P. X. Gao

SYNCHRONIZATION OF HEMISPHERIC SUNSPOT ACTIVITY REVISITED : WAVELET TRANSFORM ANALYSES

Three kinds of wavelet transform methods-continuous wavelet transform, cross-wavelet transform, and wavelet coherence-have been proposed to investigate the phase synchrony of the smoothed monthly mean sunspot areas in the time interval of 1874 May to 2008 March in the solar northern and southern hemispheres. For both time series, the Schwabe cycle is the only period of statistical significance, whose mean value is 10.61 yr. The length of the Schwabe cycle for the smoothed monthly mean sunspot areas in the northern hemisphere actually differs from that in the southern hemisphere, which should lead to phase asynchrony between the two series. Both the cross-wavelet transform and wavelet coherence analyses show an asynchronous behavior with phase mixing in the high-frequency components of hemispheric sunspot activity and a strong synchronous behavior with coherent phase angles in the low-frequency components corresponding to period scales around the Schwabe cycle. Although a phase coherence is found at timescales of about 8.5-13.5 yr (which is similar to those of Donner & Thiel, but within a shorter period), phases are not always coherent at the timescales in the considered time interval. The availability of a physical, meaningful phase definition depends crucially on the appropriate choice of reference frequencies. At the coherent period scales, the leading role is found from those conditions where processes of sunspot formation in the northern hemisphere occur earlier than in the southern one (except some exceptions in several years around the year 1900) during the years of about 1874-1926 to those where the opposite is true during the years of about 1926-1966, and returning back again during the years of about 1966-2008. The mean phase synchronization values at the coherent timescales given by wavelet coherence represent the running trend of the line of synchronization given by a cross-recurrence plot.

SUNSPOT UNIT AREA: A NEW PARAMETER TO DESCRIBE LONG-TERM SOLAR VARIABILITY

In this Letter we introduce a new parameter, the sunspot unit area (SUA), which describes the daily average size of sunspots produced by the dynamo in a solar cycle. The monthly average of the SUA is studied to show its variation during the solar cycle and is compared with the two commonly used parameters, sunspot numbers and sunspot areas. Our results show that (1) the new SUA parameter waxes and wanes during sunspot cycles in the same way as the other two parameters, but with a relatively small magnitude of fluctuations, (2) the Waldmeier effect and the Gnevyshev-Ohl rule, which appear in the variations of both sunspot numbers and sunspot areas, are not shown in the variations of SUA during solar cycles, and (3) the most pronounced period of SUA variation is about 10.13 yr, which is statistically significant at any time of the considered time span.

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. It 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.

Asymmetry of solar activity in cycle 23

Using sunspot groups and sunspot areas from May 1996 to February 2007, we find that solar activity for cycle 23 is dominant in the southern hemisphere, and our results enhance the inferred but uncertain conclusions obtained before. They are as follows: (1) each four cycles, the slope of the fitting straight lines of north-south asymmetry values changes its sign, and (2) the asymmetry signs of solar activity at both the low (>0 degrees - = 25 degrees - = 10 degrees - <25 degrees). When the former two are the same as the latter, solar activity is asymmetrically distributed in the hemispheres but symmetrically distributed when the former two differ from the latter. Moreover, asymmetry values of solar activity for the whole disk are always located between the first two and the latter and seem to be the averages of the first two and the latter, suggesting that the asymmetry of solar activity may be a function of latitude. In the forthcoming cycle 24, asymmetry of solar activity is inferred as being similar to cycle 12, and solar activity should remain dominant in the southern hemisphere.

THE LONG-TERM HEMISPHERIC SUNSPOT ACTIVITY

Sunspot activity is usually represented by either sunspot numbers (SN) or sunspot areas (SA). The smoothed monthly mean SA and SN in the northern and southern hemispheres from 1945 January to 2008 March are used to investigate the characteristics of long-term hemispheric sunspot activity. Although sunspot activity (SA and SN) is found to begin one month earlier in the northern hemisphere than in the southern hemisphere on the average of the considered time interval, the shift is so small that no long-term systematic phase shift is statistically acceptable as a first-order effect, as suggested by White & Trotter. Sunspot activity never peaks at the same time in the two hemispheres. Although the Schwabe cycle appears in hemispheric sunspot activity, its period length slightly varies during the considered time interval and seems to be longer in the southern hemisphere than in the northern hemisphere on the average. Sunspot activity is asymmetrically distributed in the hemispheres, but the largest hemispheric diversity usually does not appear around the maximum time of a cycle. The diversity of SA, respectively, in the northern and southern hemispheres runs on the Sun similarly and synchronously as the diversity of SN does. Sunspot activity is slightly asynchronous in the hemispheres.

LONG-TERM TREND OF SUNSPOT NUMBERS

Using the Hilbert-Huang Transform method, we investigate the long-term trend of yearly mean total sunspot numbers in the time interval of 1700-2015, which come from the World Data Center-the. sunspot Index and long-term solar observations. The main findings of this study are summarized below. (1) From the adaptive trend, which is extracted from the yearly mean total sunspot numbers, we can find that the value gradually increases during the time period 1700-1975, then decreases gradually from 1975 to 2015. (2) The Centennial Gleissberg Cycle is extracted from the yearly mean total sunspot numbers and confirms that. a new grand minimum is in progress; the Dalton Minimum, the Gleissberg Minimum, and low level of solar activity during solar cycle 24 (the part of the new grand minimum) all can be understood as minima of the Centennial Gleissberg Cycle. (3) Based on the adaptive (overall) trend, and the 100-year and longer timescale trend of yearly mean total sunspot numbers, we can infer that the level of solar activity during the new grand minimum may be close to that during the Gleissberg Minimum, slightly higher than that during the. Dalton Minimum, and significantly higher than that during the. Maunder Minimum. Our results do not support the suggestion. that a new grand minimum, somewhat resembling the Maunder Minimum, is in progress.

Solar-cycle related variation of solar differential rotation

Solar-cycle-related variation of differential rotation is investigated through analysing the rotation rates of magnetic fields, distributed along latitudes and varying with time at the time interval of 1976 August to 2008 April. More pronounced differentiation of rotation rates is found to appear at the ascending part of a Schwabe cycle than at the descending part on an average. The coefficient B in the standard form of differential rotation, which represents the latitudinal gradient of rotation, may be divided into three parts within a Schwabe cycle. Part 1 spans from the start to the fourth year of a Schwabe cycle, within which the absolute B is approximately a constant or slightly fluctuates. Part 2 spans from the fourth to the seventh year, within which the absolute B decreases. Part 3 spans from the seventh year to the end, within which the absolute B increases. Strong magnetic fields repress differentiation of rotation rates, so that rotation rates show less pronounced differentiation, but weak magnetic fields seem to just reflect differentiation of rotation rates. The solar-cycle-related variation of solar differential rotation is inferred to be the result of both the latitudinal migration of the surface torsional pattern and the repression of the strong magnetic activity to differentiation of rotation rates. The north-south asymmetry in solar rotation is investigated as well, and the Northern hemisphere should rotate faster than the southern in cycles 21-23.

Periodicity in the most violent solar eruptions: recent observations of coronal mass ejections and flares revisited

Using the Hilbert-Huang Transform method, we investigate the periodicity in the monthly occurrence numbers and monthly mean energy of coronal mass ejections (CMEs) observed by the Large Angle and Spectrometric Coronagraph Experiment on board the Solar and Heliographic Observatory from 1999 March to 2009 December. We also investigate the periodicity in the monthly occurrence numbers of Ha flares and monthly mean flare indices from 1996 January to 2008 December. The results show the following. (1) The period of 5.66 yr is found to be statistically significant in the monthly occurrence numbers of CMEs; the period of 10.5 yr is found to be statistically significant in the monthly mean energy of CMEs. (2) The periods of 3.05 and 8.70 yr are found to be statistically significant in the monthly occurrence numbers of Ha flares; the period of 9.14 yr is found to be statistically significant in the monthly mean flare indices.

Does High-Latitude Solar Activity Lead Low-Latitude Solar Activity in Time Phase?

Using data from the Carte Synoptique solar filaments archive, we investigate whether there is a time lag between high-latitude solar activity and low-latitude solar activity. The cross-correlation analysis of the number of high-latitude filaments per Carrington rotation (NHF) and that of low-latitude filaments per Carrington rotation (NLF) shows, although inconclusively, that NLF possibly lags behind NHF. The periodic characteristics of both NHF and NLF clearly indicate that the activity of high-latitude filaments is evidently leading the activity of low-latitude filaments. Thus, the present study suggests that high-latitude solar activity leads low-latitude solar activity in time phase.

Speed Distributions of CMEs in Cycle 23 at Low and High Latitudes

We analyzed the speed (v) distributions of 11584 coronal mass ejections (CMEs) observed by the Large Angle and Spectrometric Coronagraph Experiment on board the Solar and Heliospheric Observatory (SOHO/LASCO) in cycle 23 from 1996 to 2006. We find that the speed distributions for high-latitude (HL) and low-latitude (LL) CME events are nearly identical and to a good approximation they can be fitted with a lognormal distribution. This finding implies that statistically the same driving mechanism of a nonlinear nature is acting in both HL and LL CME events, and CMEs are intrinsically associated with the sources magnetic structure on large spatial scales. Statistically, the HL CMEs are slightly slower than the LL CMEs. For HL and LL CME events respectively, the speed distributions for accelerating and decelerating events are nearly identical and also to a good approximation they can be both fitted with a lognormal distribution, thus supplementing the results obtained by Yurchyshyn et al.