Evolution of rising helical prominences in a nonuniform atmosphere

Recent coronagraph observations of rising priminences such as in the 14 April and 5 May, 1980 coronal transient events, as well as other older observations, have shown evidence for helical structure in the prominences. If this is true, then a study of the dynamical evolution of rising helical structures in a nonuniform atmosphere is worthwhile. For this study, three important considerations become apparent: (1) Since the ends of the prominence remain rooted in the photosphere, significant stretching of the configuration will result as it rises, (2) due to the fall-off with height of the external quantities, such as gas and magnetic pressure, the prominence will experience time-varying boundary conditions as it rises, and (3) significant lateral expansion of the prominence is expected as the external conditions weaken with height. The interplay of all these effects togehter result in a quite complex dynamical behavior of the prominence.We have tried to obtain some insight into this general problem through a simple model - that of a helical pinch rising in a low beta atmosphere under the influence of an ambient external magnetic field which declines in strength with radial distance from the solar center. Under the general assumptions of an internal uniform, but time-varying, temperature and neglecting gravitational stratification within the prominence, expressions are derived for associated variations in the prominence structure as it rises. We discuss in some detail, particular quantities which are potentially most accessible to observation such as prominence radius, density, and pitch angle as they vary with height during the eruptive process.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A model for quiescent solar prominences with normal polarity

A class of 2-D models of solar quiescent prominences, with normal polarity, is presented. These represent an extension to the Kippenhahn-Schlüter model for which the prominence configuration matches smoothly onto an external non-potential coronal solution of a constant field. Using typical prominence values a model is constructed which also matches the coronal conditions. It is found that the magnetic field component along the prominence influences the internal structure of the prominence. A simple extension to the basic models is indicated as a means of taking a lower boundary of the prominence and eliminating parasitic polarities in the photosphere.     

Optimal growth of small perturbations in thin gaseous disks

A thin gaseous disk with a nearly Keplerian rotation profile and free boundaries in the external gravitational field of a point gravitating object does not generate any growing perturbation eigenmodes. In spite of this, a significant transient growth of linear perturbations measured by the evolution of their total acoustic energy is possible in such a disk. This is shown within the framework of the simplest model of an inviscid polytropic thin disk with a finite radial extent in which small adiabatic perturbations that are a linear combination of neutral eigenmodes with a corotation radius beyond the outer flow boundary are considered.     

A remark on the apsidal motion in slose binary systems

Dynamics of the apsidal motion in close binary systems are discussed. A comparison between the solution for the perfect fluid system and the solution for the rigid system reveals that some overall viscosity in the interior of distorted star has a right tendency to reconcile the observation of apsidal motion with the theory of internal structure.     

Modeling Irregularities in Solar Flux Ropes

To model irregularities in the magnetic structure of solar flux ropes or in interplanetary magnetic clouds, we propose the following approach. A local irregularity in the form of a compact toroid is added into a cylindrical linear force-free magnetic structure. The radius of the cylinder and the small radius of the toroid are the same, since the force-free parameter α is constant, that is, we have in total a linear force-free configuration, too. Meanwhile, the large radius of the toroid can be smaller. The effect of such modeling depends on the aspect ratio of the compact toroid, its location and orientation, and on its magnetic field magnitude in comparison with that of the cylinder.     

A mathematical magnetospheric field model with independent physical parameters

A quantitative magnetospheric magnetic field model has been calculated in three dimensions. The model is based on an analytical solution of the Chapman-Ferraro problem. For this solution, the magnetopause was assumed to be an infinitesimally thin discontinuity with given geometry. The shape of the dayside magnetopause is in agreement with measurements derived from spacecraft boundary crossings.The magnetic field of the magnetopause currents can be derived from scalar potentials. The scalar potentials result from solutions of Laplace's equation with Neumann's boundary conditions. The boundary values and the magnetic flux through the magnetopause are determined by all magnetic sources which are located inside and outside the magnetospheric cavity. They include the Earth's dipole field, the fields of the equatorial ring current and tail current systems, and the homogeneous interplanetary magnetic field. In addition, the flux through the magnetopause depends on two constants of interconnection which provide the possibility of calculating static interconnection between magnetospheric and interplanetary field lines. Realistic numerical values for both constants have been derived empirically from observed displacements of the polar cusps which are due to changes in the orientation of the interplanetary field. The transition from a closed to an open magnetosphere and vice versa can be computed in terms of a change of the magnetic boundary conditions on the magnetopause. The magnetic field configuration of the closed magnetosphere is independent of the amount and orientation of the interplanetary field. In contrast, the configuration of the open magnetosphere confirms the observational finding that field line interconnection occurs primarily in the polar cusp and high latitude tail regions.The tail current system reflects explicitly the effect of dayside magnetospheric compression which is caused by the solar wind. In addition, the position of the plasma sheet relative to the ecliptic plane depends explicitly on the tilt angle of the Earth's dipole. Near the tail axis, the tail field is approximately in a self-consistent equilibrium with the tail currents and the isotropic thermal plasma.The models for the equatorial ring current depend on the D_st-parameter. They are self-consistent with respect to measured energy distributions of ring current protons and the axially symmetric part of the magnetospheric field.     

大质量黑洞吸积盘的径向自引力

本文研究了大质量黑洞吸积盘的自引力,用薄盘位形上积分的方法计算了吸积盘自引力的径向与垂向分量,着重讨论了径向自引力。主要结果为:对于大质量黑洞(M～10~8—10~(10)M_⊙)吸积盘,在(R/R_g)～10~5—10~4的距离上,径向自引力会超过中心天体引力。在这个距离上,吸积盘的动力学结构完全不同于开普勒盘。提出了径向自引力不稳定扰动作为一种能源机制。本文还得到吸积盘自引力与中心天体引力量级比较的两个判据,并由此得到大质量黑洞吸积盘外半径的近似解析估计。本文结果可用于类星体和星系核吸积盘。     

Emden-chandrasekhar axisymmetric,rigidly rotating polytropes

We determine equilibrium configuration of Emden-Chandrasekhar axisymmetric, solid-body rotating polytropes, defined as EC polytropes, for polytropic indices ranging from 0 (homogeneous bodies) to 5 (Roche-type bodies). To this aim, we improve Chandrasekhar's method to determine equilibrium configurations on two respects: namely, (a) no distinction exists between undistorted and distorted terms in the expression of the potential, and (b) the comparison between the expressions of gravitational potential and its first derivatives inside and outside the body has to be made on the boundary of a sphere of radius Ξ_E, which does not necessarily coincide with the undistorted Emden's sphere of radius \(\bar \xi _0 \geqslant \Xi _{\text{E}} \) . We also allow different values of \(\bar \xi _0 \) for different physical parameters, and choose a special set which best fits more refined results (involving more complicated and more expensive computer codes) by James (1964). We find an increasing agreement with increasing values of polytropic indexn and vice-versa, while a large discrepancy arises for 0≤n<1, which makes the approximations used here too much rough tobe accepted in this range. A real slight non-monotonic trend is exhibited by axial rations and masses related to rotational equilibrium configurations — i.e., when gravity at the equator is balanced by centrifugal force-with extremum points for 4.8<n<4.85 in both cases. The same holds for masses related to spherical configurations, as already pointed out by Seidov and Kuzakhmedov (1978). Finally, it is shown that isotrophic, one-component models of this paper might provide the required correlation between the ratio of a typical rotation velocity to a typical peculiar velocity and the ellipticity, for about \(\tfrac{3}{4}\) of elliptical systems for which observations are available.     

Practical SPH models for major planets

Modelling planets is done for two main reasons – the first to further understanding of their internal structure and the second to provide models to explore astrophysical situations in which planets play a role. For the latter reason, the requirements on accuracy are less severe, although the planet must be realistic in its major features. A numerical model of a layered giant planet is developed with an iron core, a silicate mantle, an ice region and a hydrogen–helium atmosphere. The Tillotson equation of state is used and examples of two model planets are given, one reproducing the mass and radius of Jupiter quite closely and the other with two Jupiter masses. Transferring these results into a smoothed particle hydrodynamics (SPH) model presents two main difficulties. A uniform distribution of SPH points leads to too few points representing the non-atmospheric component. It is shown that using a distorted lattice enables the core + silicate + ice to be represented by several hundred points so that the evolution of these regions can be followed in detail. Another difficulty concerns the density discontinuities attendant on a layered structure. Density estimates of SPH points are either too large or too small near material interfaces leading to unrealistic pressure gradients and, consequently, to large and unphysical local forces. Algorithms are described for avoiding this difficulty both at material interfaces and near the surface of the planet. In some astrophysical situations involving SPH-modelled planets, the main bulk of the planet is so opaque that internal heat transfer can be neglected. However, surface regions should radiate and a convenient way for including radiation from a planetary surface is described.     

The rotation of the solar atmosphere

A model of the solar atmosphere is presented in which we discuss the conservation of angular momentum for the two basic states in which the solar gas can be: namely, either confined by closed field lines or outflowing along open magnetic field lines. It can be shown that the boundary conditions are in general different for these two cases. From this we obtain the results that in the closed configuration the gas can corotate at the solar surface with the magnetic field lines and its angular velocity will then increase with height, whereas for a gas flowing along an open field line the angular velocity will decrease. An exception to the latter case can be found where the open magnetic field lines are strongly nonradial and where the density is a slowly varying function of radius. In such regions the angular velocity may initially increase with height, reach a maximum and then decrease.Kitt Peak National Observatory Contribution No. 439.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Artificial Neural Network Approach of Cosmic Ray Primary Data Processing

One of the most critical points in the detection of cosmic rays by neutron monitors is the correction of the raw data. The data that a detector measures may be distorted by a variety of reasons and the subtraction of these distortions is a prerequisite for processing them further. The final aim of these corrections is to keep only the fluctuations related to the real cosmic-ray intensity. To achieve this, we analyze data from identical neutron monitor detectors which provide a configuration with the ability to exclude the distortions by comparing the counting rate of each detector. Based on this method, a number of effective algorithms have been developed: Median Editor, Median Editor Plus, and Super Editor are some of the algorithms that are being used in the neutron monitor data processing with satisfactory results. In this work, a new approach for the correction of the neutron monitor primary data with a completely different method, based on the use of artificial neural networks, is proposed. A comparison of this method with the algorithms mentioned previously is also presented.     

Behavior of planetary dynamos under the influence of external magnetic fields: Application to Mercury and Ganymede

For planets with strong intrinsic magnetic fields such as Earth and Jupiter, an external magnetic field is unlikely to affect the internal dynamo, but for bodies with weak intrinsic fields in appropriate environments, such as Mercury and Ganymede, the interaction with nearby field sources may determine the internal dynamics and overall behavior of their liquid iron cores. On the basis of simulations of such interactions using numerical models for fluid flow and dynamo generation, the parameter regimes for stable dipolar and multipolar reversing dynamo magnetic fields established for isolated systems can be substantially changed by the action of external sources. Relatively weak external background fields (as low as 2% of the averaged undisturbed field at the core-mantle boundary) may change the energy balance and alter the regime over which natural isolated dynamos operate.     

Plasma Heating by Forced Magnetic Reconnection

A model of forced magnetic reconnection in a force-free magnetic field is considered, which allows calculation of the magnetic energy release during the current sheet reconnection. The dependence of this energy on characteristics of the magnetic configuration has been studied, and it was found that the released energy becomes very large when the field is near the marginal tearing stability. A persistent plasma heating provided by ongoing external driving and internal reconnection is also derived. It shows a typical relaxation-type dependence on the driving frequency, with dissipation becoming most efficient when the time-scales of the driving and reconnection are comparable. Possible implications of the obtained results for the problem of solar coronal heating are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the internal structure of stars

A new model of the internal structure of certain types of celestial bodies is proposed. It is based on the concept that some neutron stars might have been formed earlier than all other type of stars, at an early stage of expansion of the universe, directly from continuous cosmic matter. Under such conditions, a neutron star after forming becomes an efficient center for the accretion of cosmic plasma. The plasma streams falling onto the neutron star carry magnetic fields with them that are created in the process (by thermoelectric currents and the dynamo process) and pack the fields tightly around the star. After a certain time, an extended and strongly magnetized plasma layer is formed around the neutron star. As a result, a stellar configuration is formed with an outer layer, mass, radius, and luminosity similar to those of an ordinary star. In the magnetized part of such a configuration, the gravitational attraction of the masses is compensated for by a magnetic pressure gradient, while the plasma is confifned by the magnetic field itself. Numerical estimates corroborate the possibility that magnetized stars exist. The radii and masses of the magnetized spheres of such stars are considerably less than the radii and masses of the corresponding configurations, so in observations they should not differ from ordinary stars: the outer layers (intermediate layer, photosphere, and chromosphere) of the magnetized configuration are the same as for an ordinary star. Structural differences may appear in the inner regions, however, involving magnetic activity and neutrino luminosity, for example.     

The tidal stripping of satellites

We present an improved analytic calculation for the tidal radius of satellites and test our results against N -body simulations.
The tidal radius in general depends upon four factors: the potential of the host galaxy, the potential of the satellite, the orbit of the satellite and the orbit of the star within the satellite . We demonstrate that this last point is critical and suggest using three tidal radii to cover the range of orbits of stars within the satellite. In this way we show explicitly that prograde star orbits will be more easily stripped than radial orbits; while radial orbits are more easily stripped than retrograde ones. This result has previously been established by several authors numerically, but can now be understood analytically. For point mass, power-law (which includes the isothermal sphere), and a restricted class of split power-law potentials our solution is fully analytic. For more general potentials, we provide an equation which may be rapidly solved numerically.
Over short times (≲1–2 Gyr ∼1 satellite orbit), we find excellent agreement between our analytic and numerical models. Over longer times, star orbits within the satellite are transformed by the tidal field of the host galaxy. In a Hubble time, this causes a convergence of the three limiting tidal radii towards the prograde stripping radius. Beyond the prograde stripping radius, the velocity dispersion will be tangentially anisotropic.     

Anguilar momentum transport by tidal acoustic wave

We give an analytic expression of the braking torque on a Jacobian ellipsoid rotating steadily in an environmental gas, based on the assumption that the ellipsoid rotates around its shortest principal axis with an angular momentum slightly larger than that at the bifurcation point of the Maclaurin spheroid. This braking torque is effected by the gravitational interaction between the ellipsoid matter and a spiral density configuration in the environmental gas. This spiral configuration, which we call a tidal acoustic wave, is caused by the zone of silence effect in a supersonic flow. With respect to a coordinates system rotating with the ellipsoid, a supersonic region appears outside a certain radius. In this supersonic region, the effect of the non-axisymmetric fluctuation in the ellipsoid potential propagates only along the downstream branches of the Mach waves. This one-sided response of the supersonic part causes the tidal acoustic wave. We restrict ourselves to the equatorial plane, and use an acoustic approximation of the basic equations under the assumption that the self-gravity effect of the environmental gas is negligible in comparison to the main gravity of the ellipsoid. The results are applied to the pre- and post-Main Sequence phases of a rotating star, and relating astrophysical problems are discussed.     

Effects of rotation on internal structure of the stars

The aim of the present paper will be to establish the explicit form of the equations which govern the internal structure of stars rotating with constant angular velocity formulated in terms of Clairaut coordinates (cf. Kopal, 1980) in which the radial coordinate is replaced by the total potential, which for equilibrium configurations remains constant over distorted level surfaces. The introductory Section 1 contains an account of previous work on rotating stars, commencing with Milne (1923), von Zeipel (1924) and Chandrasekhar (1933), who all employed orthogonal coordinates for their analysis. In Section 2 we shall apply to this end the curvilinear Clairaut coordinates introduced already in our previous work (cf. Kopal, 1980, 1981); and although these are not orthogonal, this disadvantage is more than offset by the fact that, in their terms, the fundamental equation of our problem will assume the form of ordinary differential equations, subject to very simple boundary conditions. The explicit form of these equations — exact to terms of fourth order in surficial distortion caused by centrifugal force—will be obtained in Section 3; while in the concluding Section 4 these will be particularized (for the sake of comparison with work of previous investigators) to stars of initially polytropic structure. These will prove to be much simpler in Clairaut coordinates than they were in any previously used frame of reference. Lastly, in Appendix A we shall present the explicit forms, in Clairaut coordinates, of the differential operators which were needed to establish the results given in Sections 3–4; while Appendix B will summarize other auxiliary algebraic relations of which use was made to formulate our fourth-order theory developed in Section 3.     

The internal evolution of planetary-sized objects

The importance of ‘creep’ in controlling the internal thermal state of large objects with physical properties corresponding to a roughly homogeneous meteoritic composition is reviewed. Some results of this study are used to justify a picture of evolution as a quasistatic process. An attempt is made to show that the viscous dissipation of the motions that occur in the lifetime of such bodies formed about 4.5 × 10⁹ yr ago gives them an innate capacity to chemically differentiate if their external radius exceeds a few hundred kilometres. The capacity to differentiate increases rapidly with external radius and for objects of lunar size and greater, the process is not yet complete. During the ‘active’ stage of evolution the convective cores of these objects tend to grow smaller and hotter with time, giving a secular change in the composition of the differentiating phases. It is suggested that by a curious coincidence of dehydration curves and the horizontally averaged temperature distribution, water of dehydration can still be present at depth in the planets and is the cause of the observed seismic attenuation at the Moon's centre and in the Earth's upper mantle. It is also noted that if water is present at tenths of a percent level the temperature within objects with radii < 3000 km is kept below the Curie point of pure iron for long periods - a situation that could have significant bearing on the present magnetisation of the planetary objects in this size range.     

Initial-Condition Influences on CME Expansion and Propagation

A general-purpose melon-seed-overpressure-expansion (MSOE) model is used to examine the dependence of the expansion and propagation of fast CMEs on average initial values of the magnetic field inside the CME, the magnetic field outside the CME, and the CME mass. The MSOE model extracts from the real situation only features that are essential in determining the expansion and propagation processes and idealizes them to obtain an adaptable “minimalist” set of equations that governs these processes yet retains enough relevant physics to give useful results. This minimalist set is used to carry out a systematic comparison of solutions against four sets of observed correlations between CME and ICME parameters in which the input parameters to the MSOE model are varied to achieve simultaneous fits to all four correlations. The fits impose relations between the three independent input variables: initial internal field strength, initial external field strength, and initial density. For example, light CMEs (e.g., those with no prominences) require the external field strength to nearly equal the internal field strength. However, heavy CMEs (e.g., those with prominences) require the external field strength to be much weaker than the internal field strength.