On particle trajectories in restricted 3-body problem including the effect of radiation: Sun-Jupiter system

In this work, we have simulated orbits of a particle moving in gravitational field of the Sun-Jupiter system. The effect of solar radiation pressure, including Poynting Robertson drag, on the evolution of particle orbits in phase space have been studied for different values of the parameter β ₁ (the ratio of radiation to gravitational force) and initial conditions. Characteristics of various computed trajectories have been studied using wavelet transform (WT), Fourier transform (FT) and Poincare surface of section method. We use wavelet analysis to identify transitions of a trajectory in time-frequency plane and further apply it to classify it as regular or chaotic in phase space. Unlike the Fourier transform method (FT), we observe that the wavelet transform (WT) also provides a basis to identify ‘sticky’ trajectories in the present dynamical system.     

Wavelet analysis of the standard map: Structure and scaling

Wavelet analysis is applied to distributions of points generated by iterating the standard map. The initial condition is chosen so that the points fill the largest chaotic region. When the standard map parameterk=1.3, the distribution of points contains many voids corresponding to islands in the chaotic region. The wavelet transform is dominated by contributions from these islands. Fork=10 the chaos fills phase space and no structure is apparent; the wavelet transform reveals statistical fluctuations in the distribution of points.     

Stability in Period and Amplitude: The High-Amplitude δ Scuti Star YZ Boötis

The variability of period and amplitude of the high-amplitude δ Scuti star YZ Boo was thoroughly investigated based on a comprehensive analysis of new time-series photometry and other available data. Fourier analysis, O–Cdiagram, and wavelet analysis establish a clear picture for the star's time-dependent behavior in period and amplitude. We detected no additional frequencies being intrinsic to the variable or caused by amplitude/frequency modulation confirming its mono-periodicity. We reveal the pulsation of YZ Boo is quite stable in both period and amplitude over the past 50 years. Short-term variations at cycle level including “anomalous cycles” are present clearly, while long-term variations in period and amplitude at annual base are insignificant. However, we note an increment from 2000 to 2003 in both period and amplitude. In 2000 the amplitude reached the lowest. This is indicated by the Fourier and wavelet results. In the long term, O–Cfits and wavelet analysis agree with the Fourier results that the period change of YZ Boo is still inconclusive.     

Merging a Line Profile Series Into an One-Dimensional Dataset, an Applied Technique for Nonradial Pulsation Mode Diagnosis

A new method of nonradial pulsation mode identification is developed. This method is based on Fourier analysis of time series line profile variations that have been merged into a one-dimensional equally spaced dataset. In principle, this method is identical to that of two-dimensional Fourier transform of line profile time series, but it is much more convenient to use for most of astronomers who have experience in period analysis of light curves. The features of both temporal frequency and Doppler spatial frequency can be accurately retrieved. This method provides an easy way to carry out mode identification from line profiles and minimizes the uncertainty of mode determination caused by random noise. Comments and assessment of related methods of mode identification are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

Evaluation of the short-term periodicities in the flare index between the years 1966–2002

The short-term periodicities of the flare index are investigated in detail using Fourier and wavelet transforms for the full disc and for the northern and the southern hemispheres of the Sun separately over the epoch of almost 4 cycles (1966–2002). The most pronounced power peaks were found by the Fourier transform to be present at 25.6, 27.0, 30.2, and 33.8 days. The wavelet transform results show that the occurrence of periodicities of flare index power is highly intermittent in time. A comparison of the results of the Fourier transform and the time-period wavelet transform of the flare index time series has clarified the importance of different periodicities, whether they are or are not the harmonics of the basic ones, as well as the temporal location of their occurrence. We found that the modulation of the flare index due to the 27-day solar rotation is more pronounced during the declining portion of solar cycle than during the rising portion.     

Daubechies小波在射电成图降噪处理中的应用

在超新星遗迹的认证中,如何有效去除观测资料中的干扰噪音,突出其中的有用信号,一直是实验工作关注的焦点。小波分析法是一种新近发展超来的新的时频分析方法。与Ｆｏｕｒｉｅｒ分析方法一样,任意的能量有限函数可以用小波正交展开。与Ｆｏｕｒｉｅｒ正交基不同的是,小波正交基具有局域性好的特性,这为分离观测资料中的局部噪音。提供了一个十分不效的工具,在利用Ｄａｕｂｅｃｈｉｅｓ４离散小波时,成功地去除了射电源成图中     

Subsecond (0.1 s) Pulsations in the 11 April 2001 Radio Event

Radio pulsations observed during the 11 April 2001 event at six single frequencies (237, 327, 408, 610, 1420, and 2695 MHz) by the Trieste radio-polarimeter with a time resolution 10 ms are analyzed. A wavelet analysis method as well as time delay and polarization measurements are used. Both methods reveal pulsations with a period of about 0.1 s at all observed frequencies. Furthermore, the 0.1 s pulsations drift toward higher and lower frequencies, starting at about 1420 MHz. The polarization of pulsations increases with frequency and time. The remarkable fact that the detected 0.1 s period of pulsations does not depend on frequency in a very broad frequency range is discussed in terms of existing models of pulsations.     

Image compression by means of wavelet transform - application to solar observations

Images and spectra contain a large amount of data. Therefore the question arises, how this data can be decreased or compressed without losing important detail. The discrete wavelet transform is a tool which can be used to compress data because of its good approximation properties. It is very easy to implement and requires approximately the same amount of calculation as the fast Fourier transform. It has the advantage of giving information both in time and frequency. Since most of the coefficients in the transformed data are very small compared to the maximum values, which means that they do not contribute much to the transform, a large number of them can be neglected. Although some data get lost, the physical results deduced from the data remain the same, as is demonstrated by various examples. By this method it is even possible to compress data containing much noise to high-compression ratios.     

Spurious results from Fourier analysis of data with closely spaced frequencies

It is shown how erroneous results can occur using some period-finding methods, such as Fourier analysis, on data containing closely spaced frequencies. The frequency spacing accurately resolvable with data of lengthT is increased from the standard value of about 1/T quoted in the literature to approximately 1.5/T.     

Horizontal convective velocity field obtained from the observations of the solar limb

Structure of horizontal convective currents in the solar atmosphere has been investigated using profiles of the λ ≈ 532.42 nm neutral iron line which were observed at the solar limb with high spatial resolution. The asymmetry of the observed line was shown to arise when approaching the solar limb. The spatial and time velocity variations were simulated using the λ-meter technique. Acoustic waves were removed using the k-ω filters. The convection currents on various spatial scales were distinguished, namely, those connected with granulation, mesogranulation, and supergranulation. The spatial and time distribution of the convection velocities in the photosphere and in the low chromosphere has been analyzed. The horizontal currents were shown to exist on granulation, mesogranulation, and supergranulation scales as low as h ≈ 250 km, and the granulation and mesogranulation horizontal velocities increase with height. In the photospheric layers, the supergranulation vertical-velocity field appears almost invariable, while the supergranulation horizontal-velocity field can vary with height. The horizontal velocity distribution within large convection currents is found to be asymmetric on granulation, mesogranulation, and supergranulation scales.     

Relative phase analyses of long-term hemispheric solar flare activity

Wavelet transform methods, including the continuous wavelet transform, cross-wavelet transform and wavelet coherence, have been proposed to investigate the phase synchrony of the monthly mean flare indices in the time interval 1966 January–2007 December in the solar northern and southern hemispheres, respectively. The Schwabe cycle is the only period of statistical significance, and its mean value is 10.7 yr for the monthly mean flare indices in the northern hemisphere but slightly smaller, 10.1 yr, in the southern hemisphere – this should lead to phase asynchrony between the two. Both the cross-wavelet transform and wavelet coherence analyses show asynchronous behaviour with strong phase mixing in the high-frequency components of hemispheric flare activity, and strong synchronous behaviour with coherent phase angles in the low-frequency components, corresponding to the period-scales around the Schwabe cycle. The northern flare activity should lead the southern for the low-frequency components.     

Synchronization of Sunspot Numbers and Sunspot Areas

Sunspot activity is usually described by either sunspot numbers or sunspot areas. The smoothed monthly mean sunspot numbers (SNs) and the smoothed monthly mean areas (SAs) in the time interval from November 1874 to September 2007 are used to analyze their phase synchronization. Both the linear method (fast Fourier transform) and some nonlinear approaches (continuous wavelet transform, cross-wavelet transform, wavelet coherence, cross-recurrence plot, and line of synchronization) are utilized to show the phase relation between the two series. There is a high level of phase synchronization between SNs and SAs, but the phase synchronization is detected only in their low-frequency components, corresponding to time scales of about 7 to 12 years. Their high-frequency components show a noisy behavior with strong phase mixing. Coherent phase variables should exist only for a frequency band with periodicities around the dominating 11-year cycle for SNs and SAs. There are some small phase differences between them. SNs lag SAs during most of the considered time interval, and they are in general more asynchronous around the minimum and maximum times of a cycle than at the ascending and descending phases.     

On the Possibility for Action Conservation in the Solar Cycle

The sunspot series are investigated in detail by use of a wavelet transform. By simple arguments, we present a reduced sunspot time-series, which can be argued to be approximately proportional to the magnetic flux density at the coronal surface. This reduced sunspot index correctly reproduces the (average) 22 year solar cycle. Closer scrutiny of the sunspot variation shows that the frequency of the solar cycle and the energy in the magnetic field vary consistently with conservation of action, i.e., energy divided by frequency. The analysis is based on the available data beginning with the year 1700, and analyzed by a wavelet transform. The present results relate to observations reported previously in the literature.     

基于小波变换的射频干扰消除方法的研究

在射电天文观测中,射频干扰(Radio Frequency Interference, RFI)会以多种形式混入望远镜接收系统,给观测带来误判或者降低观测信噪比.近年来国内国际射电天文快速发展,国内国际大型射电望远镜和阵列先后建设,观测灵敏度大为提高,射频干扰的影响尤为突出.随着科技发展和人类活动的加剧,射频干扰日益严重且不可逆转.提出利用2维离散小波变换的方法分析射电天文观测的数据,对望远镜系统输出的时间频率序列进行小波变换,根据小波系数分离出原始信号中各分量,每个分量统计得到相应的阈值,将各分量与阈值相比较识别干扰成分并标记去除.利用该方法对实际观测数据进行了处理,结果表明该方法能够很好地标记并消减干扰信号,且提高了观测的信噪比.     

Correlated fast time structures at millimeter waves and hard X-rays during a solar burst

We present an analysis of the time profiles detected during a solar impulsive flare, observed at one-millimeter radio frequency (48 GHz) and in three hard X-ray energy bands (25–62, 62–111, and 111–325 keV) with high sensitivity and time resolution. The time profiles of all emissions exhibit fast time structures of 200–300 ms half power duration which appear in excess of a slower component varying on a typical time scale of 10 s. The amplitudes of both the slow and fast variations observed at 48 GHz are not proportional to those measured in the three hard X-ray energy bands. However, the fast time structures detected in both domains are well correlated and occur simultaneously within 64 ms, the time resolution of the hard X-ray data. In the context of a time-of-flight flare model, our results put strong constraints on the acceleration time scales of electrons to MeV energies.     

Periodicities in Solar Flare Index for Cycles 21 – 23 Revisited

The periodic analyses of solar flare data have been carried out by different authors for about three decades. Controversial results appear as depending on the analysis techniques and investigated time periods. Considering that different authors applied different methods to different data sets, it seems necessary to reanalyze the periodicity of solar flare index with a unified method. In this study we used two new methods to investigate the periodic behavior of solar flare index data, first for individual cycles 21, 22 and 23, and then for all of them. We used i) the multi taper method with red- and white-noise approximations, and ii) the Morlet wavelet transform for periodicity analysis. Apart from the solar rotation periodicity of about 27 days which is of obvious significance and is found in all examined cycles with at least a 90% significance level, we obtained the following prominent periods: 152 days for cycle 21, 73 days for cycle 22, and 62 days for cycle 23. Finally, we compare our results with the ones previously found. We emphasize the fact that a lesser number of periodicities is found in the range of low frequencies (long periods) while the higher frequencies show a greater number of periodicities. This result might be useful for better predictions of the solar cycles.     

The 156-day quasi-periodicity in solar indices

This paper investigates a series of daily solar indices: the sunspot number W (1900–2008), solar flux at 2800 MHz F _10.7 (1947–2008), and a number of X-ray flares N _x (1981–2008). The methods of Fourier and wavelet analysis are used to reveal the so-called 156-day Rieger-type periodicity (RTP). The W index is observed to have a statistically significant RTP amplitude in the neighborhood of the solar maxima in most of the solar cycles under study, except for cycles 14, 15, and 23. The 156-day peak is observed to have its largest power during the declining phase of cycle 16, at the maximum of cycle 21, and during the increasing phase of cycles 20 and 23. Statistically significant RTPs are also observed at the minima of cycles 17, 18 and 19. We conclude that there is no stable dependence between RTP and the solar cycle. The wavelet analysis shows that the pattern of the RTP time dependence for the F _10.7 index is almost identical to that of the W index. The correlation coefficient between the RTP curves is 0.95. The correlation coefficients for the pairs of indices W-N _x and F _10.7-N _x are 0.36 and 0.32, respectively. No time lags are found between the RTP starting points for different indices. Thus, the 156-day quasi-periodicity involves, almost simultaneously, events that occur in active regions of the solar atmosphere at different heights. This paper discusses the possible nature of RTP.