The Sun’s Large-Scale Magnetic Field and Its Long-Term Evolution

The Sun’s large-scale external field is formed through the emergence of magnetic flux in active regions and its subsequent dispersal over the solar surface by differential rotation, supergranular convection, and meridional flow. The observed evolution of the polar fields and open flux (or interplanetary field) during recent solar cycles can be reproduced by assuming a supergranular diffusion rate of 500 – 600 km² s⁻¹ and a poleward flow speed of 10 –20 m s⁻¹. The nonaxisymmetric component of the large-scale field decays on the flow timescale of ∼1 yr and must be continually regenerated by new sunspot activity. Stochastic fluctuations in the longitudinal distribution of active regions can produce large peaks in the Sun’s equatorial dipole moment and in the interplanetary field strength during the declining phase of the cycle; by the same token, they can lead to sudden weakenings of the large-scale field near sunspot maximum (Gnevyshev gaps). Flux transport simulations over many solar cycles suggest that the meridional flow speed is correlated with cycle amplitude, with the flow being slower during less active cycles.     

A Preliminary Estimate of the Size of the Coming Solar Cycle 24, based on Ohl’s Precursor Method

For many purposes (e.g., satellite drag, operation of power grids on Earth, and satellite communication systems), predictions of the strength of a solar cycle are needed. Predictions are made by using different methods, depending upon the characteristics of sunspot cycles. However, the method most successful seems to be the precursor method by Ohl and his group, in which the geomagnetic activity in the declining phase of a sunspot cycle is found to be well correlated with the sunspot maximum of the next cycle. In the present communication, the method is illustrated by plotting the 12-month running means aa(min ) of the geomagnetic disturbance index aa near sunspot minimum versus the 12-month running means of the sunspot number Rz near sunspot maximum [aa(min ) versus Rz(max )], using data for sunspot cycles 9 – 18 to predict the Rz(max ) of cycle 19, using data for cycles 9 – 19 to predict Rz(max ) of cycle 20, and so on, and finally using data for cycles 9 – 23 to predict Rz(max ) of cycle 24, which is expected to occur in 2011 – 2012. The correlations were good (∼+0.90) and our preliminary predicted Rz(max ) for cycle 24 is 142±24, though this can be regarded as an upper limit, since there are indications that solar minimum may occur as late as March 2008. (Some workers have reported that the aa values before 1957 would have an error of 3 nT; if true, the revised estimate would be 124±26.) This result of the precursor method is compared with several other predictions of cycle 24, which are in a very wide range (50 – 200), so that whatever may be the final observed value, some method or other will be discredited, as happened in the case of cycle 23.     

10.7-cm Solar radio flux and the magnetic complexity of active regions

During sunspot cycles 20 and 21, the maximum in smoothed 10.7-cm solar radio flux occurred about 1.5 yr after the maximum smoothed sunspot number, whereas during cycles 18 and 19 no lag was observed. Thus, although 10.7-cm radio flux and Zürich suspot number are highly correlated, they are not interchangeable, especially near solar maximum. The 10.7-cm flux more closely follows the number of sunspots visible on the solar disk, while the Zürich sunspot number more closely follows the number of sunspot groups. The number of sunspots in an active region is one measure of the complexity of the magnetic structure of the region, and the coincidence in the maxima of radio flux and number of sunspots apparently reflects higher radio emission from active regions of greater magnetic complexity. The presence of a lag between sunspot-number maximum and radio-flux maximum in some cycles but not in others argues that some aspect of the average magnetic complexity near solar maximum must vary from cycle to cycle. A speculative possibility is that the radio-flux lag discriminates between long-period and short-period cycles, being another indicator that the solar cycle switches between long-period and short-period modes.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

The 73-day periodicity of the flare index during the current solar cycle 22

The flare index of the current solar cycle 22 is analysed to detect intermediate-term periodicities from Sep. 1, 1986 to Dec. 31, 1991. Power spectral analysis of the time series of solar flare index data reveals a periodicity around 73 and 53 days. We find that a periodicity of 73 days was in operation from 1988 November to the end of 1991 December. We also find that when the 73-day periodicity or the 154-day periodicity is in operation, the flare index is well correlated with the relative sunspot numbers. As a conclusion, we do not expect to see a resumption of the 154-day or 73-day periodicity, but we do expect only one of the periodicity near the integral multiples of 25^d.8 in the next solar cycles.     

Correlation and spectral analysis of daily solar radio flux

Correlation and spectral analysis of solar radio flux density and sunspot number near the maximum of the sunspot cycle has indicated the existence of

1. long period amplitude modulation of the slowly varying component (SVC) of radio emission
2. coronal storage over a period of the order of three solar rotations
3. fast decay (one solar rotation period or less) of gyromagnetic emissions from radio sources
4. shift in location of chromospheric sources compared to those of either the upper corona or the photosphere.

     

Variations of the radiation signatures of noise storm-emitting sunspot groups during a solar cycle

The flux density of a noise storm continuum is known to depend on importance parameters of the associated sunspot group, e.g., its total area A. A study of the continua at 287, 234, 113, and 64 MHz, however, reveals in case of the two cycles Nos. 20 and 21 that the radiation signatures of sunspot groups, with a value of A kept fixed, vary systematically with time indicating regular changes of relevant parameters of the overlying loop systems with the phase of the solar cycle. A trend of intense continua at high frequencies (for definition, cf. Figures 1, 2(b)) to occur preferably during the first activity maximum of a solar cycle has been obtained in either case suggesting a decrease of the emissivity of sunspot groups with time. Vice versa, intense continua at lower frequencies (for definition, cf. Figures 1, 2(b)) were mainly observed during the later phase of both cycles. The latter effect is shown to be attributed rather to a long-term variation of the spectral characteristics of the type-I continua than to an enhanced number of intense type-III continua. From the result obtained it follows that non-potential loops extending to great heights into the corona or developing at least conditions favourable for the generation of an intense type-I continuum even at the frequencies < 100 MHz tend to occur more frequently above sunspot groups during the later phase of a solar cycle than above the comparable groups of its first activity maximum.Furthermore, characteristic periods have been found for both cycles during which the emissivity, especially of the very large sunspot groups, was significantly diminished with reference to the comparable groups of the adjacent time intervals.     

Spatial distribution of solar flares in 23rd solar cycle

H-alpha flares accompanied by the X-radiation f ?? 10^?6 wm^?2 in power are examined; 2331 flares were registered during the first half of the 23rd solar cycle (1997?C2000). The specific power of the X-radiation of the flares monotonically doubles from the minimum to the maximum of the sunspot. An increase in the number of flares in each solar rotation is nonmonotonic and disproportional to the relative number of sunspots. Several longitudinal intervals with increased flare activity can be distinguished in the entire time interval of five to ten rotations. The longitudinal distributions of flares and boundaries of the sector structures of a large-scale magnetic field differ considerably. This confirms the existence of two types of zero lines; the first type is determined by active regions, and the second one is determined by large-scale structures with weak magnetic fields. The flares concentrate near Hale??s zero lines of the first type.     

High Flare Activity in the Late Declining Phase of Cycle 23

In the declining phase of the current solar cycle (23), a large number of major flares were produced. In this cycle, the monthly sunspot number continuously remained below 100 since October 2002. However, during four epochs since then, flare activity became very high. Compared to this, each of cycles 21 and 22 produced only one epoch of high activity in the declining phase. In the declining phase of cycle 20, similarly to this cycle, there were four epochs of high flare activity. During 2003 and 2004, the distribution of flare sizes measured in GOES classes was much harder (i.e., proportionately more energetic flares) than during the maximum years. Such pronounced hardening of the size distribution was not observed in the previous cycles. It is of theoretical interest to understand why some cycles are very active in the declining phase, and the high level of activity in the declining phase has practical implications for planning solar observations and forecasting space weather.     

Periodicities in the occurrence rate of solar proton events

Power spectral analyses of the time series of solar proton events during the past three solar cycles reveal a periodicity around 154 days. This feature is prominent in all of the cycles combined, cycles 19 and 21 individually but is only weak in cycle 20. These results are consistent with the presence of similar periodicities between 152 and 155 days in the occurrence rate of major solar flares, the sunspot blocking function (P _s ), the 10.7 cm radio flux (F _10.7) and the sunspot number (R _z ). This suggests that the circa 154-days periodicity may be a fundamental characteristic of the Sun. Periods around 50–52 days are also found in the combined data set and in the three individual cycles in general agreement with the detection of this periodicity in major flares in cycle 19 and inP _s ,F _10.7, andR _z in cycle 21. The cause of the 155 day period remains unknown. The spectra contain lines (or show power at frequencies) consistent with a model in which the periodicity is caused by differential rotation of active zones and a model in which it is related to beat frequencies between solar oscillations, as proposed by Wolff.     

What the Sunspot Record Tells Us About Space Climate

The records concerning the number, sizes, and positions of sunspots provide a direct means of characterizing solar activity over nearly 400 years. Sunspot numbers are strongly correlated with modern measures of solar activity including: 10.7-cm radio flux, total irradiance, X-ray flares, sunspot area, the baseline level of geomagnetic activity, and the flux of galactic cosmic rays. The Group Sunspot Number provides information on 27 sunspot cycles, far more than any of the modern measures of solar activity, and enough to provide important details about long-term variations in solar activity or “Space Climate.” The sunspot record shows: 1) sunspot cycles have periods of 131± 14 months with a normal distribution; 2) sunspot cycles are asymmetric with a fast rise and slow decline; 3) the rise time from minimum to maximum decreases with cycle amplitude; 4) large amplitude cycles are preceded by short period cycles; 5) large amplitude cycles are preceded by high minima; 6) although the two hemispheres remain linked in phase, there are significant asymmetries in the activity in each hemisphere; 7) the rate at which the active latitudes drift toward the equator is anti-correlated with the cycle period; 8) the rate at which the active latitudes drift toward the equator is positively correlated with the amplitude of the cycle after the next; 9) there has been a significant secular increase in the amplitudes of the sunspot cycles since the end of the Maunder Minimum (1715); and 10) there is weak evidence for a quasi-periodic variation in the sunspot cycle amplitudes with a period of about 90 years. These characteristics indicate that the next solar cycle should have a maximum smoothed sunspot number of about 145 ± 30 in 2010 while the following cycle should have a maximum of about 70 ± 30 in 2023.     

Cyclic and Long-Term Variation of Sunspot Magnetic Fields

Measurements from the Mount Wilson Observatory (MWO) were used to study the long-term variations of sunspot field strengths from 1920 to 1958. Following a modified approach similar to that presented in Pevtsov et al. (Astrophys. J. Lett. 742, L36, 2011), we selected the sunspot with the strongest measured field strength for each observing week and computed monthly averages of these weekly maximum field strengths. The data show the solar cycle variation of the peak field strengths with an amplitude of about 500?–?700 gauss (G), but no statistically significant long-term trends. Next, we used the sunspot observations from the Royal Greenwich Observatory (RGO) to establish a relationship between the sunspot areas and the sunspot field strengths for cycles 15?–?19. This relationship was used to create a proxy of the peak magnetic field strength based on sunspot areas from the RGO and the USAF/NOAA network for the period from 1874 to early 2012. Over this interval, the magnetic field proxy shows a clear solar cycle variation with an amplitude of 500?–?700 G and a weaker long-term trend. From 1874 to around 1920, the mean value of magnetic field proxy increases by about 300?–?350 G, and, following a broad maximum in 1920?–?1960, it decreases by about 300 G. Using the proxy for the magnetic field strength as the reference, we scaled the MWO field measurements to the measurements of the magnetic fields in Pevtsov et al. (2011) to construct a combined data set of maximum sunspot field strengths extending from 1920 to early 2012. This combined data set shows strong solar cycle variations and no significant long-term trend (the linear fit to the data yields a slope of ??0.2±0.8 G?year^?1). On the other hand, the peak sunspot field strengths observed at the minimum of the solar cycle show a gradual decline over the last three minima (corresponding to cycles 21?–?23) with a mean downward trend of ≈?15 G?year^?1.     

The Temperature of the Low Corona During Solar Cycles 21–23

Observations of the forbidden coronal lines Fe xiv 530.3 nm and Fe x 637.4 nm obtained at the National Solar Observatory at Sacramento Peak are used to determine the variation of coronal temperature at latitudes above 30^∘ during solar activity cycles 21–23. Features of the long-term variation of emission in the two lines are also discussed. Temperatures at latitudes below 30^∘ are not studied because the technique used to determine the coronal temperature is not applicable in active regions. The polar temperature varies cyclically from approximately 1.3 to 1.7 MK. The temperatures are similar in both hemispheres. The temperature near solar minimum decreases strongly from mid-latitudes to the poles. The temperature of the corona above 80^∘ latitude generally follows the sunspot cycle, with minima in 1985 and 1995–1996 (cf. 1986 and 1996 for the smoothed sunspot number, Rz) and maxima in 1989 and 2000 (cf. 1989 and 2000 for Rz). The temperature of the corona above 30^∘ latitude at solar maximum is nearly uniform, i.e., there is little latitude dependence. If the maximum temperatures of cycles 22 and 23 are aligned in time (superposed epochs), the average annual N + S temperature (average of the northern and southern hemisphere) in cycle 23 is hotter than that in cycle 22 at all times both above 80^∘ latitude and above 30^∘ latitude. The difference in the average annual N + S maximum temperature between cycles 23 and 22 was 56 kK near the poles and 64 kK for all latitudes above 30^∘. Cycle 23 was also hotter at mid-latitudes than cycle 22 by 60 kK. The last 3 years of cycle 21 were hotter than the last 3 years of cycle 22. The difference in average annual N + S temperatures at the end of cycles 21 and 22 was 32 kK near the poles and 23 kK for all latitudes above 30^∘. Cycle 21 was also hotter at mid-latitudes than cycle 22 by at least 90 kK. Thus, there does not seem to be a solar-cycle trend in the low-coronal temperature outside of active regions.     

Coronal holes,solar wind streams,and geomagnetic disturbances during 1978 and 1979

We have extended our long-term study of coronal holes, solar wind streams, and geomagnetic disturbances through the rising phase of sunspot cycle 21 into the era of sunspot maximum. During 1978 and 1979, coronal holes reflected the influence of differential rotation, and existed within a slowly-evolving large-scale pattern despite the relatively high level of sunspot activity. The long-lived 28.5-day pattern is not produced by a rigidly-rotating quasi-stationary structure on the Sun, but seems to be produced by a non-stationary migratory process associated with solar differential rotation. The association between coronal holes and solar wind speed enhancements at Earth continues to depend on the latitude of the holes (relative to the heliographic latitude of Earth), but even the best associations since 1976 have speeds of only 500–600 km s^-1 rather than the values of 600–700 km s^-1 that usually occurred during the declining phase of sunspot cycle 20.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

On the use of ‘first spotless day’ as a predictor for sunspot minimum

Defining the first spotless day of a sunspot cycle as the first day without spots relative to sunspot maximum during the decline of the solar cycle, one finds that the timing of that occurrence can be used as a predictor for the occurrence of solar minimum of the following cycle. For cycle 22, the first spotless day occurred in April 1994, based on the International sunspot number index, although other indices (Boulder and American) indicated the first spotless day to have occurred earlier (September 1993). For cycles 9–14, sunspot minimum followed the first spotless day by about 72 months, having a range of 62–82 months; for cycles 15–21, sunspot minimum followed the first spotless day by about 35 months, having a range of 27–40 months. Similarly, the timing of first spotless day relative to sunspot minimum and maximum for the same cycle reveals that it followed minimum (maximum) by about 69 (18) months during cycles 9–14 and by about 90 (44) months during cycles 15–21. Accepting April 1994 as the month of first spotless day occurrence for cycle 22, one finds that it occurred 91 months into the cycle and 57 months following sunspot maximum. Such values indicate that its behavior more closely matches that found for cycles 15–21 rather than for cycles 9–14. Therefore, one infers that sunspot minimum for cycle 23 will occur in about 2–3 years, or about April 1996 to April 1997. Accepting the earlier date of first spotless day occurrence indicates that sunspot minimum for cycle 23 could come several months earlier, perhaps late 1995.The U.S. Government right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.     

An Early Prediction of the Amplitude of Solar Cycle 25

A “Solar Dynamo” (SODA) Index prediction of the amplitude of Solar Cycle 25 is described. The SODA Index combines values of the solar polar magnetic field and the solar spectral irradiance at 10.7 cm to create a precursor of future solar activity. The result is an envelope of solar activity that minimizes the 11-year period of the sunspot cycle. We show that the variation in time of the SODA Index is similar to several wavelet transforms of the solar spectral irradiance at 10.7 cm. Polar field predictions for Solar Cycles 21?–?24 are used to show the success of the polar field precursor in previous sunspot cycles. Using the present value of the SODA index, we estimate that the next cycle’s smoothed peak activity will be about \(140 \pm30\) solar flux units for the 10.7 cm radio flux and a Version 2 sunspot number of \(135 \pm25\). This suggests that Solar Cycle 25 will be comparable to Solar Cycle 24. The estimated peak is expected to occur near \(2025.2 \pm1.5\) year. Because the current approach uses data prior to solar minimum, these estimates may improve as the upcoming solar minimum draws closer.     

Characteristics of the solar flares and their spatial distribution in cycle 22 and the first half of cycle 23

This paper considers 3246 solar flares in the line H_α, which were accompanied by X-ray emission with a power f ≥ 5 × 10^?6 Wm^?2 in the solar cycle 22 (CR1797-CR1864). During 33 rotations, the specific power of X-ray emission of the flares increased monotonically by a factor of 4 from the cycle minimum up to its first maximum. The number of flares in each solar turnover rises non-monotonically and disproportionately to the relative number of sunspots. For the entire interval of time, one can identify several longitudinal intervals with increased flare activity. They exist during 5–10 rotations. The characteristics of the flares for 33 rotations in cycles 22 and 23 (CR1797-CR1961) are compared. It is concluded that the Sun is more active in cycle 22 than in cycle 23.     

Intermediate-term periodicities in solar activity

The presence of intermediate-term periodicities in solar activity, at approximately 323 and 540 days, has been claimed by different authors. In this paper, we have performed a search for them in the historical records of two main indices of solar activity, namely, the daily sunspot areas (cycles 12–21) and the daily Zürich sunspot number (cycles 6–21). Two different methods to compute power spectra have been used, one of them being especially appropriate to deal with gapped time series. The results obtained for the periodicity near 323 days indicate that it has only been present in cycle 21, while in previous cycles no significant evidence for it has been found. On the other hand, a significant periodicity at 350 days is found in sunspot areas and Zürich sunspot number during cycles 12–21 considered all together, also having been detected in some individual cycles. However, this last periodicity must be looked into with care due to the lack of confirmation for it coming from other features of solar activity. The periodicity around 540 days is found in cycles 12, 14, and 17 in sunspot areas, while during cycles 18 and 19 it is present, with a very high significance, in sunspot areas and Zürich sunspot number. It also appears at 528 days in sunspot areas during cycles 12–21. On the other hand, it is important to note the coincidence between the asymmetry, favouring the northern hemisphere, of sunspot areas and solar flares during cycle 19, and the fact that the periodicity at 540 days was only present, with high significance, in that hemisphere during that solar cycle.     

On ‘bimodality of the solar cycle’ and the duration of cycle 21

The period-growth dichotomy of the solar cycle predicts that cycle 21, the present solar cycle, will be of long duration (>133 mo), ending after July 1987. Bimodality of the solar cycle (i.e., cycles being distributed into two groups according to cycle length, based on a comparison to the mean cycle period) is clearly seen in a scatter diagram of descent versus ascent durations. Based on the well-observed cycles 8–20, a linear fit for long-period cycles (being a relatively strong inverse relationship that is significant at the 5% level and having a coefficient of determination r ² 0.66) suggests that cycle 21, having an ascent of 42 mo, will have a descent near 99 mo; thus, cycle duration of about 141 mo is expected. Like cycle 11, cycle 21 occurs on the downward envelope of the sunspot number curve, yet is associated with an upward first difference in amplitude. A comparison of individual cycle, smoothed sunspot number curves for cycles 21 and 11 reveals striking similarity, which suggests that if, indeed, cycle 21 is a long-period cycle, then it too may have an extended tail of sustained, low, smoothed sunspot number, with cycle 22 minimum occurring either in late 1987 or early 1988.     

Predictions of the maximum amplitude for solar cycle 23 and its subsequent behavior using nonlinear methods

Two nonlinear methods are employed for the prediction of the maximum amplitude for solar cycle 23 and its declining behavior. First, a new heuristic method based on the second derivative of the (conveniently smoothed) sunspot data is proposed. The curvature of the smoothed sunspot data at cycle minimum appears to correlate (R 0.92) with the cycle's later-occurring maximum amplitude. Secondly, in order to predict the near-maximum and declining activity of solar cycle 23, a neural network analysis of the annual mean sunspot time series is also performed. The results of the present study are then compared with some other recent predictions.     

Short-Term Periodicities in Sunspot Activity and Flare Index Data during Solar Cycle 23

The short-term periodicities in sunspot numbers, sunspot areas, and flare index data are investigated in detail using the Date Compensated Discrete Fourier Transform (DCDFT) for the full disk of the Sun separately over the rising, the maximum, and the declining portions of solar cycle 23 (1996 – 2006). While sunspot numbers and areas show several significant periodicities in a wide range between 23.1 and 36.4 days, the flare index data do not exhibit any significant periodicity. The earlier conclusion of Pap, Tobiska, and Bouwer (1990, Solar Phys. 129, 165) and Kane (2003, J. Atmos. Solar-Terr. Phys. 65, 1169), that the 27-day periodicity is more pronounced in the declining portion of a solar cycle than in the rising and maximum ones, seems to be true for sunspot numbers and sunspot area data analyzed here during solar cycle 23.