The spherically-symmetrical trajectories of spin particles in the Schwarzschild field

The motion of spin particles in the Schwarzschild field is examined in this paper. It is shown that Mathisson-Papapetrou equations under additional conditions , where is the Lie derivative of the Killing vector _j , permit only radial motion, motion in the equatorial plane and in the equilibrium points. All these types of motion are considered more in detail.     

Apsidal motion in the close binary IT cassiopeiae

In 1982 and 1993, we carried out highly accurate photoelectric WBVR measurements for the close binary IT Cas. Based on these measurements and on the observations of other authors, we determined the apsidal motion $\left[ {\dot \omega _{obs} = {{(11\mathop .\limits^ \circ 0 \pm 2\mathop .\limits^ \circ 5)} \mathord{\left/ {\vphantom {{(11\mathop .\limits^ \circ 0 \pm 2\mathop .\limits^ \circ 5)} {100 years}}} \right. \kern-0em} {100 years}}} \right]$ . This value is in agreement with the theoretically calculated apsidal motion for these stars $\left[ {\dot \omega _{th} = {{(14^\circ \pm 3^\circ )} \mathord{\left/ {\vphantom {{(14^\circ \pm 3^\circ )} {100 years}}} \right. \kern-0em} {100 years}}} \right]$ .     

Apsidal motion in the eclipsing binary AS Cam

Multi-colourWBVR photoelectric observations of the eclipsing binary AS Cam have been carried out and the photometric elements, absolute dimensions, and the angular velocity of a periastron motion ( \(\mathop \omega \limits^ \cdot _{obs}\) ) are determined. The obtained value of \(\mathop \omega \limits^ \cdot _{obs}\) is almost three times smaller than that theoretically predicted.     

A wide-field corrector at the prime focus of a Ritchey-Chrétien telescope

We propose a form of a lens corrector at the prime focus of a hyperboloidal mirror that provides a flat field of view up to 3° in diameter at image quality D₈₀<0.8 arcsec in integrated (0.32–1.1 µm) light. The corrector consists of five lenses made of fused silica. All lens surfaces are spherical in shape, so the system is capable of achieving better images, if necessary, by aspherizing the surfaces. The optical system of the corrector is stable in the sense that its principal features are retained when optimized after significant perturbations of its parameters. As an example, we calculated three versions of the corrector for the Blanco 4-m telescope at Cerro Tololo Inter-American Observatory with \(2\mathop .\limits^ \circ 12\), \(2\mathop .\limits^ \circ 4\) and \(3\mathop .\limits^ \circ 0\) fields of view.     

The interaction of an obliquely incidents-polarized plane electromagnetic wave at a warm moving magnetized plasma half-space

The interaction of ans-polarized plane electromagnetic wave incident from a dielectric (or vacuum) region on awarm moving magnetized plasma half-space is considered. The external magnetic field is assumed to be normal to the direction of the wave normal and the velocity of the moving medium. Using the first three moment equations, together with Maxwell's electromagnetic equations, we construct the constitutive relations in the rest frame of the moving medium. The constitutive relations are then transformed to the laboratory frame by invokingMinkowski's equations for the moving plasma medium, and the dispersion relation for the propagating ordinary mode in the moving medium is derived. Expressions are obtained for the phase and group velocities and the index of refraction for the ordinary mode, as also for power reflection and transmission coefficients. It is found that in contrast to the case of a cold magnetized plasma, the ordinary electromagnetic mode excited in the warm magnetoplasma medium getsmodified due to the presence of an external magnetic field. In addition, the various reflection and transmission characteristics for a warm magnetoplasma depend on the velocity of the moving plasma as well as on the strength of the applied magnetic field, as against the case for a cold moving magnetized plasma. Numerical results on the reflection coefficient are presented for several values of the parameters characterizing the electron-plasma temperature, the velocity of the moving medium and the strength of the applied magnetic field.     

Electromagnetic instabilities in an anisotropic loss-cone plasma

A form of general dispersion relation for electromagnetic waves in a fully ionized anisotropic plasma with loss-cone that explicates the contribution of the loss-cone to the dispersion relation is developed. By initially ignoring effects due to anisotropy, it is shown by means of Nyquist diagram technique that an isotropic loss-cone distribution can be unstable to EM waves corresponding to the whistler mode (0<< _e ). The growth rate is then determined analytically for this distribution, assuming cyclotron resonance between the waves in the whistler mode and particles in the high energy tail of the velocity distribution. By including the effects of anisotropy, a general growth rate is obtained which is found to depend on the anisotropy, the size of the loss-cone, the softness of the energy spectrum, and the fraction of the particles which are resonant with the wave. For particular distributions the relative contributions of the anisotropy and of the loss-cone to the growth rate have been determined. It is seen that loss-cone effects, which depend on the size of the loss-cone as well as the softness of the energy spectrum, can be a significant factor in the determination of the growth rate. For the Lorentzian distribution, the half-width of unstable waves is considerably broadened and the growth rates are somewhat more severe as compared to a two-temperature Maxwellian. The threshold frequency is which confirms the presence of unstable EM waves in the magnetospheric plasma leading to turbulence.     

Continuum spectrum of the star Θ1 Ori C

Published photoelectric measurements over a wide wavelength range (0.36–18 µm) are used to study the continuum spectrum of the star Θ¹ Ori C. The model that assumes the following three radiation sources is consistent with observations: (1) a zero-age main-sequence O7 star (object 1) of mass M ₁=20M _⊙, radius R ₁=7.4R _⊙, effective temperature T ₂=37 000 K, and absolute bolometric magnitude $M\mathop {bol}\limits^1 = - 7\mathop .\limits^m 7$ ; (2) object 2 with M ₂=15M _⊙, R ₂=16.2R _⊙, T ₂=4000 K, and $M\mathop {bol}\limits^2 = - 5\mathop .\limits^m 1$ ; and (3) object 3 with R ₃10 700 R _⊙, T ₃=190 K, and $M\mathop {bol}\limits^3 = - 0\mathop .\limits^m 6$ . The visual absorption toward the system is $A_V = 0\mathop .\limits^m 95$ and obeys a normal law. The nature of objects 2 and 3 has not been elucidated. It can only be assumed that object 2 is a companion of the primary star, its spectral type is K7, and it is in the stage of gravitational contraction. Object 3 can be a cocoon star and a member of the system, but can also be a dust envelope surrounding the system as a whole.     

Theoretical emission line strengths for Ov compared to EUV solar observations

RecentR-matrix calculations of electron impact excitation rates in Ov are used to derive the emission line intensity ratios (in energy units) $$\begin{gathered} R_1 = I(2s2p^{ 3} P - 2p^{2 3} P)/I(2s^{2 1} S_0 - 2s2p^{ 1} P_1 ) = I(761.1\mathop A\limits^ \circ )/I(629.7\mathop A\limits^ \circ ), \hfill \\ R_2 = I(2s^{2 1} S_0 - 2s2p^{ 3} P_1 )/I(2s^{2 1} S_0 - 2s2p^{ 1} P_1 ) = I(1218.4\mathop A\limits^ \circ )/I(629.7\mathop A\limits^ \circ ), \hfill \\ \end{gathered} $$ and $$R_3 = I(2s2p^{ 1} P_1 - 2p^{2 1} S_0 )/I(2s^{2 1} S_0 - 2s2p^{ 1} P_1 ) = I(774.5\mathop A\limits^ \circ )/I(629.7\mathop A\limits^ \circ )$$ as a function of electron temperature (T _e) and density (N _e). These results are presented as plots ofR ₁ vsR ₂, andR ₁ vsR ₃, which should allowboth N _e andT _e to be deduced for the Ov line emitting region of a plasma. Electron densities derived from the (R ₁,R ₂) and (R ₁,R ₃) diagrams in conjunction with observational data for several solar features obtained with the Harvard S-055 spectrometer on boardSkylab are found to be compatible, and in good agreement with values ofN _e estimated from line ratios in species formed at similar electron temperatures to Ov. In addition, values ofT _e determined from (R ₁,R ₂) and (R ₁,R ₃) are generally close to that expected theoretically. These results provide experimental support for the accuracy of the diagnostic calculations presented in this paper, and hence the atomic data used in their derivation.     

Optical monitoring of the central region of the globular cluster M 15 = NGC 7078: New variable stars

We obtained a series of more than two hundred R-band CCD images for the crowded central (115″×77″) region of the metal-poor globular cluster M 15 with an angular resolution of \(0\mathop .\limits^{''} 5 - 0\mathop .\limits^{''} 9\) in most images. Optimal image subtraction was used to identify variable stars. Brightness variations were found in 83 stars, 55 of which were identified with known cluster variables and the remaining 28 are candidates for new variables. Two of them are most likely SX Phe variables. The variability type of two more stars is uncertain. The remaining stars were tentatively classified as RR Lyrae variables. A preliminary analysis of published data and our results shows that the characteristics of RR Lyrae variables in the densest part (r<35″) of the cluster probably change. More specifically, the maximum of the period distribution of first-and second-overtone (RR1, RR2) pulsating stars shifts toward shorter periods; i.e., there is an increase in the fraction of stars pulsating with periods \( < 0\mathop .\limits^d 3\) and a deficiency of stars with \(0\mathop .\limits^d 35 - 0\mathop .\limits^d 40\). The ratio of the number of these short-period RR Lyrae variables to the number of fundamental-tone (RR0) pulsating variables changes appreciably. We found and corrected the error of transforming the coordinates of variables V128–155 in M 15 into the coordinate system used in the catalog of variable stars in globular clusters.     

Sound and thermal waves propagation in a hydrogen plasma heated by an external radiation field

The thermal equilibrium of a hydrogen plasma heated and ionized by an external radiation field, diluted by a factorW _* and defined by an effective temperatureT _*, is studied. In addition, the problem of propagation of acoustic and thermal waves in the above plasma model is also analysed. It is found that an external radiation field has stabilizing effects against wave amplification. From the dispersion relation obtained, the phase velocity for sound and thermal waves and their respective scale-length of damping (or anti-damping) is calculated as a function of the frequency for representative values of the plasma temperature and the external radiation fieldT _*.     

Non-Homogeneous Charge-Consistent Model for Acceleration of Iron in the Solar Corona

Acceleration of iron ions by a spherical shock wave moving through non-homogeneous solar corona is considered. The energy dependence of the mean charge of iron, _Fe(E), is determined by the characteristic acceleration time, T _a, trapping time, T _tr, and time for charge changes, T _q. The latter varies along with plasma number density during the propagation of the shock wave in the corona. Our calculations have demonstrated that adiabatic energy changes, Coulomb losses and shock broadening do not sufficiently influence the dependence _Fe(E). According to our estimations, the photoionizing processes can scarcely affect the ionic states of accelerated iron, except probably for the most powerful X10 class events.     

Astrophysical thermonuclear functions

Stars are gravitationally stabilized fusion reactors changing their chemical composition while transforming light atomic nuclei into heavy ones. The atomic nuclei are supposed to be in thermal equilibrium with the ambient plasma. The majority of reactions among nuclei leading to a nuclear transformation are inhibited by the necessity for the charged participants to tunnel through their mutual Coulomb barrier. As theoretical knowledge and experimental verification of nuclear cross sections increases it becomes possible to refine analytic representations for nuclear reaction rates. Over the years various approaches have been made to derive closed-form representations of thermonuclear reaction rates (Critchfield, 1972; Haubold and John, 1978; Haubold, Mathai and Anderson, 1987). They show that the reaction rate contains the astrophysical cross section factor and its derivatives which has to be determined experimentally, and an integral part of the thermonuclear reaction rate independent from experimental results which can be treated by closed-form representation techniques in terms of generalized hypergeometric functions. In this paper mathematical/statistical techniques for deriving closed-form representations of thermonuclear functions, particularly the four integrals $$\begin{gathered} I_1 (z,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - zy^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ I_2 (z,d,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - zy^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ I_3 (z,t,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - z(y + 1)^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ I_4 (z,\delta ,b,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - by^\delta } e^{ - zy^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ \end{gathered} $$ will be summarized and numerical results for them will be given. The separation of thermonuclear functions from thermonuclear reaction rates is our preferred result. The purpose of the paper is also to compare numerical results for approximate and closed-form representations of thermonuclear functions. This paper completes the work of Haubold, Mathai, and Anderson (1987).     

Compatibility conditions for a non-quadratic integral of motion

Conditions are found which are satisfied by the coefficients of the expression being a second integral of the motion of an autonomous dynamical system with two degrees of freedom. The coefficientsA, B. , ,E are differentiable functions of the cartesian position coordinatesx, y. The velocity components are denoted by . It is shown that must be constant andB must be of the formB =f(x+y) +g(x-y) wheref, g are arbitrary.Given andB one can always find the remaining coefficientsA, E and also the corresponding potential and second integral. Depending on the specifica case at hand a certain number of arbitrary constants (or arbitrary functions) enter into the potential and the second integral. To each potential (which may be of the separable or nonseparable type in the coordinatesx andy)there corresponds one integral of the above form.     

Stability of motion of the restricted circular and charged three-body problem

Stabiliity is applied to characterize type of motion in which the moving body is confined to certain limited regions and in this sense we may say that the motion of the body in question is stable. This method has been used in the past chiefly in connection with the classical restricted problem of three bodies.In this paper we consider a dynamical system defined by the Lagrangian

Solution of Lambert's problem for short arcs

Approximation formulas are found for and , wherex(t) satisfies ,x(0)=x ₀,x(1)=x ₁. The results are applied to an example of two-body motion.     

A revised version of synchrotron radiation in a magnetized plasma

We analyze the propagation features of synchrotron radiation of a charge moving with a gyrating helix trajectory (3-dimensional) in a magnetoplasma. We found that a new factor (1+ cot ) should be included into the relevant spectrum radiation formulae and the usual relativistic factor has to be modified as , ifv <v _g , the radiative energy are more concentrated along the velocity of the moving charge; but ifv>v _g, the direction of maximum energy cone deviates from the direction of the moving charge.     

The velocity of pulsars and interstellar irregularities in the scintillation pattern

The scintillation theory is developed for application to the interstellar medium taking into account both the movement of the pulsars and the movement of the interstellar irregularities.It is shown that the velocity of the drifting pattern differs essentially from that for the pulsars. This difference is due to the medium extent effect and to the motion of the irregularities. The pulsar velocityv ₀ and the parameters of the motion of the irregularities ( , ) can be derived from the obtained formulae, using the known parameters of the cross-correlation function of scintillations (V _ef, ₁,S).In contrast with the interplanetary scintillation, the asymmetry of the form of the cross-correlation function of the interstellar scintillations is caused not only by the motion of the interstellar irregularities, but also by the movement of the source itself.     

Peculiarities of processing VLBI observations of pulsars

We determined the features of pulsars that were disregarded in standard amplitude-calibration procedures for VLBI observations. We suggest additional amplitude-calibration methods. These methods were used to process the VLBI observations of the pulsar PSR B0329+54 carried out with the HALCA ground—space interferometer. Data from the space radio telescope are corrected for a nonuniform reception band. We estimated the diameter of the scattering disk for this pulsar at a frequency of 1600 MHz: \( < 1\mathop .\limits^{''} 8 \times 10^{ - 3}\).