Dynamics of Enceladus and Dione inside the 2:1 mean-motion resonance under tidal dissipation

In a previous work (Callegari and Yokoyama, Celest. Mech. Dyn. Astr. 98:5–30, 2007), the main features of the motion of the pair Enceladus–Dione were analyzed in the frozen regime, i.e., without considering the tidal evolution. Here, the results of a great deal of numerical simulations of a pair of satellites similar to Enceladus and Dione crossing the 2:1 mean-motion resonance are shown. The resonance crossing is modeled with a linear tidal theory, considering a two-degrees-of-freedom model written in the framework of the general three-body planar problem. The main regimes of motion of the system during the passage through resonance are studied in detail. We discuss our results comparing them with classical scenarios of tidal evolution of the system. We show new scenarios of evolution of the Enceladus–Dione system through resonance not shown in previous approaches of the problem.     

The coupling resonance of torsional alfven wave and fast wave in coronal loops

The method of Orthogonal Function Series Expansion (OFSE) is generalized and applied to the study of the evolution of the coupling of nondissipative torsional Alfven wave and fast wave in coronal loops. Using this method, the intrinsic angular frequency of the overall wave mode can be described mathematically and that of the Alfven waves along the magnetic lines in the coronal loop during the coupling of the Alfven and fast waves can be analyzed both theoretically and numerically. Also with this method, the relation between the coupling driven term and the Alfven wave resonance may be analyzed. Results of computation reveal the place of appearance of coupling resonance as well as the characteristics of the amplitudes of the Alfven and fast waves. As found by the calculations, if the footpoint driven angular frequency is not equal to the intrinsic angular frequency of the overall wave mode of the coronal loop and when a δ section appears at the place of coupled resonance, the radial gradient of the fast wave's amplitude is quite large. Sometimes it approximates to a discontinuity, and this is extremely favorable for the dissipation of the fast wave. If the footpoint driven angular frequency is equal to the intrinsic angular frequency of the overall wave mode and when a δ section occurs in the Alfven wave amplitude, abundant small-scale structures appear in the radial direction. Then the location of resonance approximately becomes a discontinuity, very favorable to the dissipation of the Alfven wave.     

Resonance trapping and evolution of particles subject to poynting-robertson drag: Adiabatic and non-adiabatic approaches

The problem of resonance trapping for particles subject to Poynting-Robertson drag is approached initially from an adiabatic regime theory. A simplified Hamiltonian system is presented for simple eccentricity-type resonances up to order 3, and expressions related to the trapping process are deduced. The fast dissipation provoked by Poynting-Robertson leads to the employment of a numerical approach for the computation of resonance capture probabilities, for particles in the size range of practical importance. Some aspects of the dynamical evolution of a particle after capture are noticed from results of numerical integrations. Analytical methods are used in order to confirm the numerical results.     

Polarization transfer in a pulsar magnetosphere

Propagation of radio waves in the ultrarelativistic magnetized electron–positron plasma of a pulsar magnetosphere is considered. The polarization state of the original natural waves is found to vary markedly on account of the wave mode coupling and cyclotron absorption. The change is most pronounced when the regions of mode coupling and cyclotron resonance approximately coincide. In cases when the wave mode coupling occurs above and below the resonance region, the resultant polarization appears essentially distinct. The main result of the paper is that in the former case the polarization modes become non-orthogonal. The analytical treatment of the equations of polarization transfer is accompanied by numerical calculations. The observational consequences of polarization evolution in pulsar plasma are discussed as well.     

The propagation of electron fluxes in the solar corona

The problem of energetic electron flux propagation in the solar coronal plasma is solved with due regard for the influence of the oppositely directed neutralizing cold electron flux and the kinematic escape effect of the electrons with different velocities. It is shown that the flux electrons are accelerated in the process of propagation, thus forming a beam, whose velocity is constant on rather long time scales. Three regimes can be realized in this case. In the first regime, plasma waves do not have time to be excited because they escape rapidly from resonance with the beam. In the second regime, waves are excited, but the beam does not have time to relax. The third regime is quasi-linear relaxation.The generation of solar type III radio bursts in the second regime of electron flux propagation is considered.     

Energy balance in current sheets: From Petschek to gravity driven reconnection?

It has been shown earlier that energy balance processes play a very important role in the determination of the reconnection regime in the central diffusive region of a steady Petschek flow (usually considered elsewhere as isothermal and incompressible): as a consequence of the plasma thermal properties, abrupt transitions in the reconnection regime may occur for special external conditions. The regime becomes then a dynamical one, and it was suggested that onset of plasma microturbulence may result and act as a primary triggering mechanism in solar flares.In this paper we will reexamine the problem of onset of such dynamical transition and conclude that plasma microturbulence does not appear in a straightforward way. However it is possible that the canonical Petschek regime may evolute into a new one in which the dissipative sheet is no longer infinitesimal with respect to the dimensions of the structure, and in which gravity plays an important role. Flare triggering, if related to the reconnection regime, must then proceed by more complex processes, possibly related to tearing mode dynamics, or to more global properties of the magnetic structure of the active region.     

A numerical investigation of coorbital stability and libration in three dimensions

Motivated by the dynamics of resonance capture, we study numerically the coorbital resonance for inclination \(0\le I\le 180^\circ \) in the circular restricted three-body problem. We examine the similarities and differences between planar and three dimensional coorbital resonance capture and seek their origin in the stability of coorbital motion at arbitrary inclination. After we present stability maps of the planar prograde and retrograde coorbital resonances, we characterize the new coorbital modes in three dimensions. We see that retrograde mode I (R1) and mode II (R2) persist as we change the relative inclination, while retrograde mode III (R3) seems to exist only in the planar problem. A new coorbital mode (R4) appears in 3D which is a retrograde analogue to an horseshoe-orbit. The Kozai–Lidov resonance is active for retrograde orbits as well as prograde orbits and plays a key role in coorbital resonance capture. Stable coorbital modes exist at all inclinations, including retrograde and polar obits. This result confirms the robustness the coorbital resonance at large inclination and encourages the search for retrograde coorbital companions of the solar system’s planets.     

Shear flow driven counter rotating vortices in an inhomogeneous dusty magnetoplasma

The coupling of Shukla-Varma (SV) and convective cell modes is discussed in the presence of non-Boltzmannian electron response and parallel equilibrium shear flow. In the linear case, a new dispersion relation is derived and analyzed. It is found that the coupled SV and convective cell modes destabilize in the presence of electron shear flow. On the other hand, in the nonlinear regime, it is shown that Shukla-Varma mode driven counter rotating vortices can be formed for the system under consideration. It is found that these vortices move slowly by comparison with the ion acoustic or electron drift-wave driven counter rotating vortices. The relevance of the present investigation with regard to space plasmas is also pointed out.     

The plasma radiation of flare kernels

We survey the mathematics of non-linear Hamiltonian oscillations with emphasis being laid on the more recently discovered Kolmogorov instability. In the context of radial adiabatic oscillations of stars this formalism predicts a Kolmogorov instability even at low oscillation energies, provided that sufficiently high linear asymptotic modes have been excited. Numerical analysis confirms the occurrence of this instability. It is found to show up already among the lowest order modes, although high surface amplitudes are then required (¦δr¦/R ～ 0.5 for an unstable fundamental mode - first harmonic coupling). On the basis of numerical evidence we conjecture that in the Kolmogorov unstable regime the enhanced coupling due to internal resonance effects leads to an equipartition of energy over all interacting degrees of freedom. We also indicate that the power spectrum of such oscillations is expected to display two components: A very broad band of overlapping pseudo-linear frequency peaks spread out over the asymptotic range, and a strictly non-linear l/f-noise type component close to the frequency origin. It is finally argued that the Kolmogorov instability is likely to occur among non-linearly coupled non-radial stellar modes at a surface amplitude much lower than in the radial case. This lends support to the view that this instability might be operative among the solar oscillations.     

Unstable non-radial modes in radial pulsators: theory and an example

We study the possibility of the excitation of non-radial oscillations in classical pulsating stars. The stability of an RR Lyrae model is examined through non-adiabatic non-radial calculations. We also explore stability in the presence of non-linear coupling between radial and non-radial modes of nearly identical frequency.   In our model, a large number of unstable low-degree (ℓ = 1,2) modes have frequencies in the vicinity of unstable radial mode frequencies. The growth rates of such modes, however, are considerably smaller than those of the radial modes. We also recover an earlier result that at higher degrees (ℓ = 6–12) there are modes trapped in the envelope with growth rates similar to those of radial modes.   Subsequently, monomode radial pulsation of this model is considered. The destabilizing effect of the 1:1 resonance between the radial mode and nearby non-radial modes of low degrees is studied, with the assumption that the excited radial mode saturates the linear instability of all other modes. The instability depends on the radial mode amplitude, the frequency difference, the damping rate of the non-radial mode, and the strength of the non-linear coupling between the modes considered. At the pulsation amplitudes typical for RR Lyrae stars, the instability of the monomode radial pulsation and the concomitant resonant excitation of some non-radial oscillation modes is found to be very likely.     

On the spatial structure and dispersion of slow magnetosonic modes coupled with Alfvén modes in planetary magnetospheres due to field line curvature

The structure of the slow mode coupled with Alfvén mode in the axially symmetric magnetosphere is studied in the paper. Due to the coupling, the slow magnetosonic wave gets dispersion across magnetic shells and becomes not strictly guided. The slow mode is found to be captured between the resonant and cutoff surfaces, where the wave vector radial component goes to infinity and to zero, accordingly. The resonant surface is farther from the Earth than the cutoff surface. The slow mode resonance frequency is much lower than the Alfvén resonance frequency due to small value of the sound velocity near the equator. The maximum of the slow mode amplitude expressed in terms of the parallel magnetic field is concentrated near the equator, but expressed in hydromagnetic terms is concentrated near the ionospheres.     

Long Term Evolution of Solar Meridional Circulation and Phase Synchronization Viewed Through a Symmetrical Kuramoto Model

The solar-cycle oscillations of the toroidal and poloidal components of the solar magnetic field in the northern solar hemisphere have a persistent phase difference of about \(\pi \). We propose a symmetrical Kuramoto model with three coupled oscillators as a simple way to understand this anti-synchronization. We solve an inverse problem and reconstruct natural frequencies of the top and bottom oscillators under the conditions of a constant coupling strength and a non-delayed coupling. These natural frequencies are associated with angular velocities of the meridional flow circulation near the solar surface and in the deep layer of the solar convection zone. A relationship between our reconstructions of the shallow and the deep meridional flow speed during recent Solar Cycles 21?–?23 is in agreement with estimates obtained in helioseismology and flux-transport dynamo modeling. The reconstructed top oscillator speed presents significant solar-cycle like variations that agree with recent helioseismical reconstructions. The evolution of reconstructed natural frequencies strongly depends on the coupling strength. We find two stable regimes in the case of strong coupling with a change of regime during anomalous solar cycles. We see the onset of a new transition in Solar Cycle 24. We estimate the admitted range of coupling values and find evidence of cross-equatorial coupling between solar hemispheres not accounted for by the model.     

Solar p modes of high degree l: coupling by differential rotation

Accurate measurements of solar p-mode frequencies and frequency splittings at high degree l require an adequate theoretical knowledge of the effects of mode coupling, induced by the variation with latitude of the angular velocity of the solar internal rotation. Earlier results for expansion coefficients of composite solutions (coupling coefficients) are due to Woodard. In this paper, the analysis is extended to allow for the dependence of the differential rotation on depth, and the result is expressed in terms of measurable quantities (the rotational splitting coefficients), which makes it convenient for diagnostic purposes. The analysis is based on the approach of quasi-degenerate perturbation theory, and is extended further to address possible effects of mode coupling in the observational line profiles. It is shown, using approximations applicable at high degree l , that the expected line profiles of composite modes in the observational power spectra are not distorted by mode coupling.     

Drift anisotropy instability of a finite-β magnetospheric plasma

A unified theory of low frequency instabilities in a two component (cold and hot) finite-β magnetospheric plasma is suggested. It is shown that the low frequency oscillations comprise two wave modes : compressional Alfvén and drift mirror mode. No significant coupling between them is found in the long-wave approximation. Instabilities due to spontaneous excitation of these oscillations are considered. It is found that the temperature anisotropy significantly influences the instability growth rate at low frequency. A new instability due to the temperature anisotropy and density gradient appears when the frequency of compressional Alfvén waves is close to the drift mirror mode frequency. The theoretical predictions are compared in detail with the Pc5 event of 27 October 1978 observed simultaneously by the GEOS 2 satellite and the STARE radar facility. It is shown that the experimental results can be interpreted in terms of a compressional Alfvén wave driven by the drift anisotropy instability.     

Flare SOL2012-07-06: On the Origin of the Circular Polarization Reversal Between 17 GHz and 34 GHz

The new generation of multiwavelength radioheliographs with high spatial resolution will employ microwave imaging spectropolarimetry to recover flare topology and plasma parameters in the flare sources and along the wave propagation paths. The recorded polarization depends on the emission mechanism and emission regime (optically thick or thin), the emitting particle properties, and propagation effects. Here, we report an unusual flare, SOL2012-07-06T01:37, whose optically thin gyrosynchrotron emission of the main source displays an apparently ordinary mode sense of polarization in contrast to the classical theory that favors the extraordinary mode. This flare produced copious nonthermal emission in hard X-rays and in high-frequency microwaves up to 80 GHz. It is found that the main flare source corresponds to an interaction site of two loops with greatly different sizes. The flare occurred in the central part of the solar disk, which allows reconstructing the magnetic field in the flare region using vector magnetogram data. We have investigated the three possible known reasons of the circular polarization sense reversal – mode coupling, positron contribution, and the effect of beamed angular distribution. We excluded polarization reversal due to contribution of positrons because there was no relevant response in the X-ray emission. We find that a beam-like electron distribution can produce the observed polarization behavior, but the source thermal density must be much higher than the estimate from to the X-ray data. We conclude that the apparent ordinary wave emission in the optically thin mode is due to radio wave propagation across the quasi-transverse (QT) layer. The abnormally high transition frequency (above 35 GHz) can be achieved reasonably low in the corona where the magnetic field value is high and transverse to the line of sight. This places the microwave source below this QT layer, i.e. very low in the corona.     

Mixing-length theory and the excitation of solar acoustic oscillations

The stability of radial solar acoustic oscillations is studied using a time-dependent formulation of mixing-length theory. Though the radiation field is treated somewhat simplistically with the Eddington approximation, and we appreciate that any coupling of the pulsation to the radiation field is important, for the lower frequency radial modes that have been computed this should not produce too serious an error. Instead, we have concentrated upon treating the coupling with convection as accurately as is currently possible with generalized mixing-length theory in order to learn something about its pertinence. Our principal conclusion is that, according to this theory, solar radial acoustic oscillations are expected to be stable and generated by turbulence. Moreover, the theory predicts changes in mode frequency that may, in part, explain the discrepancy between solar observations and the adiabatic pulsation frequencies of theoretical models. We also compute the amplitudes of the modes using a theory of stochastic excitation. These are in good agreement with observed power spectra.     

Parametric resonance in a thin disc dynamo

The swing excitation or parametric resonance in dynamos is discussed. A simple example of the parametric resonance in a thin disc is considered by the use of Wiener integral methods. The additional growth rate of bisymmetric mode being controlled by the disc aspect ratio is shown to be relatively small and insufficient to explain the preferable generation of this mode in galaxies.     

Observations of mode coupling in the solar corona and bipolar noise storms

We review high-spatial-resolution observations of the Sun which reflect on the role of mode coupling in the solar corona, and present a number of new observations. We show that typically polarization inversion is seen at 5 GHz in active region sources near the solar limb, but not at 1.5 GHz. Although this is apparently in contradiction to the simplest form of mode coupling theory, in fact it remains consistent with current models for the active region emission. Microwave bursts show no strong evidence for polarization inversion. We discuss bipolar noise storm continuum emission in some detail, utilizing recent VLA observations at 327 MHz. We show that bipolar sources are common at 327 MHz. Further, the trailing component of the bipole is frequently stronger than the leading component, in apparent conflict with the leading-spot hypothesis. The observations indicate that at 327 MHz mode coupling is apparently strong at all mode-coupling layers in the solar corona. The 327 MHz observations require a much weaker magnetic field strength in the solar corona to explain this result than did earlier lower-frequency observations: maximum fields are 0.2 G. This is a much weaker field than is consistent with current coronal models.On leave from the Indian Institute for Astrophysics, Bangalore, India.     

Two-Way Orbits

This paper introduces a new set of compatible orbits called “Two-Way Orbits,” whose ground track path is a closed-loop trajectory that intersects at certain points with tangent intersections. The spacecraft passes over these tangent intersections once in a prograde mode and once in a retrograde mode. Motivations are found for the need to have simultaneous observations of the same target area in both Earth observation and reconnaissance systems. The general mathematical model to design a Two-Way Orbit is presented for the specific case where the tangent points are experienced at the orbit extremes, perigee and apogee. As for the general case, Two-Way Orbit conditions are formulated and numerically solved. Results show that, in general, Two-Way Orbits could be formed over any point on Earth. Since Two-Way Orbits use compatible orbits, the theory of Flower Constellations can be applied to them. Using these Two-Way Orbits, this paper also introduces the Two-Way Flower Constellations that have one spacecraft prograde and one retrograde passing simultaneously over the tangent intersection.     

A non-linear theory of vertical resonances in accretion discs

An important and widely neglected aspect of the interaction between an accretion disc and a massive companion with a coplanar orbit is the vertical component of the tidal force. As shown by Lubow, the response of the disc to vertical forcing is resonant at certain radii, at which a localized torque is exerted, and from which a compressive wave (p mode) may be emitted. Although these vertical resonances are weaker than the corresponding Lindblad resonances, the   m =2  inner vertical resonance in a binary star is typically located within the tidal truncation radius of a circumstellar disc.
In this paper I develop a general theory of vertical resonances, allowing for non-linearity of the response, and dissipation by radiative damping and turbulent viscosity. The problem is reduced to a universal, non-linear ordinary differential equation with two real parameters. Solutions of the complex non-linear Airy equation are presented to illustrate the non-linear saturation of the resonance and the effects of dissipation. It is argued that the   m =2  inner vertical resonance is unlikely to truncate the disc in cataclysmic variable stars, but contributes to angular momentum transport and produces a potentially observable non-axisymmetric structure.