Bounds on the stability of 3D magnetic equilibria in the solar corona     

A. W. Longbottom  J. P. Melville  A. W. Hood 《Solar physics》1993,146(1):93-118

A necessary and a sufficient condition are derived for the ideal magnetohydrodynamic stability of any 3D magnetohydrostatic equilibrium using the energy method and incorporating photospheric line-tying. The theory is demonstrated by application to a simple class of theoretical 3D equilibria. The main thrust of the method is the formulation of the stability conditions as two sets of ordinary differential equations together with appropriate boundary conditions which may be numerically integrated along tied field lines one at a time. In the case of the shearless fields with non-negligible plasma pressure treated here the conditions for stability arenecessary and sufficient. The method employs as a trial function a destabilizing ballooning mode, of large wave number vector perpendicular to the equilibrium field lines. These modes may not be picked up in a solution of the full partial differential equations which arise from a direct treatment of the problem.  相似文献   

Stability of outer planetary orbits around binary stars: A comparison of Hill's and Laplace's stability criteria     

A. Kubala  D. Black  V. Szebehely 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):51-68

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   

Position and velocity sensitivities at the triangular libration points     

D. G. Tuckness 《Celestial Mechanics and Dynamical Astronomy》1995,61(1):1-19

The model of the circular restricted problem of three bodies is used to investigate the sensitivity of the third body motion when it is given a positional or velocity deviation away from the L₄ triangular libration point. The x-axis is used as a criteria for defining the stability of the third body motion. Poincaré's surfaces of section are used to compare the regions of periodic, quasi-periodic and stochastic motion to the trajectories found using the definition of stability (not crossing the x-axis) defined in this study. Values of the primary/secondary mass ratios () ranging from 0 to the linear critical value 0.038521... are investigated. Using this new form of stability measure, it is determined that certain values of are more stable than others. The results of this study are compared, and found, to give agreeable results to other studies which investigate commensurabilities of the long and short period terms of periodic orbits.  相似文献   

A Systematic Study of the Stability of Symmetric Periodic Orbits in the Planar, Circular, Restricted Three-Body Problem     

Alessandra Celletti  Andrea Chessa  John Hadjidemetriou  Giovanni Battista Valsecchi 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):239-255

We investigate symmetric periodic orbits in the framework of the planar, circular, restricted, three-body problem. Having fixed the mass of the primary equal to that of Jupiter, we determine the linear stability of a number of periodic orbits for different values of the eccentricity. A systematic study of internal resonances, with frequency p/q with 2p 9, 1 q 5 and 4/3 p/q 5, offers an overall picture of the stability character of inner orbits. For each resonance we compute the stability of the two possible periodic orbits. A similar analysis is performed for some external periodic orbits.Furthermore, we let the mass of the primary vary and we study the linear stability of the main resonances as a function of the eccentricity and of the mass of the primary. These results lead to interesting conclusions about the stability of exosolar planetary systems. In particular, we study the stability of Earth-like planets in the planetary systems HD168746, GI86, 47UMa,b and HD10697.  相似文献   

Inhomogeneities in the circumstellar envelope of the A0E herbig star AB aur     

Nina Beskrovnaya  Mikhail Pogodin  Ivan Najdenov  Iosiff Romanyuk 《Astrophysics and Space Science》1995,224(1-2):429-430

Simultaneous high-resolution spectroscopy in H andUBVRI polarimetric observations are proposed as an effective method for the search for circumstellar inhomogeneities in A0-type Herbig stars. The new results for AB Aur are presented as a successful example of the use of this method. The analysis of about 100 CCD H profiles (R = 30 000) and more than 150 polarimetric measurements obtained in January, 1994 allowed to discover a long-lived stream-like inhomogeneity in the circumstellar gaseous envelope.  相似文献   

The visco-resistive stability of arcades in the corona of the Sun     

E. Bogaert  M. Goossens 《Solar physics》1991,132(1):109-124

The stability of ballooning modes in coronal arcades is studied using linear visco-resistive MHD. Rigid wall conditions are adopted for modelling the photospheric line-tying of the magnetic field. The full Braginskii viscosity stress tensor is used and particular attention is given to the effect of the viscosity coefficient ₃ which was left out of an earlier investigation by Van der Linden, Goossens, and Hood (1987, 1988). The numerical results for shearless arcades show that the coefficient ₃ has a stabilizing effect. However, for realistic values of the equilibrium quantities the stabilizing effect by ₃ can be neglected in comparison with the strong stabilizing effect of the perpendicular viscosity. The effect of magnetic field strength and mode number on stability are determined. In particular it is found that there exists a critical field strength for every mode number such that the mode is stable for weaker fields and unstable for stronger fields.  相似文献   

The stability of the equilibrium of supermassive and superdense stars     

Giulio Calamai 《Astrophysics and Space Science》1970,6(2):240-257

The second variation of the mass-energy (by constant baryon number) is analysed to inquire into the stability of the equilibrium for a spherical mass under the action of its own gravitation. The equations of general relativity are used. For zero density at the surface, the sphere is stable if (and only if) a solution of a second order equation (Jacobi equation) has only one zero in the interior (at center) of the sphere. The results obtained in this way coincide of course with those obtained by means of the Chandrasekhar-Misner-Zapolsky variational principle, but the solution of the Jacobi equation is more simple and straightforward. In particular, the stability of the several modes are analysed without making any choice of a trial function for the Lagrangian displacement.The method is applied to the GrattonR-polytropic model of supermassive stars.Work done in the Laboratorio Astrofisico, Frascati-Roma, Italy.  相似文献   

The ideal magnetohydrodynamic stability of a line-tied coronal magnetohydrostatic equilibrium     

J. P. Melville  A. W. Hood  E. R. Priest 《Solar physics》1986,105(2):291-306

An energy method is used to determine a condition for local instability of field lines in magnetohydrostatic equilibrium which are rooted in the photosphere. The particular equilibrium studied is isothermal and two-dimensional and may model a coronal arcade of loops where variations along the axis of the arcade are weak enough to be ignorable. If line tying conditions are modelled by perturbations that vanish on the photosphere, then, when the field is unsheared, the condition for stability is necessary and sufficient. However, when the axial field component is non-zero, so that the field is sheared, the stability condition is only sufficient.It is found that when < 0.34 the equilibrium is stable. When = 0.34 a magnetic neutral line appears at the photosphere and it is marginally stable. When > 0.34 a magnetic island is present and all the field lines inside the island are unstable as well as some beyond it. As increases, the size of the island and the extent of unstable field lines increase. The effect of the instability is likely to be to create small-scale filamentation in the solar corona and to enhance the global transport coefficients.  相似文献   

The Phase Space Structure Around L4 in the Restricted Three-Body Problem     

Zsolt Sándor  Bálint Érdi  Christos Efthymiopoulos 《Celestial Mechanics and Dynamical Astronomy》2000,78(1-4):113-123

The phase space structure around L ₄ in the restricted three-body problem is investigated. The connection between the long period family emanating from L ₄ and the very complex structure of the stability region is shown by using the method of Poincarés surface of section. The zero initial velocity stability region around L ₄ is determined by using a method based on the calculation of finite-time Lyapunov characteristic numbers. It is shown that the boundary of the stability region in the configuration space is formed by orbits suffering slow chaotic diffusion.  相似文献   

The post-main sequence evolution of a star of 20M ⊙ to core helium exhaustion     

S. R. Sreenivasan  K. E. Ziebarth 《Astrophysics and Space Science》1974,30(1):57-70

An evolutionary model of a Population I star of 20M and of compsitionX=0.70;Y=0.28, beyond the main sequence and up to core helium exhaustion is reported. Calculations were carried out to determine the effect of semi-convection using a method of mixing considered physically more appropriate than previous methods. Both the density as wel as the temperature stability criteria were employed in parallel calculations and reasons are advanced to prefer the temperature criterion. The results of the model calculations reported here underline the importance of the proper choice of the stability criterion and an appropriate mixing-scheme. In addition it is demonstrated that the loop phenomenon seen in the helium burning evolution of less massive stars is either absent or very unpronounced at 20M .  相似文献   

On the accuracy in the numerical solution of theN-body problem     

P. E. Zadunaisky 《Celestial Mechanics and Dynamical Astronomy》1979,20(3):209-230

There exist several widely used methods that give a qualitative estimation of the accuracy of the results in the numerical solution of theN-body problem. The reverse and closure tests are examined here critically. The author has developed a method for the estimation of global errors propagated in the numerical solution of ordinary and partial differential equations that has proven to be rather efficient in numerous cases (see P. E. Zadunaisky [17]). Applications of the method to several cases of theN-body problem are presently made and the advantages and limitations of the method are shown in a set of examples.  相似文献   

Self-consistent solutions of the semi-classical Einstein equations with cosmological constant and perfect fluid     

Luis P. Chimento  Norberto A. Zuccalá 《Astrophysics and Space Science》1993,201(2):341-345

Exact solutions of the semi-classical Einstein equations with cosmological constant for conformally invariant free quantum fields in a spatially flat Robertson-Walker metric are found when a classical perfect fluid is present. The stability of the asymptotically Friedmann-de Sitter solutions is studied. The formers are found to be stable if < 0, while the stability of the latter depends of the signs of , and A.Fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas.Supported by scholarship of the Universidad de Buenos Aires.  相似文献   

Parameter values for stable low-inclination periodic motion in the restricted three-body problem with oblateness     

E.A. Perdios 《Astrophysics and Space Science》2001,278(4):405-407

The known intervals of possible stability, on the mgr-axis, of basicfamilies of 3D periodic orbits in the restricted three-body problem areextended into -A₁ regions for oblate larger primary, A ₁ beingthe oblateness coefficient. Eight regions, corresponding to the basicstable bifurcation orbits l1v, l1v, l2v, l3v, m1v, m1v,m2v, i1v are determined and related branching 3D periodic orbits arecomputed systematically and tested for stability. The regions for l1v,m1v and m2v survive the test emerging as the regions allowing thesimplest types of stable low inclination 3D motion. For l1v, l2v,l3v, m1v and m2v oblateness seems to have a stabilising effect,while stability of i1v survives only for a very small range of A ₁values.  相似文献   

Kink instability of solar coronal loops as the cause of solar flares     

A. W. Hood  E. R. Priest 《Solar physics》1979,64(2):303-321

Solar coronal loops are observed to be remarkably stable structures. A magnetohydrodynamic stability analysis of a model loop by the energy method suggests that the main reason for stability is the fact that the ends of the loop are anchored in the dense photosphere. In addition to such line-tying, the effect of a radial pressure gradient is incorporated in the analysis.Two-ribbon flares follow the eruption of an active region filament, which may lie along a magnetic flux tube. It is suggested that the eruption is caused by the kink instability, which sets in when the amount of magnetic twist in the flux tube exceeds a critical value. This value depends on the aspect ratio of the loop, the ratio of the plasma to magnetic pressure and the detailed transverse magnetic structure. For a force-free field of uniform twist the critical twist is 3.3, and for other fields it is typically between 2 and 6. Occasionally active region loops may become unstable and give rise to small loop flares, which may also be a result of the kink instability.  相似文献   

Analytical investigation of non-linear stability of the Lagrangian pointL 4 around the commensurability 1:2     

Johannes Hagel 《Celestial Mechanics and Dynamical Astronomy》1995,63(2):205-225

The problem of stability of the Lagrangian pointL ₄ in the circular restricted problem of three bodies is investigated close to the 1 : 2 commensurability of the long and short period libration. By stability we define boundedness of the solution for a given initial finite displacement from the equilibrium point as function of the mass parameter close to the commensurability. A rigorous treatment close to the resonance condition is possible using a transformation that diagonalizes the matrix related to the linear part of the equations of motion. The so obtained equations are further transformed to action angle type variables. Then using an isolated resonance approach, only the slowly varying terms are kept in the equations and two independent isolating first integrals can be found. These integrals finally enable us to solve the stability problem in an exact way. The so obtained results are compared to numeric integration of the equations of motion and are found to be in perfect agreement.  相似文献   

Mass ratios of three bodies for stable low-inclination three-dimensional periodic motion     

E. Perodios  V. V. Markellos 《Astrophysics and Space Science》1992,192(2):291-297

The intervals of possible stability, on the -axis, of the basic families of three-dimensional periodie motions of the restricted three-body problem (determined in an earlier paper) are extended into regions of the -m ₃ parameter space of the general three-body problem. Sample three-dimensional periodic motions corresponding to these regions are computed and tested for stability. Six regions, corresponding to the vertical-critical orbitsl1v, m1v,m2v, andilv, survive this preliminary stability test-therefore, emerging as the mass parameters regions allowing the simplest types of stable low inclination three-dimensional motion of three massive bodies.  相似文献   

Stability of planar oscillations of a satellite in an elliptic orbit     

V. A. Zlatoustov  A. P. Markeev 《Celestial Mechanics and Dynamical Astronomy》1973,7(1):31-45

A problem of stability of odd 2-periodic oscillations of a satellite in the plane of an elliptic orbit of arbitrary eccentricity is considered. The motion is supposed to be only under the influence of gravitational torques.Stability of plane oscillations was investigated earlier (Zlatoustovet al., 1964) in linear approximation. In the present paper a problem of stability is solved in the non-linear mode. Terms up to the forth order inclusive are taken into consideration in expansion of Hamiltonian in a series.It is shown that necessary conditions of stability obtained in linear approximation coincide with sufficient conditions for almost all values of parameters ande (inertial characteristics of the satellite and eccentricity of the orbit). Exceptions represent either values of the parameters ,e when a problem of stability cannot be solved in a strict manner by non-linear approximation under consideration, or values of the parameters which correspond to resonances of the third and fourth orders. At the resonance of the third order oscillations are unstable, but at the resonance of the fourth order both unstability and stability of the satellite's oscillations take place depending on the values of the parameters ,e.  相似文献   

Resistive ballooning modes in line-tied coronal fields     

M. Velli  A. W. Hood 《Solar physics》1987,109(2):351-354

The resistive stability of coronal loops to perturbations with short wavelength across the magnetic field is analysed, taking full account of the line tying effect due to the presence of the photosphere. The results presented are similar to those previously obtained for arcades: configurations with a pressure profile decreasing with distance from the loop axis at some point are found to be always unstable, the growth rate increasing monotonically with the wavenumber (n) and scaling approximately as (n ² D _r)^1/3 in the limit of large n.  相似文献   

Rapidly rotating supermassive stars in the first post-Newtonian approximation to general relativity     

G. G. Fahlman  S. P. S. Anand 《Astrophysics and Space Science》1971,12(1):83-97

The structure and stability of rapidly uniformly rotating supermassive stars is investigated using the full post-Newtonian equations of hydrodynamics. The standard model of a supermassive star, a polytrope of index three, is adopted. All rotation terms up to and including those of order ⁴, where is the angular velocity, are retained. The effects of rotation and post-Newtonian gravitation on the classical configuration are explicitly evaluated and shown to be very small. The dynamical stability of the model is treated by using the binding energy approach. The most massive objects are found to be dynamically unstable when =1/c ².p _c / _c 2.2 × 10^–3, wherep _c and _c are the central pressure and density, respectively. Hence, the higher-order terms considered in this analysis do not appreciably alter the previously known stability limits.The maximum mass that can be stabilized by uniform rotation in the hydrogen-burning phase is found to be 2.9×10⁶ M , whereM is the solar mass. The corresponding nuclear-generated luminosity of 6×10⁴⁴ erg/sec^–1 is too small for the model to be applicable to the quasi-stellar objects. The maximum kinetic energy of a uniformly rotating supermassive star is found to be 3×10^–5 Mc ², whereM is the mass of the star. Masses in excess of 10¹⁰ M are required if an adequate store of kinetic energy is to be made available to a pulsar like QSO. However such large masses have rotation periods in excess of 100 yr and thus could not account for any short term periodic variability. It is concluded then that the uniformly rotating supermassive star does not provide a suitable base for a model of a QSO.  相似文献   

On the coupling of lunisolar resonances for Earth satellite orbits     

SŁawomir Breiter 《Celestial Mechanics and Dynamical Astronomy》2001,80(1):1-20

The resonance C1 occurs when the longitude of the perigee measured from the equinox becomes a slow angle in the doubly averaged equations of motion. This resonance is one of the critical inclination family with I 46°. For prograde Earth satellite orbits, up to five critical points can be identified. Only simple pitchfork bifurcations occur for the single resonance C1. A two degrees of freedom system is studied to check how a coupling of two lunisolar resonances affects the results furnished by the analysis of an isolated resonance case. In the system with two critical angles (g+h and h,+2 , seven types of critical points have been identified. The critical points arise and change their stability through 11 bifurcations. If the initial conditions are selected close to the critical points, the system becomes chaotic as shown in Poincaré maps.  相似文献