Rotational charecteristics of solar radio emissions and IMF: A comparative study Mehul Mehta1, and Hari Om Vats2 1 VP & RPTP Science college, Vallabh Vidyanagar, 388 120, INDIA. meghdhanusha@yahoo,co.in 2 Physical Research Laboratory, Navrangpura, Ahmedabad, 380 009, INDIA. [email protected] Abstract In present work we have performed autocorrelation analysis of time series of disc integrated solar flux at 2800 MHz and daily observations of Interplanetary magnetic field (IMF) for the period of 1987 to 2010 to infer rotation period. The analysis presents a comparison between rotation periods obtained from radio emissions, a coronal feature and interplanetary magnetic field. The results show a correlation between two which indicates that IMF seems to emanate from regions of low latitudes while it is expected to originate from polar regions. 1.Introduction: The problem of solar rotation is being studied systematically since mid of 19th century. It was made clear that the Sun does not rotate like a solid body. Solar rotation is measured, mainly by two methods. One is observation of tracers like sunspots, faculae, filaments etc. and other is spectroscopic observations of Doppler shift of selected spectral lines. Each of these methods has its own limitations as pointed by Howard [1], in the review of observation and interpretation of solar rotation. In last two decades it has been shown by several groups that solar radio emissions can be used to estimate solar rotation [2,3 & 4] In this paper, we have used yet another method of inferring solar rotation using daily observations of solar radio emissions at 2800 MHz and interplanetary magnetic field (IMF). We have made use of technique of auto correlation [5]. 1.1 2800 MHz radio emissions The data used in present work is disc integrated solar flux values at 2800 MHz, expressed in the solar flux unit (1 SFU = 10-22 wats/meter square-Hertz). This radio emission originates mainly from thermal free-free (Bremsstrahlung) radiation [6] and directly related to total amount of magnetic flux. The choice of 2800 MHz radio emission is based on two reasons. (1) Radio emissions at this frequency forms longest and most reliable data set after sunspot number. (2) 2800 MHz radio emissions are found to be most regular [7]. These data are obtained through National Geophysical Data Centre (NGDC,NOAA), USA. The site presents data in two forms; the observed disc integrated flux and adjusted disc integrated flux. Observed data is actually observed flux that changes with Sun- Earth distance. The adjusted flux data are scaled to the standard distance of 1 AU. The adjusted flux data is more appropriate for study of solar behavior. 1.2 Interplanetary Magnetic Flux The Interplanetary magnetic flux (IMF) originates from the Sun and propagates into inter planetary medium (IPM) by solar wind. The solar dynamo generates magnetic field with opposite polarities in northern and southern hemispheres of the Sun. The hydrodynamic expansion of coronal plasma results into solar wind. Due to large electrical conductivity, the magnetic field lines are frozen in outward flowing solar plasma stretched out to form Archimedean spiral. Near the earth, the angle between IMF and the line joining Sun-Earth has an average value of 45o. Since there are opposite polarities of magnetic field in two hemispheres of the Sun, the magnetic field near the earth has inward or outward polarity with a three dimensional Archimedean spiral orientation beyond the radius of the Sun, where the flow becomes super-Alfvanic. The spiral pattern and azimuthal field components have been explained by Parker’s model based on radial flow of the solar plasma from the rotating Sun, combined with a uniform field at some “source surface” in corona. The comparison of mean magnetic field of the Sun as a star with the IMF measurements near the earth orbit confirms that change in polarity of mean solar magnetic field is followed by subsequent change in near earth magnetic field approximately 4.5 days later. The IMF data used in present work is taken by Atmospheric Composition Explorer (ACE) satellite. 2. The data analysis and results The daily values of solar flux and IMF can be considered as time series of regular interval as (x0, x1, x2, ….. xn) and (b0, b1, b2, …. bn). Such series can be processed by auto correlation technique. The auto correlation coefficient Px(l) is calculated using equation (1) and plotted as a function of lag. n − l − 1 − − ∑ (x k x)( x k +1 x) = k =0 Px (l) n −l − 2 (1) ∑ (x k x) k =0 Typical autocorrellograms thus obtained for solar radio flux and IMF component By, for year 2003 are shown in figure 1. Radio emissions in year 2003 shows fair degree of rotational modulation while By show very strong and persistent rotational modulation. The rotation period determined from such autocorrellograms varies from 20.8 to 27.9 days for radio emissions and 24.1to 26.8 days for By. A comparison of rotation periods for these two parameters are shown in figure 2. One can find a fair degree of correlation among results of radio emissions and By component of magnetic field, however there are disagreement in years 1987, 1997, 1998 and 2007, wherein radio and IMF results vary in opposite directions. 1 By-2003 0.9 Radio flux, 2003 0.8 0.7 0.6 0.5 0.4 Coef. 0.3 0.2 0 0.1 -0.2 Auto Cor.Auto Coef. Auto Cor -0.1 -0.4 -0.3 -0.6 -0.8 -0.5 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Lag (Days) Lag (Days) Figure 1: Typical autocorrellograms for year 2003, for By, and radio emissions at 2800 MHz. 30 29 28 27 26 25 Radio 24 (Days) 23 By 22 21 Sidereal Rotation Period 20 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 Year Figure 2: Comparison of rotation periods obtained from 2800 MHz radio emissions and IMF. 3. Discussion The disc integrated radio emissions are dominated by emissions from equatorial region in solar atmosphere and represent solar corona. The comparison between results of radio emissions and IMF indicate that major part of IMF observed by ACE at L1, should have emanated from equatorial and near equatorial region in solar atmosphere, not from higher latitudes as expected by potential field model of solar magnetic field. A simultaneous observation of IMF at different distances from the Sun can throw more light on the problem. We believe that a similar analysis for IMF near Venus and Mars will be fruitful. 4. Acknowledgement The authors acknowledge National Geophysical Data Centre (NGDC) for the data. The research at Physical Research Laboratory is supported by Government of India. One of the authors, Mehul Mehta, is thankful to University Grant Commission, India, for research grant. 5. References 1. Howard R F; “Solar active regions as diagnostics of subsurface conditions” ARA&A, 1996, Volume 34, pp75-109 2. Vats H O, Deshpande M R, Shah C R and Mehta M; “Rotational modulation of microwave solar flux” Solar Physics, 1998, Volume 181, pp351-362. 3. Kane R P, Vats H O and Sawant H S; “Short term periodicities in time series of solar radio emissions at different altitudes”, Solar Physics, 2001, Volume201, pp181-190. 4. Mouradian Z, Bocchia R and Botton C; “Solar activity cycle and rotation of corona” 2002, A & A, Volume 314, pp1103-1109. 5. 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