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1.
A new analytic approach to the solution of the Sitnikov Problem is introduced. It is valid for bounded small amplitude solutions (z max = 0.20) (in dimensionless variables) and eccentricities of the primary bodies in the interval (–0.4 < e < 0.4). First solutions are searched for the limiting case of very small amplitudes for which it is possible to linearize the problem. The solution for this linear equation with a time dependent periodic coefficient is written up to the third order in the primaries eccentricity. After that the lowest order nonlinear amplitude contribution (being of order z 3) is dealt with as perturbation to the linear solution. We first introduce a transformation which reduces the linear part to a harmonic oscillator type equation. Then two near integrals for the nonlinear problem are derived in action angle notation and an analytic expression for the solution z(t) is derived from them. The so found analytic solution is compared to results obtained from numeric integration of the exact equation of motion and is found to be in very good agreement. CERN SL/AP  相似文献   

2.
The effect of a prevalent magnetic field on static and uniformly rotating self-gravitating cylinders of infinite length is examined. The magnetic field is assumed to consist ofH andH z components, which are taken to be functions of the radial coordinate alone. A variety of magnetic-field configurations are shown to be admissible solutions of equations of motion, from which some feasible cases are presented. A particular magnetic-field configuration having bothH andH z components is studied in detail. The configuration is such that the assumption of a polytropic equation of state reduces the equation governing the density function to a non-homogeneous cylindrical analogue of the Lane-Emden equation for spherical polytropes. The homogeneous case is also studied and shows interesting magnetic-field patterns.  相似文献   

3.
We studied the behavior of magnetic field, horizontal motion and helicity in a fast emerging flux region NOAA 10488 which eventually forms a δ spot. It is found that the rotation of photospheric footpoints forms in the earlier stage of magnetic flux emergence and the relative shear motion of different magnetic flux systems appears later in this active region (AR). Therefore the emerging process of the AR can be separated into two phases: rotation and shear. We have computed the magnetic helicity injected into the corona using the local correlation tracking (LCT) technique. Furthermore we determined the vertical component of current helicity density and the vertical component of induction electric fields Ez = (V× B)z in the photosphere. Particularly we have presented the comparison of the injection rate of magnetic helicity and the variation of the current helicity density. The main results are as follows: (1) The strong shear motion (SSM) between the new emerging flux system and the old one brings more magnetic helicity into the corona than the twisting motions. (2) After the maturity of the main bipolar spots, their twist decreases and the SSM becomes dominant and the major contributor of magnetic non-potentiality in the solar atmosphere in this AR. (3) The positions of the maxima of Ez (about 0.1 ∼ 0.2 V cm−1) shift from the twisting areas to the areas showing SSMs as the AR evolved from the rotation phase to the shear one, but no obvious correlation is found between the kernels of Hα flare and Ez for the M1.6 flare in this AR. (4) The coronal helicity inferred from the horizontal motion of this AR amounts to −6 × 1043 Mx2. It is comparable with the coronal helicity of ARs producing flares with coronal mass ejections (CMEs) or helicity carried away by magnetic clouds (MCs) reported in previous studies (Nindos, Zhang, and Zhang, 2003; Nindos and Andrews, 2004). In addition, the formation of the δ configuration in this AR belongs to the third formation type indicated by Zirin and Liggett (1987), i.e., collision of opposite polarities from different dipoles, and can be naturally explained by the SSM.  相似文献   

4.
We study the stability of motion in the 3-body Sitnikov problem, with the two equal mass primaries (m 1 = m 2 = 0.5) rotating in the x, y plane and vary the mass of the third particle, 0 ≤ m 3 < 10−3, placed initially on the z-axis. We begin by finding for the restricted problem (with m 3 = 0) an apparently infinite sequence of stability intervals on the z-axis, whose width grows and tends to a fixed non-zero value, as we move away from z = 0. We then estimate the extent of “islands” of bounded motion in x, y, z space about these intervals and show that it also increases as |z| grows. Turning to the so-called extended Sitnikov problem, where the third particle moves only along the z-axis, we find that, as m 3 increases, the domain of allowed motion grows significantly and chaotic regions in phase space appear through a series of saddle-node bifurcations. Finally, we concentrate on the general 3-body problem and demonstrate that, for very small masses, m 3 ≈ 10−6, the “islands” of bounded motion about the z-axis stability intervals are larger than the ones for m 3 = 0. Furthermore, as m 3 increases, it is the regions of bounded motion closest to z = 0 that disappear first, while the ones further away “disperse” at larger m 3 values, thus providing further evidence of an increasing stability of the motion away from the plane of the two primaries, as observed in the m 3 = 0 case.  相似文献   

5.
The magnetorotational instability (MRI) of differential rotation under the simultaneous presence of axial and azimuthal components of the (current‐free) magnetic field is considered. For rotation with uniform specific angular momentum the MHD equations for axisymmetric perturbations are solved in a local short‐wave approximation. All the solutions are overstable for Bz · Bϕ ≠ 0 with eigenfrequencies approaching the viscous frequency. For more flat rotation laws the results of the local approximation do not comply with the results of a global calculation of the MHD instability of Taylor‐Couette flows between rotating cylinders. – With Bϕ and Bz of the same order the traveling‐mode solutions are also prefered for flat rotation laws such as the quasi‐Kepler rotation. For magnetic Prandtl number Pm → 0 they scale with the Reynolds number of rotation rather than with the magnetic Reynolds number (as for standard MRI) so that they can easily be realized in MHD laboratory experiments. – Regarding the nonaxisymmetric modes one finds a remarkable influence of the ratio Bϕ/Bz only for the extrema. For Bϕ ≫ Bz and for not too small Pm the nonaxisymmetric modes dominate the traveling axisymmetric modes. For standard MRI with Bz ≫ Bϕ, however, the critical Reynolds numbers of the nonaxisymmetric modes exceed the values for the axisymmetric modes by many orders so that they are never prefered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

6.
We present an analysis of BV R c I c observations of the field sized around 4′ × 4′ centered at the host galaxy of the gamma-ray burst GRB021004 with the 6-m BTA telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. We measured the magnitudes and constructed the color diagrams for 311 galaxies detected in the field (S/N>3). The differential and integral counts of galaxies up to the limit, corresponding to 28.5 (B), 28.0 (V), 27.0 (R c ), 26.5 (I c ) were computed. We compiled the galaxy catalog, consisting of 183 objects, for which the photometric redshifts up to the limiting magnitudes 26.0 (B), 25.5 (V), 25.0 (R c ), 24.5 (I c ) were determined using the HyperZ code. We then examined the radial distribution of galaxies based on the z estimates. We have built the curves expected in the case of a uniform distribution of galaxies in space, and obtained the estimates for the size and contrast of the possible super-large-scale structures, which are accessible with the observations of this type.  相似文献   

7.
To investigate the relationship between solar activity and the large-scale axisymmetric magnetic field of the Sun, we inferred from sunspot data over the period 1964–1985 a latitude–time distribution of magnetic field associated with active regions. This has been done allowing for both bipolar structure of the active regions and inclination of their axes to parallels of latitude, so the inferred magnetic field characterizes latitudinal separation of magnetic polarities which might be related to the large-scale magnetic field of the Sun according to the Babcock–Leighton model. The inferred magnetic field, A z, is compared with the longitude-averaged (zonal) magnetic field of the Sun, B z, derived from series of magnetograms obtained at Mount Wilson Observatory in the years 1964–1976, and at Kitt Peak National Observatory during the period from 1976 to 1985. The inferred magnetic field, A z, exhibits a complex structure distribution of magnetic polarities with respect to latitude and time. Apart from concentration of the different polarity magnetic fields inside the high- and low-latitude portions of the sunspot belts, bipolar active regions produce an intensive, shorter-scale component of the magnetic field which varies on the time scale of about 2 years. Such a short-term variation of A z reveals substantial correlation with the short-term component of B z which has the form of the poleward-drifting streams of magnetic field. Most significant correlation takes place between the short-term variations of A z occurring at latitudes below 20° and those of the large-scale magnetic fields occurring at middle latitudes of 40–50°. Moreover we analyze harmonic coefficients a l and b l obtained by expanding A z and B z into series in terms of the spherical harmonics. Power spectra of the time-dependent harmonic coefficients indicate that both A z and B z reveal a number of resonant modes which oscillate either with the 22-year period in the case of the anti-symmetric (odd-l) modes or with periods of about 2 years in the case of the symmetric (even-l) modes, but the resonant modes of A z have significantly larger values of the spherical harmonic degree l (and, hence, smaller spatial scales) as compared to those of B z. It is found that there is a close relationship between the harmonic coefficients b l and a m for which either m–l16 (even l=4,...,10) or m–l=4 (odd l=5,...,15).  相似文献   

8.
The purpose of this paper is to study the motion of a spinless axisymmetric rigid body in a Newtonian field when we suppose the motion of the center of mass of the rigid body is on a Keplerian orbit. In this case the system can be reduced to a Hamiltonian system with configuration space of a two-dimensional sphere. We prove that the restricted planar motion is analytical nonintegrable and we find horseshoes due to the eccentricity of the orbit. In the caseI 3/I 1>4/3, we prove that the system on the sphere is also analytical nonintegrable.On leave from the Polytechnic Institute of Bucharest, Romania.  相似文献   

9.
A theoretical scheme is developed to deal with the problems of stellar winds in three-dimensional situations, and relativistic fluid equations are integrated formally under isentropic and quasi-stationary conditions, in a flat space-time.The relativistic Euler equation for a one-component plasma is expressed in the same form as the ideal-MHD condition for the effective electromagnetic field which combines the inertial and pressure terms with the true electromagnetic field. This equation and that of mass continuity are integrated formally by introducing Euler-type potentials for the effective magnetic field and for the mass flux in the rotating frame, respectively. Functional form of one of these Euler potentials, which represents the total energy per unit charge in the rotating frame, is specified as an integral of motion. For an electron-proton plasma, the integrals for both components are combined to yield the energy integral of the plasma as a whole and the integrated Ohm's law, in the limit of vanishing mass ratio of an electron to a proton.Maxwell's equations are divided in two parts: i.e., the co-rotational and non-corotational parts. It is shown that the electromagnetic potentials for these parts are derived from a scalar super-potential and a vector super-potential, respectively.  相似文献   

10.
P. B. Zuo  F. S. Wei  X. S. Feng  F. Yang 《Solar physics》2007,242(1-2):167-185
The magnetic cloud boundary layer (BL) is a disturbance structure that is located between the magnetic cloud and the ambient solar wind. In this study, we statistically analyze the characteristics of the magnetic field B z component (in GSM coordinates) inside the magnetic cloud boundary layers as well as the relationship between the magnetic cloud boundary layers and the magnetospheric substorms based on 35 typical BLs observed by Wind from 1995 to 2006. It is found that the magnetic field B z components are more turbulent inside the BLs than those inside the adjacent sheath regions and the magnetic clouds. The substorm onsets are identified by the auroral breakups that are the most reliable substorm indicators by using the Polar UVI image data. The UVI data are available only for 17 BLs. The statistical analysis indicated that 9 of the 17 events triggered the substorms when BLs crossed the magnetosphere and that the southward field in the adjacent sheath region is a necessary condition for these triggering events. In addition, the SF-type BLs, which are named by their features of the B z components inside the BLs and adjacent sheath regions, can easily trigger the substorms during their passage of the magnetosphere. SF-type BLs are characterized by sustained strong southward magnetic fields persisting for at least 30 minutes in the adjacent sheath regions and at least one change in the polarity of the B z component inside the BL. In this study, 7 out of 8 such SF-type BL events triggered the substorm expansion phase, suggesting that the SF-type BLs are another important interplanetary disturbance source of substorms.  相似文献   

11.
A comparative analysis of solar and heliospheric magnetic fields in terms of their cumulative sums reveals cyclic and long-term changes that appear as a magnetic flux imbalance and alternations of dominant magnetic polarities. The global magnetic flux imbalance of the Sun manifests itself in the solar mean magnetic field (SMMF) signal. The north – south asymmetry of solar activity and the quadrupole mode of the solar magnetic field contribute the most to the observed magnetic flux imbalance. The polarity asymmetry exhibits the Hale magnetic cycle in both the radial and azimuthal components of the interplanetary magnetic field (IMF). Analysis of the cumulative sums of the IMF components clearly reveals cyclic changes in the IMF geometry. The accumulated deviations in the IMF spiral angle from its nominal value also demonstrate long-term changes resulting from a slow increase of the solar wind speed over 1965 – 2006. A predominance of the positive IMF B z with a significant linear trend in its cumulative signal is interpreted as a manifestation of the relic magnetic field of the Sun. Long-term changes in the IMF B z are revealed. They demonstrate decadal changes owing to the 11/22-year solar cycle. Long-duration time intervals with a dominant negative B z component were found in temporal patterns of the cumulative sum of the IMF B z .  相似文献   

12.
We study the dispersion characteristics of fast MHD surface waves travelling on a plasma slab immersed in a complex magnetic field consisting of a large longitudinal B 0z component and a small sheared B 0y component. The analysis shows that for typical coronal conditions both the sausage and kink waves are generally pseudo-surface waves. The tangential magnetic field, B 0y , modifies the dispersion curves, and for sufficiently large sheared fields there is a transition from pseudo-surface to pure-surface fast kink waves.On leave from Faculty of Physics, Sofia University, BG-1126 Sofia, Bulgaria.  相似文献   

13.
In this paper, we describe the results of an investigation of magnetic field structures in two active regions. The photospheric magnetic fields were measured simultaneously in all three components with the Crimean vector magnetograph in the Fe i 5250 line. In our analysis, we compare the observed magnetic field with the potential field. The potential field vector was calculated according to the potential-field theory, and the H z component was taken as a boundary condition. From these data vertical gradients are calculated from the condition div H = 0. Averaged gradients of both fields increase with the H z field intensity and within the error limits they do not differ from one another for field strengths up to 1200 G. For larger H z the potential field gradients become higher than those of the observed field. In large spots, observed field gradients are about two times less than those of the potential field. It is shown that this difference is connected with the observed field twisting.  相似文献   

14.
The model of extended Sitnikov Problem contains two equally heavy bodies of mass m moving on two symmetrical orbits w.r.t the centre of gravity. A third body of equal mass m moves along a line z perpendicular to the primaries plane, intersecting it at the centre of gravity. For sufficiently small distance from the primaries plane the third body describes an oscillatory motion around it. The motion of the three bodies is described by a coupled system of second order differential equations for the radial distance of the primaries r and the third mass oscillation z. This problem which is dealt with for zero initial eccentricity of the primaries motion, is generally non integrable and therefore represents an interesting dynamical system for advanced perturbative methods. In the present paper we use an original method of rewriting the coupled system of equations as a function iteration in such a way as to decouple the two equations at any iteration step. The decoupled equations are then solved by classical perturbation methods. A prove of local convergence of the function iteration method is given and the iterations are carried out to order 1 in r and to order 2 in z. For small values of the initial oscillation amplitude of the third mass we obtain results in very good agreement to numerically obtained solutions.  相似文献   

15.
The minimum dissipative rate (MDR) method for deriving a coronal non-force-free magnetic field solution is partially evaluated. These magnetic field solutions employ a combination of three linear (constant-α) force-free-field solutions with one being a potential field (i.e., α=0). The particular case of the solutions where the other two α’s are of equal magnitude but of opposite sign is examined. This is motivated by studying the SOLIS (Synoptic Optical Long-term Investigation of the Sun (SOLIS), a National Solar Observatory facility) vector magnetograms of AR 10987, which show a global α value consistent with an α=0 value as evaluated by (∇×B) z /B z over the region. Typical of the current state of the observing technology, there is no definitive twist for input into the general MDR method. This suggests that the special α case, of two α’s with equal magnitudes and opposite signs, is appropriate given the data. Only for an extensively twisted active region does a dominant, nonzero α normally emerge from a distribution of local values. For a special set of conditions, is it found that (i) the resulting magnetic field is a vertically inflated magnetic field resulting from the electric currents being parallel to the photosphere, similar to the results of Gary and Alexander (Solar Phys. 186:123, 1999), and (ii) for α≈(α max /2), the Lorentz force per unit volume normalized by the square of the magnetic field is on the order of 1.4×10−10 cm−1. The Lorentz force (F L) is a factor of ten higher than that of the magnetic force d(B 2/8π)/dz, a component of F L. The calculated photospheric electric current densities are an order of magnitude smaller than the maximum observed in all active regions. Hence both the Lorentz force density and the generated electric current density seem to be physically consistent with possible solar dynamics. The results imply that the field could be inflated with an overpressure along the neutral line. However, the implementation of this or any other extrapolation method using the electric current density as a lower boundary condition must be done cautiously, with the current magnetography.  相似文献   

16.
We apply the theory of the third integral to a self-consistent galactic model, generated by the collapse of a N-body system. The final configuration after the collapse is a stationary triaxial system, that represents an almost prolate non-rotating elliptical galaxy with its longest axis in the z-direction. This system is represented by an axisymmetric potential V plus a small triaxial perturbation V 1. The orbits in the potential V are of three types: box orbits, tube orbits (corresponding to various resonances), and chaotic orbits.The intersections of the box and tube orbits by a Poincaré surface of section z=0 are closed invariant curves. The main tube orbits are like ellipses and form an island of stability on the (R,R) plane.We calculated the third integral I in the potential V for the general non-resonant case and for various resonant cases. The agreement between the invariant curves of the orbits and the level curves of the third integral is good for the box and tube orbits, if we truncate the third integral at an appropriate level. As expected the third integral fails in the case of chaotic orbits. The most important result is the form of the number density F on the Poincaré surface of section. This function decreases exponentially outwards for the box orbits, like Fexp(–bI), while it is constant, as expected, for the chaotic orbits. In the case of the island of the main tube orbits it has a minimum at the center of the island. This can be explained by the form of the near elliptical orbits that are elongated along R, thus they fail to support a self-consistent galaxy, which is elongated along the z-axis.  相似文献   

17.
Adiabatic indices for a non-dissipative anisotropic convecting plasma are analyzed, and general expressions for the effective adiabatic index and the partial adiabatic indices parallel (γ∥) and perpendicular (γ⟂) to the magnetic field are obtained. It is shown that, in the general case, the value of the effective adiabatic index is not an universal constant and depends on the plasma temperature anisotropy and on the properties of the plasma motion. The values of γ⟂ and γ∥ are shown to be independent of the plasma parameters being completely determined by the characteristics of the plasma flow.  相似文献   

18.
A consistent account of plasma turbulence in magnetohydrodynamics equations describing transport processes across the magnetic field is presented. The structure of the perpendicular shock wave generated in the solar atmosphere, as a result of either local disturbance of the magnetic field or dense plasma cloud motion with a frozen-in magnetic field, has been investigated. The region of parameters in the solar atmosphere at which the electron-ion relative drift velocity u exceeds the electron thermal velocity V eand generation of radio emission becomes possible, has been determined. The plasma turbulence inside the front has been shown, under conditions of solar corona, not to cause the oscillation structure of shock front to break down. Under chromospheric conditions, the shock profile is aperiodical. Then, the condition u > Vecan be satisfied and shock waves having an Alfvén Mach number M which exceeds the critical value M c 3.3 for aperiodical shock waves can exist (Eselevich et al., 1971a). Arguments are given in favour of the fact that perpendicular shock waves are generated in the Sun's atmosphere when dense plasma clouds, with a frozen-in magnetic field, are expanded.  相似文献   

19.
A new class of plane-symmetric inhomogeneous cosmological models of perfect fluid distribution with electro-magnetic field based on Lyra’s geometry is obtained by considering a time dependent displacement field. The source of the magnetic field is due to an electric current produced along the z-axis. Only F 12 is a non-vanishing component of electromagnetic field tensor. To get the deterministic solutions, the free gravitational field is assumed to be of Petrov type-II non-degenerate. It has been found that the displacement vector β(t) behaves like cosmological term Λ which is consistent with the recent observations of type Ia supernovae. It is also observed that β(t) affects entropy. Some geometric and physical behaviour of the models are also discussed in presence of magnetic field.   相似文献   

20.
Using polarimetric spectra obtained with the SOFIN spectrograph installed at the Nordic Optical Telescope, we detect a longitudinal magnetic field 〈Bz〉 = –168±35 G in the Of?p star HD 108. This result is in agreement with the longitudinal magnetic field measurement of the order of –150 G recently reported by the MiMeS team. The measurement of the longitudinal magnetic field in the Of?p star HD 191612 results in 〈Bz〉 = +450±153 G. The only previously published magnetic field measurement for this star showed a negative longitudinal magnetic field 〈Bz〉 = –220±38 G, indicating a change of polarity over ∼100 days. Further, we report the detection of distinct Zeeman features in the narrow Ca II and Na I doublet lines for both Of?p stars, hinting at the possible presence of material around these stars. The origin of these features is not yet clear and more work is needed to investigate how magnetic fields interact with stellar wind dynamics (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

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