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)     

太阳与地磁活动的1.3–1.7 yr振荡关系分析

太阳和地磁活动中的1.3–1.7 yr周期研究对于理解日地空间耦合系统中可能发生的物理过程十分重要.黑子是太阳光球层上最突出的磁场结构, Ap指数则是表征全球地磁活动水平的重要指标.使用同步压缩小波变换得到太阳黑子数和地磁Ap指数的1.3–1.7yr周期,并用互相关方法分析研究它们之间的相位关系.结果如下:(1)太阳黑子数和地磁Ap指数的1.3–1.7 yr周期呈现间歇性的演化特征,且随着时间的变化而不断变化;(2)地磁Ap指数在奇数活动周比相邻的偶数活动周的周期分量更高,表现出上下波动的变化特性;(3)地磁Ap指数和太阳黑子数的相位关系不是一成不变的,在大多数情况下地磁Ap指数滞后太阳黑子数,仅在第18和第22活动周黑子数在相位上滞后.     

Analysis of the 1.3–1.7 yr Oscillation Relationship between Solar and Geomagnetic Activities

The study on the 1.3–1.7 yr period of the solar and geomagnetic activities is very important for understanding the possible physical processes in the solar-terrestrial coupling system. The sunspot is the most prominent magnetic field structure in the solar photosphere, and the Ap index is an important indicator for the global geomagnetic activity level. The 1.3–1.7 yr period for the sunspot number and the geomagnetic Ap index is obtained by the synchro-squeezing wavelet transform, and the phase relationship between them is studied by the cross-correlation analysis. The main results are as follows: (1) The 1.3–1.7 yr period of the geomagnetic Ap index and sunspot number exhibits an intermittent evolutionary characteristics, and changes continuously with the time; (2) the geomagnetic Ap index has a higher periodic component in the odd solar cycles than the neighboring even solar cycles, which is characterized by fluctuations; (3) the phase relationship between the geomagnetic Ap index and the sunspot number is not always invariant, in most cases the geomagnetic Ap index lags behind the sunspot number, except in the 18th and 22th solar cycles.     

How to Reach Superequipartition Field Strengths in Solar Magnetic Flux Tubes

A number of independent arguments indicate that the toroidal flux system responsible for the sunspot cycle is stored at the base of the convection zone in the form of flux tubes with field strength close to 10⁵ G. Although the evidence for such strong fields is quite compelling, how such field strength can be reached is still a topic of debate. Flux expulsion by convection should lead to about the equipartition field strength, but the magnetic energy density of a 10⁵-G field is two orders of magnitude larger than the mean kinetic energy density of convective motions. Line stretching by differential rotation (i.e., the “Ω effect” in the classical mean-field dynamo approach) probably plays an important role, but arguments based on energy considerations show that it does not seem feasible that a 10⁵-G field can be produced in this way. An alternative scenario for the intensification of the toroidal flux system in the overshoot layer is related to the explosion of rising, buoyantly unstable magnetic flux tubes, which opens a complementary mechanism for magnetic-field intensification. A parallelism is pointed out with the mechanism of “convective collapse” for the intensification of photospheric magnetic flux tubes up to field strengths well above equipartition; both mechanisms, which are fundamentally thermal processes, are reviewed.     

Activity cycle of solar filaments

Long-term variation in the distribution of the solar filaments observed at the Observatorie de Paris, Section de Meudon from March 1919 to December 1989 is presented to compare with sunspot cycle and to study the periodicity in the filament activity, namely the periods of the coronal activity with the Morlet wavelet used. It is inferred that the activity cycle of solar filaments should have the same cycle length as sunspot cycle, but the cycle behavior of solar filaments is globally similar in profile with, but different in detail from, that of sunspot cycles. The amplitude of solar magnetic activity should not keep in phase with the complexity of solar magnetic activity. The possible periods in the filament activity are about 10.44 and 19.20 years. The wavelet local power spectrum of the period 10.44 years is statistically significant during the whole consideration time. The wavelet local power spectrum of the period 19.20 years is under the 95% confidence spectrum during the whole consideration time, but over the mean red-noise spectrum of α = 0.72 before approximate Carrington rotation number 1500, and after that the filament activity does not statistically show the period. Wavelet reconstruction indicates that the early data of the filament archive (in and before cycle 16) are more noiseful than the later (in and after cycle 17).     

Sunspot groups at high latitude

Data of sunspot groups at high latitude (35°), from the year 1874 to the present (2000 January), are collected to show their evolutional behaviour and to investigate features of the yearly number of sunspot groups at high latitude. Subsequently, an evolutional pattern of sunspot group number at high latitude is given in this paper. Results obtained show that the number of sunspot groups of a solar cycle at high latitude rises to a maximum value about 1 yr earlier than the time of the maximum of sunspot relative numbers of the solar cycle, and then falls to zero more rapidly. The results also show that, at the moment, solar activity described by the sunspot relative numbers has not yet reached its minimum. In general, sunspot groups at high latitude have not appeared on the solar disc during the last 3 yr of a Wolf solar cycle. The asymmetry of the high latitude sunspot group number of a Wolf solar cycle can reflect the asymmetry of solar activity in the Wolf solar cycle, and it is suggested that one could further use the high latitude sunspot group number during the rising time of a Wolf solar cycle, maximum year included, to judge the asymmetry of solar activity over the whole solar cycle.     

Search for magnetic field oscillations in a sunspot umbra

In order to search for oscillations in velocity and magnetic field strength within a sunspot umbra, a time series of spectra has been obtained through a circular analyzer and the Gregory-Coudé telescope at the Observatorio del Teide, Tenerife. The velocity oscillations clearly show peaks of power at periods between 2 and 7 minutes, with a maximum at 5 minutes. The apparent variations of the magnetic field strength, however, don't exhibit significant oscillations; these fluctuations are rather produced by the influence of parasitic stray light from the surrouding quiet sun which are also visible in the measured time variations of the umbral contrast of continuum intensity.     

Multiresolution Analysis of Active Region Magnetic Structure and its Correlation with the Mount Wilson Classification and Flaring Activity

Two different multiresolution analyses are used to decompose the structure of active-region magnetic flux into concentrations of different size scales. Lines separating these opposite polarity regions of flux at each size scale are found. These lines are used as a mask on a map of the magnetic field gradient to sample the local gradient between opposite polarity regions of given scale sizes. It is shown that the maximum, average, and standard deviation of the magnetic flux gradient for α,β,β γ, and β γ δ active-regions increase in the order listed, and that the order is maintained over all length scales. Since magnetic flux gradient is strongly linked to active-region activity, such as flares, this study demonstrates that, on average, the Mt. Wilson classification encodes the notion of activity over all length scales in the active-region, and not just those length scales at which the strongest flux gradients are found. Further, it is also shown that the average gradients in the field, and the average length-scale at which they occur, also increase in the same order. Finally, there are significant differences in the gradient distribution, between flaring and non-flaring active regions, which are maintained over all length scales. It is also shown that the average gradient content of active-regions that have large flares (GOES class “M” and above) is larger than that for active regions containing flares of all flare sizes; this difference is also maintained at all length scales. All of the reported results are independent of the multiresolution transform used. The implications for the Mt. Wilson classification of active-regions in relation to the multiresolution gradient content and flaring activity are discussed.     

Magnetic and thermal phase shifts in the local helioseismology of sunspots

Phase perturbations due to inclined surface magnetic field of active region strength are calculated numerically in quiet Sun and simple sunspot models in order to estimate and compare the direct and indirect (thermal) effects of the fields on helioseismic waves. It is found that the largest direct effects occur in highly inclined field characteristic of penumbrae, and scale roughly linearly with magnetic field strength. The combined effects of sunspot magnetic and thermal anomalies typically yield negative travel-time perturbations in penumbrae. Travel-time shifts in umbrae depend on details of how the thermal and density structure differs from the quiet Sun. The combined shifts are generally not well approximated by the sum of the thermal and magnetic effects applied separately, except at low field strengths of around 1 kG or less, or if the thermal shift is small. A useful rule-of-thumb appears to be that travel-time perturbations in umbrae are predominantly thermal, whereas in penumbrae they are mostly magnetic.     

Search for relationship between duration of the extended solar cycles and amplitude of sunspot cycle

Duration of the extended solar cycles is taken into the consideration. The beginning of cycles is counted from the moment of polarity reversal of large-scale magnetic field in high latitudes, occurring in the sunspot cycle n till the minimum of the cycle n + 2. The connection between cycle duration and its amplitude is established. Duration of the “latent” period of evolution of extended cycle between reversals and a minimum of the current sunspot cycle is entered. It is shown, that the latent period of cycles evolution is connected with the next sunspot cycle amplitude and can be used for the prognosis of a level and time of a sunspot maximum. The 24th activity cycle prognosis is made. The found dependences correspond to transport dynamo model of generation of solar cyclicity, it is possible with various speed of meridional circulation. Long-term behavior of extended cycle's lengths and connection with change of a climate of the Earth is considered. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solar cycles during the Maunder minimum

We have obtained new consistent versions of the 400-yr time series of the Wolf sunspot number W, the sunspot group number G, and the total sunspot area S (or the total sunspot magnetic flux Φ). We show that the 11-yr cycle did not cease during the Maunder minimum of solar activity. The characteristics of the extrema of individual 11-yr cycles in 1600–2005 have been determined in terms of the total sunspot area index. We provide arguments for using alternating (“magnetic”) time series of indices in investigating the solar cyclicity.     

On the solar rotation and activity

The interaction between differential rotation and magnetic fields in the solar convection zone was recently modelled by Brun (2004). One consequence of that model is that the Maxwell stresses can oppose the Reynolds stresses, and thus contribute to the transport of the angular momentum towards the solar poles, leading to a reduced differential rotation. So, when magnetic fields are weaker, a more pronounced differential rotation can be expected, yielding a higher rotation velocity at low latitudes taken on the average. This hypothesis is consistent with the behaviour of the solar rotation during the Maunder minimum. In this work we search for similar signatures of the relationship between the solar activity and rotation determined tracing sunspot groups and coronal bright points. We use the extended Greenwich data set (1878–1981) and a series of full-disc solar images taken at 28.4 nm with the EIT instrument on the SOHO spacecraft (1998–2000). We investigate the dependence of the solar rotation on the solar activity (described by the relative sunspot number) and the interplanetary magnetic field (calculated from the interdiurnal variability index). Possible rotational signatures of two weak solar activity cycles at the beginning of the 20th century (Gleissberg minimum) are discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Turbulent dynamo near tachocline and reconstruction of azimuthal magnetic field in the solar convection zone

In order to extend the abilities of the αΩ dynamo model to explain the observed regularities and anomalies of the solar magnetic activity, the negative buoyancy phenomenon and the magnetic quenching of the α effect were included in the model, as well as newest helioseismically determined inner rotation of the Sun were used. Magnetic buoyancy constrains the magnitude of toroidal field produced by the Ω effect near the bottom of the solar convection zone (SCZ). Therefore, we examined two “antibuoyancy” effects: i) macroscopic turbulent diamagnetism and ii) magnetic advection caused by vertical inhomogeneity of fluid density in the SCZ, which we call the ∇ρ effect. The Sun's rotation substantially modifies the ∇ρ effect. The reconstruction of the toroidal field was examined assuming the balance between mean‐field magnetic buoyancy, turbulent diamagnetism and the rotationally modified ∇ρ effect. It is shown that at high latitudes antibuoyancy effects block the magnetic fields in the deep layers of the SCZ, and so the most likely these deep‐rooted fields could not become apparent at the surface as sunspots. In the near‐equatorial region, however, the upward ∇ρ effect can facilitate magnetic fields of about 3000 – 4000 G to emerge through the surface at the sunspot belt. Allowance for the radial inhomogeneity of turbulent velocity in derivations of the helicity parameter resulted in a change of sign of the α effect from positive to negative in the northern hemisphere near the bottom of the SCZ. The change of sign is very important for direction of the Parker's dynamo‐waves propagation and for parity of excited magnetic fields. The period of the dynamo‐wave calculated with allowance for the magnetic quenching is about seven years, that agrees by order of magnitude with the observed mean duration of the sunspot cycles. Using the modern helioseismology data to define dynamo‐parameters, we conclude that north‐south asymmetry should exist in the meridional field. At low latitudes in deep layers of the SCZ, the αΩ dynamo excites most efficiency the dipolar mode of the meridional field. Meanwhile, in high‐latitude regions a quadrupolar mode dominates in the meridional field. The obtained configuration of the net meridional field is likely to explain the magnetic anomaly of polar fields (the apparent magnetic “monopole”) observed near the maxima of solar cycles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The time-delayed solar cycle luminosity modulation by sub-surface magnetic flux tubes

In order to explore the mechanism of the solar cycle luminosity change observed by the Active Cavity Radiometer Irradiance Monitor (ACRIM) I experiment on board of the spacecraft Solar Maximum Mission, we examined running mean time profiles of the daily ACRIM data from the declining phase of solar cycle 21 to the rising phase of solar cycle 22. By comparing them with those of the daily sunspot number, integrated surface magnetic field flux, integrated He I 10830 Å line equivalent width data, and two kinds of data sets of the daily integrated Ca II K line index as indices of the surface magnetic activities, we found (i) that the running mean time profiles of the six independent data sets have several peaks and valleys in common in one solar cycle with time intervals on the order of a few hundreds of days, and (ii) that the peaks and valleys of the ACRIM data profiles followed the peaks and valleys of all the other five indices of the surface activities by 40 to 60 days. This time delay phenomenon suggests (i) that the luminosity modulation was not directly caused by dark and bright features of the surface magnetic activities that the other five indices represent, and (ii) that the missing sunspot radiative flux which was blocked by sub-surface magnetic flux tubes of sunspots and sunspot groups should be re-radiated 40 to 60 days after the surface emergence of the magnetic flux tubes. The concept of the time delay resolves the enigma of the missing sunspot radiative flux and the enigma of the ACRIM experiment that the luminosity dropped when a sunspot or a sunspot group appeared on the surface while the yearly mean of the luminosity decreased and increased along with the decrease and increase of the yearly sunspot number of the 11-year solar cycle. A model of the mechanism to understand these phenomena is presented and its application to other stars is suggested.     

Sunspot Group Decay

We examine daily records of sunspot group areas (measured in millionths of a solar hemisphere or μHem) for the last 130 years to determine the rate of decay of sunspot group areas. We exclude observations of groups when they are more than 60° in longitude from the central meridian and only include data when at least three days of observations are available following the date of maximum area for a group’s disk passage. This leaves data for over 18 000 measurements of sunspot group decay. We find that the decay rate increases linearly from 28 μHem day⁻¹ to about 140 μHem day⁻¹ for groups with areas increasing from 35 μHem to 1000 μHem. The decay rate tends to level off for groups with areas larger than 1000 μHem. This behavior is very similar to the increase in the number of sunspots per group as the area of the group increases. Calculating the decay rate per individual sunspot gives a decay rate of about 3.65 μHem day⁻¹ with little dependence upon the area of the group. This suggests that sunspots decay by a Fickian diffusion process with a diffusion coefficient of about 10 km² s⁻¹. Although the 18 000 decay rate measurements are lognormally distributed, this can be attributed to the lognormal distribution of sunspot group areas and the linear relationship between area and decay rate for the vast majority of groups. We find weak evidence for variations in decay rates from one solar cycle to another and for different phases of each sunspot cycle. However, the strongest evidence for variations is with latitude and the variations with cycle and phase of each cycle can be attributed to this variation. High latitude spots tend to decay faster than low latitude spots.     

Looking inside the butterfly diagram

The suitability of Maunder's butterfly diagram to give a realistic picture of the photospheric magnetic flux large scale distribution is discussed. The evolution of the sunspot zone in cycle 20 through 23 is described. To reduce the noise which covers any structure in the diagram, a smoothing algorithm has been applied to the sunspot data. This operation has eliminated any short period fluctuation, and given visibility to long duration phenomena. One of these phenomena is the fact that the equatorward drift of the spot zone center of mass results from the alternation of several prograde (namely, equatorward) segments with other stationary or poleward segments. The long duration of the stationary/retrograde phases as well as the similarities among the spot zone alternating paths in the cycles under examination prevent us from considering these features as meaningless fluctuations, randomly superimposed on the continuous equatorward migration. On the contrary, these features should be considered physically meaningful phenomena, requiring adequate explanations. Moreover, even the smoothed spotted area markedly oscillates. The compared examination of area and spot zone evolution allows us to infer details about the spotted area distribution inside the butterfly diagram. Links between the changing structure of the spot zone and the tachocline rotation rate oscillations are proposed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The north–south asymmetry of solar activity at high latitudes

Solar long-term activity runs at high latitudes in three ways: (i) in phase with solar long-term activity at low latitudes; (ii) in antiphase with solar long-term activity at low latitudes and (iii) does not follow either (i) or (ii), and mainly occurs around the times of maxima of (i) and (ii). In the present study, we investigate the north–south asymmetry of solar activity at high latitudes and found the following. In Case (i), high-latitude filament activity, for example, is inferred to have the same dominant hemisphere as low-latitude activity in a cycle. In Case (ii), the north–south asymmetry of high-latitude activity, represented by both the polar faculae and the Sun's polar field strength, is usually different from that of low-latitude activity in a sunspot cycle, and even in a cycle of high-latitude activity (polar faculae and the Sun's polar field strength), suggesting that the north–south asymmetry of solar activity at high latitudes should have little or no connection with that of low latitudes. In Case (iii), the north–south asymmetry of solar activity at high latitudes (polar flares) should have little connection with that at low latitudes as well. The observed magnetic field at high latitudes is inferred to consist of two components: one comes from the emergence of the magnetic field from the Sun's interior and the other comes from the drift of the magnetic activity at low latitudes.     

Solar activity forecast with a dynamo model

Although systematic measurements of the Sun's polar magnetic field exist only from mid-1970s, other proxies can be used to infer the polar field at earlier times. The observational data indicate a strong correlation between the polar field at a sunspot minimum and the strength of the next cycle, although the strength of the cycle is not correlated well with the polar field produced at its end. This suggests that the Babcock–Leighton mechanism of poloidal field generation from decaying sunspots involves randomness, whereas the other aspects of the dynamo process must be reasonably ordered and deterministic. Only if the magnetic diffusivity within the convection zone is assumed to be high (of order  10¹² cm² s⁻¹  ), we can explain the correlation between the polar field at a minimum and the next cycle. We give several independent arguments that the diffusivity must be of this order. In a dynamo model with diffusivity like this, the poloidal field generated at the mid-latitudes is advected toward the poles by the meridional circulation and simultaneously diffuses towards the tachocline, where the toroidal field for the next cycle is produced. To model actual solar cycles with a dynamo model having such high diffusivity, we have to feed the observational data of the poloidal field at the minimum into the theoretical model. We develop a method of doing this in a systematic way. Our model predicts that cycle 24 will be a very weak cycle. Hemispheric asymmetry of solar activity is also calculated with our model and compared with observational data.     

Effect of noise on sunspot magnetic field parameters

Using a perturbated (noised) dipole model of a sunspot magnetic field structure we simulated the influence of background noise or apparent noise (unresolved small-scale magnetic field structure) on sunspot magnetic field parameters. We evaluated mean values of the vertical and horizontal electric current densities |j|_∥ and |j|_⊥, respectively, of the force-free parameter α and of the Lorentz force |F|. For comparison we estimated |j_⊥| and |F| of a standard sunspot magnetic field model (return-flux model, OSHEROVICH 1982). Furthermore, we compared our results with those from observations resulting in estimated values of |j|_∥ for quiet sunspots. Our investigation led to the following results: the estimated values of 〈|F|〉 show clearly that due to the noise the axisymmetric magnetic dipole model is clustered into several subsystems of fluxbundles. The latter are connected with a system of electric current densities of the order of |j|_∥ ∼ 10⁻³ Am⁻² and |j|_⊥ = 10⁻¹ Am⁻², i.e., this system is a noise-generated nonaxisymmetric magnetohydrostatic model.     

Structure of a simple sunspot from the inversion of IR spectral data

Analysis of spectral data of two neighboring infrared lines, Fe I 15648.5 Å (g = 3) and FeI 15652.9 Å (g_eff = 1.53) are carried out for a simple sunspot when it was near the solar disk center (μ = 0.92), to understand the basic structure of sunspot magnetic field. Inversions of Stokes profiles are carried out to derive different atmospheric parameters both as a function of location within the sunspot and height in the atmosphere. As a result of the inversion we have obtained maps of magnetic field strength, temperature, line‐of‐sight velocity, field inclination and azimuth for different optical depth layers between log(τ₅) = 0 and log(τ₅) = –2.0. In this paper we present few results from our inversion for a layer averaged between log(τ5) from 0.0 to –0.5.