Title: AMPLITUDE OF SOLAR CYCLE 24 BASED ON POLAR MAGNETIC FIELD OF THE SUN

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1 Solar Physics Manuscript Draft Manuscript Number: SOLA Title: AMPLITUDE OF SOLAR CYCLE BASED ON POLAR MAGNETIC FIELD OF THE SUN Article Type: Original Research Keywords: "Solar activity"; "solar cycle" Abstract: We have investigated the correlation between the relative sunspot number and magnitude of Sun's polar magnetic field in solar cycles 1-. Sunspot number is in anti-correlation with average magnitude of polar field (r = -0., P < 0.001). Maximal positive correlation between the parameters was calculated when average magnitude of polar magnetic field was time-shifted forward on about. years (r = 0., P < 0.001). Magnitude of polar field of the Sun in the minimum of solar activity between solar cycles and was used as precursor to forecast maximal amplitude of sunspot number in solar cycle. It was found that solar cycle is expected to be relatively weak cycle with maximal strength of 1.. in units of monthly sunspot numbers.

2 Manuscript Click here to download Manuscript: Pishkalo_SP_00_AMPLITUDE_SC.doc AMPLITUDE OF SOLAR CYCLE BASED ON POLAR MAGNETIC FIELD OF THE SUN MYKOLA I. PISHKALO Astronomical Observatory of Kyiv National Taras Shevchenko University,, Observatorna vul., Kyiv 0, Ukraine ( pish@observ.univ.kiev.ua) (Received October 00; accepted ) Abstract. We have investigated the correlation between the relative sunspot number and magnitude of Sun s polar magnetic field in solar cycles 1. Sunspot number is in anti-correlation with average magnitude of polar field (r = -0., P < 0.001). Maximal positive correlation between the parameters was calculated when average magnitude of polar magnetic field was time-shifted forward on about. years (r = 0., P < 0.001). Magnitude of polar field of the Sun in the minimum of solar activity between solar cycles and was used as precursor to forecast maximal amplitude of sunspot number in solar cycle. It was found that solar cycle is expected to be relatively weak cycle with maximal strength of 1.±. in units of monthly sunspot numbers. 1. Introduction The -year sunspot cycle is the most famous and most used characteristic of the solar activity. The solar activity variations cause some changes in the interplanetary space and, in particular, in the Earth s magnetosphere. The last, in turn, affect the operation of such space-borne and ground-based technological systems as manned space flights, space navigation and aeronavigation, radars, ground power lines, high-frequency radio communication, etc. The solar activity variations have also some influence on the climate and living organisms on the Earth including people. This is why knowledge of the solar activity level in advance is interesting and sometimes very important. Now, at October of 00, the solar activity is very low, it is in deep minimum between solar cycles and, although the first bipolar sunspots with magnetic polarity of solar cycle appeared as early as December 00. At the present time it is very hard to say when maximum of solar cycle will occur and what maximal amplitude of sunspot number will be achieved. Many predictions for solar cycle exist at the present time. The most extensive set of predictions was collected and published by Pesnell (00), some published predictions are also collected, for example, in (Pishkalo, 00). Several panels of predictions of solar cycle can easily be found in the internet. Maximal amplitude of sunspot number in solar cycle is predicted to be in a wide range from (Clilverd et al., 00) to about (Li et al., 00). Many methods for the prediction of solar activity have been suggested up to date (see, e.g., Lantos and Richard, 1; Obridko and Shelting, 00; Pesnell, 00; Schatten, 00; Thompson, 1 and references therein). One of them is the precursor method, which uses some indexes or values as leading indicators of solar activity. Polar magnetic field of the Sun is one of such precursors. It is in addition physically-based precursor (Schatten et al., 1). In the present paper we analyze correlation between relative sunspot number and strength of Sun s polar magnetic field and forecast maximal amplitude of solar cycle.. Sunspot number and polar field of the Sun Figure 1 shows time evolution of relative sunspot number, heliospheric current sheet (HCS) tilt and strength of Sun s polar magnetic field in solar cycles 1. Monthly sunspot numbers were taken from the Solar Influences Data analysis Center (SIDC, HCS tilts and

3 magnitudes of polar fields were taken from the Wilcox Solar Observatory (WSO, Smoothed values are shown by bold lines. Vertical solid and dashed lines at the upper panel indicate times of magnetic reversals at northern and southern poles respectively according to (Pishkalo et al., 00). Figure 1. Relative sunspot number (the top panel), average classical (solid line) and radial (dashed line) tilt of the heliospheric current sheet (the middle panel) and magnitude of Sun s polar magnetic field (the bottom panel) at the northern pole (solid line) and the southern pole (dashed line) in solar cycles 1. Smoothed values are shown by bold lines. Vertical solid and dashed lines at the top panel present times of magnetic reversals at northern and southern poles, respectively. Relative sunspot number (or the Wolf number) characterizes the number of sunspots on the visible solar surface. Polar magnetic fields of the Sun are determined every days as -day average strength of magnetic field in the near-polar regions measured with -aperture, from about to the poles. The HCS tilts are determined using coronal synoptic maps computed in the potential approach as maximal latitudes of the HCS in the northern and southern hemispheres during specific rotations and are limited in high latitudes at the range of about degrees. The HCS position reflects the position of the magnetic neutral line of the global solar magnetic field at the source surface, which, in turn, mainly defines structure of the whole heliospheric magnetic field and, in particular, the sector structure of the interplanetary magnetic field near the Earth s orbit. In other words, the HCS is a manifestation of solar magnetic equator. It divides the interplanetary space into two parts with oppositely directed open magnetic field lines and is a framework of the heliosphere. One can see form Figure 1 that polarity (or direction) of polar magnetic field in the Sun's northern hemisphere is opposite to polarity of the field in the southern hemisphere, and polar magnetic field reversals occur near the times of the sunspot activity maxima. Moreover, magnetic reversals at northern and southern poles occur at different time; sometimes (as in solar cycle ) the time difference is slightly greater than one year. A pair of even and odd -year cycles forms one -year magnetic solar cycle (the Hale cycle). Sunspot number variations are in good agreement with variations of the HCS tilts. It allows calculating HCS tilts before 1 (Pishkalo, 00).

4 Average magnitude of polar magnetic field of the Sun is in anti-correlation with sunspot number. It is easily seen at the upper panel of Figure. Maxima of polar fields strength occur at minima of solar activity and vice versa. The correlation coefficient between smoothed sunspot number and magnitude of polar field is equal to -0. (P < 0.001). Figure. Sunspot numbers and average magnitudes of Sun s polar magnetic field (both smoothed) without any time shift (the upper panel) and with the time shift of days corresponding to about. years (the bottom panel). Cross-correlation analysis of smoothed sunspot numbers and magnitudes of polar field is presented at the upper panel of Figure. Here the % confidence limits are plotted by dashed lines. They were estimated by means of the standard Fisher r to z transformation (Mitropolsky, 11). The first left and right secondary maxima at the upper panel of Figure are equal to 0.0 (P < 0.001) and 0. (P < 0.001) correspondingly and tally with the time lag of and 1 days or the time period of about. and. years. Shown at the bottom panel of Figure are sunspot numbers in solar cycles 1- and magnitudes of polar magnetic field time-shifted forward on days corresponding to the first left secondary maximum at the upper panel of Figure. It should be noted that ratio of maximal sunspot number amplitude in solar cycles to corresponding time-shifted maximal magnitude of polar magnetic field is close to the same ratio in solar cycle (1. and 1.1 respectively). Cross-correlation of cross-cutting data is presented at the bottom panel of Figure. Maximal coefficient of correlation between sunspot number and time-shifted magnitude of polar magnetic field is equal to 0. (P < 0.001). Sunspot numbers depending on time-shifted magnitudes of polar magnetic field are plotted at the upper panel of Figure. Straight dashed and curved solid lines are linear and quadratic fits correspondingly. They are presented by the equations y = x, (1) y = x + 0.0x. When we select only the sunspot number points that are equal or greater than / of maximal sunspot number amplitude in each cycle, the equation for linear fit becomes the following (see, Figure, the bottom panel)

5 y = x. () Figure. Cross-correlation between smoothed sunspot numbers and magnitudes of polar magnetic fields of the Sun: the upper panel without time shift, the bottom panel polar fields are time-shifted forward on days (about. years), corresponding to the first left secondary maximum at the upper panel. The % confidence limits estimated by means of the standard Fisher r to z transformation are shown by dashed lines. Figure. Smoothed sunspot number dependence on shifted forward on days average magnitude of polar field for the solar cycles 1 (the upper panel all the data points, the bottom panel only points with magnitude greater than / of maximal sunspot number in cycles and. Straight and curved lines represent linear and quadratic fits respectively.

6 Prediction of amplitude of solar cycle According to the dynamo theory toroidal magnetic field of the Sun in the solar activity maximum is determined by poloidal magnetic field in the previous minimum (Schatten et al., 1). Sunspots (therefore sunspot number as well) are representations of toroidal magnetic field. Strength of polar magnetic field characterizes poloidal field. So, magnitude of polar magnetic field of the Sun in the minimum between solar cycles and can inform us about maximal amplitude of sunspot numbers in maximum of the forthcoming solar cycle. The equations obtained above can be used to calculate sunspot number when time-shifted magnitude of polar magnetic field is known. Sunspot numbers calculated using equations (1) are shown at the top panel of Figure. Here observed sunspot numbers are plotted by solid line, predicted ones obtained using linear and quadratic equations (1) by dashed and dotted lines respectively. For forthcoming solar cycle maximal amplitude of sunspot number is found to be about.±. and.±. for quadratic and linear approximation respectively. It can be seen from the top panel of Figure that amplitude of maximal sunspot number in each cycle predicted using equations (1) is less than corresponding observed amplitude. Maximal observed and calculated amplitudes of sunspot numbers in solar cycles and can be leveled by multiplying calculated sunspot numbers by about 1.0 and 1. for quadratic and linear approximation respectively (see, the middle panel of Figure ). It results in maximal calculated amplitude of sunspot number in solar cycle to be equal to about. and. for quadratic and linear approximation respectively. Hence, one can conclude that solar cycle is expected to be very weak cycle. It can be seen also from the bottom panel of Figure and the upper panel of Figure that near minima of solar activity relation between sunspot number and time-shifted magnitude of polar magnetic field is less revealed. So it seems that the use of time-shifted magnitudes of polar magnetic field near maxima of solar activity to predict maximal sunspot amplitude in solar cycle is more believable. If we use only the points with magnitude greater than / of maximal sunspot number in cycles and then predicted maximal sunspot number can be found from equation (). It yields to the value 1.±. for maximal amplitude of sunspot number in solar cycle. We adopt this result as our forecast for solar cycle. It is shown by dashed line at the bottom panel in Figure. So, strength of solar cycle is expected to be about twice weaker than strength of solar cycle 1 and about only / of strength of solar cycle. When we use, for example, the points with magnitude greater than / of maximal sunspot number in cycles and then resulting prediction becomes equal to.1±.0. It is very hard to tell at the present time when the maximum of solar cycle will occur. From average parameters of solar cycle it can be concluded that the maximum of solar cycle is expected to be at the end of 01. The next solar minimum is expected to be in end of 01 or early in 00. The result obtained here is very close to the results by Schatten (00) and Svalgaard et al. (00). Their predictions for maximal amplitude of monthly smoothed sunspot number in solar cycle are equal to 0± and ± respectively and were also obtained using Sun s polar field as precursor. Svalgaard et al. (00) have used time variation of the solar magnetic axial dipole moment expressed as the difference between the polar fields in the north and in the south hemispheres for the epochs of minima since 10. Prediction by Schatten (00) is based on the SODA method which uses a combination of polar and toroidal fields. Some other predictions (see, e.g., the panel of Pesnell, 00) are also close to our result, while the majority of predictions are higher. Our previous prediction based on the correlation between cycle parameters (Pishkalo, 00) indicates that maximal amplitude of monthly sunspot number is expected to be 1.±..

7 Figure. Observed (solid line) and predicted (dashed or dotted line) sunspot number in solar cycle 1. The top panel predicted sunspot numbers are calculated using equations (1), quadratic and linear approximation are shown by dotted and dashed lines respectively. The middle panel the same when predicted values are multiplied by 1.0 and 1. respectively. The bottom panel observed sunspot number and predicted strength of solar cycle.. Conclusions According to the dynamo theory, parameters of polar magnetic field of the Sun can be used as precursors to forecast strength of solar activity in the maximum of solar cycle. We have used average magnitude of polar magnetic field in the minimum of solar activity between solar cycles and, measured at the WSO, as the precursor to forecast maximal amplitude of sunspot number in solar cycle. Monthly international relative sunspot numbers from the SIDC were also used. The correlation between the sunspot number and magnitude of Sun s polar magnetic field in solar cycles 1 was investigated. Sunspot number is in anti-correlation with average magnitude of polar field (r = -0., P < 0.001). Maximal positive correlation between the parameters (r = 0., P < 0.001) was calculated when average magnitude of polar magnetic field was time-shifted forward on about days or. years. It was found that solar cycle is expected to be relatively weak cycle with maximal strength of 1.±. in units of monthly sunspot numbers that is only about / of the strength of solar cycle. Acknowledgements Author is very grateful to Prof. T. Hoeksema and the Wilcox Solar Observatory for the data on strength of polar magnetic fields of the Sun and the HCS tilts and R.A.M. Van der Linden and the SIDC team for sunspot number data, both available via the internet. References Clilverd, M. A., Clarke, E., Ulich, T., Rishbeth, H., and Jarvis, M. J.: 00, Predicting solar cycle and beyond. Space Weather, S000. doi:./00sw0000.

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