A Method to Determine the Solar Synodic Rotation Rate and the Height of Tracers

The dependence of the measured apparent synodic solar rotation rate on the height of the chosen tracer is studied. A significant error occurs if the rotation rate is determined by tracing the apparent position of an object above the photospheric level projected on the solar disc. The centre-to-limb variation of this error can be used to determine simultaneously the height of the object and the true synodic rotation rate. The apparent (projected) heliographic coordinates are presented as a function of the height of the traced object and the coordinates of its footpoint. The relations obtained provide an explicit expression for the apparent rotation rate as a function of the observed heliographic coordinates of the tracer, enabling an analytic least-squares fit expression to determine simultaneously the real synodic rotation rate and the height of the tracer.     

Determination of the Rotation Periods of Solar Active Longitudes

There are two types of active longitudes (ALs) in terms of the distribution of sunspot areas: long-lived and intra-cyclic ALs. The rotation period of the long-lived ALs has been determined by a new method in this paper. The method is based on the property of ALs to be maintained over several cycles of solar activity. The daily values of sunspot areas for 1878 – 2005 are analyzed. It is shown that the AL positions remain almost constant over a period of about ten cycles, from cycle 13 to cycle 22. The rotation period was found to be 27.965 days during this period. The dispersion in AL positions is about 26° from cycle to cycle, which is half of the dispersion observed in the Carrington system. The ALs in the growth phase of the activity cycle are more stable and pronounced. The excess in solar activity in the ALs over adjacent longitudinal intervals is about 12 – 14%. It is shown that only one long-lived AL can be observed at one time on the Sun, as a rule.     

太阳活动区速度场的测量及其可靠性

本文介绍了暗条、耀斑、后环等各种客体通常使用的速度测量方法.采用简单模型,计算运动客体的理论光谱轮廓,从而对现有测定方法的可靠性作了讨论.指出如使用方法不当,所测得的速度不仅量值上与真实情况相差甚远,而且测得的运动方向亦可与实际相反.     

Height of Tracers and the Correction of the Measured Solar Synodic Rotation Rate: Demonstration of the Method

Two large stable solar filaments were used as test tracers to determine the apparent synodic rotation rate as a function of the central meridian distance for several filaments' segments at different heights. An analytic fitting procedure was applied to determine simultaneously the real synodic rotation rate and the height of the traced filament segments. The determined heights were compared with the values obtained from the widths of filament contours on the solar disk and with the values obtained by direct measurements at the solar limb. Furthermore, the obtained rotation rates and heights of the filaments' segments close to the filaments' pivot points were compared with the values obtained using two successive central meridian passages. Finally, sources and scales of errors were investigated and possible implications on the previous studies of the solar differential rotation were considered.     

Rotation of the Solar Equator

Regular measurements of the general magnetic field of the Sun, performed over about half a century at the Crimean Astrophysical Observatory, the J. Wilcox Solar Observatory, and five other observatories, are considered in detail for the time 1968?–?2016. They include more than twenty-six thousand daily values of the mean line-of-sight field strength of the visible solar hemisphere. On the basis of these values, the equatorial rotation period of the Sun is found to be 26.926(9) d (synodic). It is shown that its half-value coincides within error limits with both the main period of the magnetic four-sector structure, 13.4577(25) d, and the best-commensurate period of the slow motions of the major solar system bodies, 13.479(22) d (sidereal). The probability that the two periods coincide by chance is estimated to be about \(10^{-7}\). The true origin of this odd resonance is unknown.     

On Rotation of the Solar Corona

We have studied the rotation of the solar corona using the images taken at a 9.4?nm wavelength by the AIA 094 instrument on board the Solar Dynamics Observatory (SDO) satellite. Our analysis implies that the solar corona rotates differentially. It appears that ??, the angular rotation velocity of the solar corona, does not only depend on heliographic latitude but is also a function of time, while the nature of the latter dependence remains unclear. Besides measurement errors, deviations ???? from the mean rotational speed are also caused by proper motion of the observed point source (the tracer) with respect to its surroundings. The spread in ?? values at a particular heliographic latitude is a real effect, not caused by measurement errors. Most of the observations carry relative error less than 1?% in???.     

太阳活动与太阳自转速率变化关系的分析

研究发现,太阳自转速率的变化与太阳活动之间存在一定的联系,但是不同学者的研究结论存在着矛盾:有的认为两者为正相关,而有的却认为是负相关.究竟两者之间是什么关系,需要做进一步深入的分析.利用EEMD (Ensemble Empirical Mode Decomposition)等方法对太阳自转速率和太阳黑子数据序列进行相关关系以及相位关系的计算和分析,以探讨太阳自转速率变化与太阳活动之间的关系.研究发现:两者的长期趋势项分量呈显著负相关;在11 yr左右周期分量上,观测到的太阳自转速率滞后太阳黑子的变化约2 yr时,呈显著负相关关系,超前3 yr时呈现次显著的正相关;对太阳活动第12–23周各周内部太阳黑子与太阳自转速率的相关分析表明,两者的关系比较复杂,但负相关关系更为显著.这为进一步理解太阳活动变化与太阳自转速率变化之间的成因联系提供了新的依据.     

Solar Rotation in the 17th century

Sunspot drawings made by Galileo Galilei in 1612 are used to derive the law of differential rotation at that time. The main interest of the work is during the time of observations, just at the beginning of telescopic observations and some decades before the Maunder Minimum (1645 – 1715), a period where the sunspots almost disappeared from the solar surface. For this purpose we have carried out careful corrections of the different sources of errors derived from the observing technique. By comparing with other results of the same century, a significant difference is only detected by comparing with data corresponding to the deep Maunder Minimum (Paris Observatory drawings). The characteristics of the solar differential rotation, and extrapolating the behavior of solar activity, did not differ before or after the Maunder Minimum. We also include an analysis of hitherto ignored sunspot drawings by N. Bion made in October and November 1672.     

Long-Term Variations in the Solar Differential Rotation

Using Greenwich data (1879–1976) and SOON/NOAA data (1977–2002) on sunspot groups we found the following results: (i) The Sun's mean (over all the concerned cycles during 1879–1975) equatorial rotation rate (A) is significantly larger (≈0.1%) in the odd-numbered sunspot cycles (ONSCs) than in the even-numbered sunspot cycles (ENSCs). The mean rotation is significantly (≈10%) more differential in the ONSCs than in the ENSCs. North–south difference in the mean equatorial rotation rate is larger in the ONSCs than in the ENSCs. North–south difference in the mean latitude gradient of the rotation is significant in the ENSCs and insignificant in the ONSCs. (ii) The known very large decrease in A from cycle 13 to cycle 14 is confirmed. The amount of this decrease in the mean A was about 0.017 μrad s⁻¹. Also, we find that A decreased from cycle 17 to cycle 18 by about 0.008 μrad s⁻¹ and from cycle 21 to cycle 22 by about 0.016 μrad s⁻¹. From cycle 13 to cycle 14 the decrease in A was more in the northern hemisphere than in the southern hemisphere, it is opposite in the later two epochs. The time gap between the consecutive drops in A is about 44 years, suggesting the existence of a `44-yr' cycle or `double Hale cycle' in A. The time gap between the two large drops, viz., from cycle 13 to cycle 14 and from cycle 21 to cycle 22, is about 90 years (Gleissberg cycle). We predict that the next drop (moderate) in A will be occurring from cycle 25 to cycle 26 and will be followed by a relatively large-amplitude `double Hale cycle' of sunspot activity. (iii) Existence of a 90-yr cycle is seen in the cycle-to-cycle variation of the latitude gradient (B). A weak 22-yr modulation in B seems to be superposed on the relatively strong 90-yr modulation. (iv) The coefficient A varies significantly only during ONSCs and the variation has maximum amplitude in the order of 0.01 μrad s<sup>−1</sup> around activity minima. (v) There exists a good anticorrelation between the mean variation of B during the ONSCs and that during the ENSCs, suggesting the existence of a `22-yr' periodicity in B. The maximum amplitude of the variation of B is of the order of 0.05 μrad s⁻¹ around the activity minima. (vi) It seems that the well-known Gnevyshev and Ohl rule of solar activity is applicable also to the cycle-to-cycle amplitude modulation of B from cycle 13 to cycle 20, but the cycles 12 (in the northern hemisphere, Greenwich data) and 21 (in both hemispheres, SOON/NOAA data) seem to violate this rule in B. And (vii) All the aforesaid statistically significant variations in A and B seem to be related to the approximate 179-yr cycle, 1811–1989, of variation in the Sun's motion about the center of mass of the solar system.     

晚型星系金属丰度与自转速度的关系

星系物质化学组成的研究不仅对于理解有关星系形成和演化的各种物理过程具有重要意义，而且还可以对星系形成和演化的各种理论模型提供重要的约束。随着观测技术及理论工作水平的不断提高，利用星系的大量观测资料来系统地研究星系化学组成与星系宏观性质之间的关系将成为可能。星系金属丰度与光度之间的强相关性以及晚型星系金属丰度与自转速度的关系即是其中最有意义的内容之一。全面回顾了星系金属丰度与星系宏观观测性质间关系的研究历史，重点评述了晚型星系金属丰度与自转速度关系的最新研究进展，详细讨论了目前对此类关系的物理解释及其对星系形成和演化模型的影响。     

The Influence of the Evolution of Sunspot Groups on the Determination of the Solar Velocity Field

Meridional motions and differential rotation of stable recurrent sunspot groups from the Greenwich data set are investigated. Simple and complex, as well as younger and older sunspot groups are treated separately. There is no difference in behavior of the meridional motions for the simple and complex sunspot groups, while complex groups rotate faster than the simple ones. If we attribute the differences of rotational velocities to the errors in position determination, it can be concluded that the rotational velocities determined by using sunspot groups as tracers are slightly overestimated. Both the meridional motions and differential rotation show the same dependence on the age, when simple and complex recurrent sunspot groups are considered. Alexander von Humboldt Research Fellow.     

Visibility-Graph Analysis of the Solar Wind Velocity

We analyze in situ measurements of the solar wind velocity obtained by the Advanced Composition Explorer (ACE) and the Helios spacecraft during the years 1998?–?2012 and 1975?–?1983, respectively. The data mainly belong to solar cycles 23 (1996?–?2008) and 21 (1976?–?1986). We used the directed horizontal-visibility-graph (DHVg) algorithm and estimated a graph functional, namely, the degree distance (D), which is defined using the Kullback–Leibler divergence (KLD) to understand the time irreversibility of solar wind time-series. We estimated this degree-distance irreversibility parameter for these time-series at different phases of the solar activity cycle. The irreversibility parameter was first established for known dynamical data and was then applied to solar wind velocity time-series. It is observed that irreversibility in solar wind velocity fluctuations show a similar behavior at 0.3 AU (Helios data) and 1 AU (ACE data). Moreover, the fluctuations change over the phases of the activity cycle.     

On the Long-Term Modulation of Solar Differential Rotation

Long-term modulation of solar differential rotation was studied with data from Mt. Wilson and our original observations during Solar Cycles 16 through 23. The results are that i) the global B-value (i.e. latitudinal gradient of differential rotation) is modulated with a period of about six or seven solar cycles, ii) the B-values of the northern and southern hemispheres are also modulated with a period similar to the global one, but iii) they show quasi-oscillatory behavior with a phase shift between them. We examined the yearly fluctuations of the B-values in every solar cycle with reference to the phase of the sunspot cycle and found that the B-values in the sunspot-minimum years show large and erratic variations, while those in the sunspot-maximum years show small fluctuations. Positive correlation between the former B-values and the latter was found. We discuss the independent long-term behavior of solar differential rotation between the northern and southern solar hemispheres and the implication for the solar dynamo.     

A Study of the Rotation of the Solar Corona

Synoptic photoelectric observations of the coronal Fexiv and Fex emission lines at 530.3 nm and 637.4 nm, respectively, are analyzed to study the rotational behavior of the solar corona as a function of latitude, height, time and temperature between 1976 (1983 for Fex) and 2001. An earlier similar analysis of the Fexiv data at 1.15 R over only one 11-year solar activity cycle (Sime, Fisher, and Altrock, 1989, Astrophys. J. 336, 454) found suggestions of solar-cycle variations in the differential (latitude-dependent) rotation. These results are tested over the longer epoch now available. In addition, the new Fexiv 1.15 R results are compared with those at 1.25 R and with results from the Fex line. I find that for long-term averages, both ions show a weakly-differential rotation period that may peak near 80° latitude and then decrease to the poles. However, this high-latitude peak may be due to sensing low-latitude streamers at higher latitudes. There is an indication that the Fexiv rotation period may increase with height between 40° and 70° latitude. There is also some indication that Fex may be rotating slower than Fexiv in the mid-latitude range. This could indicate that structures with lower temperatures rotate at a slower rate. As found in the earlier study, there is very good evidence for solar-cycle-related variation in the rotation of Fexiv. At latitudes up to about 60°, the rotation varies from essentially rigid (latitude-independent) near solar minimum to differential in the rising phase of the cycle at both 1.15 R and 1.25 R . At latitudes above 60°, the rotation at 1.15 R appears to be nearly rigid in the rising phase and strongly differential near solar minimum, almost exactly out of phase with the low-latitude variation.     

子午环度盘对径改正测试的研究

评述了各种度盘对径改正的方法；用玫瑰系列法对DCMT进行N=180的抽样实验测试，估计DCMT度盘常规读数对径误差为±0．25"。通过对度盘所有对径测试（N=5400）的精度统计特性的分析，得出49°30'、46°40'、43°12'是最优化的玫瑰系列测试组合；此外还论证了当对精度的统计特性的随机性要求不很严格时，在DCMT上实施小玫瑰角系列是可行的，其最优化组合是0°10'、46°40'、50°24'角系列。     

Zonal Velocity Bands and the Solar Activity Cycle

We compare the zonal-flow pattern in subsurface layers of the Sun with the distribution of surface magnetic features such as sunspots and polar faculae. We demonstrate that, in the activity belt, the butterfly pattern of sunspots coincides with the fast stream of zonal flows, although part of the sunspot distribution does spill over to the slow stream. At high latitudes, the polar faculae and zonal-flow bands have similar distributions in the spatial and temporal domains.     

太阳邻域银河系薄盘标高研究

利用Hipparcos卫星精确天体测量观测数据,尝试研究由不同样本恒星所反映的太阳邻域银河系薄盘的标高.根据Tycho测光系统的色指数,并考虑观测样本的完备性,分别在主序段和水平支上选取了几类恒星样本,以考察银河系薄盘标高的演化特征.分析结果发现,在比较完备的样本空间上,由O-B型主序星定义的银盘标高为103.1±3.0 pc,太阳位于其平均平面以上的15.2±7.3 pc处;水平支恒星定义的银盘标高为144.0±10.0 pc,太阳位于其平均平面以上3.5±5.4pc处.A、F、G、K、M型的主序星由于观测样本完备性的限制而无法进行可信的标高研究.     

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.     

Helioseismic Constraints on Rotation and Magnetic Fields in the Solar Core

In recent years, more and more precise measurements have been made of solar oscillation frequencies and line widths. From space, the Solar and Heliospheric Observatory/Michelson Doppler Imager (MDI) data has led to much progress. From the ground, networks, like Global Oscillation Network Group (GONG), Taiwanese Oscillation Network (TON), and Birmingham Solar Oscillations Network (BiSON) have also led to much progress. The sharpened and enriched oscillation spectrum of data have been critically complemented by advances in the treatments of the opacities and the equation of state. All of this has led to a significantly more precise probing of the solar core. Here we discuss the progress made and suggest how the core may be better probed with seismic data on-hand. In particular, we review our knowledge of the rotation and structure of the core. We further argue that much may be learned about the core by exploiting the line width data from the aforementioned sources. Line-width data can be used to place sharper constraints on core properties, like the degree to which the Sun rotates on a single axis and the upper limit on magnetic fields that may be buried in the core.