Combined effects of perturbations,radiation, and oblateness on the nonlinear stability of triangular points in the restricted three-body problem

This paper investigates the nonlinear stability of the triangular equilibrium points under the influence of small perturbations in the Coriolis and centrifugal forces together with the effect of oblateness and radiation pressures of the primaries. It is found that the triangular points are stable for all mass ratios in the range of linear stability except for three mass ratios depending upon above perturbations, oblateness coefficients and mass reduction factors.     

Observational constraints on a ‘hidden’, turbulent magnetic field of the Sun

A search for linear polarization due to the transverse Zeeman effect in quiet regions near the heliographic north pole has been carried out. The aim is to determine new constraints on the properties of the hidden or turbulent magnetic flux of the Sun. As more than 90% of the total flux seen in magnetograms has its source in kG fluxtubes with an average filling factor of less than 1%, the term hidden magnetic flux refers to the field in the remaining 99% of the photospheric volume, which remains undetected in ordinary magnetograms (at available levels of spatial resolution and sensitivity).Simultaneous recordings of the Stokes I, Q, and V profiles of the Fei 5250.22 and 5247.06 Å lines with 5 × 5 sec of arc spatial resolution have been made with the NSO McMath solar telescope. The analysis shows how the observed Stokes Q amplitudes, as well as the Q/V ratio in combination with the 5250/5247 Stokes V line ratio, provide constraints on the field strength and the angular distribution of the field vectors of the hidden magnetic flux. The field has to be tangled with opposite polarities mixed on a subarcsec scale, and the field vectors have to have large inclinations with respect to the vertical direction, with an angular distribution not far from being isotropic in the photosphere. Constraints on the strength of this tangled or turbulent magnetic field have been obtained by previous methods, which are reconsidered in view of their dependence on the assumed angular distribution. An upper limit of 100 G comes from determinations of magnetic line broadening, a lower limit of 10 G from observed Hanle-effect depolarization.In our observations the linear polarization has been recorded with a precision of 10^-4 with good spectral resolution. Further improvements are impeded by the lack of telescopes with large photon collecting areas and small instrumental polarization.     

The effect of radiation pressure on the equilibrium points in the generalized photogravitational restricted three body problem

The existence of equilibrium points and the effect of radiation pressure have been discussed numerically. The problem is generalized by considering bigger primary as a source of radiation and small primary as an oblate spheroid. We have also discussed the Poynting-Robertson (P-R) effect which is caused due to radiation pressure. It is found that the collinear points L ₁,L ₂,L ₃ deviate from the axis joining the two primaries, while the triangular points L ₄,L ₅ are not symmetrical due to radiation pressure. We have seen that L ₁,L ₂,L ₃ are linearly unstable while L ₄,L ₅ are conditionally stable in the sense of Lyapunov when P-R effect is not considered. We have found that the effect of radiation pressure reduces the linear stability zones while P-R effect induces an instability in the sense of Lyapunov.     

On the Analysis of the Complex Forbush Decreases of January 2005

In this work an analysis of a series of complex cosmic ray events that occurred between 17 January 2005 and 23 January 2005 using solar, interplanetary and ground based cosmic ray data is being performed. The investigated period was characterized both by significant galactic cosmic ray (GCR) and solar cosmic ray (SCR) variations with highlighted cases such as the noticeable series of Forbush effects (FEs) from 17 January 2005 to 20 January 2005, the Forbush decrease (FD) on 21 January 2005 and the ground level enhancement (GLE) of the cosmic ray counter measurements on 20 January 2005. The analysis is focusing on the aforementioned FE cases, with special attention drawn on the 21 January 2005, FD event, which demonstrated several exceptional features testifying its uniqueness. Data from the ACE spacecraft, together with GOES X-ray recordings and LASCO CME coronagraph images were used in conjunction to the ground based recordings of the Worldwide Neutron Monitor Network, the interplanetary data of OMNI database and the geomagnetic activity manifestations denoted by K _p and D _st indices. More than that, cosmic ray characteristics as density, anisotropy and density gradients were also calculated. The results illustrate the state of the interplanetary space that cosmic rays crossed and their corresponding modulation with respect to the multiple extreme solar events of this period. In addition, the western location of the 21 January 2005 solar source indicates a new cosmic ray feature, which connects the position of the solar source to the cosmic ray anisotropy variations. In the future, this feature could serve as an indicator of the solar source and can prove to be a valuable asset, especially when satellite data are unavailable.     

Effect of Moon perturbation on the energy curves and equilibrium points in the Sun–Earth–Moon system

In this paper, we have considered that the Moon motion around the Earth is a source of a perturbation for the infinitesimal body motion in the Sun–Earth system. The perturbation effect is analyzed by using the Sun–Earth–Moon bi–circular model (BCM). We have determined the effect of this perturbation on the Lagrangian points and zero velocity curves. We have obtained the motion of infinitesimal body in the neighborhood of the equivalent equilibria of the triangular equilibrium points. Moreover, to know the nature of the trajectory, we have estimated the first order Lyapunov characteristic exponents of the trajectory emanating from the vicinity of the triangular equilibrium point in the proposed system. It is noticed that due to the generated perturbation by the Moon motion, the results are affected significantly, and the Jacobian constant is fluctuated periodically as the Moon is moving around the Earth. Finally, we emphasize that this model could be applicable to send either satellite or telescope for deep space exploration.     

On the large-scale diffuse magnetic field of the Sun – II. The Contribution of Active Regions

Dikpati and Choudhuri (1994, 1995) developed a model for the poleward migration of the weak diffuse magnetic field on the Sun's surface. This field was identified with the poloidal component produced by the solar dynamo operating at the base of the convection zone, and its evolution was studied by considering the effects of meridional circulation and turbulent diffusion. The earlier model is extended in this paper by incorporating the flux from, the decay of tilted active regions near the solar surface as an additional source of the poloidal field. This extended model can now explain various low-latitude features in the time-latitude diagram of the weak diffuse fields. These low-latitude features could not be accounted for in the earlier model, which was very successful in modeling the behavior at high latitudes. The time-latitude diagrams show that regions of a particular polarity often have tongues of opposite polarity. Such tongues can be produced in the theoretical model by incorporating fluctuations in the source term arising out of the decaying active regions.     

Effect of radiation on the stability of equilibrium points in the binary stellar systems: RW-Monocerotis,Krüger 60

We have studied the stability of location of various equilibrium points of a passive micron size particle in the field of radiating binary stellar system within the framework of circular restricted three body problem. Influence of radial radiation pressure and Poynting-Robertson drag (PR-drag) on the equilibrium points and their stability in the binary stellar systems RW-Monocerotis and Krüger-60 has been studied. It is shown that both collinear and off axis equilibrium points are linearly unstable for increasing value of β ₁ (ratio of radiation to gravitational force of the massive component) in presence of PR-drag for the binary systems. Further we find that out of plane equilibrium points (L _i , i=6,7) may exists for range of values of β ₁>1 for these binary systems in the presence of PR-drag. Our linear stability analysis shows that the motion near the equilibrium points L _6,7 of the binary systems is unstable both in the absence and presence of PR-drag.     

Revealing the “fingerprints” of the magnetic precursor of C-shocks

We present the first C-shock and radiative transfer model that calculates the evolution of the line profiles of neutral and ion species like SiO, H¹³CO⁺ and HN¹³C for different flow times along the propagation of the shock through the unperturbed gas. We find that the line profiles of SiO characteristic of the magnetic precursor stage have very narrow linewidths and are centered at velocities close to the ambient cloud velocity, as observed toward the young shocks in the L1448-mm outflow. Consistently with previous works, our model also reproduces the broad SiO emission detected in the high velocity gas in this outflow, for the downstream postshock gas in the shock. This implies that the different velocity components observed in L1448-mm are due to the coexistence of different shocks at different evolutionary stages.     

Evolution of the Sun’s Polar Fields and the Poleward Transport of Remnant Magnetic Flux

Observations of the solar photosphere show spatially compact large-amplitude Doppler velocity events with short lifetimes. In data from the Imaging Magnetograph eXperiment (IMaX) on the first flight of the Sunrise balloon in 2009, events with velocities in excess of 4\(\sigma \) from the mean can be identified in both intergranular downflow lanes and granular upflows. We show that the statistics of such events are consistent with the random superposition of strong convective flows and p-mode coherence patches. Such coincident superposition complicates the identification of acoustic wave sources in the solar photosphere, and may be important in the interpretation of spectral line profiles formed in solar photosphere.

     

An Analysis of the Sunspot Groups and Flares of Solar Cycle 23

Designing a statistical solar flare forecasting technique can benefit greatly from knowledge of the flare frequency of occurrence with respect to sunspot groups. This study analyzed sunspot groups and Hα and X-ray flares reported for the period 1997 – 2007. Annual catalogs were constructed, listing the days that numbered sunspot groups were observed (designated sunspot group-days, SSG-Ds) and for each day a record for each associated Hα flare of importance category one or greater and normal or bright brightness and for each X-ray flare of intensity C 5 or higher. The catalogs were then analyzed to produce frequency distributions of SSG-Ds by year, sunspot group class, likelihood of producing at least one flare overall and by sunspot group class, and frequency of occurrence of numbers of flares per day and flare intensity category. Only 3% of SSG-Ds produced a substantial Hα flare and 7% had a significant X-ray flare. We found that mature, complex sunspot groups were more likely than simple sunspot groups to produce a flare, but the latter were more prevalent than the former. More than half of the SSG-Ds with flares had a maximum intensity flare greater than the lowest category (C-class of intensity five and higher). The fact that certain sunspot group classes had flaring probabilities significantly higher than the combined probabilities of the intensity categories when all SSG-Ds were considered suggest that it might be best to first predict the flaring probability. For sunspot groups found likely to flare, a separate diagnosis of maximum flare intensity category appears feasible.     

The Recovery of CME-Related Dimmings and the ICME’s Enduring Magnetic Connection to the Sun

It is generally accepted that transient coronal holes (TCHs, dimmings) correspond to the magnetic footpoints of CMEs that remain rooted in the Sun as the CME expands out into the interplanetary space. However, the observation that the average intensity of the 12 May 1997 dimmings recover to their pre-eruption intensity in SOHO/EIT data within 48 hours, whilst suprathermal unidirectional electron heat fluxes are observed at 1 AU in the related ICME more than 70 hours after the eruption, leads us to question why and how the dimmings disappear whilst the magnetic connectivity is maintained. We also examine two other CME-related dimming events: 13 May 2005 and 6 July 2006. We study the morphology of the dimmings and how they recover. We find that, far from exhibiting a uniform intensity, dimmings observed in SOHO/EIT data have a deep central core and a more shallow extended dimming area. The dimmings recover not only by shrinking of their outer boundaries but also by internal brightenings. We quantitatively demonstrate that the model developed by Fisk and Schwadron (Astrophys. J. 560, 425, 2001) of interchange reconnections between “open” magnetic field and small coronal loops is a strong candidate for the mechanism facilitating the recovery of the dimmings. This process disperses the concentration of  “open” magnetic field (forming the dimming) out into the surrounding quiet Sun, thus recovering the intensity of the dimmings whilst still maintaining the magnetic connectivity to the Sun. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

The effect of two-temperature post-shock accretion flow on the linear polarization pulse in magnetic cataclysmic variables

The temperatures of electrons and ions in the post-shock accretion region of a magnetic cataclysmic variable (mCV) will be equal at sufficiently high mass flow rates or for sufficiently weak magnetic fields. At lower mass flow rates or in stronger magnetic fields, efficient cyclotron cooling will cool the electrons faster than the electrons can cool the ions and a two-temperature flow will result. Here we investigate the differences in polarized radiation expected from mCV post-shock accretion columns modeled with one- and two-temperature hydrodynamics. In an mCV model with one accretion region, a magnetic field ?30 MG and a specific mass flow rate of ～0.5 g?cm^?2?s^?1, along with a relatively generic geometric orientation of the system, we find that in the ultraviolet either a single linear polarization pulse per binary orbit or two pulses per binary orbit can be expected, depending on the accretion column hydrodynamic structure (one- or two-temperature) modeled. Under conditions where the physical flow is two-temperature, one pulse per orbit is predicted from a single accretion region where a one-temperature model predicts two pulses. The intensity light curves show similar pulse behavior but there is very little difference between the circular polarization predictions of one- and two-temperature models. Such discrepancies indicate that it is important to model some aspect of two-temperature flow in indirect imaging procedures, like Stokes imaging, especially at the edges of extended accretion regions, were the specific mass flow is low, and especially for ultraviolet data.     

Study of Hα Jets on the Quiet Sun

High-speed jets of solar quiet regions have been observed at Big Bear Solar Observatory in H–1.0 Ú, and compared with high-resolution magnetograms. Over the whole Sun, the birthrate of the H–1.0 Ú jets is about 19±3 events s^–1, which is much lower than the birthrate of spicules. The average lifetime of these jets is 2±1 min. H–1.0 Ú jets are very different from spicules, in the sense of birthrate, lifetime, and shape. Jets tend to recur in the same sites, always located in boundaries of supergranules. Under the best observing conditions, we found that 80% of the major jet sites are associated with converging magnetic dipoles – mainly the sites where intranetwork elements are canceling with opposite polarity network elements. In order to establish a possible relationship between the disk H jets and limb macrospicules, we have also obtained time sequences of H center-line images at the limb. These images are enhanced by median filtering so that jet structures over the limb are easily studied. We found that these limb H jets (above the spicule forest) repeatedly occur in the same sites, which is the property shared by the disk H–1.0 Ú jets. However, their mean lifetime is 10 min, substantially longer than that of disk jets. Comparison with simultaneous SOHO/EIT Heii 304 Ú images shows that every Heii 304 Ú jet over the limb coincides with an H jet, although Heii 304 Ú jets extend much farther out. Some H jets do not have associated He jets, probably due to the difference in image resolutions. H spectra of selected jets are analyzed, and we found that jets are not simply blue-shifted; instead, the line profiles are broadened with significantly larger broadening on the blue side. Two-component fitting finds that the velocity of the blue-shifted component (an optically-thin component) is around 20 to 40 km s^–1.     

Statistical interrelation of 22-yr-long variations in the data on parameters of the Earth’s rotation and magnetic fields of the Earth and the Sun

By means of spectral analysis, oscillations have been detected in many-year time series of deviations in the duration of days from the standard that cannot be explained within the framework of existing gravitational theory. The solution of the problem of the origin and structure of these oscillations is associated with the essence of the phenomena taking place inside the Earth and the mechanisms of energy transfer by external fields and the Sun. The effect of the Sun on the Earth’s rotation also leads to the formation of a unified cyclic background, resulting in correlated oscillations in all shells of the Earth, as well as in its atmosphere and its nucleus. Ground magnetic fields of the Earth and the Sun play the leading role in the abovementioned unified cyclic process. The results of spectral autoregressive and wavelet analyses of experimental data concerning deviations in the duration of days from the standard in the years 1832–2006, ground geomagnetic field intensities in 1832–2006, and the mean magnetic field of the Sun during the period from 1975 to 2005 have been discussed in this paper to reveal and compare correlating oscillations. To analyze a short-period (31-yr-long) series of daily data on the mean magnetic field of the Sun, the results of wavelet transformations (the Morlet wavelet) of the detected amplitude of a burst envelope with a carrier frequency of 13 cycles/yr have been obtained.     

Global Effects of Local Sound-Speed Perturbations in the Sun: A Theoretical Study

We study the effect of localized sound-speed perturbations on global mode frequencies by applying techniques of global helioseismology to numerical simulations of the solar acoustic wave field. Extending the method of realization-noise subtraction (e.g., Hanasoge, Duvall, and Couvidat, Astrophys. J. 664, 1234, 2007) to global modes and exploiting the luxury of full spherical coverage, we are able to achieve very highly resolved frequency differences that are then used to study sensitivities and the signatures of the thermal asphericities. We find that i) global modes are almost twice as sensitive to sound-speed perturbations at the bottom of the convection zone in comparison to anomalies well inside the radiative interior (r?0.55R _⊙), ii) the m degeneracy is lifted ever so slightly, as seen in the a coefficients, and iii) modes that propagate in the vicinity of the perturbations show small amplitude shifts. Through comparisons with error estimates obtained from Michelson Doppler Imager (MDI; Scherrer et al., Solar Phys. 162, 129, 1995) observations, we find that the frequency differences are detectable with a sufficiently long time series (70?–?642 days).     

Evolution of isolated G-band bright points： size,intensity and velocity

We study the evolution pattern of isolated G-band bright points(GBPs)in terms of their size, intensity and velocity. Using a high resolution image sequence taken with the Hinode/Solar Optical Telescope(SOT), we detect GBPs in each image by the Laplacian and Morphological Dilation algorithm, and track their evolutions by a 26-adjacent method in a three-dimensional space-time cube. For quantifying the evolution, we propose a quantification method based on lifetime normalization which aligns the different lifetimes to common stages. The quantification results show that, on average, the diameter of isolated GBPs changes from 166 to 173 km, then down to 165 km; the maximum intensity contrast changes from 1.012 to 1.027, then down to 1.011; however, the velocity changes from 1.709 to 1.593 km s-1, then up to 1.703 km s-1. The results indicate that the evolution follows a pattern such that the GBP is small, faint and fast-moving at the birth stage, becomes big, bright and slow-moving at the middle stage, then gets small, faint and fast-moving at the decay stage until disappearance. Although the differences are very small, a two-sample t-test is used to demonstrate there are significant differences in means between the distributions of the different stages. Furthermore, we quantify the relationship between the lifetimes of GBPs and their properties. It is found that there are positive correlations between the lifetimes and their sizes and intensities with correlation coefficients of0.83 and 0.65, respectively; however, there is a negative correlation between the lifetimes and velocities with a correlation coefficient of –0.49. In summary, the longer the GBP persists, the bigger, brighter and slower it will be.     

Signatures of Emerging Subsurface Structures in Acoustic Power Maps of the Sun

We show that under certain conditions, subsurface structures in the solar interior can alter the average acoustic power observed at the photosphere above them. By using numerical simulations of wave propagation, we show that this effect is large enough for it to be potentially used for detecting emerging active regions before they appear on the surface. In our simulations, simplified subsurface structures are modeled as regions with enhanced or reduced acoustic wave speed. We investigate the dependence of the acoustic power above a subsurface region on the sign, depth, and strength of the wave-speed perturbation. Observations from the Solar and Heliospheric Observatory/Michelson Doppler Imager (SOHO/MDI) prior and during the emergence of NOAA active region 10488 are used to test the use of acoustic power as a potential precursor of the emergence of magnetic flux.     

Are Planetary Tides on the Sun and the Birthplace of Sunspots Related?

We study whether the birthplaces of sunspots (defined as the location of first appearance in the photosphere) are related to the planetary tides on the Sun. The heliocentric longitudes of newly emerging sunspots are statistically compared to the longitudes of tidal peaks caused by the tidal planets Mercury, Venus, Earth, and Jupiter. The longitude differences between new sunspots and tidal planets (and their conjugate locations) as well as the magnitudes of the vertical and horizontal tidal forces at the birthplace of new sunspots are calculated. The statistical distributions are compared with simulation results calculated using a random sunspot distribution. The results suggest that the birthplaces of sunspots (in the photosphere) are independent of the positions of tidal planets and the strength of tidal forces caused by them. However, since the sunspots actually originate near the tachocline (well below the photosphere) and it takes considerable time for the disturbances to reach photosphere, we hesitate to conclude that the formation of sunspots are not related to planetary positions.     

A magnetic core in the Sun? The solar rotator

The previously found solar distortion rotating rigidly and wave-like on the surface with a 12 day period is interpreted as the shape of the gravitational potential induced by the solar core distorted by an internal magnetic field and rotating rigidly with this period. The distortion does not have a symmetry axis and the necessary magnetic field is not compatible with the axial symmetry required of a quasi-static field locked in the rotating core. It is concluded that if the solar distortion is due to such a process the core is oscillating with a very long period, a toroidal oscillation with a period of the order of years.This research was supported in part by the National Science Foundation.     

Is there an oblique magnetic rotator inside the Sun?

The size of the rotational splitting recently observed (Claverie et al., 1981) is correlated with the 12.2^d variation in the measurements of solar oblateness observed by Dicke (1976) and implies a convection zone of depth of 0.1 R . The near equality of amplitudes of global velocity oscillations (Claverie et al., 1981) of the various m components of the l = 1 and l = 2 modes as seen from the Earth viewing the Sun nearly along the equator is unexpected for pure rotational splitting. It is suggested that a magnetic perturbation is present and an oblique asymmetric magnetic rotator with magnetic fields of a few million gauss is responsible. A more detailed account was submitted to Nature.Proceedings of the 66th IAU Colloquium: Problems in Solar and Stellar Oscillations, held at the Crimean Astrophysical Observatory, U.S.S.R., 1–5 September, 1981.