Periodicities in the coronal rotation and sunspot numbers

Mon. Not. R. Astron. Soc. 414, 3158–3165 (2011) doi:10.1111/j.1365-2966.2011.18611.x Periodicities in the coronal rotation and sunspot numbers Satish Chandra1 and Hari Om Vats2 1 Department 2 Physical of Physics, PPN College, Kanpur 208 001, India Research Laboratory, Ahmedabad 380 009, India Accepted 2011 February 28. Received 2011 January 20; in original form 2010 April 19 This study is an attempt to investigate the long-term variations in coronal rotation by analysing the time-series of the solar radio emission data at 2.8 GHz frequency for the period 1947–2009. Here, daily adjusted radio flux (known as Penticton flux) data are used. The autocorrelation analysis shows that the rotation period varies between 19.0–29.5 sidereal days (mean sidereal rotation period is 24.3 d). This variation in the coronal rotation period shows evidence of two components in the variation: (1) 22-yr component which may be related to the solar magnetic field reversal cycle or Hale’s cycle; and (2) a component which is irregular in nature, but dominates over the other components. The cross-correlation analysis between the annual average sunspot number and the coronal rotation period also shows evidence of its correlation with 22-yr Hale’s cycle. The 22-yr component is found to be almost in phase with the corresponding periodicities in the variation of the sunspot number. Key words: Sun: corona – Sun: radio radiation – Sun: rotation. 1 I N T RO D U C T I O N Coronal rotation can be observed through various solar tracers at different frequencies, like the coronal green line (Fe XIV emission line at 530.3 nm), white light, He I line (at 1083 nm), soft X-rays, ultraviolet (UV) rays and radio waves. The coronal green line has been used to measure the rotation rate of the solar corona at higher latitudes by Waldemier (1950), Trellis (1957), Cooper & Billing (1962), Sýkora (1971), Sime, Fisher & Altrock (1989), Rybák (1994), Badalyan, Obridko & Sýkora (2006), Badalyan & Sýkora (2006b) and others. The results of Waldemier (1950) and Cooper & Billing (1962) indicate a faster rate of rotation as compared to the rate of rotation of the sunspots, suggesting a much lower differential rotation rate in the corona. In his work on the green corona, Sýkora (1971) found that the Sun shows little or no differential rotation for six latitudinal zones ±7.5, ±27.5 and ±47.5. For low latitudes, the rotation period was near to that found by Trellis (1957). The green (Fe XIV at 530.3 nm) emission line for the period 1973–2000 and red (Fe X at 637.4 nm) emission line for the period 1984–2000 were analysed by Altrock (1997, 2003). It was reported that the corona, at green and red emission lines, shows more rigid rotation than does the photosphere. Sime et al. (1989) also concluded, after analysing the Sacramento Peak Observatory data observed between 1973 and 1985, that the Fe XIV corona rotates more rigidly than do features in the photosphere or chromosphere. The synodic period obtained by Rybák (1994) for the period 1964–89 again confirmed the differential rotation of the green corona. Badalyan et al. (2006) and  E-mail: (SC); (HOV) Badalyan & Sýkora (2006b) carried out a comprehensive analysis using a long data base (1939–2001) on the brightness of the coronal green line. The results support previous conclusions that the differential rotation in the corona is less pronounced than in photospheric tracers. Hansen, Hansen & Loomis (1969) used the K-coronometer for coronal rotation measurement at different latitudes, for heights ranging from 1.125 to 2 R . The rotation found at the equator is in good agreement with the sunspot’s rotation results and shows less variation with the latitude at higher latitudes in comparison to the rotation of the chromosphere. A detailed study of the white-light corona, from 1.1 to 30 R , was done with the LASCO onboard the SoHO spacecraft. It was concluded that the rotation of the corona displayed a radially rigid rotation of 27.5 d synodic period from 2.5 R to >15 R (Lewis et al. 1999). The He I 1083-nm maps, from the National Solar Observatory, have been used to determine the rotation. It is found, both from observations and from magnetic extrapolation methods, that the corona becomes more rigid with height. By considering coronal holes as tracers (from an atlas of coronal holes mapped in He I 1083-nm data) of the differential rotation, Insley, Moore & Harrison (1995) demonstrated that the mid-latitude corona rotates more rigidly than the photosphere, but still exhibits significant differential rotation, with an equatorial rate of 13.◦ 30 ± 0.◦ 04 per day and at 45◦ latitude, a rate of 12.◦ 57 ± 0.◦ 13 per day. An analysis of the rotation of coronal holes spanning 18 yr (from 1973 to 1991) was done based on data from the Catalogue of Coronal Holes (Navarro-Peralta & SanchezIbarra 1994). Isolated coronal holes showed a typical differential rotation, but polar coronal hole extensions displayed two different types of behaviour: a rotation rate below approximately 40◦ ± 5◦ of  C 2011 The Authors C 2011 RAS Monthly Notices of the Royal Astronomical Society  ABSTRACT Periodicities in the coronal rotation  C 2011 The Authors, MNRAS 414, 3158–3165 C 2011 RAS Monthly Notices of the Royal Astronomical Society  gradient of differential rotation show similar values during periods of low and high activity. Mouradian, Bocchia & Boston (2002) analysed the 2.8-GHz radio emission flux with the maximum entropy method and showed that the 2.8-GHz radio emission rotation varies according to the activity level. But Mehta (2005), after analysing the radio emission data could not find any systematic relationship between the coronal rotation period and the phase of the solar cycle. Chandra et al. (2009, 2010) calculated the equatorial rotation rate for each year separately (using radio images at 17 GHz for the years 1999–2001 and SXT data for the years 1992–2001, respectively) and compared it with the annual sunspot numbers. The comparison shows that the equatorial rotation rate seems largely to be a function of the phases of the solar cycle. Javaraiah (2000) used the Greenwich Photoheliographic Results data on sunspot groups compiled during 1879–1975 to study the variations in the differential rotation coefficients A and B during the odd-numbered solar cycles (ONSCs) and during the even-numbered solar cycles (ENSCs). The parameters A and B are measures of the equatorial rotation rate and latitude gradient of the rotation rate, respectively. It is seen that the variation in A is significant only in the ONSCs (Waldmeier cycle numbers 13, 15, 17 and 19), whereas, the variation in B is quite significant in both ONSCs and ENSCs (Waldmeier cycle numbers 12, 14, 16, 18 and 20). There exists a good anticorrelation between the mean variations of B during ONSCs and ENSCs, suggesting the existence of a 22-yr periodicity in B. Different methods and different tracers have been employed (...truncated)