Temporal variation of solar flare index during solar cycles 21–24

The present investigation attempts to quantify the temporal variation of Solar Flare Index(SFI)with other activity indices during solar cycles 21-24 by using different techniques such as linear regression,correlation,cross-correlation with phase lag-lead,etc.Different Solar Activity Indices(SAI)considered in this present study are Sunspot Number(SSN),10.7 cm Solar Radio Flux(F10.7),Coronal Index(CI)and MgⅡCore-to-Wing Ratio(MgⅡ).The maximum cycle amplitude of SFI and considered SAI has a decreasing trend from solar cycle 22,and cycle 24 is the weakest solar cycle among all other cycles.The SFI with SSN,F10.7,CI and MgⅡshows hysteresis during all cycles except for solar cycle 22 where both paths for ascending and descending phases are intercepting each other,thereby representing a phase reversal.A positive hysteresis circulation exists between SFI and considered SAI during solar cycles 22 and 23,whereas a negative circulation exists in cycles 21 and 24.SFI has a high positive correlation with coefficient values of 0.92,0.94,0.84 and 0.81 for SSN,F10.7,CI and MgⅡrespectively.According to crosscorrelation analysis,SFI has a phase lag with considered SAI during an odd-number solar cycle(solar cycles21 and 23)but no phase lag/lead during an even-numbered solar cycle(solar cycles 22 and 24).However,the entire smoothed monthly average SFI data indicate an in-phase relationship with SSN,F10.7 and MgⅡ,and a one-month phase lag with CI.The presence of those above characteristics strongly confirms the outcomes of different research work with various solar indices and the highest correlation exists between SFI and SSN as well as F10.7 which establishes that SFI may be considered as one of the prime activity indices to interpret the characteristics of the Sun’s active region as well as for more accurate short-range or long-range forecasting of solar events.     

Asymmetric behavior of different solar activity features over solar cycles 20–23

This paper presents the study of normalized north–south asymmetry, cumulative normalized north–south asymmetry and cumulative difference indices of sunspot areas, solar active prominences (at total, low (?40°) and high (?50°) latitudes) and Hα solar flares from 1964 to 2008 spanning the solar cycles 20–23. Three different statistical methods are used to obtain the asymmetric behavior of different solar activity features. Hemispherical distribution of activity features shows the dominance of activities in northern hemisphere for solar cycle 20 and in southern hemisphere for solar cycles 21–23 excluding solar active prominences at high latitudes. Cumulative difference index of solar activity features in each solar cycle is observed at the maximum of the respective solar cycle suggesting a cyclic behavior of approximately one solar cycle length. Asymmetric behavior of all activity features except solar active prominences at high latitudes hints at the long term periodic trend of eight solar cycles. North–south asymmetries of SAP (H) express the specific behavior of solar activity at high solar latitudes and its behavior in long-time scale is distinctly opposite to those of other activity features. Our results show that in most cases the asymmetry is statistically highly significant meaning thereby that the asymmetries are real features in the N–S distribution of solar activity features.     

Heliospheric modulation of cosmic rays in solar cycles 19–23

The previously developed basic theory of the heliospheric modulation of high-energy cosmic rays is generalized to lower energies. Comparison of the theory with the results of long-term observations of cosmic rays in the stratosphere carried out by the group from the Lebedev Institute of Physics inMoscow andMurmansk shows satisfactory agreement. The cosmic rays are shown to behave quite differently when even and odd solar cycles alternate. Possible causes of the anomalously high cosmic-ray intensity recorded during the last solar activity minimum are discussed.     

Are short-time variations of the solar S-component emission identical with microwave bursts?

Extended time series (time resolution about 2–3 min) of spatially resolved observations (≫ 17 arcsec) in one dimension of solar S-component sources obtained at the Siberian Solar Radio Telescope (SSRT) at 5.2 cm wavelength allow the detection of evolutional features of the growth and decay of active regions in the solar corona. Characteristic slow flux variations with timescales of about 1–2 hours occurring during the decay phase of the radio emission in the low corona above plages and sunspots are compared with recently detected step-like flux increases on timescales of about 10–20 min followed by quasi-constant periods appearing in the initial phase of the development of active regions. Superimposed on this basic behaviour, also fluctuations at shorter timescales (or even periodic oscillations) have been observed. As it is well known from emission-model calculations, the variations of the S-component radiation can be due to variations of the magnetic field and/or changes of the energy of the radiating particles, which is basically the same emission mechanism as for microwave bursts. Since the “S-component” is originally defined by its long timescale behaviour derived from whole-Sun flux density measurements, the presently detected small-timescale features in S-component sources require either a revised definition of S-component emission or must be considered as “burst-like”.     

Mid-term periodicities and heliospheric modulation of coronal index and solar flare index during solar cycles 22–23

We applied fast Fourier transform techniques and Morlet wavelet transform on the time series data of coronal index, solar flare index, and galactic cosmic ray, for the period 1986–2008, in order to investigate the long- and mid-term periodicities including the Rieger (\({\sim }130\) to \({\sim }190\) days), quasi-period (\({\sim }200\) to \({\sim }374\) days), and quasi-biennial periodicities (\({\sim }1.20\) to \({\sim }3.27\) years) during the combined solar cycles 22–23. We emphasize the fact that a lesser number of periodicities are found in the range of low frequencies, while the higher frequencies show a greater number of periodicities. The rotation rates at the base of convection zone have periods for coronal index of \({\sim }1.43\) years and for solar flare index of \({\sim }1.41\) year, and galactic cosmic ray, \({\sim }1.35\) year, during combined solar cycles 22–23. In relation to these two solar parameters (coronal index and solar flare index), for the solar cycles 22–23, we found that galactic cosmic ray modulation at mid cut-off rigidity (\(\hbox {Rc} = 2.43\hbox {GV}\)) is anti-correlated with time-lag of few months.     

The height stratification of solar magnetic fields in cycles 21–23

The radial component of the solar magnetic field, Br, was calculated in the potential approximation in the height range from 1 to 2.5 solar radii, Ro. According to these data, synoptic maps of the magnetic field for solar cycles 21–23 were constructed. For each 10-degree latitudinal zone, the proportion of its area, S _+field, that was occupied by the “+” field in each rotation was found. In the entire latitudinal zone, the radial component of the field is assumed to be positive if S_+field ≥ 80% and negative if S _+field ≤ 20%. The field proved to be virtually unipolar at the level of the photosphere (R = Ro) during most of the cycle, from the poles to the north and south latitude ≈60°. In the vicinity of minimums between cycles 21 and 22, as well as cycles 22 and 23, for a few rotations of the Sun, the field was almost unipolar within the range of latitudes (?40°)-90°. At R = 2.5 Ro, for most of each cycle, the field was unipolar in the range of latitudes (?20°-(-90°)) and (20°–90°). According to our interpretation, the shift of the polar-field boundary to the equator with height reflects superradial expansion of open magnetic flux tubes from the polar coronal holes. It was found that the reversal of the polar fields began with 1–2 rotations and ended from 2 to 14 solar rotations earlier at great heights than at the surface of the Sun. This indicates that the reversal of the large-scale field occurs first and then that of the small-scale one. In the study of the sectoral structure of the magnetic field at different heights it was found that the boundaries that rotate with a period of less than the Carrington revolution extend to greater heights than the boundaries with a Carrington or longer period. We assume that the boundaries of the first type are formed by the large-scale structures of the magnetic field and the boundaries of the second type are determined by the active regions.     

Solar modulation of galactic cosmic rays during 19–23 solar cycles

We make a detailed analysis of cross-correlation and time-lag between monthly data of galactic cosmic rays (GCRs) intensity and different solar activity indices (e.g., sunspot number, sunspot area, green coronal Fe line and 10.7 cm solar radio flux) during 19–23 solar cycles. GCRs time-series data from Kiel neutron monitor station and solar data from the last 50 years period, covering five solar cycles (19–23), and alternating solar polarity states (i.e., five A < 0 and four A > 0) have been investigated. We find a clear asymmetry in the cross-correlation between GCRs and solar activity indicators for both odd and even-numbered solar cycles. The time-lags between GCRs and solar parameters are found different in different solar cycles as well as in the opposite polarity states (A < 0 and A > 0) within the same solar cycle. Possible explanations of the observed results are discussed in light of modulation models, including drift effects.     

On the cyclicity of solar magnetic fields during cycles 21–23

The cyclicity of weak local and strong large-scale components of the low-latitude solar magnetic field during the last three cycles of solar activity is studied using the average monthly values for the total area of sunspots and general magnetic field of the sun as a star. A local decrease in the value of magnetic flux is found for both components of the magnetic field in the phase of growing solar activity. This decrease coincides in time with the intervals of monopolarity for the polar magnetic field of the sun.     

Statistical characteristics of large sunspots in solar activity cycles 17–23

Integral and differential distributions of sunspot diameters are studied for the last seven 11-year cycles of solar activity. Data of the Greenwich catalogue, Pulkovo’s database, and the “Solniechnyie Dannyie” bulletin are used. We found that the average index of integral distribution α is 6.0 for the diameters from 50 to 90 Mm and independent of the Wolf’s numbers, but it depends on a cycle phase in the majority of cycles (four of seven), i.e., it is higher during the ascending phase, of intermediate value during the maximum phase and minimum during the declining phase. Cycles 17, 18, and 22 behave differently: the index α is either invariable with phase or the variations differ from the above ones. It turned out that cycles 17 and 18 are peculiar by sunspot diameters, i.e., sunspots of up to 140–180 Mm in diameter, the largest over the last 80 years, have been observed. Three assumptions concerning the nature of these gigantic sunspots have been proposed: (a) these sunspots occur due to changes in differential rotation of the sun, (b) these sunspots are a certain independent statistical assembly formed in a sporadic discrete region of the convective zone, and (c) these sunspots are surface “fragments” of the relict magnetic field of the solar nucleus.     

What are solar faculae?

Results are presented of observations of the facula area near the solar disc center. Observations were performed at the German Vacuum Tower Telescope of the Observatorio del Teide (Tenerife) with the simultaneous use of two instruments, i.e., TESOS in the Ba IIλ 455.4 nm line to measure intensity variations in the photosphere and, at the same time, TIP in the Fe I (λλ 1564.3–1565.8 nm) line to measure Stokes parameters. Using the Fourier filtering technique, we separated the convective and wave components of the intensity field. Stokes parameters Fe I λ 1564.8 nm and λ 1565.2 nm were inverted by the SIR inversion code to estimate the magnetic field strength. We found that the contrast of intergranular lines of the facula in the continuum is almost independent of the magnetic field strengh (in the range from 30 to 160 mT). This result casts doubt on the assertion that solar faculae are a cluster of magnetic flux tubes. Most likely, due to the decrease of transparency of the matter in a strong (approximately 1 kilogauss) magnetic field, we can see the hot walls of granules.     

The north–south asymmetry of filaments in solar cycles 16–21

In the present study, the north–south asymmetry of filaments in solar cycles 16–21 is investigated with the use of the solar filaments observed at the Observatoire de Paris, Section de Meudon from March 1919 to December 1989. Filament activity is found regularly dominated in each of cycles 16–21 in the same hemisphere as that inferred by sunspot activity, and it is found to run in a different asymmetrical behavior at different latitudinal bands, suggesting that the north–south asymmetry of filament activity should be a function of latitudes. The regularity on the north–south asymmetry of sunspot activity given by Li et al. (2002b) is demonstrated by filament activity. The periods in the north–south asymmetry of solar filament activity are 9.13, and 12.8 years without the solar cycle found.     

Recurring coronal holes and their rotation rates during the solar cycles 22–24

Coronal holes (CHs) play a significant role in making the Earth geo-magnetically active during the declining and minimum phases of the solar cycle. In this study, we analysed the evolutionary characteristics of the Recurring CHs from the year 1992 to 2016. The extended minimum of Solar Cycle 23 shows unusual characteristics in the number of persistent coronal holes in the mid- and low-latitude regions of the Sun. Carrington rotation maps of He 10830 Å and EUV 195 Å observations are used to identify the Coronal holes. The latitude distribution of the RCHs shows that most of them are appeared between \(\pm 20^{\circ }\) latitudes. In this period, more number of recurring coronal holes appeared in and around \(100^{\circ }\) and \(200^{\circ }\) Carrington longitudes. The large sized coronal holes lived for shorter period and they appeared close to the equator. From the area distribution over the latitude considered, it shows that more number of recurring coronal holes with area \(<10^{21}~\mbox{cm}^{2}\) appeared in the southern latitude close to the equator. The rotation rates calculated from the RCHs appeared between \(\pm 60^{\circ }\) latitude shows rigid body characteristics. The derived rotational profiles of the coronal holes show that they have anchored to a depth well below the tachocline of the interior, and compares well with the helioseismology results.     

Does the solar magnetic field increase?

We consider measurements of the general magnetic field (GMF) of the Sun as a star at four world observatories from 1968 until 1999. We show that, within the error limits, the mean strength of the photospheric magnetic field H (of its longitudinal component, in magnitude) has not changed over the last 32 years. This is in conflict with the recent conclusion by Lockwood et al. (1999) that the solar coronal magnetic field increased by 40% from 1964 until 1996 and has almost doubled in the last 100 years. The causes of discrepancies in the results are discussed. At the same time, the GMF exhibits a natural 11-year variation associated with the solar cycle. The strength of the photospheric longitudinal magnetic field (in absolute value) averaged over 32 years is 0.46 G (at an rms GMF strength of 0.57 G). The mean GMF for all years of measurements had a south polarity: $\bar H = - 0.030 \pm 0.018 G$ . The difference from zero is statistically significant at 1.7σ (90%) and may be directly related to the outstanding problem of the solar magnetic “monopole.”     

Predicting monthly sunspot numbers of solar cycle 23 by the method of “similar cycles”

We briefly describe the concept and method of “similar cycles” to be used in sunspot prediction. We have checked on the reliability of this method and made the comparison of the predictions and observations for the 23rd solar activity cycle.     

Prediction verification of solar cycles 18–24 and a preliminary prediction of the maximum amplitude of solar cycle 25 based on the Precursor Method

Predictions of the strength of solar cycles are important and are necessary for planning long-term missions.A new solar cycle 25 is coming soon,and the amplitude is needed for space weather operators.Some predictions have been made using different methods and the values are drastically different.However,since 2015 July 1,the original sunspot number data have been entirely replaced by the Version 2.0 data series,and the sunspot number values have changed greatly.In this paper,using Version 2 smoothed sunspot numbers and aa indices,we verify the predictions for cycles 18–24 based on Ohl’s Precursor Method.Then a similar-cycles method is used to evaluate the aa minimum of 9.7(±1.1)near the start of cycle 25 and based on the linear regression relationship between sunspot maxima and aa minima,our predicted Version 2maximum sunspot number for cycle 25 is 121.5(±32.9).     

Are collisions with electrons important for modeling the polarization of the lines of the C_2 solar molecule?

Observations of the second solar spectrum(SSS) revealed the existence of prominent linear polarization signals due to lines of the C_2 molecule.Interpretation of the SSS is the only tool to obtain the weak and turbulent magnetic field which is widespread in the Quiet Sun.However,this interpretation is conditioned by the determination of accurate collisional data.In this context,we present a formulation of the problem of the calculation of the polarization transfer rates by collisions of polarized C_2 states with electrons.The obtained formulae are applied to determine,for the first time,the polarization transfer rates between the C_2 states of the Swan band electronic system(a ~3Π_u d ~3Π_q) and electrons for temperatures going up from 1000 to 10000 K.However,due to the closeness of the electronic states of the C_2 molecule,the two electronic d ~3Π_g and a ~3Π_u cannot be disconnected from the other electronic levels and,thus,a model based on only two states is not sufficient to describe the formation of the lines in the Swan band.Consequently,we also calculated the collisional polarization transfer rates in the case where the first eight electronic states of C_2 are taken into account.All rates are given as functions of the temperature by power laws.Our results should be useful for future solar applications.     

What do the solar activity indices represent?

Sunspot number, sunspot area, and radio flux at 10.7 cm are the indices which are most frequently used to describe the long‐term solar activity. The data of the daily solar full‐disk magnetograms measured at Mount Wilson Observatory from 19 January 1970 to 31 December 2012 are utilized together with the daily observations of the three indices to probe the relationship of the full‐disk magnetic activity respectively with the indices. Cross correlation analyses of the daily magnetic field measurements at Mount Wilson observatory are taken with the daily observations of the three indices, and the statistical significance of the difference of the obtained correlation coefficients is investigated. The following results are obtained: (1) The sunspot number should be preferred to represent/reflect the full‐disk magnetic activity of the Sun to which the weak magnetic fields (outside of sunspots) mainly contribute, the sunspot area should be recommended to represent the strong magnetic activity of the Sun (in sunspots), and the 10.7 cm radio flux should be preferred to represent the full‐disk magnetic activity of the Sun (both the weak and strong magnetic fields) to which the weak magnetic fields mainly contribute. (2) On the other hand, the most recommendable index that could be used to represent/reflect the weak magnetic activity is the 10.7 cm radio flux, the most recommendable index that could be used to represent the strong magnetic activity is the sunspot area, and the most recommendable index that could be used to represent the full‐disk magnetic activity of the Sun is the 10.7cm radio flux. Additionally, the cycle characteristics of the magnetic field strengths on the solar disk are given. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Statistical properties of X-class flares and their relationship with super active regions during solar cycles 21–23

We investigate the statistical distribution of X-class flares and their relationship with super active regions (SARs) during solar cycles 21–23. Analysis results show that X1.0–X1.9 flares accounted for 52.71 % of all X-class flares, with X2.0–X2.9 flares at 20.59 %, X3.0–X4.9 at 13.57 %, X5–X9.9 at 8.37 % and ≥X10 at 4.75 %. All X-class flares occurred around the solar maximum during solar cycle 22, while in solar cycle 23, X-class flares were scattered in distribution. In solar cycle 21, X-class flares were distributed neither in a concentrated manner like cycle 22 nor in a scattered manner as cycle 23. During solar cycles 21–23, 32.2 % of the X1.0–X1.9 flares, 31.9 % of the X2.0–X2.9 flares, 43.3 % of the X3.0–X4.9 flares, 81.08 % of the X5.0–X9.9 flares, and 95.2 % of the ≥X10 flares were produced by SARs.     

Dynamic screening in solar p-p reactions: is the mean-field approach applicable in solar plasma?

Although the Salpeter approximation for static screening is widely accepted and used in stellar modeling, the question of dynamic screening has been revisited. Here we reproduce Shaviv and Shaviv’s numerical analysis of the screening energy for p-p reactions in the solar core using the techniques of molecular dynamics to directly calculate the motion of ions and electrons due to Coulomb interactions without the mean-field assumption that is inherent in the Salpeter approximation. We conclude that the effects of dynamic screening are relevant and should be included in the treatment of the plasma, especially in the computation of nuclear reaction rates.     

Are QSOs local objects?

The similarities of the spectra of QSOs with those of Wolf-Rayet stars are pointed out. The emission spectrum of the earliest discovered QSO, 3C 273, in the ultraviolet and visible regions is interpreted as that of an object deficient in hydrogen like Wolf-Rayet stars but havingno redshift. The visible emission spectra of two other QSOs, 3C 48 and 3C 280.1, are also similarly interpreted. It is further assumed that the absorption lines of QSOs are produced in an expanding atmosphere so that they are violet shifted as in Wolf-Rayet stars. Fifty-four out of 55 narrow absorption lines of the QSO Q 1246-057 are interpreted on the assumption that the average velocity of the absorbing ions is 500 km s^–1, although the redshift theory can explain only 23 lines by invoking six different redshifts: Four of the five emission lines of the same object can be identified assuming no shift. Since the QSOs are here assumed to be comparatively local objects, the problems of energy supply, superluminal velocities, etc., raised by the conventional explanation do not arise in this case.Presently at the Institut für Physikalische und Theoretische Chemie, Universität Erlangen, F.R.G.