Long-term variations of the coronal rotation and solar activity

Mon. Not. R. Astron. Soc. 423, 3584–3588 (2012) doi:10.1111/j.1365-2966.2012.21155.x Long-term variations of the coronal rotation and solar activity K. J. Li,1,2 X. J. Shi,1,3 W. Feng,4 J. L. Xie,1,3 P. X. Gao,1 L. S. Zhan5 and H. F. Liang6 1 National Astronomical Observatories/Yunnan Observatory, CAS, Kunming 650011, China 2 Key Laboratory of Solar Activity, National Astronomical Observatories, CAS, Beijing 100012, China 3 Graduate School of the Chinese Academy of Sciences, Beijing, China 4 Research Center of Analysis and Measurement, Kunming University of Science and Technology, Kunming 650093, China 5 Jingdezhen Ceramic Institute, Jingdezhen 333001, Jiangxi, China 6 Department of Physics, Yunnan Normal University, Kunming 650093, China ABSTRACT Recently, Chandra and Vats have obtained the yearly period length of the solar coronal rotation cycle by analysing the daily adjusted solar radio flux at the 10.7-cm wavelength for the years 1947–2009. In this paper, we use the time series (series I) of the yearly period length to investigate the long-term variation of the rotation of radio emission corona, and we find a weak decreasing trend in the time series. We use the empirical mode decomposition to decompose both the yearly mean value (series II) of the solar radio flux at the 10.7-cm wavelength and series I into different periodical components. There is a secular trend for each of the two series, and we find a negative correlation in the two trends. The decomposed 11-yr-cycle components of the two series show different and complicated periods and there is a phase relation between them. We investigate the cycle-related variation of the coronal rotation length, and we find that there is no Schwable cycle of statistical significance for the long-term variation of the rotation cycle length. Key words: methods: data analysis – Sun: activity – Sun: corona – Sun: rotation. 1 I N T RO D U C T I O N It is well known that the Sun rotates differentially at the photosphere and the chromosphere. The equatorial region of the Sun rotates faster than the higher latitude regions, and the latitudinal profiles of rotation vary slightly for different features (Howard 1984; Beck 2000; Chu et al. 2010). However, the differential rotation in the solar corona is not profound (Howard 1984; Karachik, Pevtsov & Sattarov 2006). Solar coronal rotation can be measured by various tracers and different methods, as has been done for the low solar atmosphere (Brajs̆a, Ruz̆djak & Wöhl 2006). Coronal differential rotation has been investigated mainly using the coronal green line. Waldmeier (1950) and Cooper & Billing (1962) studied the rotation of the green corona. They found a faster rotation rate in the corona than those rotation rates deduced from observations of the low solar atmosphere, which suggests a much lower differential rotation rate in the solar corona. Sykora (1971) investigated the longitudinal distribution of the green corona activity, and the Sun was found to show very small differential rotation, supporting the theory of under-photospheric rigid-body rotation. Antonucci  E-mail: & Svalgaard (1974) and Antonucci & Dodero (1977) studied the coronal rotation using the green corona line, and the differential rotation in the corona was found to be profound at the maximum and descending phases of the sunspot cycle, compared to the rotation at the rising phase. Sime, Fisher & Altrock (1989) concluded that the green corona should rotate more rigidly than features at the photosphere and chromosphere, and that the coronal differential rotation should be most profound at the late stages of the ascending phase of a sunspot cycle. Altrock (1997, 2003) has analysed the synoptic observations of the green (Fe XIV at 530.3 nm) emission line during the years 1973–2001 and the red (Fe X at 637.4 nm) emission line in the period 1984–2001. The solar corona was found to present a weak, solar-cycle-dependent differential rotation in both spectral lines, showing more rigid rotation than the photosphere. Rybák (1994) utilized the synoptic photoelectric observations of the coronal Fe XIV 530.3 nm for the period 1964–1989 in order to investigate the rotational behaviour of the green solar corona. The differential rotation of the green solar corona was confirmed: local maxima of the rotation period exist at latitudes 45◦ and −60◦ , and a minimum at the equator. However, no clear cyclic variation of the rotation was found for the epoch examined (Rybák 1994). Badalyan, Obridko & Sykora (2006) and Badalyan & Sykora (2006) made a comprehensive analysis of the brightness of the coronal  C 2012 The Authors C 2012 RAS Monthly Notices of the Royal Astronomical Society  Accepted 2012 April 21. Received 2012 March 5; in original form 2011 May 10 Coronal rotation and activity 2 L O N G - T E R M VA R I AT I O N S O F T H E C O RO N A L ROTAT I O N A N D S O L A R AC T I V I T Y 2.1 Data Here, we use the yearly mean value of the solar radio adjusted flux at the 10.7-cm wavelength in solar flux units (one solar flux unit is equal to 10−22 W m−2 Hz−1 ) in the years 1947–2009, as measured at Ottawa and Penticton. The radio flux clearly exhibits the 11-yr cycle that is generally demonstrated by the number of sunspots on the photosphere, and there is well-established evidence of a good  C 2012 The Authors, MNRAS 423, 3584–3588 C 2012 RAS Monthly Notices of the Royal Astronomical Society  Figure 1. Temporal evolution of the yearly rotation period length (asterisks) during the period 1947–2009, obtained by Chandra & Vats (2011) using an autocorrelation analysis of solar radio emissions at 2.8 GHz. The solid line shows the linear regression trend. correlation between sunspots and radio emission (Chandra & Vats 2011). Using the autocorrelation method, Chandra & Vats (2011) have analysed the time series of the daily solar adjusted radio flux at the 10.7-cm wavelength (2.8-GHz frequency) during the period 1947–2009. Then, they obtained the length of the yearly rotation period in the time interval, as given in their table 1. Here, Fig. 1 shows the length of the yearly rotation period. A linear regression is performed to fit the length of the rotation period; the regression line is also given. Their correlation coefficient is −0.1163, which indicates a decreasing trend in the length of the coronal rotation cycle, but this is statistically insignificant. Thus, no secular trend is found to be statistically prominent. Li et al. (2011a,b) have also found a secular decreasing trend in the length of the Sun’s rotation cycle by analysing sunspot activity. Furthermore, such a trend is statistically significant. The mean value of the length of the yearly rotation period is 24.3 d, which means that the radio corona should rotate faster than the features at the photosphere and chromosphere. 2.2 Empirical mode decomposition of the temporal variations of rotation cycle length and solar radio flux The empirical mode decompositi (...truncated)