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???.     

Solar Rotation Rate during Solar Activity Cycle 23

We studied the solar rotation rate and its temporal change, using the sunspot data obtained during activity cycle 23 (1996 – 2006). The equatorial rotation rate is nearly the same as in the former cycle 22, while the latitudinal gradient of differential rotation considerably increased. Comparison of our results with others indicates the existence of a long-term periodicity of about eight cycles in differential rotation. In addition, no significant asymmetry in differential rotation between the northern and southern hemispheres during cycle 23 was found. The equatorial rotation rate and the latitudinal gradient of the differential rotation in the period of cycle 23 are approximately constant, except for the initial and final phases in the cycle.     

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 And Cycle Length

A positive correlation is suggested between solar rotation rate and solar cycle length for cycles 12 to 20. This result seems to be opposite to recent observations in solar-type stars and the Sun and yields inverse correlations between cycle lengths and chromospheric activity, but it agrees with previous work with solar-type stars and the Sun suggesting a positive correlation between cycle length and rotation rate. Estimates of solar cycle length for the Maunder minimum suggest a length 17 yr.     

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.     

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.     

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.     

Inferring Small-Scale Flatfields from Solar Rotation

We present a method to infer small-scale flatfields for imaging solar instruments using only regular-observation intensity images with a fixed field of view. The method is related to the flatfielding method developed by Kuhn, Lin, and Loranz (Publ. Astron. Soc. Pac. 103, 1097 – 1108, 1991), but does not require image offsets. Instead, it takes advantage of the fact that the solar image is changing in the CCD reference frame due to solar rotation. We apply the method to data sets of MDI filtergrams and compare the results to flat fields derived with other methods. Finally, we discuss the planned implementation of this method in the data processing for Helioseismic and Magnetic Imager on the Solar Dynamics Observatory.     

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.     

Rotation Characteristics of Large-Scale Solar Magnetic Fields

The rotation characteristics of large-scale (global) magnetic fields (GMF) and their relation to the activity of local fields (LMF) are studied over a long time interval (1915–1996). The main results are as follows. The GMF rotation rates and LMF activity vary in anticorrelation. Both variations have similar periods (11 years and a quasi-secular period of about 55–60 years), but are shifted relative to each other by half an 11-year cycle. Therefore, (1) the GMF rotation rate increases at the minimum of the 11-year cycle of LMF activity. (2) The GMF rotation rate is faster in the less active hemisphere. (3) The GMF rotation period slows down at the maximum of the secular LMF activity (cycles 18 and 19).     

A Measure of the Solar Rotation During the Maunder Minimum

In this paper we present a measure of the synodic solar rotation rate derived from an analysis of a Flamsteed drawing, corroborating the decrease of the solar rotation in the deep Maunder minimum (1666–1700).     

Iodine-Cell Spectroscopy Applied to Investigating the Solar Differential Rotation

In an attempt to examine whether the spectroscopic Doppler method with an iodine cell (which is known to be successful for precise radial-velocity determinations in stellar astronomy) could be effective for investigating the solar differential rotation, we carried out intensive observations to collect spectra at a large number of points on the solar disk by using the Domeless Solar Telescope along with the horizontal spectrograph of the Hida Observatory. Having converted the resulting line-of-sight velocity component into the angular rotational rate (ω), we derived a differential rotation law, w_sidereal  (deg day^-1) = 14.03 (±0.06)-1.84 (±0.57) sin²y-1.92 (±0.85) sin⁴y\omega_{\mathrm{sidereal}}\; (\mathrm{deg}\,\mathrm{day}^{-1}) =14.03 (\pm0.06)-1.84 (\pm0.57) \sin^{2}\psi-1.92 (\pm0.85) \sin^{4}\psi (ψ: heliographic latitude), which is reasonably consistent with other spectroscopic determinations published so far. Our analysis also revealed several practical points to note for successful application (e.g., exclusion of those data that are not well distant from the meridian; mutual data subtraction/averaging for symmetric counterparts at the eastern and western hemisphere). Considering its easiness and cheapness, this iodine-cell-featured spectroscopic method may be regarded as an effective and practical tool for studying the differential rotation of the Sun.     

High-Latitude Solar Rotation Traced by Magnetic Elements

Sequential observations at Huairou Solar Observation Station, China, and Kitt Peak, U.S.A., show that polar magnetic elements can live from several to more than 58 hours. This enables measurement of the solar rotation rate near the polar region by tracing magnetic element motions. With observations carried out on 8–15 July 1997, we identify and trace more than 1300 elements at north heliographic latitudes between 55°–85° using two methods, and fit the mean sidereal rotation rate as =14.0±0.54–(2.24±1.22)sin²–(1.78±0.79)sin⁴ deg per day.     

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.     

Variations of the Solar Differential Rotation Associated with Polarity Reversal

Variations of solar differential rotation have been studied using observations of solar quiescent Hα filaments obtained during 1965–1993 at the Abastumani Astrophysical Observatory. In both hemispheres of the Sun, propagation of a quasi-biennial pulse of residual rotation velocities of filaments was found. There is a pulse drift from high latitudes to the equator in the northern hemisphere in 1968–1970, 1979–1981, 1988–1990 and in the southern one in 1969–1971, 1979–1981, 1989–1991. Propagation of a pulse starts near the time of the polarity reversal of the circumpolar regions of the Sun. High-latitude double peaks of rapid motion were found in the northern hemisphere for cycle 20 and in the southern hemisphere for cycle 22. The relation of the appearance of suggested double pulse peaks of residual velocities with the threefold polarity changing of the circumpolar areas is suggested.     

Differential Rotation of the Solar Corona from Magnetic Field Data

A method for investigating the differential rotation of the solar corona using the coronal magnetic field as a tracer is proposed. The magnetic field is calculated in the potential approximation from observational data at the photospheric level. The time interval from June 24, 1976, to December 31, 2004, is considered. The magnetic field has been calculated for all latitudes from the equator to ±75? with a 5? step at distances from the base of the corona 1.0 R_⊙ to 2.45 R_⊙ near the source surface. The coronal rotation periods at 14 distances from the solar center have been determined by the method of periodogram analysis. The coronal rotation is shown to become progressively less differential with increasing heliocentric distance; it does not become rigid even near the source surface. The change in the coronal rotation periods with time is considered. At the cycleminimumthe rotation has been found to bemost differential, especially at small distances from the solar center. The change in coronal rotation with time is consistent with the tilt of the solar magnetic equator. The results from the magnetic field are compared with those obtained from the brightness of the green coronal Fe XIV 530.3 nm line. The consistency between these results confirms the reliability of the proposed method for studying the coronal rotation. Studying the rotation of the coronal magnetic field gives hope for the possibility of using this method to diagnose the differential rotation in subphotospheric layers.     

Measurements of Faraday Rotation Through the Solar Corona During the 2009 Solar Minimum with the MESSENGER Spacecraft

Measurements of Faraday rotation through the solar corona were collected using the radio beacon aboard the MESSENGER spacecraft during the longest solar minimum in a century. As MESSENGER entered superior conjunction, the plane of polarization of its radio signal was observed to rotate as it traversed the circularly birefringent plasma of the Sun’s atmosphere. On time scales of less than three hours, these uncalibrated plane of polarization observations of Faraday rotation can be used to investigate the dynamic processes in the solar plasma, such as magnetohydrodynamic (MHD) waves and coronal mass ejections (CMEs). Here we describe the MESSENGER Faraday rotation experiment, the data processing conducted to obtain the plane of polarization, and the estimation of error.