Periodicities in the coronal rotation and sunspot numbers

Hari Om Vats 0 0 Physical Research Laboratory , Ahmedabad 380 009, India 1 Department of Physics, PPN College , Kanpur 208 001, India A B S T R A C T 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. 1 I N T R O 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), Sykora (1971), Sime, Fisher & Altrock (1989), Rybak (1994), Badalyan, Obridko & S ykora (2006), Badalyan & S ykora (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, S ykora (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 19732000 and red (Fe X at 637.4 nm) emission line for the period 19842000 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 Rybak (1994) for the period 196489 again confirmed the differential rotation of the green corona. Badalyan et al. (2006) and Badalyan & S ykora (2006b) carried out a comprehensive analysis using a long data base (19392001) 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 sunspots 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 the heliographic latitude, increasing to the equator, and a rotation rate above the same heliographic latitude but increasing towards the poles. Coronal holes, as observed from the Skylab and Yohkoh spacecrafts, have also been used to determine the rotation rate of the outer corona. Soft X-ray observations of an elongated coronal hole shows the almost rigid rotation of the coronal hole (Timothy, Krieger & Vaiana 1975; Kozuka et al. 1994). The solar full disc (SFD) images, obtained by the soft X-ray telescope (SXT) onboard the Yohkoh Space Observatory, were used by different scientific groups to study the rotation rate of the corona. Weber et al. (1999), Weber & Sturrock (2002) and Chandra, Vats & Iyer (2010) concluded, after analysing SXT data by different methods, that the rotation profile of the corona across the latitude is shallower than the rotation profile of its lower atmospheric levels. Kariyappa (2008) tracked the X-ray bright points (XBPs) on SFD images observed through the SXT and XRT onboard the Yohkoh and Hinode spacecrafts, respectively. Kariyappa 2008 found, contrary to all expectations, that the corona rotates differentially with respect to the latitude, as in the case of the photosphere and the chromosphere. Karachik, Pevtsov & Sattarov (2006) analysed the coronal bright points (CBPs) on SFD filtergrams observed through the SoHO/EIT (Fe XII line at 19.5 nm) and reported that the rotation of CBPs closely follows the latitudinal rotation profile of the photospheric magnetic field. It was also shown that coronal features at different heights in the corona exhibit different rotation rates. Brajsa et al. (2002, 2004), Mulec et al. (2007) and Brajsa et al. (2008) determined the solar differential rotation by tracing CBPs on SFD filtergrams observed through the SoHO/EIT (Fe XV line at 28.4 nm ). For the declining phase of solar cycle 23, Zaatri et al. (2009) compared the differential rotation of subphotospheric layers derived from Global Oscillation Network Group (GONG++) Doppler grams with the small bright coronal structures (SBCS) observed through the SoHO/EIT. It is found at the equator that the SBCS rotate faster than the upper subphotospheric layer (3 Mm) by about 0.5 per day. The latitude gradients of the rotati (...truncated)