2 Data

Our analysis of inner corona rotation related to the solar cycle is based on the radio flux at 10.7 cm (2800 MHz) monitored by the Dominion Astrophysical Observatory of the National Research Council of Canada (Covington 1969). These observations started in late 1946 and are still continuing. The daily recorded flux is the integrated emission over the solar disk. The quoted flux values are measured around local noon (17:00 UT) and have a relative error of $\pm$2%. Covington mentions that the 10.7 cm flux is correlated with the active region (sunspots and plages), so that this emission becomes a good index of solar activity. The origin of 2800 MHz radiation is the thermal emission of plasma trapped in magnetic loops of the active region and is consequently related to the photospheric magnetic field flux of active regions. The 10.7 cm emission is mainly due to free-free radiation, as mentioned by Tapping & DeTracey (1990). The 10.7 cm rotation rate concerns the global activity component of the solar corona. The review of Rabin et al. (1991) shows the good correlation of 10.7 cm flux to solar activity.

The 10.7 cm emission is located in the low corona. From high-resolution observation of 8 sources Swarup et al. (1963) found that the average altitude of radio emission is 15 000 km above the photosphere. But Kundu (1965) mentioned emission altitudes two or three times higher for some active regions observed by Swarup. Covington (1969) determined even a height of 0.2 solar radius, but Vats et al. (2001) gives the altitude as 60 000 km. These discrepancies in 10.7 cm emission height are due to different magnetic complexity and strength of the active regions. Because we use the recurrence method in the present search, the results are independent of the altitude.

The radio flux we use is the Slowly Varying component (S component) consisting of pulses superimposed on a background. Figure 1 shows a thousand days' recording (February 25, 1977 to November 21, 1979) that cover the growing to maximum phases of cycle 21. It can be seen that the background intensity is changing during the cycle and is related to the global solar magnetic flux. This is clearly due to the active regions distributed outside of active longitudes, whose number varies with the phase of the activity cycle. For our search we used the "Series D" data, which is adjusted for solar-terrestrial distance variation and corrected to absolute units. The S component is free of bursts of transient events (flares, surges or other).

Figure 2: Radio flux record showing cycles 19 to 22. The low frequency ($\leq$1/365 d) effect is removed.

Figure 3: The power spectrum of the same period as in Fig. 2, in abscissa frequencis 1/d.

The modulation of the S component is due to the presence of complex of activity (Gaizauskas et al. 1983) on the solar disk. Van Driel-Gesztelyi et al. (1992) mentioned that more than a third of the active regions are clustered around "active longitudes". SOHO/EIT data analyzed by Benevolenskaya et al. (2000) confirm the reality of active longitudes in the corona. As the life time of the active longitudes is several times longer than the solar rotation period, their successive passages on the solar disk modulate the 10.7 cm flux and determine the S component. Becker (1955) gives 10 to 12 solar rotations as an average life time for sunspots "hearth" and Brouwer & Zwaan (1990) give 4 to 6 rotations. The the solar flux is thus modulated by the recurrence of active longitudes, thereby allowing measurement of the rotation rate. Consequently, we introduce a new method for measuring solar rotation rate, based on solar activity rotation with respect to Earth. This way, our method provides solar rotation parametres in absolute units.

The emergence of any new big active region or an active longitude on the solar disk introduces a "perturbation" in the flux modulation, such as those visible in Fig. 1 at day 450, or a longer period around day 700. The computed power spectra integrate the 480 d domain, including all disturbances. In our data, the signal was neither less than 65 nor greater than 370 sfu. We use the Butterworth numerical filter (Stearns 1975) to cut off frequencies below 1/365 d and give in Fig. 2 the whole period analyzed (February 3, 1947 to November 9, 1998, or JD 2 432 258 to 2 451 127), covering four solar cycles, 19 to 22.

A preliminary study of rotation rate versus cycle, based on the material mentioned above, was already given by Mouradian et al. (2000). In order to determine the period of rotation we used a method of counting emission summits in a given lapse of time, around the maximum, intermediary and minimum epochs of solar activity. We found longer periods of rotation during the minima and shorter ones during the activity maxima. In the present paper, we perform the same task using the spectral analysis method.