotation is composed of multiple frequencies and therefore has to be studied in detail. We can distinguish two groups of frequencies, one between 0.034 and 0.040 and the second between 0.030 and 0.034 1/d. The first group is composed of well-defined frequencies, but the second one is more confused. Later on we shall see that they correspond respectively to active and quiet sun.

Various solar activity analyses have revealed a period of 150 to 160 d (Ichimoto et al. 1985; Oliver et al. 1998; the present data and others). To sample the 10.7 cm data we first chose a time lapse of 160 d and in order to reduce the noise, we considered three times this period, i.e. 480 d (approximately 18 solar rotations or 1.3 y). Consequently, the length of 51.7 y was covered by 77 overlapping periods of 480 d, shifted by 240 d steps. For each time interval of 480 d, we computed the power spectrum using the Maximum Entropy Method (Press et al. 1990), which determines the frequency variation more accurately than other methods (Radoski et al. 1975). Each spectrum was normalized to its maximum, so that the frequencies occurring in low-activity periods were brought out too, thereby showing the rotation frequencies at any point in the cycle.

 

 

Table 1: Coronal rotation characteristics.

		maxima				minima			quiet sun
cycle		date	$P^{\oplus}\rm d$	$\Omega^{\star ~\rm\circ}/\rm d$		$P^{\oplus}\rm d$	$\Omega^{\star ~\rm\circ}/\rm d$		$P^{\oplus}\rm d$	$\Omega^{\star ~\rm\circ}/\rm d$
1		2	3	4		5	6		7	8
19		1957 Jul.	25.35	15.19		31	13		32	12.1
20		1969 Jan.	25.30	15.21		29	13		31	12.6
21		1980 Jun.	25.55	15.08		30	13		32	12.2
22		1890 Jun.	25.40	15.16		28	14		32	12.2

Figure 4: Contour maps of power spectra for four cycles studied in the rotation period range from 25 to 33.5 days. M and m on the y-axis indicate the dates of cycle maximum and of minimum. CR on x-axis indicates the Carrington Rotation period in 1/d. The dotted lines join the lower limit of rotation periods.