1 Introduction

The rotation of solar atmospheric structures is mainly affected by magnetic tubes rooted in the convective zone. There are two causes of the variation of rotation rates for the various structures: the dynamics of the solar interior (differential rotation, North/South hemisphere asymmetry, depth of anchorage of magnetic ropes and variation of rotation according to solar activity) and local conditions in the atmosphere (magnetic field structure, strength, and height). The review papers of Howard (1984), Schröter (1985), Howard et al. (1991), Libbrecht & Morrow (1991) and Beck (1999) summarized and analyzed the general aspects of rotation of the solar atmosphere and quoted articles on the target.

The highest precision in rotation measurement is obtained with sunspots. These measurements benefit from more than 100 years of high quality photographic observation. They are generally considered as a reference for the rotation of the solar atmosphere. Numerous authors reported sunspot rotation rates which are in good agreement (Lustig 1983; Gilman & Howard 1984; Howard et al. 1984; Balthasar et al. 1986; Hathaway & Wilson 1990; Howard et al. 1999). Some papers approach the problem of sunspot rotation in relation to the solar cycle (Livinston & Duvall 1979; Lustig 1983; Gilman & Howard 1984; Balthasar et al. 1986; Pulkkinen & Tuominen 1998; Gupta et al. 1999) and they conclude that the sun rotates faster during minimum activity. More general results of Woodard & Libbrecht (1993) from helioseismology, or Mordvinov & Plyusinia (2000) from MDI data, confirm the time variation of solar rotation during the cycle of activity. We remind the reader that the Carrington Rotation period was defined by sunspot rotation and it is the reference of solar rotation.

Studies of coronal rotation in relation to the solar cycle and observed at the limb or on the disk, were performed by Hansen et al. (1969), Henze & Dupree (1973), Antonucci & Dodero (1977), Fisher & Sime (1984), Parker (1986), Hoeksema & Scherrer (1987) and Weber et al. (1999). According to these authors, coronal rotation is characterized by a less pronounced differential rotation than photospheric rotation and a near rigid rotation during minimum activity. We found that the B coefficient (from the differential rotation rule $\Omega^{\star}=A-B \times \sin^2\varphi)$, which characterizes only the differential rotation, is about 1 for the corona and about $2.5^{\circ}/$d for sunspots. From Fig. 1 of Hoeksema & Scherrer, we obtain that the synodic rotation period variation of sunspots and of the corona, between the equator and $30^{\circ}$ latitude, is respectively 1.32 and 0.41 d. This last property made coronal rotation less latitude-dependent throughout the cycle. Sky-Lab observations long ago showed that coronal holes rotate rigidly as well as differentially. From green line data ( $\rm\lambda = 5305 ~\AA$), Badalian & Livshits (1997) assert that coronal rotation changes during the cycle, whereas Rybak (1994) do not find a clear signature. On the other hand Vats et al. (1999) derive the variation of synodic periods of coronal rotation ranging from 22 to 30 d.

In the present article we analyse corona rotation from 10.7 cm radio flux. Our aim is to find the dependence of the active coronal rotation rate on the 11-y solar cycle. We use the day (d) as the unit of synodic rotation period and the degree per day ($^{\circ}/$d) as the sideral rotation rate. Note that, for the latter, case the conversion to other units is ${\rm 1^{\circ}/d} = 0.202~ \mu {\rm rad}~ {\rm s} ^{-1} = 32.15~n$Hz. In Sect. 2, we display the data we used in this study. In Sect. 3 we briefly give the technique used to measure the rotation rate. In Sect. 4 we show the results and the dependency of the rotation rate on activity cycle. The paper ends with conclusions.

Figure 1: A thousand-day record of the slowly-varying component of 10.7 cm radio flux (February 25, 1977 to November 21, 1979). The y-axis is the flux, in sfu and the abscissa is in days.