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1.
Oscillations of magnetic flux tubes are of great importance as they contain information about the geometry and fine structure of the flux tubes. Here we derive and analytically solve in terms of Kummer’s functions the linear governing equations of wave propagation for sausage surface and body modes (m=0) of a magnetically twisted compressible flux tube embedded in a compressible uniformly magnetized plasma environment in cylindrical geometry. A general dispersion relation is obtained for such flux tubes. Numerical solutions for the phase velocity are obtained for a wide range of wavenumbers and for varying magnetic twist. The effect of magnetic twist on the period of oscillations of sausage surface modes for different values of the wavenumber and vertical magnetic field strength is calculated for representative photospheric and coronal conditions. These results generalize and extend previous studies of MHD waves obtained for incompressible or for compressible but nontwisted flux tubes. It is found that magnetic twist may change the period of sausage surface waves of the order of a few percent when compared to counterparts in straight nontwisted flux tubes. This information will be most relevant when high-resolution observations are used for diagnostic exploration of MHD wave guides in analogy to solar-interior studies by means of global eigenoscillations in helioseismology.  相似文献   

2.
The analytical stability criterion applicable to coplanar hierarchical three-body systems described in the first paper of this series, Walkeret al. (1980), is modified to give an exact representation ofHill-type stability in all such cases. The dependence of the stability on all orbital parameters (in the coplanar case) is taken into account. The criterion for stability is now dependant upon the participating masses, the elements of the initial osculating Keplerian orbits of the system (viz. the orbits ofm 2 aboutm 1 andm 3 about the mass-centre of the (m 1,m 2) system) and the positions within these orbits.The behaviour of the stability of such systems is demonstrated (both analytically and numerically) with respect to certain of the parameters involved to consider effects not dealt with in the above-mentioned paper. In particular two interesting real cases of triple systems in the Solar System are discussed, namely Sun-Jupiter-Saturn and Earth-Moon-Sun. The results of the present paper are compared with those of past authors who considered the same systems.Finally some general features arising out of our analysis are discussed.  相似文献   

3.
Volume extinction factorsV c have been evaluated for spherical grains at several refractive indices (m=1.6,m=1.5,m=1.33,m=1,16,m=1.1). From these results it is found that grains with higher-refractive index are more efficient for visual extinction than grains with low-refractive index.  相似文献   

4.
In this paper we study the chameleon Jordan-Brans-Dicke (JBD) cosmological models under the hypothesis of self-similarity. Since there are several ways to define the matter Lagrangian for a perfect fluid: L m =?ρ and L m =γρ, we show that they bring us to obtain two completely different cosmological models. In the first approach, L m =?ρ, there is ordinary matter conservation, while in the second approach, L m =γρ, we get matter creation processes. We deduce for each approach the behaviour of each physical quantity, under the self-similar hypothesis, by employing the Lie group method. The results are quite general and valid for any homogeneous geometry (FRW, Bianchi types, etc.). As example, we calculate exact solutions for each approach by considering the case of a Bianchi II geometry. In this way we can determine the exact behaviour of each physical quantity and in particular of G eff and U (the potential that mimics the cosmological constant).We compare the solutions with the obtained ones in the framework of the usual JBD models.  相似文献   

5.
Numerical and analytical comparisons are made between three methods of obtaining stability information on satellite motion using the model of the restricted problem of three bodies. Kuiper's (1961) and Szebehely's (1978) approximate results are compared with computer solutions obtained by successive iterations. The three methods show close agreement regarding the maximum values of the orbital radii for stability. The lowest result and therefore the most conservative estimate is obtained by the simplest formula, max=(/81)1/3 where is the ratio of the satellite's orbital radius to the distance between the primaries with massesm 1>m 2 and is the mass-ratio given bym 2/(m 1+m 2).  相似文献   

6.
Twisted magnetic flux tubes are often used to model the filed in coronal loops, and much attention has been given to analysing their stability. Previous astrophysical studies have concentrated on establishing the existence of an instability or determining stability bounds, and little information seems available on the associated eigenvalues, which give crucial information on the energy released. This paper develops methods of determining eigenvalues for infinitely long flux tubes. The most striking feature of the results is that the eigenvalues are always small-of order 10–2 (in dimensionless units) even for the fastest helical kink modes (m=1). The more localized higher-m modes have even smaller eigenvalues. A family of flux tubes with field line twist proportional tor is investigated, and it appears that the most energetic instabilities occur in the Gold-Hoyle tube with uniform twist (=0). Implications of these results are discussed.  相似文献   

7.
Results from optical photometric observations of the PMS star V 1735 Cyg are reported. The star is located in the IC 5146 dark cloud complex—a region of active star formation. On the basis of observed outburst and spectral properties, V 1735 Cyg was classified as a FUor object. We present data from BVRI CCD photometric observations of the star, collected from March 2003 to January 2009. Plates from the Rozhen Schmidt telescope archive were scanned for a brightness estimation of the star. A sequence of sixteen comparison stars in the field of V 1735 Cyg was calibrated in BVRI bands. The data from photographic observations made from 1986 to 1992 show a strong light variability (ΔV=1⋅m2). In contrast, the recent photometric data obtained from 2003 to 2009 show only small amplitude variations (ΔI=0⋅m3). The analysis of existing photometric data shows a very slow decrease in star brightness—1⋅m8 (R) for a 44 year period. The possibilities for future photometric investigations of V 1735 Cyg using the photographical plate archives is discussed briefly.  相似文献   

8.
The only existing photoelectric light curve of AI Cru has been re-analysed using the Wilson and Devinney (1971) direct method of solution. The system is found to be a semi-detached system of spectral type (B5 v+B8 v), with a mass ratioq=m c /m h =0.6. This solution differs somewhat from that obtained by Giuricinet al. (1980), using Wood's (1972) method, but seems more realistic because of the smaller value ofq and the reduced temperature difference between the components, which amounts to about 3300 K.  相似文献   

9.
We consider n bodies (with equal mass m) disposed at the vertices of a regular n-gon and rotating rigidly around an additional mass m 0(at its center) with a constant angular velocity (relative equilibrium). In the present paper, we prove results on the existence and on the linear stability of equilibrium positions for a zero-mass particle submitted to the gravitational field generated by the previous system. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

10.
The Sun-Earth-Moon system is modeled by the restricted problem of three bodies, and the curves of zero velocity are used to define the limits of stability of the Moon's orbit about the Earth. By holding the relative distances fixed, and maintaining the circular velocities of the Earth and Moon while their masses are varied by a common factor (=m E/m E=m M/m M), it is found that the possibility of the Moon leaving Earth orbit and orbiting the Sun exists for the range of values 0.005<<0.4.  相似文献   

11.
In this paper, new trigonometric series representations of the orbital inclination functionF imp (i) in multiples of cosines or sines will be established for all possible values ofl, m, andp. For such representations, the literal analytical expressions and the recurrence formulae satisfied by their coefficients will be established. Moreover, an economic algorithm for the table formulation of these coefficients for the possible values ofl, m, andp is given. Finally, numerical examples of the representations forl=2(1)4;m=0(1)l;p=0(1)l are also included.  相似文献   

12.
A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and co-workers and the general, numerically integrated results of Laplace's method by Graziani and Black are compared for varying values of the mass parameter =m 2/(m 1+m 2). For 00.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For >0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of .  相似文献   

13.
Recurrent power series methods are particularly applicable to problems in celestial mechanics since the Taylor coefficients may be expressed by recurrence relations. However, as the number of Taylor coefficients increases as is often necessary because of accuracy requirements, the computing time grows prohibitively large. In order to avoid this unfavorable situation, Dr E. Fehlberg introduced in 1960 Runge-Kutta methods that use the firstm Taylor coefficients obtained by recursive relations, or some other technique.Optimalm-fold Runge-Kutta methods are introduced. Embedded methods of order (m+3)[m+4] and (m+4)[m+5] are presented which have coefficients that produce minimum local truncation errors for the higher order pair of solutions of the method, as well as providing a near maximum absolute stability region. It is emphasized that the methods are formulated such that the higher order pair of solutions is to be utilized. These optimal methods are compared to the existingm-fold methods for several test problems. The numerical comparisons show that the optimal methods are more efficient. It is stressed that these optimal methods are particularly efficient whenm is small.  相似文献   

14.
In this paper we study the asymptotic solutions of the (N+1)-body ring planar problem, N of which are finite and ν=N−1 are moving in circular orbits around their center of masses, while the Nth+1 body is infinitesimal. ν of the primaries have equal masses m and the Nth most-massive primary, with m 0=β m, is located at the origin of the system. We found the invariant unstable and stable manifolds around hyperbolic Lyapunov periodic orbits, which emanate from the collinear equilibrium points L 1 and L 2. We construct numerically, from the intersection points of the appropriate Poincaré cuts, homoclinic symmetric asymptotic orbits around these Lyapunov periodic orbits. There are families of symmetric simple-periodic orbits which contain as terminal points asymptotic orbits which intersect the x-axis perpendicularly and tend asymptotically to equilibrium points of the problem spiraling into (and out of) these points. All these families, for a fixed value of the mass parameter β=2, are found and presented. The eighteen (more geometrically simple) families and the corresponding eighteen terminating homo- and heteroclinic symmetric asymptotic orbits are illustrated. The stability of these families is computed and also presented.  相似文献   

15.
We derive general results on the existence of stationary configurations for N co-orbital satellites with small but otherwise arbitrary masses m i , revolving on circular and planar orbits around a massive primary. The existence of stationary configurations depends on the parity of N. If N is odd, then for any arbitrary angular separation between the satellites, there always exists a set of masses (positive or negative) which achieves stationarity. However, physically acceptable solutions (m i > 0 for all i) restrict this existence to sub-domains of angular separations. If N is even, then for given angular separations of the satellites, there is in general no set of masses which achieves stationarity. The case N=3 is treated completely for small arbitrary satellite masses, giving all the possible solutions and their stability, to within our approximations.  相似文献   

16.
Families of asymmetric periodic orbits at the 2/1 resonance are computed for different mass ratios. The existence of the asymmetric families depends on the ratio of the planetary (or satellite) masses. As models we used the Io-Europa system of the satellites of Jupiter for the case m1>m2, the system HD82943 for the new masses, for the case m1=m2 and the same system HD82943 for the values of the masses m1<m2 given in previous work. In the case m1≥ m2 there is a family of asymmetric orbits that bifurcates from a family of symmetric periodic orbits, but there exist also an asymmetric family that is independent of the symmetric families. In the case m1<m2 all the asymmetric families are independent from the symmetric families. In many cases the asymmetry, as measured by and by the mean anomaly M of the outer planet when the inner planet is at perihelion, is very large. The stability of these asymmetric families has been studied and it is found that there exist large regions in phase space where we have stable asymmetric librations. It is also shown that the asymmetry is a stabilizing factor. A shift from asymmetry to symmetry, other elements being the same, may destabilize the system.  相似文献   

17.
From 44 spectra obtained at Asiagno in 1969–1971, we infer the orbital elements of the double lines system LY Aur. The mass-functions indicate rather massive components, with mass ratio 0.58±0.03. This is in good agreement with a contact photometric solution found by Eaton (1978). Combination of spectroscopic and photometric data yields the following absolute elements:m 1=13,m 2=22, separation 34.5,R 1=11,R 2=15, in solar units.A short comment on the large number of massive contact systems is given.  相似文献   

18.
The oscillations and stability of a homogeneous self-gravitating rotating cylinder in a toroidal magnetic field are investigated. It is assumed that the field is proportional to the distance to the axis of the cylinder. We show the existence of four infinite discreta spectra of magnetic (or rotational) modes. Rotation stabilizes the magneticm=1 instability. The magnetic field decreases the growth rate of rotational instability and reduces the interval of unstable wavenumbers. Ifm=1, instability always occurs with the exception of the equipartition state. Ifm>1, the instability can be suppressed by a sufficiently large magnetic field. Resistivity decreases the growth rate of magnetic instability, but increases the growth rate of rotational instability. For zero wavenumber perturbations secular instability occurs due to the action of resistivity before a neutral point is attained where a second secular instabiliity initiates due to the action of resistivity.  相似文献   

19.
This paper presents the study of a nonlinear process in the solar corona where dispersive Alfvén waves (DAWs) may lead to coronal heating. We present the model equations governing the nonlinear excitation of the fast waves (FWs) by DAWs in low-β plasmas (β≪m e/m i as applicable to the solar corona). By properly considering the ponderomotive nonlinearity, we have derived the equations for the decay waves, namely the FWs and other DAWs. The expressions for the coupling coefficients of the three-wave interaction have been derived. The growth rate of the instability is also calculated; we have found that the value of the decay growth time turns out to be of the order of milliseconds at the pump DAW amplitude B 0y /B 0=10−3. This time scale is much shorter than the observed time scales (a minute or less) for coronal heating, as inferred from images obtained by instruments on board Yohkoh and the Solar and Heliospheric Observatory (SOHO).  相似文献   

20.
Power spectra of the 1979 solar differential observations (Bos, 1982) have been analyzed for evidence of intermediate-degreef-modes. A set of 19 intermediate-degreef-mode multiplets has been identified and classified based on more than 300 classified modes of oscillation. The angular degree of the multiplets ranges from 18 to 36. Them=0 eigenfrequency spectrum, measured with an accuracy of typically 0.01–0.02 Hz, was found to be on the average 10 Hz greater than that predicted by the standard solar model of Saio (1982). Rotational splitting effects up to fifth order inm were obtained. The multiplet fine structure that is linear inm was found to be consistent with the internal rotation curve obtained by Hillet al. (1986a). The multiplet fine structure that is described by terms that are cubic and fifth order inm were found to be consistent with the differential rotation curve of Hillet al. (1986b). The probability that this set of 19 Zeeman-like frequency patterns were obtained from a set of peaks randomly distributed in frequency was estimated to be 10–9. The effectiveness of the mode detection and classification program in this work has been established in part by observing the horizontal spatial properties of thef-mode eigenfunctions. One consequence obtained from the study of the horizontal spatial properties of the modes is the estimate, obtained observationally, of the number of correct mode identifications: these results indicate that 73±6% of the 374 modes are correctly classified.SCLERA is an acronym for Santa Catalina Laboratory for Experimental Relativity by Astrometry, a facility operated by the University of Arizona.  相似文献   

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