Stability of the triangular libration points of the circular restricted problem in the presence of resonances

The stability of triangular libration points, when the bigger primary is a source of radiation and the smaller primary is an oblate spheroid. has been investigated in the resonance cases ₁ = 2₂ and ₁ = 3₂. The motion is unstable for all the values of parameters q and A when ₁ = 2₂ and the motion is unstable and stable depending upon the values of the parameters q and A when ₁ = 3₂. Here q is the radiation parameter and A is the oblateness parameter.     

The distribution law of stellarp-modes

We show that the overall densityg() of asymptotic acoustic frequencies of a star obeys a Weyl lawg() ^D–1, whereD is the dimensionality of the oscillating stellar configuration. For realistic stars with a finite non-zero surface sound speed,D is equal to the actual dimensionality of the star,D=3. For formal models with a vanishing sound velocity at the surface, heuristic arguments lead to a dimensionality parameterD=4.5. The empirical frequencies of Eddington's standard model are found to be consistent with the latter distribution, with reasonable agreement already occurring in the low-frequency range > _i 2× fundamental radial mode. We argue that real stars obey this 3.5-power law in some finite frequency interval _i << _f , _f being a very high frequency critically depending on the surface sound velocity, while the full asymptotic law, withD=3, holds for > _f .     

A nonlinear tensor field and the second metric tensor

In our preceding paper {see [L. Sh. Grigorian and S. Gottlöber, Astrofizika (in press)]} we investigated a self-gravitating system consisting of a scalar field and a linear tensor field _ik= _ki with minimal coupling and with allowance for the action of vacuum polarization effects. In the present paper we investigate the case of a nonlinear tensor field _ik. The action S ⁽⁾ of the field _ik is determined by the difference R_ik — _ik, where R_ik is the space-time Ricci tensor and Rik is the analogous quantity constructed using the metric _ik=g_ik+_ik induced by _ik ( is a free parameter). Here S ⁽⁾ coincides with the previously known expression for the action of a linear field _ik. Equations of motion are derived for _ik in curved space-time. The energy-momentum metric tensor, determining the contribution of _ik to the gravitational field equations, is calculated.Translated from Astrofizika, Vol. 39, No. 1, pp. 135–144, January-March, 1996.     

Compton scattering of relativistic electrons in compact X-ray sources

The problem of single Compton scattering is considered and the resulting spectrum, angular distribution and polarization of scattered photons in a general case are obtained. The inverse Compton scattering (ICS) for arbitrary energies of electronsE and photons ₀ is investigated in detail. In the case of isotropically-distributed initial photons and relativistic electrons, a strong rise of the scattered spectrum near the upper edge takes place, starting from the values of the characteristic parameterb4E ₀10 (in units of mc²=1). The energy-loss rate of relativistic electrons due to ICS is calculated. It is shown that the relativistic electrons of the energiesE100 MeV, when scattering on the X-rays with ₀~10KeV, transmit the dominant part of their energy to the photons which fall after scattering into the energy range of the electrons (100 MeV).The radiation spectrum of ICS, as well as the energy-losses of relativistic electrons distributed by power-lawE ^–, are calculated. The radiation spectrum reveals the power-law behaviour with the different indices in two limits: the dependence ^–(1)/2 at ₀1 gradually changes to ^–(+1) ln (₀) law for ₀1.     

Pulsar radio emission from expanding charge sheets

We semi-quantitatively calculate the distribution of energy in frequency and angle emitted from a sheet of charges that are moving out relativistically along dipolar magnetic field lines originating near the magnetic polar caps of a rotating neutron star. The angular distribution is conical with the angle of maximum intensity varying with frequency as ^–1/4 for _c 2 _c /(R _M ²), whereR_M is the initial angular radius of the charge sheet at the surface of the star of radiusR. At higher frequencies the width of the angular cone remains constant. The radiation is linearly polarized with the polarization vector in the plane of the line of sight and the magnetic axis. A sheet of uniform charge density and finite thickness has a frequency spectrum that varies from ^–3/2 to ^–4 for _c and _c , respectively. These features are in good general agreement with the observed characteristics of the intensity, pulse shape, and frequency spectrum of the radio pulses from pulsars.Operated by Associated Universities, Inc., under contract with the National Science Foundation.     

On the origin of type III fundamental

A two-component scheme for the generation of type III fundamental radiation is proposed. The first component of the fundamental arises at a plasma level _{L t} because of the Rayleigh scattering of the plasma waves into electromagnetic radiation. The other component arises at _{L t} /2 because of the decay of the first component into plasma waves and the subsequent rescattering of the plasma waves into electromagnetic radiation _t 2( _t /2). By its properties (location, directivity, polarization) the second component is essentially the same as the second harmonic radiation produced by a stream of fast electrons at _L ( _t /2). This scheme is used to solve the main problems (localization and directivity of the source, polarization of type III fundamental) of the harmonic theory of type III solar bursts.     

Lower hybrid wave model for aurora

In the framework of non-linear fluid theory we use a lower hybrid (LH) wave of the form as a pump which interacts with the small fluctuations with the low-frequency vibrations _i or =0, where _i , is the hydrogen ion-cyclotron (HIC) gyrofrequency. The ponderomotive force generated by the beating of the high-frequency pump wave ₀ and the sideband LH waves (±₀) produces a non-linear coupling between the high- and low-frequency motions of electrons and ions. Under certain conditions the HIC waves and the zero-frequency waves both become parametrically unstable and start to grow. These excited waves then heat the ions by stochastic acceleration in the transverse direction, thus explaining the formation of ion comics along the auroral field lines. Electrons would be heated in the parallel direction directly by the pump field as well as by low-frequency waves. Thus a single mechanism can explain the existence of ion-cyclotron waves, zero-frequency waves, ion conics, and energetic electrons along the auroral field lines.     

The 4∶1 resonance

We study the resonance ₁₂ = 41 and some near-resonance cases. The main peculiarity of this resonance is that for ₁₂ < 4 the characteristic of the central periodic orbits is broken into two and each part is joined with a resonant characteristic. This behaviour is described theoretically by means of the third integral. It seems that there are infinite families of simple periodic orbits near the escape region. Finally, a comparison is made with the cases near the ₁₂ = 21 resonance.     

Asymptotic properties of disk dynamo

The asymptotic properties of a turbulent disk dynamo at large dimensionless numbersR andR characterizing the helicity and the differential rotation are analysed. Three types of generations in the dependence of the relations betweenR andR are found: ²-dynamo and two types of -dynamo. For each of these types the rates of growth are obtained and the forms of solution are pointed out. Boundaries of the disk dynamo approximation are given.     

Existence of the continuations in theN-body problem

The method of obtaining the estimates of the maximalt-interval ( _–, ₊) on which the solution of theN-body problem exists and which is such that some fixed mutual distance (e. g. ₁₂) exceeds some fixed non-negative lower bound, for allt contained in ( _–, ₊), is considered. For given masses and initial data, the increasing sequences of the numbers _k , each of which provides the estimate ₊ > _k , are constructed. It appears that if ₊ = +, then .     

Prompt proton and electron acceleration to relativistic energies in solar flares

As a possible mechanism for particle acceleration in the impulsive phase of solar flares, a new particle acceleration mechanism in shock waves is proposed; a collisionless fast magnetosonic shock wave can promptly accelerate protons and electrons to relativistic energies, which was found by theory and relativistic particle simulation. The simultaneous acceleration of protons and electrons takes place in a rather strong magnetic field such that _{ce pe} . For a weak magnetic field ( _{ce pe} ), strong acceleration occurs to protons only. Resonant protons gain relativistic energies within the order of the ion cyclotron period (much less than 1 s for solar plasma parameters). The electron acceleration time is shorter than the ion-cyclotron period.     

Electrostatic Wave Instability and Plasma Radiation from Coronal Loops

Polarization properties of solar and stellar radio emission require, in some cases, emission below the third or fourth coronal electron gyro level, < 3,_c; 4, _c. In the context of plasma radiation, the source parameters should be such that the intermediate magnetic field condition 1 < _p ² / _c ² < 3 is satisfied. Supposing this condition, we investigate the generation of electrostatic waves in a warm background plasma with a high-energy component of magnetically trapped electrons. We invoke the conversion of upper-hybrid waves and Bernstein waves into electromagnetic radiation as being responsible for intense radio emission from a coronal magnetic loop. Moreover, odd-half harmonic emissions in the solar radio spectrum as well as the o-mode polarization at the second harmonic of the plasma frequency are natural consequence of this proposed model.     

Vertical motions in an intense magnetic flux tube

The recent discovery of localised intense magnetic fields in the solar photosphere is one of the major surprises of the past few years. Here we consider the theoretical nature of small amplitude motions in such an intense magnetic flux tube, within which the field strength may reach 2 kG. We give a systematic derivation of the governing expansion equations for a vertical, slender tube, taking into account the dependence upon height of the buoyancy, compressibility and magnetic forces. Several special cases (e.g., the isothermal atmosphere) are considered as well as a more realistic, non-isothermal, solar atmosphere. The expansion procedure is shown to give good results in the special case of a uniform basic-state (in which gravity is negligible) and for which a more exact treatment is possible.The form of both pressure and velocity perturbations within the tube is discussed. The nature of pressure perturbations depends upon a critical transition frequency, _p , which in turn is dependent upon depth, field strength, pressure and density in the basic (unperturbed) state of the tube. At a given depth in the tube pressure oscillations are possible only for frequencies greater than _p for frequencies below _p exponentially decaying (evanescent) pressure modes occur. In a similar fashion the nature of motions within the flux tube depends upon a transition frequency, _v . At a given depth within the tube vertically propagating waves are possible only for frequencies greater than _v ; for frequencies below _v exponentially decaying (evanscent) motions occur.The dependence of both _v and _p on depth is determined for each of the special cases, and for a realistic solar atmosphere. It is found that the use of an isothermal atmosphere, instead of a more realistic temperature profile, may well give misleading results.For the solar atmosphere it is found that _v is zero at about 12 km above optical depth ₅₀₀₀= 1, thereafter rising to a maximum of 0.04 s^–1 at some 600 km above ₅₀₀₀ = 1. Below ₅₀₀₀ = 1, in the convection zone, _v has a maximum of 0.013 s^–1. The transition frequency, _p , for the pressure perturbations, is peaked at 0.1 s^–1 just below ₅₀₀₀ = 1, falling to a minimum of 0.02 s^–1 at about one scale-height deeper in the tube     

Concerning isothermal self-similar blast waves

We investigate the one-dimensional self-similar flow behind a blast wave from a plane explosion in a medium whose density varies with distance asx _– with the assumption that the flow is isothermal. If <0 a continuous solution passing through the origin and the shock does not exist. If 1/3>>0 one critical point exists. To be physically acceptable the flow must by-pass this critical point. It is shown that a continuous solution passing through both the origin and through the shock and by-passing the critical point does exist. If 1>>1/3 the first critical point does not exist but a second one appears. To be physically acceptable the flow must again by-pass this new critical point. We show that a continuous solution passing through both the origin and the shock and by-passing the new critical point exists in this case. If >1 no physically acceptable solution exists since the mass behind the shock is infinite.The dependence of the solutions on the parameter is analytic for >0 so that interpolation between neighboring values of is permitted.We investigate the stability of these isothermal blast waves to one-dimensional but non-self-similar perturbations. If 0<<5/7, the solutions are shown to be linearly unstable against short wavelength perturbations near the origin. If the solution crosses the shock with a normalized velocityu>2 the solution is linearly unstable against short wavelength perturbations near the shock for 1>>0. If the solution crosses the shock with normalized velocity 2>u>1 (and it must cross the shock withu>1), the solution is certainly unstable against short wavelength perturbations near the shock for >11/19 and, depending on the crossing velocity, can be unstable there for all .Thus for 1>>0, the solution is always unstable somewhere. Since there is no characteristic time scale in the system all instabilities grow as a power law of time rather than exponentially. The existence of these instabilities implies that initial deviations do not decay and the system does not tend to a self-similar form.     

Adiabatic-drift-loss modification of the electromagnetic loss-cone instability for anisotropic plasma

Observation of the adiabatic behaviour of energetic particle pitch-angle distributions in the magnetosphere (Lyons, 1977, and others) in the past indicated the development of pronounced minima or drift-loss cones on the pitch-angle distributions centred at 90° in connection with storm-time changes in magnetospheric convection and magnetic field. Using a model of a drift-modified loss-cone distribution (MLCD) of the butterfly type, the linear stability of electromagnetic whistler or ion-cyclotron waves propagating parallel to the magnetic field has been investigated. The instability is shown to be quenched at high frequencies < _m =A/(A+1), whereA is the thermal anisotropy. This quenching becomes stronger the higher are the respective parallel hot particle thermal velocityA _h and cold plasma densityn _c . Particles around pitch-angles 90° are identified as generating electromagnetic cyclotron waves near the marginally stable frequency _m . It is concluded that the absence of electromagnetic VLF and ELF noise during times when MLCD develops is the result of the shift of the unstable spectrum to low frequencies.     

Models of pulsating low-massive yellow supergiants

The nonlinear self-excited oscillations of the envelopes of low-massive highly luminous stars are described. The parameters for these models wereM=0.8M ,M _bol=–5.5, –5.84 mag,T _eff=4500, 5000, 5500 K. The oscillations have been found to consist of the standing wave pulsation near the envelope bottom and running waves in outer layers. The ratio of the standing wave frequency _s to the average frequency of the running waves _r increases with the stellar luminosity: _s / _r =1.7 whenM _bol=–5.5 mag and _s / _r =2.4 whenM _bol=–5.84 mag. The frequency of oscillations near the photosphere is found to be in close agreement with the critical frequency for running waves. Mass loss from these stars is caused by shocks. It has been shown that agreement between FG Sge's period change observed during the last decade and the period-luminosity relation for double shell stars takes place when FG Sge's luminosity isM _bol=–5.96 mag.     

A Razin-Tsytovich effect for bremsstrahlung

It is shown that bremsstrahlung from electrons with Lorentz factor 1 is suppressed for >_p in a plasma with plasma frequency _p compared with emission in vacuo. For _p the ratio of the power emitted per unit frequency in the plasma to that in vacuo varies as ².This suppression effect is analogous to the suppression of synchrotron radiation in a plasma (Razin-Tsytovich effect). It is argued that such suppression is a characteristic property of emission by relativistic particles in a plasma.     

Interpretation of distinct type IVmA- and IVμ-bursts on the basis of micro-instabilities and of resonant nonlinear interaction of waves

The generation of space charge waves by micro instabilities of the Harris type and their conversion into electromagnetic waves is discussed in the framework of the dispersion curves of the extraordinary wave mode in the warm plasma. Acceleration of electrons as also nonlinear interactions of waves are taken into account. A survey of the parameter regions of the Harris instabilities is given. Distinct values _p / _c and _p / _c result, enabling the instability as well as the conversion. The moving type IVmA bursts, and on the other side the impulsive cm-bursts and the first phase of type IV bursts are correlated to different values _p / _c and corresponding heights in the corona. The space charge waves can produce hydromagnetic waves by parametric excitation, too (type II bursts). The proposed mechanism is discussed with respect to the energy balance and to the magnetic configurations derived from observations with the Culgoora radioheliograph.     

Thermal and electrical conductivities of crystals in neutron stars and degenerate dwarfs

Thermal and electrical conductivities due to electron scattering on phonons are calculated for degenerate cores of white dwarfs and envelopes of neutron stars for wide ranges of density, temperature and ion charge. In the stellar zones, in which T _pi(Z^1/3e²/_F) (_piis the ion plasma frequency and _F the Fermi velocity of electrons), the main contribution into scattering comes from the Umklapp processes. In the zones with lowerT, the Umklapp processes are frozen out, that results in a sharp growth of electrical and thermal conductivities. This, for instance, should make nuclear burning more stable in such zones.     

Stability and motion in two degree-of-freedom hamiltonian systems for two-to-one commensurability

The two time variable method is used to investigate the stability of and the motion about the equilibrium point of an autonomous Hamiltonian system of two degrees of freedom when the HamiltonianH is indefinite and the relation between the frequencies ₁ and ₂ of the linearized system is ₁ 2₂. Also, the conditions for periodic orbits and the stability of these orbits are obtained.