Long-Term Pulses of Dynamic Coupling Between Solar Hemispheres

The north–south (N–S) asymmetry of solar activity is a known statistical phenomenon, but its significance is difficult to prove or to explain theoretically. Here we consider each solar hemisphere as a separate dynamical system connected with the other hemisphere via an unknown coupling parameter. We use a nonlinear dynamics approach to calculate the scale-dependent conditional dispersion (CD) of sunspots between hemispheres. Using daily Greenwich sunspot areas, we calculate the Neumann and Pearson chi-squared distances between CDs as indices showing the direction of coupling. We introduce an additional index of synchronization that shows the strength of coupling and allows us to distinguish between complete synchronization and independency of hemispheres. All indices are evaluated in a four-year moving window showing the evolution of coupling between hemispheres. We find that the driver-response interrelation changes between hemispheres have a few pulses during 130 years of Greenwich data with an at least 40-year-long period of unidirectional coupling. These sharp nearly simultaneous pulses of all causality indices are found at the decay of some 11-year cycles. The pulse rate of this new phenomenon of dynamic coupling is irregular: although the first two pulses repeat after the 22-year Hale cycles, the last two pulses repeat after three and four 11-year cycles, respectively. The last pulse occurs at the decay phase of Cycle 23, which means that the next pulse will likely appear during the decay of the future Cycle 25 or later. This new phenomenon of dynamic coupling reveals additional constraints for understanding and modeling the long-term behavior of solar activity cycles.     

Mode coupling due to twisting of magnetic field lines

A new approach to the theory of mode coupling in an inhomogeneous, birefringent medium is used to treat mode coupling in a magnetized plasma with a twisted magnetic field. The twist introduces a resonance, corresponding to the rate of twisting being equal to the rate of generalized Faraday rotation. When this resonance occurs it introduces a new regime of strong mode coupling. The implications of this regime are discussed in connection with the long-standing problem in solar radiophysics that mode coupling appears to be stronger than theory implies, but no obvious resolution of the problem is found.     

A theoretically derived energy coupling function for the magnetosphere

The energy coupling function between the solar wind and the magnetosphere can be obtained for two extreme situations, in which the magnetospheric geometry is determined primarily by either (i) the interplanetary magnetic field, or (ii) the solar wind pressure. In this paper, we obtained an expression for the energy coupling function by assuming a simple interpermeation of the interplanetary and geomagnetic fields. Two important quantities in this case are the potential difference between the two neutral points and the amount of open flux. From these two overall quantities, the voltage and the current of the magnetospheric dynamo are calculated. The dynamo power output represents the rate at which energy is transferred from the solar wind to the magnetosphere. The derived functional dependence on the interplanetary conditions provides a theoretical basis for the energy coupling function previously deduced from observations.     

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.     

A core-mantle interaction in the rotation of the Earth

Effects of an interaction between the mantle and the core of the Earth on its rotational motion are investigated. Assuming that the Earth consists of a rigid mantle and a rigid core with a frictional coupling and a kind of inertial coupling between them, the equations of motion are derived, and they are solved in a close approximation. The solution gives the expressions for the precession, the nutation, the secular changes in the obliquity and the rotational speed, the polar motion and so on as functions of the magnitudes of these forces. A numerical estimation shows that the effect of the friction on the amplitude and phase of the nutation is small for a reasonable intensity of the friction while inertial coupling force has a decisive influence on the amplitude, and an appropriately chosen value of the latter force gives a nutation which closely agrees with observations. It is also indicated that this torque remarkably lessens the rates of the secular changes in the obliquity and the rotational speed. The possibility of a periodical change in the amplitude of the polar motion is suggested as a result of the interaction between the two consituents.     

磁化黑洞吸积盘的演化及放能效率

采用等效电路模型讨论了两种不同类型的磁场对黑洞的旋转能量和角动量的提取机制；Blandford-Znajek(BZ)过程和磁耦合过程，在研究磁化吸积盘中心黑洞自转参量演化特征的基础上，详细比较了纯吸积过程，BZ过程和磁耦合过程对黑洞吸积盘放能效率的贡献，结果表明，磁耦合过程是提取黑洞旋转能量重要的新机制，其放能效率与BZ过程几乎相等，在黑洞自转不是特别大的情况，纯吸积过程的放能效率高于BZ过程和磁耦合过程的放能效率，但是当黑洞自转接近极端Kerr黑洞的自转状态时，放能效率主要由BZ过程和磁耦合过程贡献。     

Magnetorotational Instability in Weakly Ionised, Stratified Accretion Discs

We present a linear analysis of the vertical structure and growth of the magnetorotational instability in weakly ionised, stratified accretion discs. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and assumed constant with height. The Hall effect causes the perturbations to grow faster and act over a much more extended section of the disc, when the magnetic coupling is low. As a result, significant accretion can occur closer to the midplane, despite the weak magnetic coupling, because of the high column density of the fluid. This is an interesting alternative to the commonly held view that accretion is relevant mainly in the surface regions of discs, which have a better coupling, but a much lower fluid density.     

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.     

The energy coupling function and the power generated by the solar wind-magnetosphere dynamo

A solar wind parameter ε, known as the energy coupling function, has been shown to correlate with the power consumption in the magnetosphere. It is shown in the present paper that the parameter ε can be identified semi-quantitatively as the dynamo power delivered from the solar wind to an open magnetosphere. This identification not only provides a theoretical basis for the energy coupling function, but also constitutes an observational verification of the solar wind-magnetosphere dynamo along the magnetotail. Moreover, one can now conclude that a substorm results when the dynamo power exceeds 10₁₈ ergs ^?1.     

Magnetorotational instability in stratified, weakly ionized accretion discs

We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionized accretion discs, such as protostellar and quiescent dwarf novae systems. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and is assumed to be constant with height.
We obtained solutions for the structure and growth rate of global unstable modes for different conductivity regimes, strengths of the initial magnetic field and coupling between ionized and neutral components of the fluid. The envelopes of short-wavelength perturbations are determined by the action of competing local growth rates at different heights, driven by the vertical stratification of the disc. Ambipolar diffusion perturbations peak consistently higher above the midplane than modes including Hall conductivity. For weak coupling, perturbations including the Hall effect grow faster and act over a more extended cross-section of the disc than those obtained using the ambipolar diffusion approximation.
Finally, we derived an approximate criterion for when Hall diffusion determines the growth of the magnetorotational instability. This is satisfied over a wide range of radii in protostellar discs, reducing the extent of the magnetic 'dead zone'. Even if the magnetic coupling is weak, significant accretion may occur close to the midplane, rather than in the surface regions of weakly ionized discs.     

A Maunder Minimum Scenario Based on Cross-Hemispheric Coupling and Intermittency

A novel scenario for Maunder minimum-like grand minima epochs of reduced solar activity is proposed, based on diffusive coupling between both solar hemispheres, each susceptible to stochastically-driven intermittent behavior. After introducing cross-hemispheric coupling into a well-validated reduced model of the solar cycle based on the Babcock–Leighton mechanism for poloidal field regeneration, simulations are presented demonstrating that even weak coupling can lead to a high degree of synchronicity between the two hemispheres. This is in qualitative agreement with the similar onset and recovery times of sunspot activity at and around the Maunder minimum. Moreover, even weak coupling manages to greatly reduce the frequency and duration of quiescent episodes, again in qualitative agreement with the relative paucity of grand minima in the sunspot and radioisotope records.     

Time-resolved studies of hypervelocity vertical impacts into porous particulate targets: Effects of projectile density on early-time coupling and crater growth

The depth and duration of energy and momentum coupling in an impact shapes the formation of the crater. The earliest stages of crater growth (when the projectile transfers its energy and momentum to the target) are unrecoverable when the event is described by late stage parameters, which collapse the initial conditions of the impact into a singular point in time and space. During the coupling phase, the details of the impact are mapped into the ejecta flow field. In this experimental study, we present new experimental and computational measurements of the ejecta distribution and crater growth extending from early times into main-stage ballistic flow for hypervelocity impacts over a range of projectile densities. Specifically, we assess the effect of projectile density on coupling depth and location in porous particulate (sand) targets. A non-invasive high-speed imaging technique is employed to capture the velocity of individual ejecta particles very early in the cratering event as a function of both time and launch position. These data reveal that the effects of early-stage coupling, such as non-constant ejection angles, manifest not only in early-time behavior but also extend to main-stage crater growth. Time-resolved comparisons with hydrocode calculations provide both benchmarking and insight into the parameters controlling the ejection process. Measurements of the launch position and metrics for the transient diameter to depth ratio as a function of time demonstrate non-proportional crater growth throughout much of excavation. Low-density projectiles couple closer to the surface, thereby leading to lower ejection angles and larger effective diameter to depth ratios. These results have implications for the ballistic emplacement of ejecta on planetary surfaces, and are essential to interpreting temporally resolved data from impact missions.     

Interference coupling analysis based on a hybrid method: application to a radio telescope system

Working in a way that passively receives electromagnetic radiation from a celestial body,a radio telescope can be easily disturbed by external radio frequency interference as well as electromagnetic interference generated by electric and electronic components operating at the telescope site.A quantitative analysis of these interferences must be taken into account carefully for further electromagnetic protection of the radio telescope. In this paper, based on electromagnetic topology theory, a hybrid method that combines the Baum-Liu-Tesche(BLT) equation and transfer function is proposed.In this method, the coupling path of the radio telescope is divided into strong coupling and weak coupling sub-paths, and the coupling intensity criterion is proposed by analyzing the conditions in which the BLT equation simplifies to a transfer function. According to the coupling intensity criterion, the topological model of a typical radio telescope system is established. The proposed method is used to solve the interference response of the radio telescope system by analyzing subsystems with different coupling modes separately and then integrating the responses of the subsystems as the response of the entire system. The validity of the proposed method is verified numerically. The results indicate that the proposed method, compared with the direct solving method, reduces the difficulty and improves the efficiency of interference prediction.     

Influence of a uniform coronal magnetic field on solar p modes: coupling to slow resonant MHD waves

The influence of a constant coronal magnetic field on solar global oscillations is investigated for a simple planar equilibrium model. The model consists of an atmosphere with a constant horizontal magnetic field and a constant sound speed, on top of an adiabatic interior having a linear temperature profile. The focus is on the possible resonant coupling of global solar oscillation modes to local slow continuum modes of the atmosphere and the consequent damping of the global oscillations. In order to avoid Alfvén resonances, the analysis is restricted to propagation parallel to the coronal magnetic field. Parallel propagating oscillation modes in this equilibrium model have already been studied by Evans and Roberts (1990). However, they avoided the resonant coupling to slow continuum modes by a special choice of the temperature profile. The physical process of resonant absorption of the acoustic modes with frequency in the cusp continuum is mathematically completely described by the ideal MHD differential equations which for this particular equilibrium model reduce to the hypergeometric differential equation. The resonant layer is correctly dealt with in ideal MHD by a proper treatment of the logarithmical branch cut of the hypergeometric function. The result of the resonant coupling with cusp waves is twofold. The eigenfrequencies become complex and the real part of the frequency is shifted. The shift of the real part of the frequency is not negligible and within the limit of observational accuracy. This indicates that resonant interactions should definitely be taken into account when calculating the frequencies of the global solar oscillations.     

Jet disc coupling in black hole binaries

In the last decade multi-wavelength observations have demonstrated the importance of jets in the energy output of accreting black hole binaries. The observed correlations between the presence of a jet and the state of the accretion flow provide important information on the coupling between accretion and ejection processes. After a brief review of the properties of black hole binaries, I illustrate the connection between accretion and ejection through two particularly interesting examples. First, an INTEGRAL observation of Cygnus X-1 during a ‘mini-’ state transition reveals disc jet coupling on time scales of orders of hours. Second, the black hole XTEJ1118+480 shows complex correlations between the X-ray and optical emission. Those correlations are interpreted in terms of coupling between disc and jet on time scales of seconds or less. Those observations are discussed in the framework of current models.     

Lagrange’s planetary equations for the motion of electrostatically charged spacecraft

A spacecraft that generates an electrostatic charge on its surface in a planetary magnetic field will be subject to a perturbative Lorentz force. Active modulation of the surface charge can take advantage of this electromagnetic perturbation to modify or to do work on the spacecraft’s orbit. Lagrange’s planetary equations are derived using the Lorentz force as the perturbation on a Keplerian orbit, incorporating orbital inclination and true anomaly for the first time for an electrostatically charged vehicle. The planetary equations reveal that orbital inclination is a second-order effect on the perturbation, explaining results found in earlier studies through numerical integration. All of the orbital elements are coupled, but the coupling notably does not depend on the magnitude of the electrostatic charge or on the strength of the magnetic field. Analytical expressions that characterize this coupling are tested with a propellantless escape example at Jupiter. A closed-form solution exists that constrains the set of equatorial orbits for which planetary escape is possible, and a sufficient condition is identified for escape from inclined orbits. The analytical solutions agree with results from the numerically integrated equations of motion to within a fraction of a percent.     

On Magnetic Coupling Between the Two Hemispheres in Solar Dynamo Models

By introducing an asymmetry between the two hemispheres, we study whether the solar dynamo solutions in the two hemispheres remain coupled with each other. Our calculations are based on the solar dynamo code SURYA, which incorporates the helioseismically-determined solar-rotation profile, a Babcock–Leighton α effect concentrated near the surface, and a meridional circulation. When the magnetic coupling between the hemispheres is enhanced by either increasing the diffusion or introducing an α effect distributed throughout the convection zone, we find that the solutions in the two hemispheres evolve together with a single period even when we make the meridional circulation or the α effect different in the two hemispheres. On the other hand, when the hemispheric coupling is weaker for other values of parameters, an asymmetry between the hemispheres can make solutions in the two hemispheres evolve independently with different periods.     

Modulation of energetic particle fluxes due to long-period geomagnetic oscillations

Mechanism of flux modulations of energetic protons and electrons, associated with the long-period geomagnetic pulsations in the outer magnetosphere, is examined theoretically. In the first part, a linear perturbation theory of the guiding centre distribution function averaged over the bounce phase of an interacting particle is developed for the case of the three-dimensional magnetic oscillations with a sufficiently long period compared with the bounce time of the particle. Secondly we extend the formulation to include some effects of the perturbed drift orbit on the particle distribution such as the particle trapping in the wave field and the phase bunching process. The latter is important for the interaction with the coupling Alfvén mode of magnetic oscillations. Applying these results together with the basic characteristics of the coupling hydromagnetic oscillations in a non-uniform plasma, we discuss the possibilities for the observed particle flux modulations in two different cases, separately, i.e. flux oscillations due to the compressional magnetic perturbation and those from the nearly transverse magnetic variations.