Can the Solar Cycle Amplitude Be Predicted Using the Preceding Solar Cycle Length?

In this work, the evolution of the relationship between Solar Cycle Length of solar cycle n (SCL _n ) and Solar Cycle Amplitude of the solar cycle n+1 (SCA _n+1) is studied by using the R _Z and R _G sunspot numbers. We conclude that this relationship is only strongly significant in a statistical sense during the first half of the historical record of R _Z sunspot number whereas it is considerably less significant for the R _G sunspot number. In this sense we assert that these simple lagged relationships should be avoided as a valid method to predict the following solar activity amplitude.     

An Analysis of the Sunspot Groups and Flares of Solar Cycle 23

Designing a statistical solar flare forecasting technique can benefit greatly from knowledge of the flare frequency of occurrence with respect to sunspot groups. This study analyzed sunspot groups and Hα and X-ray flares reported for the period 1997 – 2007. Annual catalogs were constructed, listing the days that numbered sunspot groups were observed (designated sunspot group-days, SSG-Ds) and for each day a record for each associated Hα flare of importance category one or greater and normal or bright brightness and for each X-ray flare of intensity C 5 or higher. The catalogs were then analyzed to produce frequency distributions of SSG-Ds by year, sunspot group class, likelihood of producing at least one flare overall and by sunspot group class, and frequency of occurrence of numbers of flares per day and flare intensity category. Only 3% of SSG-Ds produced a substantial Hα flare and 7% had a significant X-ray flare. We found that mature, complex sunspot groups were more likely than simple sunspot groups to produce a flare, but the latter were more prevalent than the former. More than half of the SSG-Ds with flares had a maximum intensity flare greater than the lowest category (C-class of intensity five and higher). The fact that certain sunspot group classes had flaring probabilities significantly higher than the combined probabilities of the intensity categories when all SSG-Ds were considered suggest that it might be best to first predict the flaring probability. For sunspot groups found likely to flare, a separate diagnosis of maximum flare intensity category appears feasible.     

Phase Space Analysis: The Equilibrium of the Solar Magnetic Cycle

We present the results of a statistical study of the solar cycle based on the analysis of the superficial toroidal magnetic field component phase space. The magnetic field component used to create the embedded phase space was constructed from monthly sunspot number observations since 1750. The phase space was split into 32 sections (or time instants) and the average values of the orbits on this phase space were calculated (giving the most probable cycle). In this phase space it is shown that the magnetic field on the Sun’s surface evolves through a set of orbits that go around a mean orbit (i.e., the most probable magnetic cycle that we interpret as the equilibrium solution). It follows that the most probable cycle is well represented by a van der Pol oscillator limit curve (equilibrium solution), as can be derived from mean-field dynamo theory. This analysis also retrieves the empirical Gnevyshev – Ohl’s rule between the first and second parts of the solar magnetic cycle. The sunspot number evolution corresponding to the most probable cycle (in phase space) is presented.     

Short-Term Periodicities in Sunspot Activities During the Descending Phase of Solar Cycle 23

In the present study, the short-term periodicities in the daily data of the sunspot numbers and areas are investigated separately for the full disk, northern, and southern hemispheres during Solar Cycle 23 for a time interval from 1 January 2003 to 30 November 2007 corresponding to the descending and minimum phase of the cycle. The wavelet power spectrum technique exhibited a number of quasi-periodic oscillations in all the datasets. In the high frequency range, we find a prominent period of 22 – 35 days in both sunspot indicators. Other quasi-periods in the range of 40 – 60, 70 – 90, 110 – 130, 140 – 160, and 220 – 240 days are detected in the sunspot number time series in different hemispheres at different time intervals. In the sunspot area data, quasi-periods in the range of 50 – 80, 90 – 110, 115 – 130, 140 – 155, 160 – 190, and about 230 days were noted in different hemispheres within the time period of analysis. The present investigation shows that the well-known “Rieger periodicity” of 150 – 160 days reappears during the descending phase of Solar Cycle 23, but this is prominent mainly in the southern part of the Sun. Possible explanations of these observed periodicities are delivered on the basis of earlier results detected in photospheric magnetic field time series (Knaack, Stenflo, and Berdyugina in Astron. Astrophys. 438, 1067, 2005) and solar r-mode oscillations.     

Solar Wind Sources in the Late Declining Phase of Cycle 23: Effects of the Weak Solar Polar Field on High Speed Streams

The declining phases of solar cycles are known for their high speed solar wind streams that dominate the geomagnetic responses during this period. Outstanding questions about these streams, which can provide the fastest winds of the solar cycle, concern their solar origins, persistence, and predictability. The declining phase of cycle 23 has lasted significantly longer than the corresponding phases of the previous two cycles. Solar magnetograph observations suggest that the solar polar magnetic field is also ～?2?–?3 times weaker. The launch of STEREO in late 2006 provided additional incentive to examine the origins of what is observed at 1 AU in the recent cycle, with the OMNI data base at the NSSDC available as an Earth/L1 baseline for comparisons. Here we focus on the year 2007 when the solar corona exhibited large, long-lived mid-to-low latitude coronal holes and polar hole extensions observed by both SOHO and STEREO imagers. STEREO provides in situ measurements consistent with rigidly corotating solar wind stream structure at up to ～?45° heliolongitude separation by late 2007. This stability justifies the use of magnetogram-based steady 3D solar wind models to map the observed high speed winds back to their coronal sources. We apply the WSA solar wind model currently running at the NOAA Space Weather Prediction Center with the expectation that it should perform its best at this quiet time. The model comparisons confirm the origins of the observed high speed streams expected from the solar images, but also reveal uncertainties in the solar wind source mapping associated with this cycle’s weaker solar polar fields. Overall, the results illustrate the importance of having accurate polar fields in synoptic maps used in solar wind forecast models. At the most fundamental level, they demonstrate the control of the solar polar fields over the high speed wind sources, and thus one specific connection between the solar dynamo and the solar wind character.     

Organization of Energetic Particles by the Solar Wind Structure During the Declining to Minimum Phase of Solar Cycle 23

We investigate the organization of the low energy energetic particles (≤1 MeV) by solar wind structures, in particular corotating interaction regions (CIRs) and shocks driven by interplanetary coronal mass ejections, during the declining-to-minimum phase of Solar Cycle 23 from Carrington rotation 1999 to 2088 (January 2003 to October 2009). Because CIR-associated particles are very prominent during the solar minimum, the unusually long solar minimum period of this current cycle provides an opportunity to examine the overall organization of CIR energetic particles for a much longer period than during any other minimum since the dawn of the Space Age. We find that the particle enhancements associated with CIRs this minimum period recurred for many solar rotations, up to 30 at times, due to several high-speed solar wind streams that persisted. However, very few significant CIR-related energetic particle enhancements were observed towards the end of our study period, reflecting the overall weak high-speed streams that occurred at this time. We also contrast the solar minimum observations with the declining phase when a number of solar energetic particle events occurred, producing a mixed particle population. In addition, we compare the observations from this minimum period with those from the previous solar cycle. One of the main differences we find is the shorter recurrence rate of the high-speed solar wind streams (～10 solar rotations) and the related CIR energetic particle enhancements for the Solar Cycle 22 minimum period. Overall our study provides insight into the coexistence of different populations of energetic particles, as well as an overview of the large-scale organization of the energetic particle populations approaching the beginning of Solar Cycle 24.     

Influence of the 11-Year Solar Cycle on Variations of Cosmic Ray Intensity

The monthly cosmic ray intensity (CRI) time series from Climax, Huancayo, Moscow, Kiel, and Calgary are used to investigate the presence of the 11-year periodic component with special attention paid to the solar influence on these variations. The results show obvious 11-year temporal characteristics in CRI variations. We also find a close anticorrelation between the 11-year solar cycle and CRI variations and time delays of the CRI relative to solar activity.     

Statistical Comparison of Magnetic Clouds with Interplanetary Coronal Mass Ejections for Solar Cycle 23

We compare the number and characteristics of interplanetary coronal mass ejections (ICMEs) to those of magnetic clouds (MCs) by using in-situ solar wind plasma and magnetic field observations made at 1 AU during solar cycle 23. We found that ≈ 28% of ICMEs appear to contain MCs, since 103 magnetic clouds (MCs) occurred during 1995  – 2006, and 307 ICMEs occurred during 1996 – 2006. For the period between 1996 and 2006, 85 MCs are identified as part of ICMEs, and six MCs are not associated with ICMEs, which conflicts with the idea that MCs are usually a subset of ICMEs. It was also found that solar wind conditions inside MCs and ICMEs are usually similar, but the linear correlation between geomagnetic storm intensity (Dst _min) and relevant solar wind parameters is better for MCs than for ICMEs. The differences between average event duration (Δt) and average proton plasma β (〈β〉) are two of the major differences between MCs and ICMEs: i) the average duration of ICMEs (29.6 h) is 44% longer than for MCs (20.6 hours), and ii) the average of 〈β〉 is 0.01 for MCs and 0.24 for ICMEs. The difference between the definition of a MC and that for an ICME is one of the major reasons for these average characteristics being different (i.e., listed above as items i) and ii)), and it is the reason for the frequency of their occurrences being different.     

Automated detection of EUV Polar Coronal Holes during Solar Cycle 23

A new method for automated detection of polar coronal holes is presented. This method, called perimeter tracing, uses a series of 171, 195, and 304 Å full disk images from the Extreme ultraviolet Imaging Telescope (EIT) on SOHO over solar cycle 23 to measure the perimeter of polar coronal holes as they appear on the limbs. Perimeter tracing minimizes line-of-sight obscurations caused by the emitting plasma of the various wavelengths by taking measurements at the solar limb. Perimeter tracing also allows for the polar rotation period to emerge organically from the data as 33 days. We have called this the Harvey rotation rate and count Harvey rotations starting 4 January 1900. From the measured perimeter, we are then able to fit a curve to the data and derive an area within the line of best fit. We observe the area of the northern polar hole area in 1996, at the beginning of solar cycle 23, to be about 4.2% of the total solar surface area and about 3.6% in 2007. The area of the southern polar hole is observed to be about 4.0% in 1996 and about 3.4% in 2007. Thus, both the north and south polar hole areas are no more than 15% smaller now than they were at the beginning of cycle 23. This compares to the polar magnetic field measured to be about 40% less now than it was a cycle ago.     

Solar Cycle Variation of Magnetic Flux Ropes in a Quasi-Static Coronal Evolution Model

The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free “potential-field” extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this model – in particular the flux ropes – varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes.     

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.     

A Possible Cause of the Diminished Solar Wind During the Solar Cycle 23 – 24 Minimum

Interplanetary magnetic field and solar wind plasma density observed at 1 AU during Solar Cycle 23?–?24 (SC-23/24) minimum were significantly smaller than those during its previous solar cycle (SC-22/23) minimum. Because the Earth’s orbit is embedded in the slow wind during solar minimum, changes in the geometry and/or content of the slow wind region (SWR) can have a direct influence on the solar wind parameters near the Earth. In this study, we analyze solar wind plasma and magnetic field data of hourly values acquired by Ulysses. It is found that the solar wind, when averaging over the first (1995.6?–?1995.8) and third (2006.9?–?2008.2) Ulysses’ perihelion (\({\sim}\,1.4~\mbox{AU}\)) crossings, was about the same speed, but significantly less dense (\({\sim}\,34~\%\)) and cooler (\({\sim}\,20~\%\)), and the total magnetic field was \({\sim}\,30~\%\) weaker during the third compared to the first crossing. It is also found that the SWR was \({\sim}\,50~\%\) wider in the third (\({\sim}\,68.5^{\circ}\) in heliographic latitude) than in the first (\({\sim}\,44.8^{\circ}\)) solar orbit. The observed latitudinal increase in the SWR is sufficient to explain the excessive decline in the near-Earth solar wind density during the recent solar minimum without speculating that the total solar output may have been decreasing. The observed SWR inflation is also consistent with a cooler solar wind in the SC-23/24 than in the SC-22/23 minimum. Furthermore, the ratio of the high-to-low latitude photospheric magnetic field (or equatorward magnetic pressure force), as observed by the Mountain Wilson Observatory, is smaller during the third than the first Ulysses’ perihelion orbit. These findings suggest that the smaller equatorward magnetic pressure at the Sun may have led to the latitudinally-wider SRW observed by Ulysses in SC-23/24 minimum.     

Wavelet Analysis of the Schwabe Cycle Properties in Solar Activity

Properties of the Schwabe cycles in solar activity are investigated by using wavelet transform. We study the main range of the Schwabe cycles of the solar activity recorded by relative sunspot numbers, and find that the main range of the Schwabe cycles is the periodic span from 8-year to 14-year. We make the comparison of 11-year‘s phase between relative sunspot numbers and sunspot group numbers. The results show that there is some difference between two phases for the interval from 1710 to 1810, while the two phases are almost the same for the interval from 1810 to 1990.     

Automated Detection of Oscillating Regions in the Solar Atmosphere

Recently observed oscillations in the solar atmosphere have been interpreted and modeled as magnetohydrodynamic wave modes. This has allowed for the estimation of parameters that are otherwise hard to derive, such as the coronal magnetic-field strength. This work crucially relies on the initial detection of the oscillations, which is commonly done manually. The volume of Solar Dynamics Observatory (SDO) data will make manual detection inefficient for detecting all of the oscillating regions. An algorithm is presented that automates the detection of areas of the solar atmosphere that support spatially extended oscillations. The algorithm identifies areas in the solar atmosphere whose oscillation content is described by a single, dominant oscillation within a user-defined frequency range. The method is based on Bayesian spectral analysis of time series and image filtering. A Bayesian approach sidesteps the need for an a-priori noise estimate to calculate rejection criteria for the observed signal, and it also provides estimates of oscillation frequency, amplitude, and noise, and the error in all of these quantities, in a self-consistent way. The algorithm also introduces the notion of quality measures to those regions for which a positive detection is claimed, allowing for simple post-detection discrimination by the user. The algorithm is demonstrated on two Transition Region and Coronal Explorer (TRACE) datasets, and comments regarding its suitability for oscillation detection in SDO are made.     

Grand Minima of Solar Activity and the Mean-Field Dynamo

We demonstrate that a simple solar dynamo model, in the form of a Parker migratory dynamo with random fluctuations of the dynamo governing parameters and algebraic saturation of dynamo action, can at least qualitatively reproduce all the basic features of solar Grand Minima as they are known from direct and indirect data. In particular, the model successfully reproduces such features as an abrupt transition into a Grand Minimum and the subsequent gradual recovery of solar activity, as well as mixed-parity butterfly diagrams during the epoch of the Grand Minimum. The model predicts that the cycle survives in some form during a Grand Minimum, as well as the relative stability of the cycle inside and outside of a Grand Minimum. The long-term statistics of simulated Grand Minima appears compatible with the phenomenology of the Grand Minima inferred from the cosmogenic isotope data. We demonstrate that such ability to reproduce the Grand Minima phenomenology is not a general feature of the dynamo models but requires some specific assumption, such as random fluctuations in dynamo governing parameters. In general, we conclude that a relatively simple and straightforward model is able to reproduce the Grand Minima phenomenology remarkably well, in principle providing us with a possibility of studying the physical nature of Grand Minima.     

Estimating the Size and Timing of the Maximum Amplitude of Solar Cycle 24

A simple statistical method is used to estimate the size and timing of maximum amplitude of the next solar cycle (cycle 24). Presuming cycle 23 to be a short cycle (as is more likely), the minimum of cycle 24 should occur about December 2006 (±2 months) and the maximum, around March 2011 (±9 months), and the amplitude is 189.9 ±15.5, if it is a fast riser, or about 136, if it is a slow riser. If we presume cycle 23 to be a long cycle (as is less likely), the minimum of cycle 24 should occur about June 2008 (±2 months) and the maximum, about February 2013 (±8 months) and the maximum will be about 137 or 80, according as the cycle is a fast riser or a slow riser.     

Prediction of the Maximum Amplitude and Timing of Sunspot Cycle 24

Precursor techniques, in particular those using geomagnetic indices, often are used in the prediction of the maximum amplitude for a sunspot cycle. Here, the year 2008 is taken as being the sunspot minimum year for cycle 24. Based on the average aa index value for the year of the sunspot minimum and the preceding four years, we estimate the expected annual maximum amplitude for cycle 24 to be about 92.8±19.6 (1-sigma accuracy), indicating a somewhat weaker cycle 24 as compared to cycles 21 – 23. Presuming a smoothed monthly mean sunspot number minimum in August 2008, a smoothed monthly mean sunspot number maximum is expected about October 2012±4 months (1-sigma accuracy).     

Oscillatory Response of the 3D Solar Atmosphere to the Leakage of Photospheric Motion

The direct propagation of acoustic waves, driven harmonically at the solar photosphere, into the three-dimensional solar atmosphere is examined numerically in the framework of ideal magnetohydrodynamics. It is of particular interest to study the leakage of 5-minute global solar acoustic oscillations into the upper, gravitationally stratified and magnetised atmosphere, where the modelled solar atmosphere possesses realistic temperature and density stratification. This work aims to complement and bring further into the 3D domain our previous efforts (by Erdélyi et al., 2007, Astron. Astrophys. 467, 1299) on the leakage of photospheric motions and running magnetic-field-aligned waves excited by these global oscillations. The constructed model atmosphere, most suitable perhaps for quiet Sun regions, is a VAL IIIC derivative in which a uniform magnetic field is embedded. The response of the atmosphere to a range of periodic velocity drivers is numerically investigated in the hydrodynamic and magnetohydrodynamic approximations. Among others the following results are discussed in detail: i) High-frequency waves are shown to propagate from the lower atmosphere across the transition region, experiencing relatively low reflection, and transmitting most of their energy into the corona; ii) the thin transition region becomes a wave guide for horizontally propagating surface waves for a wide range of driver periods, and particularly at those periods that support chromospheric standing waves; iii) the magnetic field acts as a waveguide for both high- and low-frequency waves originating from the photosphere and propagating through the transition region into the solar corona. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Verification of a Similar Cycle Prediction for the Ascending and Peak Phases of Solar Cycle 23

Reviews of long-term predictions of solar cycles have shown that a precise prediction with a lead time of 2 years or more of a solar cycle remains an unsolved problem. We used a simple method, the method of similar cycles, to make long-term predictions of not only the maximum amplitude but also the smoothed monthly mean sunspot number for every month of Solar Cycle 23. We verify and compare our prediction with the latest available observational results.