L. S. Zhan

On the Latitudinal Distribution of Sunspot Groups over a Solar Cycle

The latitudinal distribution of sunspot groups over a solar cycle is investigated. Although individual sunspot groups of a solar cycle emerge randomly at any middle and low latitude, the whole latitudinal distribution of sunspot groups of the cycle is not stochastic and, in fact, can be represented by a probability density function of the Γ distribution having maximum probability at about 15.5°. The maximum amplitude of a solar cycle is found to be positively correlated against the number of sunspot groups at high latitude (≥35°) over the cycle, as well as the mean latitude. Also, the relation between the asymmetry of sunspot groups and its latitude is investigated, and a pattern of the N-S asymmetry in solar activity is suggested.

VARIATIONS OF SOLAR ROTATION AND SUNSPOT ACTIVITY

The continuous wavelet transformation is used to study the temporal variations of the rotational cycle length of daily sunspot numbers from 1849 January 1 to 2010 February 28, from a global point of view. The rotational cycle length of the Sun is found to have a secular trend, which statistically shows a linear decrease by about 0.47 days during the time interval considered. The empirical mode decomposition analysis of the temporal variations of the rotational cycle length shows an acceleration trend for the surface rotation rate from cycles 11 to 19, but a deceleration trend from the beginning of cycle 20 onward. We cannot determine whether the rotation rate around the maximum times of the Schwable cycles should be faster or slower than that around the minimum times, implying no Schwable cycle in the long-term variations of rotation. The results obtained are compared to those from the literature. It is inferred that the variation of the rotational cycle length may be related to the variation of sunspot activity in the long run.

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.

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.

A method for the prediction of relative sunspot number for the remainder of a progressing cycle with application to cycle 23

In this paper, we investigate the prospect of using previously occurring sunspot cycle signatures to determine future behavior in an ongoing cycle, with specific application to cycle 23, the current sunspot cycle. We find that the gross level of solar activity (i.e., the sum of the total number of sunspots over the course of a sunspot cycle) associated with cycle 23, based on a comparison of its first several years of activity against similar periods of preceding cycles, is such that cycle 23 best compares to cycle 2. Compared to cycles 2 and 22, respectively, cycle 23 appears 1.08 times larger and 0.75 times as large. Because cycle 2 was of shorter period, we infer that cycle 23 also might be of shorter length (period less than 11 years), ending sometime in late 2006 or early 2007.

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.

Phase Relation Between Activities of Solar Active Prominences Separately at low and High Latitudes

In the present work, the phase relation between activities of solar active prominences respectively at low and high latitudes in the period 1957–1998 has been studied. We found that from the solar equator to the solar poles, the activity of the solar active prominences occurs earlier at higher latitudes, and that the cycle of the solar active prominences at high latitudes (larger than 50°) leads by 4 years both the sunspot cycle and the corresponding cycle of the solar active prominences at low latitudes (less than 40°).