General trends in the changes of indices of solar activity in the late XX - early XXI century
aa r X i v : . [ a s t r o - ph . S R ] O c t GENERAL TRENDS IN THE CHANGES OF INDICES OFSOLAR ACTIVITY IN THE LATE XX - EARLY XXI CENTURY
E.A. Bruevich a , G.V. Yakunina ba,b, Sternberg Astronomical Institute, Moscow State University,Universitetsky pr., 13, Moscow 119992, Russiae-mail: a red-fi[email protected], b [email protected] Abstract.
The analysis of the observations of solar activity indexes SSN(NOAA Sunspot Numbers), the radio flux at a wavelength of 10.7 cm ( F . )and the solar constant (TSI) during the cycles 22 - 24 is presented. Wefound a decrease of the observed values of the SSN obs which was calculatedwith
SSN syn (using regression relationships between SSN and F . ) after1990 year on 20 - 25% instead of 35%, as was previously assumed. Thechanges in characteristics of the most popular index, SSN, such as decreasein the number of sunspots, the reduction of the magnetic field in small andmedium-sized spots are not in full compliance with the proposed scenario ofsolar activity predicted by radio flux F . in the cycles 23 and 24, and cannotbe fully explained by the influence on the SSN values of additional minimumof 50 - 70 year cycle. We have also showed that the observed changes of SSNlead to a slight increase of the solar constant TSI during the cycles 23 - 24compared to the cycle 22. Key words. solar cycle, observations, solar activity indices.
Solar activity is concentrated mostly in active regions. It is reflected differ-ently in various layers of the solar atmosphere. Depending on the method ofobservation, we then observe various manifestations of this activity which,provided they have a suitable quantitative expression, we use as characteristicindices of solar activity.Indices of solar activity studied in this paper are very important not onlyfor analysis of solar radiation which comes from different altitudes of solaratmosphere. 1ince all the manifestations of active regions require the presence of in-tensified magnetic fields, we have to assume that there is a more or less closeassociation between their individual characteristics.The most important for solar-terrestrial physics is the study of solar ra-diation influence on the different layers of terrestrial atmosphere (mainly thesolar constant TSI and radiation in EUV/UV spectral range which effectivelyheats the thermosphere of the Earth and so affects to our climate).Solar irradiance is the total amount of solar energy at a given wavelengthreceived at the top of the earth’s atmosphere per unit time. When integratedover all wavelengths, this quantity is called the total solar irradiance (TSI)previously known as the solar constant. Regular monitoring of TSI has beencarried out since 1978. From 1985 the total solar irradiance was observed byEarth Radiation Budget Satellite (EBRS).All the indices of solar activity are in most cases closely related, as themain source of all their variations is an variable magnetic field. We havestudied monthly averaged values of three global solar activity indices (SSN,TSI and F . ) during activity cycles 21, 22 and 23. Most of these observeddata we used in our paper were published in Solar-Geophysical Data Bul-letin (2009) and in Reports of National Geophysical Data Center Solar andTerrestrial Physics (2014).Monthly averages allowed us to take into consideration the fact that themajor modulation of solar indexes are the consequence of 27 - 28 days vari-ations of radiative fluxes (these variations correspond to the mean solar ro-tation period). After monthly averaging we reduced the influence of the ro-tational modulation on the observational data, see Bruevich et al . (2014a),Bruevich and Yakunina (2015). The various activity indices which character-ized the different aspects of the solar magnetic activity correlate quite wellwith the most popular solar index such as the sunspot numbers and withothers indices over long time scales.When various reconstructions of the past (and the predictions of thefuture) there means that the relationship between the indices of the activityremains unchanged over time. This is true for indices that are closely related,as, for example, fluxes in radio and UV ranges.Floyd et al . (2005) showed that the mutual relation between sunspotnumbers and also between three solar UV/EUV indices, the F . flux andthe Mg II core-to-wing ratio (which is the well known chromospheric UVindex, see (Viereck et al . (2001), Viereck et al . (2004)), remained stable for25 years until 2000. At the end of 2001 these mutual relations dramatically2hanged due to a large enhancement which took place after actual sunspotmaximum of the cycle 23. On the other hand the connection between theradiation fluxes and indirect indices, such as the SSN is not so obvious:processes of formation and evolution of spots are different and are poorlystudied.For all activity indices in the rd solar activity cycle one can see twomaximums separated one from another on 1,5 year approximately. We seethe similar double-peak structure in the cycle 22 but for the cycle 21 thedouble-peak structure is not so evident. We see that there are displacementsin both maximum occurrence time of all these indices in the rd solar cycle.We assume that the probable reason of such double-peak structures is amodulation of the 11-year fluxes variations by both of the quasi-biennial and5,5 year cyclicities of solar magnetic activity, see Bruevich and Kononovich(2011)Indeed, while a time there was a confidence in the close connection be-tween the radio flux F . and the SSN that we can always possible to cal-culate the value of one from another, see Bruevich and Yakunina (2011),now we see that this relationship has being not so stable. We have to pointout that close interconnection between radiation fluxes characterized the en-ergy release from different atmosphere’s layers is the widespread phenomenonamong the stars of late-type spectral classes. Bruevich & Alekseev (2007)confirmed that there exists the close interconnection between photosphericand coronal fluxes variations for solar-type stars of F, G, K and M spectralclasses with widely varying activity of their atmospheres. It was shown thatthe sum of areas of spots and the values of X-ray fluxes increase graduallyfrom the Sun and HK project stars with the low spotted discs to the highlyspotted K and M-stars.Observers believe that low values of global activity indices in 23-rd and24-th solar cycles can be explained in recent years with help of the overlapof the current 11-year cycle with the minimum of 50 - 70 year cycle. Theratio of SSN to the radio flux F . (which is considered the most reliablesolar index) from 1950 to 1990 was almost constant, and from 1990 to 2012began to decrease parabolically 30 - 35% (Livingston et al . (2012); Svalgaard(2013)).The magnetic activity of the Sun is called the complex of electromag-netic and hydrodynamic processes in the solar atmosphere and in the under-photospheric convective zone, see Rozgacheva and Bruevich (2002). Ob-servers found that the magnetic field strength of sunspots, averaged over all3pots, was gradually decreases from 1998 to 2011 by about 25%, see Liv-ingston et al . (2012). If these two trends (the ratio of SSN to the radio flux F . decreasing simultaneously with magnetic field strength of sunspots de-creasing) would develop in the same direction, the spots on the Sun would bedisappeared, as in the era of the Maunder minimum, see Svalgaard (2013).Other indices of activity associated with surface magnetic fields also areacting by unusual way in recent time. The analysis of the total area ofsunspots as well as the total space of the flare regions has made on thebasis of observational data from Observatory of San Fernando (Spain), seeChapman et al . (2014).It was shown that the relative amplitude of the total areas of the sunspotswere reduced from 1.0 in the maximum of the cycle 22 to 0.74, and 0.37 inthe maximums of cycles 23 and 24 respectively.Also at the Observatory of San Fernando the rations of total area of facu-lae to the total area of chromospheric network (the ratio of faculae/networkimages in the CaII K line) has been measured for the cycles 22, 23 and 24.In Chapman et al . (2014) was also found that the total area of faculae whichwere observed in the line of CaII K
CaII or MgII indices), see Fontenla et al . (2004),Krivova et al . (2003).The aim of this work is the analysis of recent general trends in the be-4avior of monthly averages of global indices of solar activity, such as relativespot numbers SSN, radio flux F . and the solar constant TSI in the cycles22 - 24 . The SSN - relative sunspot numbers index has decreased by a quarter over thepast 30 years according to the observations of Penn and Livingston (2006).Analysis of the data of Penn and Livingston (2006), Penn and Livingston(2011) held in Nagovitsyn et al . (2012) showed that along with the detectedtrend towards decreasing magnetic field spot, averaged over all spots, for thelargest spots such reduction of the magnetic field is not observable but thenormal variations typical of the 11-year cycle.
50 100 150 200 250050100150200250
SSN versus F F , sfu SSN a SSN synt F - 68, sfuSSN SSN synt SSN versus (F - 68) 1950 - 1990 b Figure 1: Dependences: a) - SSN from F . ; b) - SSN from ( F . - F min . ) .Observations from 1950 to 1990. 5n the period 1998 - 2011 the number of large spots decreased in accor-dance with the predictions of cyclical activity, whereas the number of smalland medium-sized spots increased. So, a negative correlation between thenumber of small and big spots was found, and an explanation for this con-tradiction was given. It turned out that only in the separation of the spotson small and large we have the opportunity to explain the contradictionsbetween the forecast and observations in the trends in changes of magneticfields in spots in the cycles 22, 23 and 24.The ratio of the SSN to the magnitude of the radiation flux on the waveof 10.7 cm remained almost constant from 1950 to 1990, after which thisratio has steadily decreased, see Livingston et al . (2012).For an objective assessment of this trend for observations 1950 - 1990with using the coefficients of the polynomial regression between SSN and theradiation flux F . , the SSN syn values were calculated, see Fig. 1.According to our calculations of the coefficients of the polynomial regres-sion from Fig. 1a the dependence of SSN from F . is described by thefollowing formula: SSN syn = − .
63 + 1 . · F . − . · F . (1) Fig. 1b shows the dependence of SSN from 10.7 cm radio flux where,instead of a full flux F . , we use only its variable part which is equal to F . − F min . .It is known that the lowest value of the 10.7 cm radio flux in the minimumsof 22 - 24 cycles is F min . = 68 sf u ( sf u = 10 − W att · m − · Hz − ), whichroughly corresponds to the radiation flux of the Sun in the complete absenceof spots.The dependence of the SSN from ( F . − F min . ) according to the poly-nomial regression from Fig. 1b is described by the following formula: SSN syn = 6 .
70 + 1 . · ( F . − − . · ( F . − (2) For each month of the observation based on the F . data with using theformulas (1) and (2) the SSN syn values are computed.Then we have computed the relationship
SSN obs (observed) to
SSN syn (calculated). Time series of these relations are shown in Fig. 2 in accor-dance with the method of constructing of annual averages
SSN obs /SSN syn according to Svalgaard (2013). 6
950 1960 1970 1980 1990 2000 20100.00.20.40.60.81.01.21.41.61.82.0 ** ******** ************ ****** ************ * *** SSN obs divided SSN synt as a function of F *** ** * * SSN obs divided SSN synt as a function of F - 68
SSN obs / SSN’ synt b years SSN>10
SSN>10
SSN obs / SSN synt a SSN synt
Svalgaard, L., 2013
Figure 2: a) - the time dependence of the average ratio of the observed num-bers of sunspots
SSN obs to values
SSN syn , calculated (crosses) using thecoefficients of the polynomial regression between SSN and the radiation flux F . . Annual average SSN obs / SSN syn from Svalgaard (2013) are markedwith asterisks; b) - the time dependence of the ratio of the observed averagemonthly number of sunspots
SSN obs to values
SSN syn calculated using thecoefficients of the polynomial regression between SSN and the flux of radia-tion ( F . − F min . ) . The months with SSN>10 are included in consideration.In Fig. 2a we show a time series of monthly averages of SSN obs / SSN syn (crosses) from 1950, extended by us until the beginning of 2015.We can see that in 2013 - 2014, the number of sunspots increased markedly,and ultimately a reduction in the amount
SSN obs / SSN syn was not so greatas in Livingston et al . (2012); Svalgaard (2013) and is of about 20%.In the case where SSN syn is calculated depending on the variable part ofthe radiation flux by the formula (2) the decrease in the
SSN obs / SSN syn inrecent years was 25% (Fig. 2b). Annual averages of
SSN obs / SSN syn , shownby asterisks in Figure 2a, were taken from Svalgaard (2013). It is seen that7he Svalgaard’s ratio
SSN obs / SSN syn has reduced by 35 %. by 2012.The difference with our results is due to the fact that in the period from2013 to 2015, which were not included in earlier papers, the number of spots
SSN obs has increased noticeably and the main trend was changed. Thereforethe value
SSN obs / SSN syn decreased only by 20 - 25% in our analysis.We also analysed the ratio of the monthly averaged number of spots tothe radio flux ( F . taking into account only the variable components of theradio flux: SSN obs / ( F . − F min . ) . SSN divided by the radio flux (F - 68) yearsSSN obs /(F - 68)
Linear FitPolinomial Fit
Figure 3: The time dependence of the ratios of the observed monthly averagedvalues of the sunspot numbers to the variable component of radio flux values:
SSN obs / ( F . − F min . ) . Observations from 1950 to 2015.As we can see in Fig. 3 a decrease in the relative number of sunspots after1990, In the case of linear regression, the reduction is about 15%, and in thecase of a polynomial (it is more suitable for the analysis of cross-correlationbetween solar indices) - about 25%.Note to the cyclical nature of SSN obs / ( F . − F min . ) dependence. Thedeviations from regression lines reach maximum values in the minima of the81-year cycles, when the relative error of observations of indices of activityincreases. Because of this fact we have to exclude from consideration themonths when SSN < .On the other hand, the dispersion of the deviations decreases and therelationship SSN obs / ( F . − F min . ) becomes closer to the regression line onthe rise and decline phases of the 11-year cycles, which is consistent with thefindings obtained by us earlier Bruevich et al . (2014b) about the maximumcorrelation between solar indices during these periods.Our analysis showed that the assumption Livingston et al . (2012) andSvalgaard (2013) about the desire of the average annual values of sunspotnumbers to zero, and in the near future is waiting for another Maunderminimum, is not confirmed.We have tried to reveal the effect of increasing the radiation flux from thesolar photosphere, and with it the increase in TSI as a result of the reductionof deficit of brightness of photospheric radiation in dark spots. A comparisonwas made of TSI in cycle 22 with TSI in the cycle 23 and the rising phase ofcycle 24 relatively to resistant solar index - radiation flux ( F . .In Fig. 4a and Fig. 4b we present the dependence of TSI from the radioflux at 10.7 cm. We used the observations of the total solar irradiance TSIfrom the entire solar disk, integrated over the entire solar spectrum. Thedata of TSI monitoring from 1978 to 2013, observed by various instrumentsduring the flight of multiple satellites that is standardized to the uniformobservational data, which are presented in National Geophysical Data CenterSolar and Terrestrial Physics data of observations, see NGDC (2013).In Fig. 4c we show a set of observations of TSI used to analyse. Separatelyfor the cycles 22 and 23+24 we built regression: in Fig. 4a - linear, in Fig. 4b -polynomial for the cycle 22 and linear for the cycles 23+24. It is known thatpolynomial regression best describes the relationship between the activityindices in the maxima of the cycles. Fig. 4 shows that for large values of F . the TSI values in the different cycles are different: the value of the solarconstant during the periods 2000 to 2013 is higher than in 1985 - 1996.The rms (mean-square) deviation of the TSI values from regression linesfor linear and polynomial is about . W att/m . When F . = 240 sf u thedifference between TSI in the 22-nd cycle and TSI in the cycles 23+24 isabout . W att/m for the dependencies in Fig. 4a and . W att/m for thedependencies in Fig. 4b.Thus, the difference between the two regression dependencies in Fig. 4aand in Fig. 4b are statistically significant with a significance level of 0.059 Watt / m c F , sfu cycle 221985-1996cycle 23 + rising phase of cycle 24 1997-2013 TSI, Watt/m a
80 120 160 200 240 F , sfu cycle 221985-1996 cycle 23 + rising phase of cycle 24 1997-2013 TSI, Watt/m b polinomial Figure 4: The dependence of TSI from radio flux F . for 22, and 23+24cycles of solar activity: a) - linear regression for 22 and (23+24) cycles; b)- linear regression for (23+24) cycles and polynomial regression for 22 cycle;c) - the set of TSI observations from 1978 to 2013.when F . is equal to sf u , and with a significance level of 0.01 in themaximum cycle when F . is equal to sf u .This effect was predicted in Svalgaard (2013). It was assumed that thevalue of the solar constant should be increased when reducing the number ofsunspots and the magnetic field strength in them.It increases the radiation flux from the photosphere due to the decreasingof deficit of bright photosphere’s flux in dark spots. Moreover, the relativeamplitudes of the total areas of spots in the cycle’s maximums decrease in thecycles 23+24 compared to the cycle 22, and the ratio of total areas of faculaeto total areas of spots in the cycle 24 is growing according to Chapman et al . (2014). This also leads to an increase of the radiation flux from thephotosphere.It is obvious that the detection of this effect is difficult, as the maximum10ariation of TSI in the cycle of activity is not more than 0.1 - 0.15% of theaverage value in the cycle. The analysis of relationship of mean monthly observed values
SSN obs (NOAASunspots Numbers) depending on
SSN syn from 1950 to 2015 which werecalculated using the coefficients of the polynomial regression between SSNand the radio flux F . according to the observations 1950 - 1990, showedthat for the monthly averages SSN obs / SSN syn the scatter of the devia-tions from the regression line is greater than in the case of yearly averages
SSN obs / SSN syn from Svalgaard (2013). We also show the cyclical natureof
SSN obs / ( F . − F min . ) dependence. The period of this cycle is equal tohalf part of 11 yr, see Fig. 3. The deviations from regression lines reachmaximum values in the minima of the 11-year cycles, when the relative errorof observations of indices of activity increases.While an observations show marked increase in 2013 - 2014 of the numbersof sunspots we received a reduction in the amount SSN obs / SSN syn only 20%(Fig. 2a), and this value is less than 35% of Livingston et al . (2012)andSvalgaard (2013).As we noted earlier in Bruevich et al . (2014b) the relationships betweenthe indices are much stronger in the moments related to the rising and de-clining phases of the 11-year cycle and worse in moments of maximums andminimums of the cycle, which is confirmed by Fig. 3.Our detailed analysis of the variation of TSI fluxes in the cycles 22 - 24showed that the assumption in Svalgaard (2013) which was done on obser-vational data of Penn and Livingston (2006), (2011) and Chapman et al . (2014) is true: at one and the same level of F . the value of TSI at thecycles 23 - 24 increases, see Fig. 4. This assumption is based on the fol-lowing effect: when reducing the average number of spots and with reducingof their contrasts the deficit of the overall flux of radiation from the solarphotosphere is slightly increased, and with it the TSI grows.11 eferences Sun and Geosphere , , N2, 91.[4] Bruevich E., and Yakunina G. 2015, Moscow University Physics Bul-letin , , N4, 282-290. DOI: 10.3103/S0027134915040062[5] Floyd, L., Newmark, J., Cook, J., Herring, L. and McMullin, D. 2005, Journal of Atmospheric and Solar-Terrestrial Physics , , 3.[6] Viereck, R., Puga, L., McMullin, D., Judge, D., Weber, M. and Tobiska,K. 2001, J. Geophys. Res. , , 1343.[7] Viereck, R.A., Floyd, L.E., Crane, P.C., Woods, T.N., Knapp, B.G.,Rottman, G., Weber, M., Puga, L.C. and Deland, M.T. 2004, in SpaceWeather II , S10005.[8] Bruevich E.A., Kononovich E.V. 2011,
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