The Flare-Energy Distributions Generated by Kink-Unstable Ensembles of Zero-Net-Current Coronal Loops

It has been proposed that the million-degree temperature of the corona is due to the combined effect of barely detectable energy releases, called nanoflares, that occur throughout the solar atmosphere. Unfortunately, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release; thus we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory; i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold.     

A viable mechanism for the production of energy in active galactic nuclei

It is suggested that a collapsing supermassive object, which acts as an ultra-high energy particle accelerator, is the precursor of an active galactic nucleus and that the gravitational energy released during the collapse of the object is locked in the quark-gluon plasma permeated by leptons into which the entire matter in the core of the object is converted as a result of the collapse. It is also pointed out that the collapse of the object to a space-time singularity is inhibited by Pauli's exclusion principle as well as by Heisenberg's uncertainty principle and that the object explodes, before it could collapse to a singularity, thereby releasing the enormous amount of energy locked in the quark-gluon plasma.     

The use of integrals in numerical integrations of theN-body problem

The numerical integration of systems of differential equations that possess integrals is often approached by using the integrals to reduce the number of degrees of freedom or by using the integrals as a partial check on the resulting solution, retaining the original number of degrees of freedom.Another use of the integrals is presented here. If the integrals have not been used to reduce the system, the solution of a numerical integration may be constrained to remain on the integral surfaces by a method that applies corrections to the solution at each integration step. The corrections are determined by using linearized forms of the integrals in a least-squares procedure.The results of an application of the method to numerical integrations of a gravitational system of 25-bodies are given. It is shown that by using the method to satisfy exactly the integrals of energy, angular momentum, and center of mass, a solution is obtained that is more accurate while using less time of calculation than if the integrals are not satisfied exactly. The relative accuracy is ascertained by forward and backward integrations of both the corrected and uncorrected solutions and by comparison with more accurate integrations using reduced step-sizes.     

Modèle d'éjection de matière des novae

We have found that the gas of the premaximum, diffuse-enhanced and orion systems is produced by the nova itself and is ejected by shock waves in the form of discrete layers. The principal envelope originates in the gas responsible for the premaximum system, as a result of considerable, sudden increase of the radiation pressure of Lα, a certain time after the beginning of the nova explosion. The radiation pressure accelerates a part of the premaximum envelope and it is this accelerated part of the premaximum envelope that forms the principal envelope of nova. This acceleration is then transferred to the outer regions of the envelope. The mass of the principal envelope therefore increases continuously. We have rejected all the previous theories that have been proposed for the formation of the principal envelope, because the authors of the theories have supposed that the principal envelope is formed at the moment of the luminosity maximum, while in the case of Nova Delphini 1967, we have found that the principal envelope was formed about 125 days before the luminosity maximum. By accepting that the premaximum, diffuse-enhanced and orion layers are ejected by shock waves and that the principal system is produced by radiation pressure, we can interpret the luminosity curve and the variation of the radial velocity of each system as a function of time and the observed sporadic changes of luminosity or radial velocity. We have found that the luminosity comes from the gas associated with the principal envelope and that its mass is about 80% of the mass of the all matters ejected by a nova, during its activity. We have discussed the cause of the nova explosion and have concluded that there is no satisfactory theory of novae.     

Formation flying solar-sail gravity tractors in displaced orbit for towing near-Earth asteroids

Several methods of asteroid deflection have been proposed in literature and the gravitational tractor is a new method using gravitational coupling for near-Earth object orbit modification. One weak point of gravitational tractor is that the deflection capability is limited by the mass and propellant of the spacecraft. To enhance the deflection capability, formation flying solar sail gravitational tractor is proposed and its deflection capability is compared with that of a single solar sail gravitational tractor. The results show that the orbital deflection can be greatly increased by increasing the number of the sails. The formation flying solar sail gravitational tractor requires several sails to evolve on a small displaced orbit above the asteroid. Therefore, a proper control should be applied to guarantee that the gravitational tractor is stable and free of collisions. Two control strategies are investigated in this paper: a loose formation flying realized by a simple controller with only thrust modulation and a tight formation realized by the sliding-mode controller and equilibrium shaping method. The merits of the loose and tight formations are the simplicity and robustness of their controllers, respectively.     

Shock focusing and jet collimation in young stars

We study the collimation of a initially uncollimated outflow from a young star by its environment, a cloud core with a toroidal density distribution. It is shown that when cooling is unimportant the shape of the inner shock and the internal structure of the bubble will collimate the outflow and it is shown that in some cases cooling is unimportant. The effects of the focusing by an elliptical shock are studied. Numerical simulations show that when cooling is important, the collimation is actually much better and interesting combinations of energy- and momentum-conserving flow occur.     

Twisted magnetic flux tubes: Effect of small twist

The shape of a magnetic flux tube is investigated when photospheric motion causes small twist at the magnetic footpoints. Using a Fourier-Bessel series expansion, the previous results of Zweibel and Boozer (1985) and Steinolfson and Tajima (1987), when the twist is small, are substantiated. A twisting motion that is restricted to a finite region is investigated. Inside the twisted region, the tube contracts, but in the outer region the field remains straight, except for a slight expansion at the outside of the loop near the footpoints. The amount of twist depends on the radial position and can in fact be larger in the contracted region with the twist decreasing as the tube expands. An axial boundary-layer region is present, as noted by the above authors, through which the field adjusts to the line-tied magnetic footpoint positions. An analysis of the boundary layer shows that the thickness remains constant as the loop-length is increased with the result that the main part of the loop has constant cross-sectional area and can be described by cylindrically-symmetric fields. This new 1-D model predicts the main behaviour of the loop without the need to solve the more complicated 2-D problem directly. It is speculated that the boundary layers will remain even when the twist becomes large and a simple example is presented. A detailed parametric study of different twist profiles shows how the central part of the loop responds.Using the result that the majority of the loop can be described by a constant cross-sectional area, a model for a toroidal loop is presented that models coronal loops in a more realistic manner. The main result from this section is that the coronal loops can only remain in equilibrium if they are confined by an external magnetic field (possibly potential in nature) and not by a gas pressure unless additional physical effects are included.     

The jet power extracted from a magnetized accretion disc

We consider the power of a relativistic jet accelerated by the magnetic field of an accretion disc. It is found that the power extracted from the disc is mainly determined by the field strength and configuration of the field far from the disc. Comparing it with the power extracted from a rotating black hole, we find that the jet power extracted from a disc can dominate over that from the rotating black hole. However, in some cases, the jet power extracted from a rapidly rotating hole can be more important than that from the disc, even if the poloidal field threading the hole is not significantly larger than that threading the inner edge of the disc. The results imply that the radio-loudness of quasars may be governed by its accretion rate, which might be regulated by the central black hole mass. It is proposed that the different disc field generation mechanisms might be tested against observations of radio-loud quasars if their black hole masses are available.     

The Importance of Photospheric Intense Flux Tubes for Coronal Heating

Dissipation of magnetic energy in the corona requires the creation of very fine scale-lengths because of the high magnetic Reynolds number of the plasma. The formation of current sheets is a natural possible solution to this problem and it is now known that a magnetic field that is stressed by continous photospheric motions through a series of equilibria can easily form such sheets. Furthermore, in a large class of 3D magnetic fields without null points there are locations, called quasi-separatrix layers (QSLs), where the field-line linkage changes drastically. They are the relevant generalisation of normal separatrices to configurations without nulls: along them concentrated electric currents are formed by smooth boundary motions and 3D magnetic reconnection takes place when the layers are thin enough. With a homogenous normal magnetic field component at the boundaries, the existence of thin enough QSL to dissipate magnetic energy rapidly requires that the field is formed by flux tubes that are twisted by a few turns. However, the photospheric field is not homogeneous but is fragmented into a large number of thin flux tubes. We show that such thin tubes imply the presence of a large number of very thin QSLs in the corona. The main parameter on which their presence depends is the ratio between the magnetic flux located outside the flux tubes to the flux inside. The thickness of the QSLs is approximately given by the distance between neighbouring flux tubes multiplied by the ratio of fluxes to a power between two and three (depending on the density of flux tubes). Because most of the photospheric magnetic flux is confined in thin flux tubes, very thin QSLs are present in the corona with a thickness much smaller than the flux tube size. We suggest that a turbulent resistivity is triggered in a QSL, which then rapidly evolves into a dynamic current sheet that releases energy by fast reconnection at a rate that we estimate to be sufficient to heat the corona. We conclude that the fragmentation of the photospheric magnetic field stimulates the dissipation of magnetic energy in the corona.     

The formation of an eccentric gap in a gas disc by a planet in an eccentric orbit

We investigate the effect of a planet on an eccentric orbit on a two-dimensional low-mass gaseous disc. At a planet eccentricity above the planet's Hill radius divided by its semimajor axis, we find that the disc morphology differs from that exhibited by a disc containing a planet in a circular orbit. An eccentric gap is created with eccentricity that can exceed the planet's eccentricity and precesses with respect to the planet's orbit. We find that a more massive planet is required to open a gap when the planet is on an eccentric orbit. We attribute this behaviour to spiral density waves excited at corotation resonances by the eccentric planet. These act to increase the disc's eccentricity and exert a torque opposite in sign to that exerted by the Lindblad resonances. The reduced torque makes it more difficult for waves driven by the planet to overcome viscous inflow in the disc.     

A dynamical model of prominence loops

A dynamical model of prominence loops is constructed on the basis of the theory of hydromagnetic buoyancy force. A prominence loop is regarded as a flux rope immersed in the solar atmosphere above a bipolar region of the photospheric magnetic field. The motion of a loop is partitioned into a translational motion, which accounts for the displacement of the centroidal axis of the loop, and an expansional motion, which accounts for the displacement of the periphery of the loop relative to the axis. The translational motion is driven by the hydromagnetic buoyancy force exerted by the surrounding medium of the solar atmosphere and the gravitational force exerted by the Sun. The expansional motion is driven by the pressure gradient that sustains the pressure difference between internal and external gas pressures and the self-induced Lorentz force that results from interactions among internal currents. The main constituent of the hydromagnetic buoyancy force on a prominence loop is the diamagnetic force exerted on the internal currents by the external currents that sustain the pre-existing magnetic field. By spatial transformation between magnetic and mechanical stresses, the diamagnetic force is manifested through a mechanical force acting at various mass elements of the prominence. For a prominence loop in equilibrium, the gravitational force is balanced by the hydromagnetic buoyancy force and the Lorentz force of helical magnetic field is balanced by a gradient force of gas pressure.     

Multi-Wavelength Analysis of the Flare on 2 October 1993

By use of Yohkoh hard X-ray flux and soft X-ray images, and of vector magnetograms and 2D spectral observations, a 1N/C6.5 flare observed on 2 October 1993 is analysed in detail. Evidence is provided not only morphologically but also quantitatively that the dynamics at kernels A and C of the flare in the impulsive phase were controlled mainly by electron beam bombardment, while the heating of kernel B is mainly due to heat conduction. By plotting the energy gradient of the electron energy flux as a function of energy for the various spectral indexes observed during the flare, the acceleration mechanism is found to be such that there is a constant energy E₀, close to 20 keV, for which the electron flux d F₁/dE is constant. It is shown that such a conclusion can be reached more directly by using the photon flux, which in that case must be constant for E=E₀, whatever the value of the power index. This result implies also that the electron spectrum is represented by a power law and that the X-ray photons are produced in a thick target. Instantaneous momentum balance is shown to exist between the upflowing soft X-ray-emitting and the downflowing Hα- emitting plasma at the kernels of the flare. The observed Hα red asymmetry is well reproduced by the non-LTE computation, with the down-moving condensation included. The observation of the magnetic field suggests that the flare was triggered probably by magnetic flux emergence.     

Internal stellar rotation and orbital period modulation in close binary systems

The orbital period modulation, observed in close binary systems with late-type secondary stars, is considered in the framework of a general model that allows us to test the hypothesis proposed by Applegate. It relates the orbital period variation to the modulation of the gravitational quadrupole moment of their magnetically active secondary stars produced by angular momentum exchanges within their convective envelopes. By considering the case of RS CVn binary systems, it is found that the surface angular velocity variation of the secondary component required by Applegate's hypothesis is between 4 and 12 per cent, i.e. too large to be compatible with the observations and that the kinetic energy dissipated in its convection zone ranges from 4 to 43 times that supplied by the stellar luminosity along one cycle of the orbital period modulation. Similar results are obtained for other classes of close binary systems by applying a scaling relationship based on a simplified internal structure model. The effect of rapid rotation is briefly discussed finding that it is unlikely that the rotational quenching of the turbulent viscosity may solve the discrepancy. Therefore, the hypothesis proposed by Applegate is not adequate to explain the orbital period modulation of close binary systems with a late-type secondary.     

Dynamic Monte Carlo radiation transfer in SPH: radiation pressure force implementation

We present a new framework for radiation hydrodynamics simulations. Gas dynamics is modelled by smoothed particle hydrodynamics (SPH), whereas radiation transfer is simulated via a time-dependent Monte Carlo approach that traces photon packets. As a first step in the development of the method, in this paper we consider the momentum transfer between radiation field and gas, which is important for systems where radiation pressure is high. There is no fundamental limitation on the number of radiation sources, the geometry or the optical depth of the problems that can be studied with the method. However, as expected for any Monte Carlo transfer scheme, stochastic noise presents a serious limitation. We present a number of tests that show that the errors of the method can be estimated accurately by considering Poisson noise fluctuations in the number of photon packets that SPH particles interact with per dynamical time. It is found that, for a reasonable accuracy, the momentum carried by photon packets must be much smaller than the typical momentum of SPH particles. We discuss numerical limitations of the code, and future steps that can be taken to improve performance and applicability of the method.     

Some critical issues on magnetospheric substorms

Several evidences for the directly driven aspect of magnetospheric substorms are presented by reinterpreting what have been thought to be supporting evidences for the unloading process. Further, it is stressed that some of our confusions in substorm studies could be resolved by understanding that the magnetospheric substorm is primarily a directly driven phenomenon, but has a variety of internal processes. A method is suggested tto identify the directly driven and the unloading components. It is also demonstrated that the magnetosphere is intrinsically a non-linear system and that a quantitative study of magnetospheric substorms is not possible without taking into account this non-linearity.     

A New Approach for Studying Hubble Diagrams of Quasars

In this paper, a new approach for studying Hubble diagrams of quasars is introduced. The purpose is to reduce the well-known very large scatter in the diagram. We believe that the scatter is mainly caused by the wide spread of luminosity distribution of quasars. Based on a large number of quasars having been discovered, we introduce a new quantity, the collective apparent magnitude of certain amount of quasars in a corresponding redshift interval, and make a plot of the collective apparent magnitude versus redshift with the data published by Hewitt and Burbidge (1993). The quantity is contributed by individual apparent luminosities as well as the luminosity distribution of quasars. Scatter is expected to be largely reduced in the corresponding diagram, and this is indeed true as shown by the figures. By discussing several possible effects and from the figures, we find that the assumption that redshifts of quasars are distance indicators is confirmed, and the standard cosmological model is supported. This revised version was published online in July 2006 with corrections to the Cover Date.     

Basic properties of magnetic flux tubes and restrictions on theories of solar activity

It is shown that the mean longitudinal field in a magnetic flux tube is reduced, rather than enhanced, by twisting the tube to form a rope. It is shown that there is no magnetohydrostatic equilibrium when one twisted rope is wound around another. Instead there is rapid line cutting (neutral point annihilation). It is shown that the twisting increases, and the field strength decreases, along a flux tube extending upward through a stratified atmosphere.These facts are at variance with Piddington's recent suggestion that solar activity is to be understood as the result of flux tubes which are enormously concentrated by twisting, which consist of several twisted ropes wound around each other, and which came untwisted where they emerge through the photosphere.This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001.     

A long-term modulation in XTE J1716−389: an SS433-like system

We report on the properties of a 99.3-d periodic modulation in the X-ray transient XTE J1716−389. We associate this source with the transient KS J1716−389, first detected by the Mir /Kvant module in 1994. The spectral characteristics of XTE J1716−389, a high intrinsic absorption column, strong emission features and a power-law spectrum, make it very similar to the class of highly absorbed X-ray binaries detected by INTEGRAL . We associate the 99.3-d periodic behaviour with the geometrical obscuration that results from a precessing circumbinary disc that is moving in and out of the field of view, comparable to what has been proposed for SS 433. We therefore propose that XTE J1716−389 is a high-mass X-ray binary with a supergiant companion that is similar not only to SS 433, but also to the new class of highly obscured X-ray binaries, suggesting that SS 433 is a member of much wider population that is now being detected by INTEGRAL .     

单位矢量法的数学模型(MMUVM)及其简化形式(PUVM1)的迭代法的收敛性

利用人造地球卫星观测资料测定有摄初轨的单位矢量法(PUVM1),已得到了非常广泛地实际应用.为了对单位矢量法作进一步地完善和改进,首先在考虑测量误差模型的基础上,建立单位矢量法所对应的数学模型MMUVM.它本质上就是一个非线性最优化问题.针对MMUVM,先分别使用多圈仿真数据和实测数据,形成了与之相对应的目标函数,再利用求解最优化问题的一种三对角二次插值模型的直接搜索方法,分别对其进行了数值处理.计算结果表明,所建立的优化模型MMUVM正确合理,所采用的直接搜索方法实用有效.其次,进一步指明了PUVM1和MMUVM之间关系,即:从本质上讲,PUVM1就是MMUVM的一种简化形式.从数学原理上,清楚地解释了利用PUVM1的准法化方程,只能使用单圈短弧段数据进行初始轨道确定,而不能使用长弧段多圈资料进行轨道确定或轨道改进的根本原因.最后,对PUVM1的迭代算法的收敛性问题进行了初步的理论分析,并给出了相应的数值验证实例,指出了PUVM1的迭代格式是条件收敛的,即:只有在满足一定条件后,才能收敛.这也就意味着:有的时候,尽管准法化方程是合情合理的,但是,此时该迭代法却是发散的,无法迭代求出所要的解.     

The magnetohydrodynamics of stellar structures

The equation governing the equilibrium of a centrally-symmetric, self-gravitating distribution of matter is obtained by assuming that matter is described by magnetofluid and it is shown that the equation of stellar structure described by an ideal fluid is recovered when magnetic fieldh is vanishing