Kinetic Alfvén waves in extended radio sources

We study a model of extended radio sources (ERS), in particular, extragalactic jets and radio lobes, which are inhomogeneous and where noncompressive Alfvén and surface Alfvén waves (and not shocks and magnetosonic waves) are primarily excited. We assume that a negligible thermal population exists (i.e., the ion density at the low-energy cut-off of the power law distribution is greater than the ion density of the thermal population, if present). Due to internal instabilities and/or the interaction of the ERS with the ambient medium, surface Alfvén waves (SAW) are created. We show that even very small amplitude SAW are mode converted to kinetic Alfvén waves (KAW) which produce large moving accelerating potentials , parallel to the magnetic field. Neglecting nonlinear perturbations, and for typical physical parameters of ERS, we obtaine1 MeV. Wesuggest that these potentials are important in acceleration (e.g., injection energy) and reacceleration of electrons in ERS. We show that energy losses by synchrotron radiation can be compensated by reacceleration by KAW. The relation between KAW acceleration, and previously studied cyclotron-resonance acceleration by Alfvén waves, is discussed.     

The motion of a satellite in an axi-symmetric gravitational field

The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C _jk ⁿ (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin²t - i inclination of the orbit - J _n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S _jk ⁿ (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M₊+m) (gravitational constant times the sum of the masses of Earth and satellite) - _n,k coefficients ofR component of disturbing acceleration (funtions off) - _n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X ₀ ^n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node     

Implications of a strongly peaked polar magnetic field

Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed _m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin ^p cos ^q which peaks near the equator (q p) will correspond to a cos ⁿ magnetic field at high latitudes only if p = 1 and _m = n /R. Recent measurements of n 8 and 600 km² s^–1 would then give _m 7 m s^–1.     

Alfvén instabilities in streaming plasmas with anisotropic pressures and their relevance for the solar wind

Low frequency or Alfvén waves in streaming plasmas can become unstable when the square of the Alfvén velocity is smaller than the mean square of the bulk motion in a co-moving reference frame, (u –u )², whereu stands for the bulk velocity of each species and u is the average bulk velocity of the plasma as a whole. For these new Alfvén instabilities the streaming effects can be enhanced by a suitable pressure anisotropy. Perpendicular pressure effects are stabilizing, parallel pressure effects are destabilizing, as in the usual firehose instability. The observed velocity differences between helium and the main (hydrogen) flow in the solar wind plasma are such that the Alfvén waves are getting close to marginal instability. These new Alfvén instabilities limit the velocity differences between helium and hydrogen and thus provide a possible mechanism for accelerating the helium particles up to the order of the main flow velocity.     

On the dissipation rates for Alfvén waves in the solar transition region

The present paper concerns Alfvén waves, in a resistive and viscous atmosphere, under a steep temperature gradient (Section 1). The dissipative Alfvén wave equation is deduced assuming uniform vertical background magnetic field, and allowing for arbitrary profiles of Alfvén speed, and viscous and resistive diffusivities as functions of altitude (Section 2). A three-parameter family of temperature profiles, allowing for independent choice of initial and asymptotic temperature, and of initial temperature gradient, is used to re-write the wave equation, with the temperature as the independent variable, instead of altitude (Section 3). It is shown that, for the conditions prevailing in the solar transition region between the chromosphere and corona, two approximations of the dissipative wave equations may be considered, the simplest leading to solution in terms of Gaussian hypergeometric functions (Section 4). The exact analytical solution allows calculation of the (i) velocity and (ii) magnetic field perturbations, (iii) kinetic, (iv) magnetic and (v) total energy density, (vi) energy flux, (vii) rate-of-strain and (viii) electric current, and (ix) viscous, (x) resistive and (xi) total rate of dissipation (Section 5). These are plotted versus temperature, across the transition region from the chromosphere to the corona, for the quiet and active Sun (Section 6). The feasibility of heating of the transition region by dissipation of Alfvén waves is discussed (Section 7), by comparing empirical heating rates, with theoretical values for a range of physical conditions, including initial velocity perturbations 5 to 15 km s ^–1, background magnetic field 12 to 120 G, wave periods 60 to 300 s, thickness of the transition region 100 to 300 km, resistive and anomalous diffusivities to 100 and viscous and turbulent diffusivities to 100 . The conclusion is that dissipation of Alfvén waves is not an effective heating mechanism for the transition region and corona, although it may be for the chromosphere (see Campos and Mendes, 1995, and references therein).     

Cherenkov emissions of Langmuir plasmons and light neutrinosby the flux of neutrinos

We consider the system of neutrino-antineutrino – plasma taking into account theirweak Fermi interaction, when the density of neutrinos andthe plasma particles are rather high and their collective interactionplays a vital role. New fluid instabilities driven by strong neutrino flux in aplasma are observed. It is shown that a bunch of neutrinos, drifting witha constant velocity across a homogeneous plasma, can also induce emission oflower energy neutrinos due to scattering, i.e. the decay of a heavy neutrino_H into a heavy and a light neutrino _L(_HHL) in a plasma. Furthermore we find thatthe neutrino production in stars does not lead in general to energy lossesfrom the neutron stars.     

The three principal secular resonances ν5, ν6, and ν16 in the asteroidal belt

We review theoretical and numerical results obtained for secular resonant motion in the asteroidal belt. William's theory (1969) yields the locations of the principal secular resonances ₅, ₆, and ₁₆ in the asteroidal belt. Theories by Nakai and Kinoshita (1985) and by Yoshikawa (1987) allow us to model the basic features of orbital evolution at the secular resonances ₁₆ and ₆, respectively. No theory is available for the secular resonance v₅. Numerical experiments by Froeschlé and Scholl yield quantitative and new qualitative results for orbital evolutions at the three principal secular resonances ₅, ₆, and ₁₆. These experiments indicate possible chaotic motion due to overlapping resonances. A secular resonance may overlap with another secular resonance or with a mean motion resonance. The role of the secular resonances as possible sources of meteorites is discussed.     

Approximate expressions for Gyrosynchrotron radiation in Transverse Propagation

Two sets of accurate approximate expressions for the gyrosynchrotron radiation in the transverse propagation case are presented for the first time. They contain emissivity _–/BNand absorptivity _– B/Nfor e-mode, effective temperature T _effand frequency of peak brightness _p. The expressions are designed for the range 2 to 7 of electron energy spectral index and for the ranges from 2 to 10 and 10 to 100 of harmonic numbers s(=/_B). Their statistical error is, respectively, ±18% and ±29% for _–/BNand _– B/Nfor 10/_B100, ±128% and and ±170% for 2/_B10.     

The universal solution of Einstein's equations of general relativity

Einstein's equations of general relativity are solved in terms of gravitational potential derivatives, withT equal to mass and/or field energy such thatT 0 outside a body. The line element equation then describes the variance of test particle internal geometrical structure and time-rate due to work done in a field, not the space-time curvature. Specific properties of gravitational fields and bodies come from this new solution: (a) The gravitational field consists of electromagnetic spin 2 gravitons which produce the gravitational force through the magnetic vector. (b) The gravitational mass is the Newtonian mass, not the relativistic mass, of a moving body. (c) An action principle exists in gravitation theory. (d) Attractive gravity exists between matter and antimatter. (e) Unification with quantum physics appears possible.     

The restricted problem of n+ν bodies

The simplest, conventional, and original form of the circular restricted problem of three bodies is briefly described in sidereal and synodic systems using dimensional and non-dimensional variables. This dynamical system is generalized to n2 primary bodies (from n=2) with masses M_i, 1in, interacting with arbitrary force laws (instead of only gravitational forces). The number of bodies of small mass mM_i not perturbing the primaries is increased from =1 to 1 where 1 and the minor bodies are allowed to interact with one another under arbitrary force laws. While the minor bodies (m) do not affect the motions of the primaries (M_i), the primaries influence the motions of the minor bodies with arbitrary force laws.For the case where n=2, 1, and only gravitational forces act on the system, an integral of the system is derived. It is shown that the energy integral of the general problem of N bodies and the Jacobian integral of the classical restricted problem of three bodies are limiting cases of this integral. The role of the integral in bounding the motion of the minor bodies is discussed. Several applications of this system are given.     

Tunneling and interference of Alfvén waves

The propagation and interference of Alfvén waves in magnetic regions is studied. A multilayer approximation of the standard models of the solar atmosphere is used. In each layer, there is a linear law of temperature variation and a power law of Alfvén velocity variation. The analytical solutions of a wave equation are stitched at the layer boundaries. The low-frequency Alfvén waves (P > 1 s) are able to transfer the energy from sunspots into the corona by tunneling only. The chromosphere is not a resonance filter for the Alfvén waves. The interference and resonance of Alfvén waves are found to be important to wave propagation through the magnetic coronal arches. The transmission coefficient of Alfvén waves into the corona increases sharply on the resonance frequences. To take into account the wave absorption in the corona, a method of equivalent schemes is developed. The heating of a coronal arch by Alfvén waves is discussed.     

A two-density neutron star model with continuity of density

Tolman's V solution has found wide application to the redshift problems in astrophysics but it has a drawback that there is singularity at the centre. We have developed a two-density model with a parabolic density distribution in the core ande r ²ⁿ in the envelope. The most distinctive feature of the model is that there is a continuity of all four variables (E, P, , and ) at the boundary. In other analytic core-envelope models the continuity of only three varaibles is possible. This two-density structure has been used to model neutron stars and their mass, size, and red shifts have been obtained.     

Kinetic theory of MHD instabilities in a nonuniform plasma

Most of the MHD instabilities originating from the nonuniformity of a plasma excite MHD surface wave. When the excited wave has a frequency _s which corresponds to the local shear Alfvén wave resonance (_s = k v _a (x), where v _a is the Alfvén speed and k is the wave number in the direction of the magnetic field), the surface wave resonantly mode converts to the kinetic Alfvén wave, the Alfvén wave having a perpendicular wavelength comparable to the ion gyroradius and being able to propagate across the magnetic field. We discuss various linear and nonlinear effects of this kinetic Alfvén wave on the plasma including particle acceleration and heating. A specific example for the case of a MHD Kelvin-Helmholtz instability is given.     

A self-consistent model for the storm radio emission from the Sun

A self-consistent theoretical model for storm continuum and bursts is presented. We propose that the Langmuir waves are emitted spontaneously by an anisotropic loss-cone distribution of electrons trapped in the magnetic field above active regions. These high-frequency electrostatic waves are assumed to coalesce with lower-hybrid waves excited either by the trapped protons or by weak shocks, making the observed brightness temperature equal to the effective temperature of the Langmuir waves.It is shown that whenever the collisional damping ( _c ) is more than the negative damping (- _A ) due to the anisotropic distribution, there is a steady emission of Langmuir waves responsible for the storm continuum. The type I bursts are generated randomly whenever the collisional damping ( _c ) is balanced by the negative damping (- _A ) at the threshold density of the trapped particles, since it causes the effective temperature of Langmuir waves to rise steeply. The number density of the particles responsible for the storm radiation is estimated. The randomness of type I bursts, brightness temperature, bandwidth and transition from type I to type III storm are self-consistently explained.On leave from Indian Institute of Astrophysics, Bangalore 560034, India.     

An Improved Optical Model for the Non-LTE Problem for the CO2 Molecule in the Atmosphere of Mars: Nighttime Populations of Vibrational States and the Rate of Radiative Cooling of the Atmosphere

The estimates of the population of excited vibrational states of the CO₂ molecule and of the rate of radiative cooling of the atmosphere in the 15-m CO₂ band are given for the nighttime mesosphere and thermosphere of Mars. For the first time, these estimates are made (1) with allowance for the overlap of lines in the 15-m band; (2) for a wide set of vibrational states of seven isotopes of the CO₂ molecule, which was used earlier in the solution of a similar terrestrial problem; and (3) using the rate constant for quenching of the CO₂(01¹0) state in collisions with oxygen atoms, which has been recently measured for low temperatures by Khvorostovskaya et al. (2002). The main results are as follows. 1. The approximation of isolated lines provides a satisfactory accuracy of determining the radiative cooling rate and overestimates vibrational temperatures of the states of the ₂ mode by no more than 3 K for the ¹²C¹⁶O₂ molecule and by no more than 2 K for low-abundant isotopes of the CO₂ molecule. 2. A reasonably high accuracy of estimating the cooling rate can be achieved by taking into account only fundamental vibrational transitions in ¹²C¹⁶O₂, ¹³C¹⁶O₂, ¹⁶O¹²C¹⁸O, and ¹⁶O¹²C¹⁷O molecules and the hot transitions 2_{2 2} and 3₂ 2₂ in the ¹²C¹⁶O₂ molecule. 3. The vertical profile of the total rate of radiative cooling displays two peaks. The maximum near a height of 130 km is very sensitive to temperature and to the ratio of the mixture for oxygen in the atmosphere.     

The ‘sleeping beauty’ galaxy NGC 4826: an almost textbook example of the abelian higgs vorto-source (-sink)

It is demonstrated that the kinematic peculiarity of the early Sab galaxy NGC 4826 can easily be understood in terms of the Abelian Higgs (AH) model of spiral galaxies. A cylindrically symmetric AH vorto-source (-sink) with a disk-to-bulge ratio > 1 is discussed and the distributions of the diagonal components of the corresponding stress-energy tensorT are presented. It is argued that the sign-changing componentT could account for the existence of twocounter-rotating gas disks whilenegative values ofT imply inward gas motions as observed in the outer and transition regions of the galaxy.     

The kink instability in infinite cylindrical flux tubes: Eigenvalues for power-law twist profiles

We develop simple accurate methods of calculating ideal MHD instability eigenvalues for infinitely-long cylindrical tubes, with twist functionT(r)=B /rB _z . A complete theoretical treatment is presented for force-free magnetic equilibria with arbitraryT(r), and detailed semi-analytic results for the kink instability are given for the particular case of a power-law twistT(r)=r , where the index is non-negative. Our results show that the most rapidly growing and energetic instabilities occur in the Gold-Hoyle =0 field, with the instability progressively weakening with increasing . However, the maximum force eigenvalue is always small, so that even in the Gold-Hoyle case (where =O(10^–2) in dimensionless units) only a small proportion of the available magnetic energy can be released in the linear phase. Our results also confirm that the linear pinch (=) is remarkably weak (=O(10^–3)) yet relatively resistant to line-tying! It is shown that the weakness of the force eigenvalue implies that the influence of uniform gas pressure on stability is negligible. Implications for the energy-release mechanism in solar flares are discussed.     

Analysis of Multicolor Observations of 3C 66A in 1993-1998

The results of multicolor observations of the blazar 3C 66A, obtained in the course of the project OJ-94, are analyzed. It is established that the energy distribution of the variable source in the optical and IR ranges can be represented, on the average, by a power law: F ^-0.92. Since the blazar's emission is strongly polarized, there is no doubt of the synchrotron nature of the variable source responsible for the blazar's activity.     

Non-inductive current driven by Alfvén waves in solar coronal loops

It has been shown that Alfvén waves can drive non-inductive current in solar coronal loops via collisional or collisionless damping. Assuming that all the coronal-loop density of dissipated wave power (W= 10–3 erg cm^–3 s^–1), which is necessary to keep the plasma hot, is due to Alfvén wave electron heating, we have estimated the axial current density driven by Alfvén waves to be jz 10³–10⁵ statA cm^–2. This current can indeed support the quasi-stationary equilibrium and stability of coronal loops and create the poloidal magnetic field up to B 1–5 G.     

Discrete Alfvén waves in solar loop prominences

It is shown that a discrete Alfvén wave can explain the natural oscillations of solar loop prominences by considering the existence of a current flow. Discrete Alfvén waves are a new class of Alfvén waves which is described by the inclusion of the finite ion cyclotron frequency (/ _cl 0) and/or the equilibrium plasma current. In this paper we consider only the effect of the current since in solar prominences (/ _cl 0). We have modeled the solar prominences as a cylindrical plasma, surrounded by vacuum (corona), with L a where L and a are the plasma column, length, and radius, respectively. We have calculated the spectrum of the discrete Alfvén waves as function of the magnitude and shape of the plasma current.