Expected hysteresis of the 23-rd solar cycle in the heliosphere

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Adv. Space Res. Vol. 29, No. 3, pp. 475--479, 2002 © 2002 COSPAR. Published by Elsevier Science Ltd. All fights reserved. Printed in Great Britain 0273-1177/02 $22.00 + 0.00 PII: S0273-1177(01)00615-9

EXPECTED HYSTERESIS OF THE 23-RD SOLAR CYCLE IN THE HELIOSPHERE A.V. Dmitriev, A.V. Suvorova, and I.S. Veselovsky Skobeltsyn Institute of Nuclear Physics Moscow State University, Moscow 119899, Russia

ABSTRACT Solar wind and interplanetary magnetic field parameters are investigated using the data obtained at the Earth's orbit for the 20-23 solar cycles. The time-epoch analysis and hysteresis curves of the heliospherie parameters show some general and specific properties of the cycles. We have found specific hysteresis behaviour when the solar wind energy flow and the induced electric field are plotted against the sunspot number during 20-22 solar cycles. Based on these finding and using measured heliospberic parameters during the rising phase of the current 23-rd solar cyele we are able to present some semi-quantitative estimations of the expected solar wind energy flux and the induced electric field for the time period after the solar maximum. The similarity between the rising phases of the 23-rd and 20-th solar cycles presents additional grounds for expectations of the lower maximum of the current solar cycle and the geomagnetic activity in the present solar cycle as compared with the 21-st and 22-nd solar cycles. © 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

INTRODUCTION Cyclic variations of the heliospheric plasma and magnetic field parameters are produced by the solar activity changes (Veselovsky et al., 1998; 1999). The most often used indices of the solar activity are related to the sunspot numbers (Vitinsky et al., 1986). It is known that average solar wind velocity at the Earth's orbit attains a maximal value during the declining phase of the solar activity. The strongest average interplanetary magnetic field (IMF) strength is observed just after the solar maxima. The average solar wind density is enhanced during rising and declining phase of the solar cycles as measured by sunspots. These qualitative regularities are still basic in the technique of the solar cycle forecasting. There are no quantitative relations for interdependence between solar and heliospheric parameters both in single solar cycle and in different ones. The purpose of this paper is the quantitative analysis of the relations between the Wolf numbers and solar wind and interplanetary magnetic field parameters in three past solar cycles from 20°ato 22no. On the base of this analysis the dynamics of the heliospheric parameters at the rising phase of the current 23-rd solar cycle is compared with previous ones. The result of this comparison is discussed in frame of the relation with previous well-known regularities in the solar activity cyclic variations. DATA ANALYSIS Hourly averaged solar wind and interplanetary magnetic field parameters at the Earth's orbit are used from the data base OMNIWeb (http://nssde.gsfc.nasa.gov/omniweb/ in 1964-1996), SOHO (http://umtof.umd.edu/pm/crn/crn data.html from 1997 to 2000) and ACE

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(ftp://sec.noaa.gov/pub/lists/ace2/from

1998 to the March 2000) together with the dally Wolf number (ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/). Logarithms of all parameters were calculated and averaged over the time periods one and thirteen solar rotations. The results are presented in Figures 1-4 respectively for the Wolf number W, the interplanetary magnetic field IMF strength B, the solar wind density n, and the velocity V for the given month. We also calculated average solar wind energy flux density Sk=mp.n.V3/2 (erg/cm2s) (Figure 5), here mp - the proton mass.

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Fig. 1. Variations of the monthly averaged sunspot number W. The plots and the horizontal scales correspond to each other as follows: 20-th solar cycle - the black solid line, 21-st - the grey line, 22-nd the dashed line, current 23-rd - the thick grey line. 1966

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Fig. 2. Left panel - variations of the monthly averaged IMF strength B. Right panel - the "hysteresis" diagram: yearly averaged IMF strength B versus Wolf number W. The grey code is the same as in Fig. 1.

Expected Hysteresis of the 23-rd Solar Cycle

477

The plots in Figure 1 and on the left panels in Figure 2-5 are constructed in a way, which is most comfortable for epoch analysis and comparison of the cycles. For this purpose, each cycle has its own time scale in that the minima of the different solar cycles are superimposed. The grey-scale coding refers to the cycles (corresponding to the axis colour). The superimposed plots have their own and common features allowing to investigate the dynamics. It is seen that regular and irregular variations are comparable and attain tens per cent for the averages and their deviations during the cycles. The comparison shows that the heliospheric quantities during the rising phase of the 23-rd solar cycle in general better follow the averages and deviations of the 20-th solar cycle, and not the 21-st or 22-nd solar cycles. It is especially truth for the IMF B (Figure 2), solar wind density n (Figure 3), and energy flux density Sk (Figure 5), as well as for sunspot numbers W (Figure 1). The same tendency - a good correspondence between the rising phase of the 23-rd and the 20-th solar cycle is demonstrated by the heliospheric "hysteresis" diagrams (right panels of Figure 2-5) for the averages over 13 solar rotations. The grey scale codes are the same as in top panels. These diagrams clearly show the non-uniqueness of the yearly averaged heliospheric parameter dependencies on the Wolf numbers. The parameters attain different values for the same Wolf numbers at the rising part and at the declining part of the given solar cycle and in the minima and maxima of different solar cycles. The common tendency is clearly seen on the "hysteresis" diagrams that the heliospheric parameters have higher values on the declining phase than on the rising phase of the solar cycle. For example, the IMF B average value is higher on declining phase and maximum of the solar activity at least on 20% relatively to the solar minimum and rising phase. One can see also that the average solar wind velocity V is nearly the same in the maximum and the minimum of the solar cycle (Figure 4). It is interesting to note that the average value of the solar wind density n (Figure 3) in the maxima of large solar cycles (21 st and 22 nd) is about twice higher than one in the maximum of the low cycles (20 th and 23rd). At the same time, for any solar minima the solar wind density value is similar and high n-8-9 cm"3. Most prominent difference of the values on rising and declining phases of the solar cycle is observed for the average solar wind kinetic energy flux Sk - more than 50%. The dynamics of Sk has the most stable and large hysteresis behaviour in the solar cycle. Furthermore, large and low solar cycles are significantly different on the "hysteresis" diagram for Sk. For the large cycles, the solar wind kinetic energy flux in average about twice higher than for the low ones. DISCUSSION Solar cycles represent complicated nonlinear dynamical phenomena. Their primary physical nature and drivers are still elusive in spite of the large amount of secondary observational manifestations on the Sun, in the heliosphere. The non-linear character of the solar cycles is seen, first of all, in the shorter and steeper rising parts as compared with the declining parts of the same cycle. Moreover, the steeper the rising part the shorter and more powerful cycle will be, as a rule. This last property seems to be useful in attempts of a rough estimation of an expected power of the current solar cycle judged by the rising part only. Based on this predictor, one can expect that the 23 rd solar cycle will be similar to the 20th solar cycle and not of a big power as the 21 st and the 22 nd solar cycles. If this really happens, this would mean the violation of the empirical Gnevyshev-Ohl rule [Gnevishev and Ohl', 1948] according to which the consecutive even-odd pairs of the solar cycles are ordered in the way, that each odd cycle is higher than the previous even one in the pair. Such violations happened about hundred years ago and earlier in the past. Nevertheless the rule "worked" well during most of the 20 th century and was also often used in attempts to make some long term forecasts. The physical grounds of this rule are not known, but the observed violations are sometimes supposed to be explained by the secular or chaotic variations in the solar activity. Hence only further observations could reveal regular and irregular dynamical properties of the cycles.

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Fig. 3. Left panel - variations of the monthly averaged solar wind density n. Right panel - the "hysteresis" diagram: yearly averaged n versus Wolf number W. The grey code is the same as in Fig. 1. 1966

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Expected Hysteresis of the 23-rd Solar Cycle

479

The observed hysteresis behaviour of the heliospheric parameters in dependence on the Wolf number is connected to the phase shifts between these characteristics. The maximal values of several heliospheric parameters are attained not at the sunspot maxima, but later on the declining phase. Strong fluctuations of the solar activity with the time scale of the order of the characteristic lifetime of the largest active regions (months) prevent the precise determination of the times of the minima and maxima of the solar activity. The resulting precision is not better than several months. Comparisons of the averaged heliospheric conditions in the rising phase of the current and the 20 th solar cycles show not only the good similarity but also some differences as well between both these cycles. The average solar wind velocity was lower at the rising phase of the current solar cycle than for the 20th one. On the contrary, the average solar wind density value is lower at the rising phase of the current 23 rd solar cycle than in the 20 th solar cycle. The continuation of observations of the Sun and the heliosphere are needed together with theoretical efforts for a better understanding of the predictability limits, which remain unclear. Nevertheless, based on the marked similarity and hysteresis behaviour of cycles one could expect average St values which will be up to a factor of two higher after the 23-rd solar maximum than observed at the rising part of the cycle in 1997-2000. CONCLUSIONS The current solar cycle develops in a way, which is generally similar to the 20 th solar cycle. This lends some additional grounds for expectations, that the 23 rd solar cycle will be lower than two previous cycles in the solar and heliospheric manifestations. Wolf numbers are not sufficient for the one-valued ordering of the heliospheric conditions at the Earth's orbit and corresponding solar-planetary relations. It is because of the "hysteresis" between solar activity indices and heliospheric parameters. The stable hysteresis is observed for Sk versus W in 20th - 22 nd solar cycles. The amplitude of the hysteresis for St varies from ~30% in the large solar cycles to 200% in the moderate ones. ACKNOWLEDGEMENTS This work was partially supported by RFBR grants 98-02-17660, 99-02-17630, the Federal Program "Astronomy" project 1.5.6.2, and the Program "Universities of Russia" grants N 992281, 99.

REFERENCES Gnevishev M.N., and Ohl', A. I., On the 22-year cycle of the solar activity, Astronomicheskii Zhumal, 25, 1, 18-20, 1948 (in Russian). Veselovsky, I.S., A.V. Dmitriev, and A.V. Suvorova, Average parameters of the solar wind and interplanetary magnetic field at the Earth's orbit for the last three solar cycles, Solar System Research, 32, 4, 310-315, 1998. Veselovsky I.S., A.V. Dmitriev, O.A. Panassenko, and A.V. Suvorova, Solar cycles in the energy and mass outputs of the heliospheric plasma, Astronomy Reports, 43, 7, 485-486, 1999. Vitinsky Yu.I., Kopecky M., Kuklin G.V., Statistics of the sunspot activity, Moscow, Nauka, 1986 (in Russian).