A note on the solution of the saturation flux limited solar wind equations

The solution curves of the differential equations determining the behavior of the solar wind are calculated for the case where the heat flux has its maximum value 3/2 nkTv _th. All the supersonic solutions are asymptotically adiabatic, T r ^-4/3.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The asymptotic behavior of the supersonic solutions of the two-fluid solar wind equations

Three different asymptotic branches of the two-fluid equations are found with _e ^m , _p ⁿ , where, is the inverse distance from the Sun, with (m, n) = (2/7, 2/7), (2/7, 6/7), (4/3, 4/3); other special solutions are also found but they correspond to special choices of density and temperature at the corona. In all the (4/3, 4/3) solutions, the electron and proton temperatures tend to equality at large distances.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

An equation of state at subnuclear densities

An equation of state for cold matter above white dwarf densities is evaluated. The gas is considered to be a mixture of degenerate neutrons, protons and electrons combined with nuclei of one type (that is only oneA andZ value). We derive the equilibrium equations for the mixture and calculate the number densities as well as theA andZ of the nucleus. Finally we calculate an equation of state, which smoothly goes over to that of a neutron, proton electron gas mixture at a density of 5×10¹³ g/cm³.     

3-D period doubling and magnetic moments of particles

Several invariant properties of matter seem to fit remarkably well to quantized values obtained from Planck domain units by period doubling in three dimensions. The units are defined using natural constants only. Such properties include the elementary electric charge, electron and proton rest energies and others. It has been shown by W. G. Tifft that the quantized redshifts of galaxies fit the pattern, too. Magnetic moments of the electron, proton, neutron, muon and lambda particles also seem to obey the doubling rule. The same number of doublings seems to yield the electron and proton rest masses and magnetic moments correspondingly. The proton rest mass is E₀×2^–64 and the magnetic moment µ _o × 2⁶⁴, where E₀ and µ _o are the Planck domain units. The corresponding exponent of 2 for the electron is 75.66. The units for the proton and the electron differ by a factor of . The magnetic moment of the muon suggests a close relationship between the magnetic structures of the muon and the proton, whereas the lambda particle seems to be related to the neutron. Reasons for the supposed existence of quantized 3-d time are represented.     

Populations of highly excited atoms and ions in the optically thin plasma

Treating it as a boundary-value problem, the equations of highly excited state populations of atoms and ions are theoretically studied in case of recombining plasma. Scattering and spontaneous transitions as well as those induced by background radiation, are taken into account in the kinetic equations. The kinetic coefficients for inelastic scattering of incident charged particles on highly excited atoms and ions have been calculated in the asymptotically exact case: 1.6×10⁵ (z/n)²)T _e ^–1 1.The distribution functions over the Rydberg states, analytically found, allow to determine amplification factor and optical depth of radio-recombination lines as functions of cosmic plasma parameters.     

Some new exact solutions with finite central parameters and?uniform radial motion of sound

We present three new categories of exact and spherically symmetric Solutions with finite central parameters of the general relativistic field equations. Two well behaved solutions in curvature coordinates first category are being studied extensively. These solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, one of the solution (I₁) is studied extensively. The solution (I₁) gives us wide range of Schwarzschild parameter u (0.138≤u≤0.263), for which the solution is well behaved hence, suitable for modeling of Neutron star. For this solution the mass of Neutron star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to u=0.263, the maximum mass of Neutron star comes out to be 3.369 M _Θ with linear dimension 37.77 km and central and surface redshifts are 4.858 and 0.4524 respectively. We also study some well known regular solutions (T-4, D-1, D-2, H, A, P) of Einstein’s field equations in curvature coordinates with the feature of constant adiabatic sound speed. We have chosen those values of Schwarzschild parameter u for which, these solutions describe perfect fluid balls realistic equations of state. However, except (P) solution, all these solutions have monotonically non-decreasing feature of adiabatic sound speed. Hence (P) solution is having a well behaved model for uniform radial motion of sound. Keeping in view of well behaved nature of the solution for this feature and assuming the surface density; ρ _b =2×10¹⁴ g/cm³, the maximum mass of Neutron star comes out to be 1.34 M _Θ with linear dimension 28.74 km. Corresponding central and surface redshifts are 1.002 and 0.1752 respectively.     

Thermal properties of the solar wind plasma

In the solar wind, electrostatic ion cyclotron waves can be excited by electrons when the flow velocity becomes supersonic. The waves reduce the proton temperature anisotropy and heat the protons effectively. Temperature equations for T _e ,T _p and T _p are solved numerically in the region from 1 AU to the Sun, with the non-thermal proton heating rate included as a parameter. Distributions of T _e ,T _p , T _p and the proton heating rate are determined and found to be in good agreement with the proton heating rate expected from the linear growth rate of electrostatic ion cyclotron waves. The electron thermal conductivity is reduced approximately 2–3 times smaller than the usual collisional one due to the plasma wave instabilities. Effective energy exchange rates from proton-proton and electron-proton interactions are 1–10 and 10–100 times larger than the Coulomb collision rates v ppand v ep,respectively.     

Note on the helium-like ion line emission in solar plasmas

An analysis is presented of the rate coefficients occurring in the Gabriel-Jordan theory on the relative intensities of the forbidden, intercombination, and resonance lines of helium-like ions in a steady-state plasma. Simple expressions are given to show the dependence on atomic number and electron temperature. The influence of proton collisions on the excitation 2³ S2³ P is estimated and deviations from the theory under non-equilibrium conditions are briefly discussed.     

The Einstein-Maxwell field equations,II

In order to arrive at more general results solving Einstein-Maxwell's equations our investigation is centered around an electromagnetic spin tensor, which must be chosen in such a way that conservation laws still hold. This notion of the combined tensor is of course closely linked with the unified field equations. We shall avoid in this way the problem of the form of the matter tensor and neglect non-linear gravitational terms in the Ricci tensor. Then, the field equations have as solutionsh _ij=h _ij ^(P) +h _ij ^(h) , whereh _ij ^(P) are particular solutions, which are obtained by direct calculations andh _ij ^(h) are solutions of h _ij ^(h) =0. The quantitiesh _ij ^(P) are purely electromagnetic in nature, whileh _ij ^(h) may represent purely gravitational terms. The results obtained complete the ones which have been published already in the preceeding paper (Dionysiou, 1980a; which will hereafter be referred to as Paper I).     

Normal form,Lie-Poisson structure and reduction for the Henon-Heiles system

The reduced Henon-Heiles system is investigated as a Hamiltonian dynamical system obtained by applying the normalization of the HamiltonianH=1/2(p ₁ ² +p ₂ ² +q ₁ ² +q ₂ ² )+1/3q ₁ ³ –q ₁ q ₂ ² to fourth-degree terms. The related equations of motion are bi-Hamiltonian and possess the Lie-Poisson structure. Each Lie-Poisson structure possesses an associated Casimir function. When reduced to level sets of these functions, the equations of motion take various symplectic forms. The various reductions give different coordinate representations of the solutions. These coordinate representations are used to seek the simplest representation of the solutions.     

Eigenschaften singularitätenfreier,statischer, zentralsymmetrischer Lösungen gewisser Gravitationsfeldgleichungen 4. Ordnung

FIEDLER and SCHIMMING (1983) proved that the fourth order gravitational field equations with a linear combination of Bach's and Einstein's tensors on the left-hand side, which were proposed by TREDER , admit static centrally symmetric solutions which are analytical and non-flat in some neighbourhood of the centre of symmetry. The existence of these solutions, known at first only in a small neighbourhood of r = o (r radius), can now be extended to intervals o ≦ r ≦ α with arbitrarily large α , using the abstract theorem on inverse functions. Further it is proved that the Schwarzschild metrics are in a certain sense the only solutions of the above equations that are analytic, asymptotically flat, static and centrally symmetric around r = +∞.     

Determination of Libration Characteristics of Asteroids near Mean Motion Commensurabilities 1/1, 4/3, 3/2, 2/1, 7/3, 5/2, and 3/1

The possibility of using a generalized perfect resonance for the study of libration motions of asteroids near the (p+ q)/p-type commensurabilities of the mean motions of asteroids and Jupiter is considered. Based on the equations of the planar circular restricted three-body problem, the libration-motion equations are derived and their solutions for the intermediate Hamiltonian, as well as a solution taking into account perturbations of the order O(m ^3/2), are determined.     

Stationary equations of hydrogen excitation and ionization in prominences

The statistical equilibrium equations for the continuum and first 10 levels of a hydrogen atom show that the radiation of a bright prominence (the brightness of the H line has attained 56 mÅ of the disc centre spectrum) is completely due to scattering of the Sun radiation. The basic unknowns are separated with certainty: electron concentration (n _e = 3.0 × 10¹⁰ cm^–3), effective thickness (l = 4.2 × 10⁸ cm) and electron temperature (T _e = 5000 K).Radiation of a very bright prominence (A (H) = 213 mÅ; T _e = 7300 K; n _e = 5.0 × 10¹¹ cm^–3; l = 1.3 × 10⁷ cm) is on account of electron impacts (40%) and the Sun radiation scattering (60%).The parameters are shown to depend greatly on the prominence optical thickness in the lines of the first subordinate series of a hydrogen atom. In the course of determination all the parameters and 100 interconnected integral equations of the radiation diffusion have been thickness-averaged; the population of levels has been calculated by observations using the self-absorption factors.     

Asymptotic and Periodic Orbits Around L 3 in the Photogravitational Restricted Three-Body Problem

Asymptotic motion near the collinear equilibrium points of the photogravitational restricted three-body problem is considered. In particular, non-symmetric homoclinic solutions are numerically explored. These orbits are connected with periodic ones. We have computed numerically the families containing these orbits and have found that they terminate at both ends by asymptotically approaching simple periodic solutions belonging to the Lyapunov family emanating from L₃.     

A model for GRB jets

By using relativistic, axisymmetric, ideal MHD, we examine the motion of the baryon/e^±/ photon fluid that emanates from a stellar-mass compact object/debris-disk system (a common outcome of many progenitor models). We prove that the motion can be described as a frozen pulse, which permits the study of each shell of the pancake-shaped outflow using steady-state equations. The ejected energy flux is dominated by the electromagnetic (Poynting) contribution, but it can also have a non negligible e^±/radiation (thermal fireball)component. We demonstrate, through exact self-similar solutions, that the flow is first thermally and subsequently magnetically accelerated up to equipartition between kinetic and Poynting fluxes, i.e., ～ 50% of the total energy is converted into baryonic kinetic energy. The electromagnetic forces also collimate the flow, reaching a cylindrical structure asymptotically.     

Cosmological models in semi-classical and higher order gravitational theories

We have studied semiclassical models with a classical scalar field, givingexact solutions in the cases of a ⁴ and an exponentialself-interaction potential, in the last case we have also studied theinfluence of the vacuum polarization terms on the stability of the power-lawsolutions. We have also found cosmological exact solutions to the higherorder gravitational equations derived from a Lagrangian with a R ^k Rstructure, and investigated the stability of the de Sitter and Minkowskispace-time in the sixth order approximation of this theory.     

Analysis of the chromospheric hydrogen spectrum at the 1962 eclipse

Slitless spectrograms of the chromosphere obtained during the eclipse of 4–5 February 1962 have been analyzed to obtain the decrements of the level populations of hydrogen, the self-absorption in the Balmer lines, and parameters useful in construction of models of the low chromosphere.The decrement of the high energy levels of hydrogen inferred under the optically thin assumption does not vary significantly with height, and it appears to be unnecessary to seek large deviations from local thermodynamic equilibrium in the high levels. The observed Balmer-to-Paschen line intensity ratios have been used to infer self-absorption and opacities in the Balmer lines. The resulting population of the second energy level is about an order of magnitude smaller than that found by Athay and Thomas from the 1952 data.The chromospheric continuum was generally underexposed; the absence of observed continuum in the visible region of the spectrum made it impossible to derive a unique model from the 1962 data alone. However, the high Balmer line data and new theoretical solutions of the statistical equilibrium equations for hydrogen combined with corrected 1952 observations at 4700 A are compatible with a model having approximately the same temperature and neutral hydrogen structure as the 1952 model by Pottasch and Thomas but half the electron density: T _e = 6200K, N ₁ = 7.4 × 10¹³ cm^-3, N _e = 2.3 × 10¹¹ cm^-3 at 500 km and T _e = 7200K, N ₁ = 2.6 × 10¹² cm^-3, N _e = 1.7 × 10¹¹ cm^-3 at 1000 km.Based in part on a Ph.D. thesis submitted to the Department of Astro-Geophysics, University of Colorado.Now at the Department of Astronomy, Indiana University.     

Exact solutions: classical electron model

Rahaman et al. (Astrophys. Space. Sci. 331:191–197, 2010) discussed some classical electron models (CEM) in general relativity. Bijalwan (Astrophys. Space. Sci. 334:139–143, 2011) present a general exact solution of the Einstein-Maxwell equations in terms of pressure. We showed that charged fluid solutions in terms of pressure are not reducible to a well behaved neutral counter part for a spatial component of metrice ^λ . Hence, these solutions represent an electron model in general relativity. We illustrated solutions in terms of pressure briefly with de-Sitter equation of state and charged analogues of Kohler Chao interior solution as a special cases.     

The extended phase space formulation of the Vinti problem

The Vinti problem, motion about an oblate spheroid, is formulated using the extended phase space method. The new independent variable, similar to the true anomaly, decouples the radius and latitude equations into two perturbed harmonic oscillators whose solutions toO(J ₂ ⁴ ) are obtained using Lindstedt's method. From these solutions and the solution to the Hamilton-Jacobi equation suitable angle variables, their canonical conjugates and the new Hamiltonian are obtained. The new Hamiltonian, accurate toO(J ₂ ⁴ ) is function of only the momenta.     

The excitation of the forbidden coronal lines

The excitation of the 2s²2p² ground configuration of Caxv is calculated for coronal densities and temperatures. The calculations include electron and proton excitation of the forbidden transitions and electron excitation via the first excited (2s2p³) configuration. It is shown that measurements of the line intensity ratio I( 5694)/I( 5446) are in good agreement with the predictions. The line to continuum observations for limb flares and coronal condensations are discussed. It is suggested that the calcium abundance in condensations is enhanced owing to diffusion processes.Present address: Department of Astronomy, University of Texas, Austin, Texas, U.S.A.