Numerical Exploration of Chermnykh’s Problem

We study the equilibrium points and the zero-velocity curves of Chermnykh’s problem when the angular velocity ω varies continuously and the value of the mass parameter is fixed. The planar symmetric simple-periodic orbits are determined numerically and they are presented for three values of the parameter ω. The stability of the periodic orbits of all the families is computed. Particularly, we explore the network of the families when the angular velocity has the critical value ω = 2√2 at which the triangular equilibria disappear by coalescing with the collinear equilibrium point L₁. The analytic determination of the initial conditions of the family which emanate from the Lagrangian libration point L₁ in this case, is given. Non-periodic orbits, as points on a surface of section, providing an outlook of the stability regions, chaotic and escape motions as well as multiple-periodic orbits, are also computed. Non-linear stability zones of the triangular Lagrangian points are computed numerically for the Earth–Moon and Sun–Jupiter mass distribution when the angular velocity varies.     

Some results of the photospheric large-scale velocity research from Belgrade observations

On the basis of the possibility of sight-line velocity observations by a special equatorial solar spectrograph, a research programme for detection of photospheric large-scale velocities has been initiated. The first series of observations in the FeI 6302 Å absorption line has been limited to the central meridian.The combined limb effect assumed to incorporate an unresolved stationary photospheric motion, has been evaluated. The observed asymmetry of the obtained curve is mainly explained by dB ₀/dt.The remaining sight-line velocities along the central meridian, taken as random, gave an r.m.s. value of 32 m s^–1. In a few cases a certain kinematic situation in some areas along the central meridian lasted for 2 to 4 consecutive days. It is assumed that such velocity features belong to the kinematic picture of a large-scale photospheric motion which, as a whole, has not yet been clearly seen.     

Differential Rotation of Stable Recurrent Sunspot Groups

Stable recurrent sunspot groups from the Greenwich data set which were identified in at least two subsequent solar rotations were traced. The solar rotation was determined by the period method from the time difference of the two central meridian passages of each of the 327 identified groups. Sidereal rotation periods were calculated from the synodic ones by a seasonal-dependent procedure taking into account the details of the Earth's motion around the Sun. Growing recurrent sunspot groups rotate on the average faster than decaying recurrent sunspot groups, while sunspot groups of all types taken together rotate faster than both growing and decaying recurrent sunspot groups. A north–south rotational asymmetry and a cycle-dependence of rotational velocity of recurrent sunspot groups were analyzed. Positive rotation velocity deviations are larger, but less numerous than the negative ones. Signatures of torsional oscillations were not found analyzing the rotation velocity residual of recurrent sunspot groups as a function of the distance from the average latitude of activity.     

A study of the magnetic and velocity fields in an active region

A time sequence of magnetograms and velocity-grams in the H and Fe i 6569 Å lines has been made at a rate of 12 h^–1 of McMath Region 10385 from 26 to 29 October, 1969. The 14 flares observed during this period have been studied in relation to the configuration and changes in the magnetic and velocity fields. There was little correlation between flare position and the evolutionary changes in the photospheric magnetic and velocity field, except at large central meridian distances where the velocity observations suggested shearing taking place at flare locations. At central meridian distances > 30° we found that flares are located in areas of low line-of-sight photospheric velocity surrounded by higher velocity hills. The one exception to this was the only flare which produced a surge. Blue-shifted velocity changes in the photosphere of 0.3 to 1 km s^–1 were observed in localized areas at the times of 8 of 14 flares studied.Visiting Astronomer, Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

The age dependence of photospheric tracer rotation

From the analysis of the motions of sunspot groups recorded at Catania Astrophysical Observatory over a 7-years period from 1972 to 1978 the mean angular velocity as a function of latitude and age is calculated. The results suggest that the age of photospheric tracer (sunspot groups) affects the rotation curve slope. The implications of this result are discussed.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Simulation of compact groups of galaxies

Self-consistent simulations of seven groups of galaxies with halos have been performed to find a constraint upon the size of missing halos around spiral galaxies. An initial galaxy, which consists of 100 superstars, has half-mass radius 41 kpc and central velocity dispersion 235 km s^–1. The simulations start from the epoch of maximum expansion. The initial conditions involve a variety of spatial distributions of galaxies, and the velocity dispersion of galaxies as would be permitted for maximum expansion. Dense groups having collapse times shorter than (2/3)H ₀ ^–1 are shown to form multiple mergers in a Hubble timeH ₀ ^–1 . From a comparison of the frequencies of cD galaxies, or multiple mergers, in observed and simulated groups, it is concluded that the effective radius of missing halos is less than 41 kpc.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Dependence of the meridional motions of sunspot groups on life spans and age of the groups,and on the phase of the solar cycle

We have analyzed data on sunspot groups compiled during 1874–1981 and investigated the following: (i) dependence of the `initial' meridional motion (v <sub>ini</sub>()) of sunspot groups on the life span () of the groups in the range 2–12 days, (ii) dependence of the meridional motion (v(t)) of sunspot groups of life spans 10–12 days on the age (t) of the spot groups, and (iii) variations in the mean meridional motion of spot groups of life span 2–12 days during the solar cycle. In each of the latitude intervals 0°–10°, 10°–20° and 20°–30°, the values of both v <sub>ini</sub>() and v(t) often differ significantly from zero. In the latitude interval 20°–30°, the forms of v <sub>ini</sub>() and v(t) are largely systematic and mutually similar in both the north and south hemispheres. The form of v(t) suggests existence of periodic variation in the solar meridional motion with period of 4 days and amplitude 10–20 m s<sup>–1</sup>. Using the anchoring depths of magnetic structures for spot groups of different and testimated earlier, (Javaraiah and Gokhale, 1997), we suggest that the forms of v <sub>ini</sub>() and v(t) may represent radial variation of meridional flow in the Sun's convection zone, rather than temporal variation of the flow. The meridional flows (v <sub>e</sub>(t)) determined from the data during the last few days (i.e., age t: 10–12 days) of spot groups of life spans of 10–12 days are found to have magnitudes (10–20 m s<sup>–1</sup>) and directions (poleward) similar to the those of the surface meridional plasma flows determined from the Dopplergrams and magnetograms. The mean meridional velocity of sunspot groups living 2–12 days seems to vary during the solar cycle. The velocity is not significantly different from zero during the rising phase of the cycle and there is a suggestion of equatorward motion (a few m s<sup>–1</sup>at lower latitudes and 10 m s<sup>–1</sup>at higher latitudes) during the declining phase (last few years) of the cycle. The variation during the odd numbered cycles seems to anticorrelate with the variation during the even numbered cycles, suggesting existence of 22-year periodicity in the solar meridional flow. The amplitude of the anticorrelation seems to be depending on latitude and the cycle phase. In the latitude interval 20°–30° the `surface plasma meridional motion', v _e(t), is found to be poleward during maximum years (v _e(t) 20 m s^–1at 4th year) and equatorward during ending years of the cycle (v _e(t) –17 m s^–1at 10th year).     

Two-dimensional classification of globular clusters

The metallicities of 75 globular clusters are determined in the Pilachowskiet al. scale from the slopes of their giant branches in theV, B-V diagram. In the diagram giant branch slope, horizontal branch morphology type, the clusters form two sequences: a vertical sequence (group I) with blue horizontal branches and [Fe/H] from –2.2 to –1.2 and a diagonal sequence (group II) with horizontal branches changing from the blue to the red parallel with an increase of metallicity from –1.8 to –1.0. The differences in horizontal branch morphology of both cluster groups are probably caused by the difference in age, which is found to be of the order 1–2 billion years. It is shown that integrated reddening-free quantitiesQ and integrated spectral types cannot be used to determine metalicity without a previous division of clusters into groups.     

The secular modulation of solar rotation from 1943 to 1992 and its time-delayed correlation with the 55-year grand cycle of the 11-year solar cycle

We devised a new method, which we call the running-segment method, to achieve high-resolution time series of indices of solar rotation for determining the latitude dependence of the differential rotation by a least-squares fitting of the daily translation of positions of sunspot groups during a fixed time segment of 11 years. The segment is moved by an amount of one year to determine the differential profile of the next point of time. Time of the determined rotation data is defined by an arithmetic mean of the beginning and ending years of the segment. The rotation underwent an acceleration from 1948 to 1974 and a deceleration from 1974 to 1987. We found that the time profile of the indexM, the angular momentum surface layer density defined by integration of the angular momentum volume density over the whole surface, follows almost exactly the time profile of the 11-year running mean of the yearly mean of the sunspot relative number with a delay time of about 20 years. The acceleration (deceleration) phase corresponds to the ascending (descending) phase of amplitude of the 11-year solar cycle of cycle 16 (19) to cycle 19 (20) with a delay time of about 20 years. The cycles 15–20 correspond to the 55-year grand cycle V of the 11-year cycle. The delay time of about 20 years agrees well with the delay time predicted by a nonlinear dynamo theory of the solar cycle for driving the 55-year modulation of the 11-year solar cycle. The agreement suggests that the Lorentz force of the magnetic field of the solar cycle during grand cycle V drives the solar rotation modulation from 1948 to 1987 and that the force needed about 20 years to modify the rotation during 1943–1992.     

Possible effects of internal rotation in low-mass stars

The influence of internal rotation on the evolution of a 0.85M star is investigated by the construction of model sequences. Rotation is treated by a simple one-dimensional approximation. The calculations assume solid-body rotation on the zero-age Main Sequence, followed by conservation of angular momentum in shells. The 4 cases considered have the initial angular velocities 0,2×10^–4, 6×10^–4, and 8×10^–4/sec. All cases but the last are followed to helium ignition. Compared with the non-rotating case, the rotating models are older at Main-Sequence turnoff, develop fast-spinning central regions on the red-giant branch, and ignite helium at higher surface luminosities and at larger helium-core masses. The increases in the last two quantities are roughly proportional to the square of the initial angular velocity.The 6×10^–4 case is followed through the helium core flash to the zero-age horizontal branch. Under the assumption of spherical symmetry, the non-central ignition of helium leads to a sequence of flashes of decreasing amplitude occurring progressively closer to the center. The flashes are weaker than those encountered in previous studies and do not produce mixing.     

Synoptic charts of solar 9.1 cm and coronal hole data

Synoptic charts for Carrington rotations 1601–1605 (May–August, 1973) were prepared using the central meridian column of the daily 9.1 cm Stanford solar radio maps. These charts were especially contoured to emphasize temperatures near the quiet solar disk level. Synoptic charts of coronal holes from the ATM-Skylab were superimposed on the radio data to investigate the ability of the radio charts to show coronal holes. This brief period is unfortunately the only interval for which both sets of data are available. The conclusion reached is that in spite of certain problems due to active regions, side-lobe effects and a rather large beamwidth, the 9.1 cm synoptic charts can be of substantial value in identifying large coronal holes, especially during periods of low solar activity. Such synoptic charts, therefore, for the years 1962–1973 that Stanford data are available, could enhance significantly the meagre data pool for coronal holes prior to the Skylab mission.     

On changes of the rotation velocities of stable,recurrent sunspots and their interpretation with a flux tube model

The angular rotation velocities of stable, recurrent sunspots were investigated using data from the Greenwich Photoheliographic Results 1940 until 1968. We found constant rotation velocities during the passages on the solar disk with errors of about ±4 m s^–1. During their lifetime these spots show a decreasing braking of their rotation velocities from 0.8 to 0.3 m s^–1 per day. A plausible interpretation is found by assuming the spots to be coupled to a slowly rising subsurface flux tube and a rotation velocity which increases with depth.Mitteilungen aus dem Kiepenheuer-Institut Nr. 201.     

Spiral structure of galaxies two alternatives

At present the wave theory of the spiral structure of the galaxies includes two alternative viewpoints. Two types of spiral waves—short-wave and long-wave modes—can be excited. According to Lin and Shu (1964) the short-wave modeK is responsible for the spiral structure of the galaxies and, according to Marochniket al. (1972), the long-wave mode (K ₀). In our Galaxy theK -mode corresponds to the wave with an angular rotation velocity _p =11–13 kms^–1 kps^–1 and a radial group velocity directed from the periphery to the center. TheK ₀-mode corresponds to the wave having an angular rotation velocity _p =23 ± 3 kms^–1 kps^–1 and a radial group velocity directed from the center of the Galaxy to its periphery. The theoretical and observational evidences in favour of Marochniket al.'s (1972) model are given.     

Jumps in pulsar angular velocity and their relaxation with allowance for pinning and depinning of quantum vortex filaments

The dynamics of the rotating two-component system in the core of a neutron star is considered. Equations of motion are derived with allowance for the pinning and depinning of neutron vortices, and general solutions of these equations are found for relatively small changes in the star's angular velocity. It is shown that these solutions can describe both a jump in a pulsar's angular velocity and its subsequent relaxation. The characteristic pinning and depinning times are estimated qualitatively from observational data for jumps in the angular velocity of the Vela pulsar.Translated from Astrofizika, Vol. 39, No. 4, pp. 593–604, October–December, 1996.     

Das ProduktAR 0 und Weitere Galaktische Parameter

According to the tangential method the productAR ₀ is determined with 145.7 km s^–1 from measurements of the line profiles of the 21-cm line of the neutral hydrogen by Weaver and Williams (1973). The recent individual measurements of Oort's constantA and of the distanceR ₀ of the Sun from the galactic centre yields 138.5 km s^–1. The mean value 142.1 kms^–1 leads toA=14.56 km s^–1 kpc^–1 andR ₀=9.76 kpc. At the galactocentric distanceR nearR ₀ the angular velocity is represented by (R)=25.84–2.98 (R–9.76)+0.075 (R–9.76)². The mass of the Galaxy amounts to 1-92×10¹¹ .

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Herrn Kollegen Prof. Dr W. Gleisberg zum 70. Geburtstag am 26.12.1973 gewidmet.

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Mitteilungen Serie A.     

Limb effect of solar absorption lines

Low-noise limb-effect observations of the non-magnetic line Fei 557.6 nm are presented. Separate measurements along the solar equator and the meridian have been carried out and have been corrected for scattered light. The limb-effect line shifts at the pole and at the equatorial limb are found to be equal. The detailed shape of the limb effect along the meridian is found to differ significantly from that along the equator. This difference can be explained by the presence of a meridional circulation pattern, with horizontal flows < 50 m^–1 from both the equator and poles toward ± 45° latitude. Alternatively the meridian/equator difference may be caused by a combination of latitude dependence of the granular parameters. An increase with latitude of the granular velocity scale height, contrast, or mean sizes could explain the observations.     

An atlas of coronal hole boundary positions May 28 to November 21, 1973

This atlas shows the boundary locations of the coronal holes observed in soft X-rays (2–32, 44–54 Å) by the AS & E X-ray spectrographic telescope on Skylab. The data are presented as tracings of the boundaries as they appeared when the holes were near central meridian.Center for Astrophysics - Harvard College Observatory, Smithsonian Astrophysical Observatory.     

Geomagnetic disturbances and complex sunspots

Statistical result shows that a large geomagnetic disturbance is most likely to occur at the time when a complex sunspot is in 6.7° E-19.9° E from the central meridian of the solar disk during the period 1968–1972.     

The large-scale polarization of the microwave foreground

Most of the useful information about inflationary gravitational waves and reionization is on large angular scales where Galactic foreground contamination is the worst, so a key challenge is to model, quantify and remove polarized foregrounds. We use the Leiden radio surveys to quantify the polarized synchrotron radiation at large angular scales, which is likely to be the most challenging polarized contaminant for the WMAP satellite. We find that the synchrotron E- and B-contributions are equal to within 10% from 408–820 MHz with a hint of E-domination at higher frequencies. We quantify Faraday rotation and depolarization effects and show that they cause the synchrotron polarization percentage to drop both towards lower frequencies and towards lower multipoles.     

A possible interpretation of the optical spectrum for BL Lac-type objects

On the basis of Sobolev's method, the population of 30 levels of hydrogen atom is determined allowing for the radiative and collision processes of the heating and ionization of the medium with velocity gradient gradv=10^–9–10^–11s^–1, electron temperatureT _e=10⁴ K-2×10⁴ K and electron densityN _e=10¹⁰ cm^–3–10¹¹ cm^–3. The central source radiation is characterized by a power spectrum with spectral indices varying from 0 to 2. A region of possible physical conditions is found where the thermal diffuse radiation of the envelope exceeds the emission in the Balmer H line.