Early latitude observations at the Pulkovo observatory

Pulkovo astrometric observations began in the 1840s using the Repsold transit instrument in the prime vertical and Ertel vertical circle. The first observers on these instruments were W.I. Struve, 1840–1856, and Kh.I. Peters, 1842–1849. In the present work, we collected and analyzed different series of latitude variations from observations made by M.O. Nuren, B. Wanach, A.A. Ivanov, I.N. Bonsdorf, and A.Ya. Orlov. In addition, results are given of investigations of a specific behavior of the Chandler polar motion in this interval, obtained by C. Chandler, Ivanov, Kh. Kimura, Orlov, and N. Sekiguchi. The aim of this paper is to search for and analyze the earliest series of Pulkovo latitudes, in order to evaluate the possibility of their use to study the motion of the pole at the maximum available range of observations. Different methods were used to isolate and analyze the sum of Chandler and annual latitude variations. The annex provides a series of Pulkovo latitude variations for 1840–1848, which may be used to extend latitude variation back to 1840.     

研究Chandler摆动的一个随机激发模型

基于同运动激发了Chandler摆动的假设，提出一个研究Chandler摆动的随机非线性模型，它是由一个随机性阶梯函数和一个具有阻尼的线性谐振子的Euler中心差分格式混合而成，研究此模型中各个参数与Chandler摆动振幅的关系，通过对基于实测资料获得的有效大气角动量时间序列的统计分析，初步发现其中含有随机噪声成份，它可以激发目前观测到的Chandler摆动振幅的28－40％，最后，对Chandler摆胡机激发的假设作了一些讨论。     

Excitation of Annual Polar Wobble by Global Oceans

A reasonable and quantitative result on the variation of polar wobble excited by the oceans is not available at present. Numerous researches have shown that atmospheric motion is the greatest excitation source for the seasonal variations in the polar wobble and that oceanic motion is one of the main remaining excitation sources. The excitation of variation in the annual polar wobble caused by oceans from 1992 to 2004 both globally and in latitude dependence, have been studied in depth by means of the new generation of SODA oceanic data assimilation (SODA-1.4.2 and SODA-1.4.3) and the ECCO oceanic data assimilation. The result shows that the variation in the seasonal polar wobble excited by the SODA oceans is very close to that of the residual after the action of the atmosphere and land water is deducted from the geodesic excitation function for a large part of the investigated time interval, and that there is overall agreement between the two as regards the annual amplitude and phase. In addition, in comparison with the result of early SODA-Bata 7, the new generation of SODA oceanic excitation has achieved obvious improvements. The latitude distributions of the excitations of the annual polar wobble by the SODA and ECCO oceans are consistent in the Greenwich direction, while having obvious differences in the direction of 90° E.     

Astrometric studies of the series of photographic and CCD observations of the Saturnian system with the 26-inch Pulkovo refractor in 1995-2007

The results of the reduction, investigation, and comparison of the photographic observations of the major Saturnian satellites and CCD observations with an ST6 CCD camera obtained at the 264nch Pulkovo refractor in 1995–2007 are presented. A comparison of the observational results with the TASS 1.7 theory of motion of the Saturnian satellites has served as the basis for investigating and comparing the series of observations. The period-averaged (O-C) residuals and observational errors have been calculated. A comparison of the series of CCD and photographic observations has shown the same external accuracy of the observations at a higher internal accuracy of the CCD observations than that of the photographic ones. A comparison of the Pulkovo results with those of other authors has shown them to be close in accuracy. The accuracy of the theory has been estimated by comparing simultaneous (on the same night) CCD and photographic observations. The errors of the observations and the theory have been found from this comparison to be the following: 0.081“ and 0.067” for the observations and 0.077“ and 0.115” for the theory (inxandy, respectively). An analysis of the dependence of (O-C)x,y for three satellites (the sixth, seventh, and eighth) on the satellite positions in Saturn-centered orbits has revealed systemat ic deviations for the seventh satellite in both coordinates. The positions of Saturn have been determined from satellite observations without measuring its images on photographic plates with accuracies of 0.121“ and 0.105” in right ascension and declination, respectively.     

Mid-Term Periodicities in the Solar Magnetic Flux

In this paper we report an analysis of the solar magnetic fluxes estimated in the period 1971–1998. We applied the wavelet technique to find the significant periodicities of these series. We concentrate particularly in the mid-term quasi-periodicities (1–2 years). The mid-term periodicity of 1.7 year is the dominant fluctuation for all the types of fluxes analyzed (total, closed, open, low and high latitude open fluxes) and has a strong tendency to appear during the descending phase of solar activity. The mid-term fluctuation of 1 year is significantly present in total and closed fluxes, but it is less important in open fluxes. It is recognizable in the high latitude open flux, but it is absent in the low latitude open flux. Due to the uncertainties involved in estimating the exact period of the quasi-annual peak, this component may not be different from the previously-reported 1.3 year periodicity. The high frequency fluctuations of all the fluxes but the high latitude open flux are in phase with the 11 years solar cycle. The high latitude flux tends to be present all the time, showing that along the cycle both the low latitude bipolar active regions and the polar coronal holes regulate this flux. These findings rule out the possibility of a more basic periodicity different from the 11 years cycle.     

地极移动的非线性动力机制

用非线性动力学原理和非线性振动方法,结合Chandler摆动的时间序列反演,证实了Chandler摆动的衰减能量是由周年激发的非线性共振所补充的．由高布锡归算的ILS参数,按共振激发模型反演出的Chandler摆动衰减指数和频率品质因数等结果,符合已有的大量基本结论,反演出的非齐次项的强迫频率基本都在周年频率的周围．非线性共振模型还表明,Chandler频率的不稳定性是由于存在频率转换和漂移,摆动振幅的不稳定性是由于存在共振跳跃,非线性的存在还将引出组合共振频率．同时用推广的最小公倍数证实和频差频的存在,提供了非整数的最小公倍数算法,为数论的非线性推广和在天文中的应用提供了工具．     

Analysis of periodic perturbations in the multiple system ADS 15571

The visual binary star ADS 15571 has been observed with the 26″ refractor at Pulkovo since 1960. Periodic perturbations in the relative motion of the components are studied in this paper. The visible motion of the component B was resolved into orbital motion of the barycenter relative to component A and an elliptical motion of the photocenter relative to the barycenter. The visible ellipse of the photocenter motion is used to determine the elements of the orbit by the direct geometric method of A. A. Kiselev and estimate the perturbing mass. The minimum mass of the invisible companion is 0.62 M_⊙. __________ Translated from Astrofizika, Vol. 49, No. 3, pp. 467–474 (August 2006).     

Temperature of Polar Corona of the Sun According to Kislovodsk Observations During 1957–2002

We continued a study of the long-term variations of temperature in the solar corona at all latitudes (Makarov, Tlatov, and Callebaut, 2002a). The series of the green (Fe xiv 530.3 nm; KI₅₃₀₃) and red (Fe x 637.4 nm; KI₆₃₇₄) coronal intensities for 1957–2002 has been obtained using the coronal observations at the Kislovodsk Solar Station. The mean monthly coronal intensities have been calculated at all latitudes (0–90^˚) and in the high latitude (45–90^˚) zones. It was found that the value of KI₆₃₇₄/KI₅₃₀₃increased about 2.0 times at the high latitudes during the last 45 years. This corresponds to a decrease of the average temperature by 0.1 ×10⁶K of the polar corona. We suppose that a polar decrease of coronal temperature is connected with an increase of the area of polar zones A _PZoccupied by unipolar magnetic fields (Makarov et al., 2002) and, probably, with an increase of the area of polar coronal holes. The maximum ratio KI₆₃₇₄/KI₅₃₀₃is observed during the minimum sunspot activity.     

Estimates of Chandler's Component of Polar Motion as Derived from Various Data Sets

Data sets consisting of several combinations of classical and modern techniques (Doppler and laser ranging to artificial sattellites) have been analysed by autoregressive (AR), sinusoidal and autoregressive moving averag (ARMA) methods in order to obtain estimates of the frequency and quality factor of the Chandler component of polar motion. The ARMA method shows advantages over the other methods and the results obtained do not furnish evidence of temporal variation in these polar motion parameters. The disadvantages associated with smoothing the data sets and the difficulties as sociated with short time intervals for the data are cleary demonstrated. There is a great need for regular and long observational series obtained by the modern techniques.     

Long-term evolution of orbits about a precessing oblate planet. 2. The case of variable precession

We continue the study undertaken in Efroimsky [Celest. Mech. Dyn. Astron. 91, 75–108 (2005a)] where we explored the influence of spin-axis variations of an oblate planet on satellite orbits. Near-equatorial satellites had long been believed to keep up with the oblate primary’s equator in the cause of its spin-axis variations. As demonstrated by Efroimsky and Goldreich [Astron. Astrophys. 415, 1187–1199 (2004)], this opinion had stemmed from an inexact interpretation of a correct result by Goldreich [Astron. J. 70, 5–9 (1965)]. Although Goldreich [Astron. J. 70, 5–9 (1965)] mentioned that his result (preservation of the initial inclination, up to small oscillations about the moving equatorial plane) was obtained for non-osculating inclination, his admonition had been persistently ignored for forty years. It was explained in Efroimsky and Goldreich [Astron. Astrophys. 415, 1187–1199 (2004)] that the equator precession influences the osculating inclination of a satellite orbit already in the first order over the perturbation caused by a transition from an inertial to an equatorial coordinate system. It was later shown in Efroimsky [Celest. Mech. Dyn. Astron. 91, 75–108 (2005a)] that the secular part of the inclination is affected only in the second order. This fact, anticipated by Goldreich [Astron. J. 70, 5–9 (1965)], remains valid for a constant rate of the precession. It turns out that non-uniform variations of the planetary spin state generate changes in the osculating elements, that are linear in , where is the planetary equator’s total precession rate that includes the equinoctial precession, nutation, the Chandler wobble, and the polar wander. We work out a formalism which will help us to determine if these factors cause a drift of a satellite orbit away from the evolving planetary equator.By “precession,” in its most general sense, we mean any change of the direction of the spin axis of the planet—from its long-term variations down to nutations down to the Chandler wobble and polar wander.     

A New Method for Polar Field Interpolation

The photospheric magnetic field in the Sun’s polar region is not well observed compared to the low-latitude regions. Data are periodically missing due to the Sun’s tilt angle, and the noise level is high due to the projection effect on the line-of-sight (LOS) measurement. However, the large-scale characteristics of the polar magnetic field data are known to be important for global modeling. This report describes a new method for interpolating the photospheric field in polar regions that has been tested on MDI synoptic maps (1996 – 2009). This technique, based on a two-dimensional spatial/temporal interpolation and a simple version of the flux transport model, uses a multi-year series of well-observed, smoothed north (south) pole observations from each September (March) to interpolate for missing pixels at any time of interest. It is refined by using a spatial smoothing scheme to seamlessly incorporate this filled-in data into the original observation starting from lower latitudes. For recent observations, an extrapolated polar field correction is required. Scaling the average flux density from the prior observations of slightly lower latitudes is found to be a good proxy of the future polar field. This new method has several advantages over some existing methods. It is demonstrated to improve the results of global models such as the Wang–Sheeley–Arge (WSA) model and MHD simulation, especially during the sunspot minimum phase.     

Investigation of Long-Period Oscillations of Sunspots with Ground-Based (Pulkovo) and SOHO/MDI Data

We applied special data-processing algorithms to the study of long-period oscillations of the magnetic-field strength and the line-of-sight velocity in sunspots. The oscillations were investigated with two independent groups of data. First, we used an eight-hour-long series of solar spectrograms, obtained with the solar telescope at the Pulkovo Observatory. We simultaneously measured Doppler shifts of six spectral lines, formed at different heights in the atmosphere. Second, we had a long time series of full-disk magnetograms (10 – 34 hour) from SOHO/MDI for the line-of-sight magnetic-field component. Both ground- and space-based observations revealed long-period modes of oscillations (40 – 45, 60 – 80, and 160 – 180 minutes) in the power spectrum of the sunspots and surrounding magnetic structures. With the SOHO/MDI data, one can study the longer periodicities. We obtained two new significant periods (> 3σ) in the power spectra of sunspots: around 250 and 480 minutes. The power of the oscillations in the lower frequencies is always higher than in the higher ones. The amplitude of the long-period magnetic-field modes shows magnitudes of about 200 – 250 G. The amplitude of the line-of-sight velocity periodicities is about 60 – 110 m s⁻¹. The absence of low-frequency oscillations in the telluric line proves their solar nature. Moreover, the absence of low-frequency oscillations of the line-of-sight velocity in the quiet photosphere (free of magnetic elements) proves their direct connection to magnetic structures. Long-period modes of oscillation observed in magnetic elements surrounding the sunspot are spread over the meso-granulation scales (10″ – 12″), while the sunspot itself oscillates as a whole. The amplitude of the long-period mode of the line-of-sight velocity in a sunspot decreases rapidly with height: these oscillations are clearly visible in the spectral lines originating at heights of approximately 200 km and fade away in lines originating at 500 km. We found a new interesting property: the low-frequency oscillations of a sunspot are strongly reduced when there is a steady temporal trend (strengthening or weakening) of the sunspot’s magnetic field. Another important result is that the frequency of long-period oscillations evidently depends on the sunspot’s magnetic-field strength.     

The Moon’s physical librations and determination of their free modes

The Lunar Laser Ranging experiment has been active since 1969 when Apollo astronauts placed the first retroreflector on the Moon. The data accuracy of a few centimeters over recent decades, joined to a new numerically integrated ephemeris, DE421, encourages a new analysis of the lunar physical librations of that ephemeris, and especially the detection of three modes of free physical librations (longitude, latitude, and wobble modes). This analysis was performed by iterating a frequency analysis and linear least-squares fit of the wide spectrum of DE421 lunar physical librations. From this analysis we identified and estimated about 130–140 terms in the angular series of latitude librations and polar coordinates, and 89 terms in the longitude angle. In this determination, we found the non-negligible amplitudes of the three modes of free physical libration. The determined amplitudes reach 1.296′′ in longitude (after correction of two close forcing terms), 0.032′′ in latitude and 8.183′′ × 3.306′′ for the wobble, with the respective periods of 1056.13 days, 8822.88 days (referred to the moving node), and 27257.27 days. The presence of such terms despite damping suggests the existence of some source of stimulation acting in geologically recent times.     

Observations of the binary star 61 Cyg on the 26 inch refractor at the Pulkovo observatory

Results from an analysis of a forty year series of photographic observations of the binary star 61 Cyg on the 26 inch refractor at the Pulkovo Observatory are presented. The orbit is constructed and the sum of the masses of the components is determined from the relative positions of the components. A study of the individual motions of the components of 61 Cyg relative to the surrounding stars yields their mass ratio and the masses of the main and secondary components, 0.74 and 0.46 solar masses, respectively. The relative motion of the components is found to have a fluctuating component with a period of 6.5 years which may be caused, in particular, by the presence in the system of a dark, low-mass companion. __________ Translated from Astrofizika, Vol. 49, No. 3, pp. 453–465 (August 2006).     

Nova Cygni 1975 (V1500 Cyg) in 2000–2009 and the nature of its synodic period

Multicolor photometric data are presented for the asynchronous polar V1500 Cyg during 2000–2009, i.e., 23–35 years after its outburst. Some examples of individual light curves of the system are shown. An analysis of these reveals large variations in its brightness and color with the phase of the orbital period owing to a “reflection effect” caused by reradiation from the side of the red dwarf facing the hot white dwarf and heated by its hard ultraviolet radiation. The variations in the O-C residuals and in the maximum intensity with the phase of the synodic period are illustrated. It is found that the amplitude A of the orbital fluctuations increases in proportion to the intensity I at a rate dA/dI=0.64. This behavior of V1500 Cyg is most likely caused by periodic shading of the illuminated part of the red dwarf, where the degree of shading depends on the phase of the synodic cycle.     

Physical parameters of the continuum emission layer of Mira-type stars. I. Spectrophotometric temperatures

The spectrophotometric temperatures of five Mira-type variable stars are determined using observations in the Pulkovo spectrophotometric data base in the range from 320–1080 nm. All the resulting temperatures are below the effective temperatures of stars in the corresponding subclasses. Near the brightness maximum, the temperatures are found to be lower with increasing separation in time from the maximum. __________ Translated from Astrofizika, Vol. 50, No. 3, pp. 415–426 (August 2007).     

Independent Global Modes of Solar Magnetic Field Fluctuations

Observed solar, interplanetary and geomagnetic time series contain quasi periodicities on scales of 1–2.5 years. The further discovery of 1.3 year fluctuations in helioseismic observations suggests that a variety of signals may be related to the underlying dynamo in the Sun. We use independent component analysis to study the temporal and spatial variations of a few statistically independent global modes of the axisymmetric solar magnetic field over a period of 25 years. Five modes capture the salient properties of the data. Two modes describe the polar and high latitude fields, and present 1–1.5 year quasi periodicities. The other three modes correspond to low and mid-latitude phenomena and show both 1.3 and 1.7-year variations. By comparing the characteristic time scales, dates of occurrence and heliocentric latitudes of these modes, we connect them to their manifestations in heliospheric time series.     

Predicting the Amplitude of a Solar Cycle Using the North – South Asymmetry in the Previous Cycle: II. An Improved Prediction for Solar Cycle 24

Recently, using Greenwich and Solar Optical Observing Network sunspot group data during the period 1874 – 2006, Javaraiah (Mon. Not. Roy. Astron. Soc. 377, L34, 2007: Paper I), has found that: (1) the sum of the areas of the sunspot groups in 0° – 10° latitude interval of the Sun’s northern hemisphere and in the time-interval of −1.35 year to +2.15 year from the time of the preceding minimum of a solar cycle n correlates well (corr. coeff. r=0.947) with the amplitude (maximum of the smoothed monthly sunspot number) of the next cycle n+1. (2) The sum of the areas of the spot groups in 0° – 10° latitude interval of the southern hemisphere and in the time-interval of 1.0 year to 1.75 year just after the time of the maximum of the cycle n correlates very well (r=0.966) with the amplitude of cycle n+1. Using these relations, (1) and (2), the values 112±13 and 74±10, respectively, were predicted in Paper I for the amplitude of the upcoming cycle 24. Here we found that the north – south asymmetries in the aforementioned area sums have a strong ≈44-year periodicity and from this we can infer that the upcoming cycle 24 will be weaker than cycle 23. In case of (1), the north – south asymmetry in the area sum of a cycle n also has a relationship, say (3), with the amplitude of cycle n+1, which is similar to (1) but more statistically significant (r=0.968) like (2). By using (3) it is possible to predict the amplitude of a cycle with a better accuracy by about 13 years in advance, and we get 103±10 for the amplitude of the upcoming cycle 24. However, we found a similar but a more statistically significant (r=0.983) relationship, say (4), by using the sum of the area sum used in (2) and the north – south difference used in (3). By using (4) it is possible to predict the amplitude of a cycle by about 9 years in advance with a high accuracy and we get 87±7 for the amplitude of cycle 24, which is about 28% less than the amplitude of cycle 23. Our results also indicate that cycle 25 will be stronger than cycle 24. The variations in the mean meridional motions of the spot groups during odd and even numbered cycles suggest that the solar meridional flows may transport magnetic flux across the solar equator and potentially responsible for all the above relationships. The author did a major part of this work at the Department of Physics and Astronomy, UCLA, 430 Portola Plaza, Los Angeles, CA 90095-1547, USA.