H. F. Liang

Regularity of the north-south asymmetry of solar activity

In the present work, the dominant hemisphere of solar activity in each of solar cycles 12 to 22 has been clarified by calculating the actual probability of the hemispheric distribution of several solar activity phenomena using long-term observational records. An attempt is made to demonstrate that a long characteristic time scale, about 12-cycle length, is inferred to occur in solar activity.

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.

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.

STATISTICAL BEHAVIOR OF SUNSPOT GROUPS ON THE SOLAR DISK

In the present study we have produced a diagram of the latitude distribution of sunspot groups from the year 1874 through 1999 and examined statistical characteristics of the mean latitude of sunspot groups. The reliability of the observed data set prior to solar cycle 19 is found quite low as compared with that of the data set observed after cycle 19. A correlation is found between maximum latitude at which first sunspot groups of a new cycle appear and the maximum solar activity of the cycle. It is inferred that solar magnetic activity during the early part of an extended solar cycle may contain some information about the strength of forthcoming solar cycle. A formula is given to describe latitude change of sunspot groups with time during an extended solar cycle. The latitude-migration velocity is found to be largest at the beginning of solar cycle and decreases with time as the cycle progresses with a mean migration velocity of about 1.61° per year.

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.

Phase shifts of the paired wings of butterfly diagrams

Sunspot groups observed by the Royal Greenwich Observatory/US Air Force/NOAA from 1874 May to 2008 November and the Carte Synoptique solar filaments from 1919 March to 1989 December are used to investigate the relative phase shift of the paired wings of butterfly diagrams of sunspot and filament activities. Latitudinal migration of sunspot groups (or filaments) does asynchronously occur in the northern and southern hemispheres, and there is a relative phase shift between the paired wings of their butterfly diagrams in a cycle, making the paired wings spatially asymmetrical on the solar equator. It is inferred that hemispherical solar activity strength should evolve in a similar way within the paired wings of a butterfly diagram in a cycle, demonstrating the paired wings phenomenon and showing the phase relationship between the northern and southern hemispherical solar activity strengths, as well as a relative phase shift between the paired wings of a butterfly diagram, which should bring about almost the same relative phase shift of hemispheric solar activity strength.

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°).

Periodicity of the solar radius revisited by using empirical mode decomposition and the Lomb–Scargle method*

Using the Hilbert–Huang transform and the Lomb–Scargle method, we investigate periodicities in the daily solar radius data during the time interval from February 1978 to October 1999 derived from Calern Observatory. The following prominent periods are found: (1) the rotation cycle signal; (2) several mid-term periods including 122, 162.9 and 225 days, annual-variation periodicities (319 and 359 days), quasi-triennial oscillations (3.46 and 3.94 years); (3) the 11-year Schwabe cycle, which is in anti-phase with solar activity. This result indicates that the strong magnetic field associated with the Sun has a greater inhibitive effect on the radius variation.