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.     

Modeling Solar Spectral Irradiance and Total Magnetic Flux Using Sunspot Areas

We show that daily sunspot areas can be used in a simple, single parameter model to reconstruct daily variations in several other solar parameters, including solar spectral irradiance and total magnetic flux. The model assumes that changes in any given parameter can be treated mathematically as the response of the system to the emergence of a sunspot. Using cotemporal observational data, we compute the finite impulse response (FIR) function that describes that response in detail, and show that the response function has been approximately stationary over the time period for which data exist. For each parameter, the impulse response function describes the physical evolution of that part of a solar active region that is the source of the measured variability. We show that the impulse response functions are relatively narrow functions, no more than 3 years wide overall. Each exhibits a pre-active, active, and post-active region component; the active region component dominates the variability of most of the parameters studied.     

太阳黑子月平均面积数活动周及其特征

我们对第12周至第22周的太阳黑子月平均面积数进行统计分析,并与相应的太阳黑子月平均数相比较,结果表明太阳黑子月平均面积数活动周与太阳黑子月平均数活动周有一定的关系。在多数情况下,太阳黑子出现最大值的时间与太阳黑子面积数出现最大值的时间上不一致;太阳黑子平滑月平均数活动周上升期与太阳黑子平滑月平均面积数上升期在大多数情况下不相同;太阳黑子平滑月平均数活动周平均效果的瓦德迈尔效应(Waldmeiereffect)一般要比太阳黑子平滑平均面积数的活动周明显;文中还对太阳黑子平滑月平均面积数活动周的特征进行了分析。     

The Shape of Sunspot Cycles Described by Monthly Sunspot Areas

In this paper, we used the same four-parameter function as Hathaway, Wilson, and Reichmann (1994) proposed and studied the temporal behavior of sunspot cycles 12–22. We used the monthly averages of sunspot areas and their 13-point smoothed data. Our results show the following. (1) The four-parameter function may reduce to a function of only two parameters. (2) As a cycle progresses, the two-parameter function can be accurately determined after 4–4.5 years from the start of the cycle. A good prediction can be made for the timing and size of the sunspot maximum and for the behavior of the remaining 5–10 years of the cycle. (3) The solar activity in the remaining and forthcoming years of cycle 23 is predicted. (4) The smoothed monthly sunspot areas are more suitable to be employed for prediction at the maximum and the descending period of a cycle, whereas at the early period of a cycle the (un-smoothed) monthly data are more suitable.     

The Ten-Rotation Quasi-periodicity in Sunspot Areas

Sunspot-area fluctuations over an epoch of 12 solar cycles (12?–?23) are investigated in detail using wavelets. Getko (Universal Heliophysical Processes, IAU Symp. 257, 169, 2009) found three significant quasi-periodicities at 10, 17, and 23 solar rotations, but two longer periods could be treated as subharmonics of the ten-rotation quasi-periodicity. Therefore we focused the analysis on the occurrence of this quasi-periodicity during the low- and high-activity periods of each solar cycle. Because of the N?–?S asymmetry, each solar hemisphere was considered separately. The skewness of each fluctuation-probability distribution suggests that the positive and negative fluctuations could be examined separately. To avoid the problem that occurs when a few strong fluctuations create a wavelet peak, we applied fluctuation transformations for which the amplitudes at the high- and the low-activity periods are almost the same. The wavelet analyses show that the ten-rotation quasi-periodicity is mainly detected during the high-activity periods, but it also exists during a few low-activity periods. The division of each solar hemisphere into 30^°-wide longitude bins and the wavelet calculations for the areas of sunspot clusters belonging to these 30^° bins enable one to detect longitude zones in which the ten-rotation quasi-periodicity exists. These zones are present during the whole high-activity periods and dominate the integrated spectra.     

太阳黑子面积数与黑子数指标在大气预报中的应用对比分析

分别应用太阳黑子视面积数和太阳黑子相对数代表太阳活动水平与天津夏季降水总量进行相关分析,结果表明黑子面积指标明显优于黑子数.     

Total Solar Irradiance Variation During Rapid Sunspot Growth

Large sunspot areas correspond to dips in the total solar irradiance (TSI), a phenomenon associated with the local suppression of convective energy transport in the spot region. This results in a strong correlation between sunspot area and TSI. During the growth phase of a sunspot other physics may affect this correlation; if the physical growth of the sunspot resulted in surface flows affecting the temperature, for example, we might expect to see an anomalous variation in TSI. In this paper we study NOAA active region 8179, in which large sunspots suddenly appeared near disk center, at a time (March 1998) when few competing sunspots or plage regions were present on the visible hemisphere. We find that the area/TSI correlation does not significantly differ from the expected pattern of correlation, a result consistent with a large thermal conductivity in solar convection zone. In addition we have searched for a smaller-scale effect by analyzing white-light images from MDI (the Michelson Doppler Imager) on SOHO. A representative upper-limit energy consistent with the images is on the order of 3×10³¹ ergs, assuming the time scale of the actual spot area growth. This is of the same order of magnitude as the buoyant energy of the spot emergence even if it is shallow. We suggest that detailed image analyses of sunspot growth may therefore show `transient bright rings' at a detectable level.     

Toward Waveform Heliotomography: Observing Interactions of Helioseismic Waves with a Sunspot

We investigate how helioseismic waves that originate from effective point sources interact with a sunspot. These waves are reconstructed from observed stochastic wavefields on the Sun by cross-correlating photospheric Doppler-velocity signals. We select the wave sources at different locations relative to the sunspot, and investigate the p- and f-mode waves separately. The results reveal a complicated picture of waveform perturbations caused by the wave interaction with the sunspot. In particular, it is found that for waves originating from outside of the sunspot, p-mode waves travel across the sunspot with a small amplitude reduction and slightly higher speed, and wave amplitude and phase get mostly restored to the quiet-Sun values after passing the sunspot. The f-mode wave experiences some amplitude reduction passing through the sunspot, and the reduced amplitude is not recovered after that. The wave-propagation speed does not change before encountering the sunspot and inside the sunspot, but the wavefront becomes faster than the reference wave after passing through the sunspot. For waves originating from inside the sunspot umbra, both f- and p-mode waves show significant amplitude reductions and faster speed for all propagation paths. A comparison of positive and negative time lags of cross-correlation functions shows an apparent asymmetry in the waveform changes for both the f- and p-mode waves. We suggest that the waveform variations of the helioseismic waves interacting with a sunspot found in this article can be used for developing a method of waveform heliotomography, similar to the waveform tomography of the Earth.     

大黑子群对太阳总辐照度的影响

本文用云南天文台在第２２周太阳活动峰年期间拍摄到的大太阳黑子群照相资料，太阳黑子目视描述资料，以及Ｎｉｍｂｕｓ—７卫星上辐射计测量的太阳总辐照度，分别计算了太阳总辐射照度与大黑子群的本影视面积，大黑子群全群视面积和日面上全部黑子的总视面积的相关系数。结果表明，太阳总辐射照度与这三种视面积均存在强的负相关。其中与大黑子群本影视面积的相关最强，其次是与全群视面积的相关，最后是与日面上全部黑子的总视面积的相关。并对以上结果和其它有关结果进行了分析和讨论。     

卫星黑子衰减触发的喷流事件

详细分析了一次太阳低层大气磁场重联触发的喷流事件.这次喷流发生在2014年8月1日,爆发自美国国家海洋和大气管理局(National Oceanic and Atmospheric Administration, NOAA)活动区12127边缘的一个卫星黑子处.该喷流爆发包括日浪、紫外喷流、极紫外高温和低温喷流.大熊湖太阳天文台(Big Bear Solar Observatory,BBSO)的Goode Solar Telescope (GST)高分辨率氧化钛(TiO)谱线的光球观测显示,喷流爆发过程中,卫星黑子一直衰减.到喷流结束,卫星黑子面积共减少了80%.在此过程中,太阳动力学天文台(Solar Dynamics Observatory, SDO)日球磁场成像仪(Helioseismic and Magnetic Imager, HMI)的视向磁场观测表明,该卫星黑子对应的负极磁场与相邻的正极磁场发生明显对消,产生喷流足部亮点.根据SDO卫星太阳大气成像仪(Atmospheric Imaging Assembly, AIA)的多波段观测,该足部亮点首先出现在紫外1600?波段.待紫外(1600?)喷流从紫外足部亮点顶部向上喷发,在极紫外波段也观测到相应的亮源.随着足点源亮度突然增强,有明显的极紫外低温喷流和日浪从足部亮点侧面喷发.从GST的高分辨率Hα图像上,可见日浪由许多精细纤维组成,这些纤维扎根在足点源的东南侧.根据从光球层过色球层再到日冕层的多波段高分辨率观测,色球中下层的磁场对消触发了这次喷流事件.向上喷发的物质流可以携带能量进入上层大气,并加热上层大气.研究结果表明,低层大气磁重联可能对解决日冕加热问题起重要作用.     

Group Sunspot Numbers: A New Solar Activity Reconstruction

In this paper, we construct a time series known as the Group Sunspot Number. The Group Sunspot Number is designed to be more internally self-consistent (i.e., less dependent upon seeing the tiniest spots) and less noisy than the Wolf Sunspot Number. It uses the number of sunspot groups observed, rather than groups and individual sunspots. Daily, monthly, and yearly means are derived from 1610 to the present. The Group Sunspot Numbers use 65941 observations from 117 observers active before 1874 that were not used by Wolf in constructing his time series. Hence, we have calculated daily values of solar activity on 111358 days for 1610–1995, compared to 66168 days for the Wolf Sunspot Numbers. The Group Sunspot Numbers also have estimates of their random and systematic errors tabulated. The generation and preliminary analysis of the Group Sunspot Numbers allow us to make several conclusions: (1) Solar activity before 1882 is lower than generally assumed and consequently solar activity in the last few decades is higher than it has been for several centuries. (2) There was a solar activity peak in 1801 and not 1805 so there is no long anomalous cycle of 17 years as reported in the Wolf Sunspot Numbers. The longest cycle now lasts no more than 15 years. (3) The Wolf Sunspot Numbers have many inhomogeneities in them arising from observer noise and this noise affects the daily, monthly, and yearly means. The Group Sunspot Numbers also have observer noise, but it is considerably less than the noise in the Wolf Sunspot Numbers. The Group Sunspot Number is designed to be similar to the Wolf Sunspot Number, but, even if both indices had perfect inputs, some differences are expected, primarily in the daily values.     

Group Sunspot Numbers: A New Solar Activity Reconstruction

In this paper, we construct a time series known as the Group Sunspot Number. The Group Sunspot Number is designed to be more internally self-consistent (i.e., less dependent upon seeing the tiniest spots) and less noisy than the Wolf Sunspot Number. It uses the number of sunspot groups observed, rather than groups and individual sunspots. Daily, monthly, and yearly means are derived from 1610 to the present. The Group Sunspot Numbers use 65941 observations from 117 observers active before 1874 that were not used by Wolf in constructing his time series. Hence, we have calculated daily values of solar activity on 111358 days for 1610–1995, compared to 66168 days for the Wolf Sunspot Numbers. The Group Sunspot Numbers also have estimates of their random and systematic errors tabulated. The generation and preliminary analysis of the Group Sunspot Numbers allow us to make several conclusions: (1) Solar activity before 1882 is lower than generally assumed and consequently solar activity in the last few decades is higher than it has been for several centuries. (2) There was a solar activity peak in 1801 and not 1805 so there is no long anomalous cycle of 17 years as reported in the Wolf Sunspot Numbers. The longest cycle now lasts no more than 15 years. (3) The Wolf Sunspot Numbers have many inhomogeneities in them arising from observer noise and this noise affects the daily, monthly, and yearly means. The Group Sunspot Numbers also have observer noise, but it is considerably less than the noise in the Wolf Sunspot Numbers. The Group Sunspot Number is designed to be similar to the Wolf Sunspot Number, but, even if both indices had perfect inputs, some differences are expected, primarily in the daily values.     

Long-Term Variations in Solar Differential Rotation and Sunspot Activity

The solar equatorial rotation rate, determined from sunspot group data during the period 1879–2004, decreased over the last century, whereas the level of activity has increased considerably. The latitude gradient term of the solar rotation shows a significant modulation of about 79 year, which is consistent with what is expected for the existence of the Gleissberg cycle. Our analysis indicates that the level of activity will remain almost the same as the present cycle during the next few solar cycles (i.e., during the current double Hale cycle), while the length of the next double Hale cycle in sunspot activity is predicted to be longer than the current one. We find evidence for the existence of a weak linear relationship between the equatorial rotation rate and the length of sunspot cycle. Finally, we find that the length of the current cycle will be as short as that of cycle 22, indicating that the present Hale cycle may be a combination of two shorter cycles. Presently working for the Mt. Wilson Solar Archive Digitization Project at UCLA.     

Tilt of Sunspot Bipoles in Solar Cycles 15 to 24

We use recently digitized sunspot drawings from Mount Wilson Observatory to investigate the latitudinal dependence of tilt angles of active regions and its change with solar cycle. The drawings cover the period from 1917 to present and contain information as regards polarity and strength of magnetic field in sunspots. We identified clusters of sunspots of same polarity, and used these clusters to form “bipole pairs”. The orientation of these bipole pairs was used to measure their tilts. We find that the latitudinal profile of tilts does not monotonically increase with latitude as most previous studies assumed, but instead, it shows a clear maximum at about 25?–?30 degree latitudes. Functional dependence of tilt (\(\gamma\)) on latitude (\(\varphi\)) was found to be \(\gamma= (0.20\pm0.08) \sin(2.80 \varphi) + (-0.00\pm0.06)\). We also find that latitudinal dependence of tilts varies from one solar cycle to another, but larger tilts do not seem to result in stronger solar cycles. Finally, we find the presence of a systematic offset in tilt of active regions (non-zero tilts at the equator), with odd cycles exhibiting negative offset and even cycles showing the positive offset.     

Temporal Variations of the Solar Rotation Determined by Sunspot Groups

The extended Greenwich data set consisting of positions of sunspot groups is used for the investigation of cycle-related variations of the solar rotation in the years 1874–1981. Applying the residual method, which yields a single number for each year describing the average deviation from the mean value of the solar rotation, the dependence of the rotation velocity residual on the phase of the solar cycle is investigated. A secular deceleration of the solar rotation was found: the slope being statistically significant at the 3σ level. Periods of 33, 22, 11, 5.2, and 3.5 years can be identified in the power spectra. The rotation velocity residuals were averaged for all years with the same solar cycle phase relative to the nearest preceding sunspot minimum. The variation pattern reveals a higher than average rotation velocity in the minimum of activity and, to a lesser extent, also around the maximum of activity. The analysis was repeated with several changes in the reduction method, such as elimination of the secular trend, application of statistical weights, different cutoffs of the central meridian distance, division of the latitude into subregions and treating data from the years of activity minima separately. The results obtained are compared with those from the literature, and an interpretation of the observed phenomena is proposed.     

From Sunspot Area to Solar Variability: A Linear Transformation

The relationship between sunspot area and other observable solar parameters, such as spectral solar irradiance or total magnetic flux, is frequently sought by examining scatterplots of daily data, which generally show a non-linear distribution of points. We show that the scatterplots are consistent with our published result that these observable solar parameters are related to sunspot area by a transformation that is both linear and time invariant, namely by convolution with a finite impulse response function. Most solar parameters are affected by extended active regions, not just by sunspots. The fact that a complex active region evolves much more slowly than its associated sunspots provides a simple physical explanation of the observed non-linearities in scatterplots.     

Sunspot Positions and Areas from Observations by Galileo Galilei

Sunspot records in the seventeenth century provide important information on the solar activity before the Maunder minimum, yielding reliable sunspot indices and the solar butterfly diagram. Galilei’s letters to Cardinal Francesco Barberini and Marcus Welser contain daily solar observations on 3?–?11 May, 2 June?–?8 July, and 19?–?21 August 1612. These historical archives do not provide the time of observation, which results in uncertainty in the sunspot coordinates. To obtain them, we present a method that minimizes the discrepancy between the sunspot latitudes. We provide areas and heliographic coordinates of 82 sunspot groups. In contrast to Sheiner’s butterfly diagram, we found only one sunspot group near the Equator. This provides a higher reliability of Galilei’s drawings. Large sunspot groups are found to emerge at the same longitude in the northern hemisphere from 3 May to 21 August, which indicates an active longitude.     

Long-Term Variations of Solar Differential Rotation and Sunspot Activity: Revisited

Long-term variations of solar differential rotation and sunspot activity are investigated through re-analyzing the data on parameters of the differential-rotation law obtained by Makarov, Tlatov, and Callebaut (Solar Phys. 170, 373, 1997), Javaraiah, Bertello, and Ulrich (Astrophys. J. 626, 579, 2005a; Solar Phys. 232, 25, 2005b), and Javaraiah et al. (Solar Phys. 257, 61, 2009). Our results indicate that the solar-surface-rotation rate at the Equator (indicated by the A-parameter of the standard solar-rotation law) shows a secular decrease since Cycle 12 onwards, given by about 1?–?1.5×10^?3 (deg?day^?1?year^?1). The B-parameter of the standard differential-rotation law seems to also show a secular decrease since Cycle 12 onwards, but of weak statistical significance. The rotation rate averaged over latitudes 0^°?–?40^° does not show a secular trend of statistical significance. Moreover, the average sunspot area shows a secular increase of statistical significance since Cycle 12 onwards, while a negative correlation is found between the level of sunspot activity (indicated by the average sunspot area) and the solar equatorial rotation on long-term scales.