Effects of a deformation of a star on the gravitational lensing

We study analytically a gravitational lens due to a deformed star, which is modelled by using a monopole and a quadrupole moment. Positions of the images are discussed for a source on the principal axis. We present explicit expressions for the lens equation for this gravitational lens as a single real 10th-order algebraic equation. Furthermore, we compute an expression for the caustics as a discriminant for the polynomial. Another simple parametric representation of the caustics is also presented in a more tractable form. A simple expression for the critical curves is obtained to clarify a topological feature of the critical curves; the curves are simply connected if and only if the distortion is sufficiently large.     

FAST单元面板面型检测算法研究

500 m口径球面射电望远镜(Five-hundred-meter Aperture Spherical Radio Telescope,FAST)是一个超大口径的可动望远镜,有三项技术创新,一是选址,二是轻型馈源索支撑,三是主动反射面。在主动反射面上,单元面板的面型和面板的出厂加工精度对电磁波在反射面的汇聚有很大影响。FAST主反射面由4 600块三角形反射面板拼接而成,每块面板为边长11 m三角形,这对FAST反射面面板的测量技术提出了更高的要求。摄影测量直接在影像上进行量测,无需接触物体本身;所摄影像信息丰富,可以从中获得所研究物体的大量几何信息和物理信息;适用于大范围、多目标测量,效率高。目前世界上最大的射电望远镜,如GBT和ARECIBO都是采用摄影测量技术进行反射面面形检测。在对现有的面型检测技术调研并试验后,提出基于数字近景摄影测量的方法,对FAST反射面11 m单元面板的面型进行检测,数分钟完成反射面板面型的一次检测,测量精度达到2.5 mm,经过调整后的单元面板的面型精度达到了3.0 mm,结果表明摄影测量应用于FAST反射面单元面板面型检测是可行的。     

Estimating the significance of a signal in a multi-dimensional search

In experiments that are aimed at detecting astrophysical sources such as neutrino telescopes, one usually performs a search over a continuous parameter space (e.g. the angular coordinates of the sky, and possibly time), looking for the most significant deviation from the background hypothesis. Such a procedure inherently involves a “look elsewhere effect”, namely, the possibility for a signal-like fluctuation to appear anywhere within the search range. Correctly estimating the p-value of a given observation thus requires repeated simulations of the entire search, a procedure that may be prohibitively expansive in terms of CPU resources. Recent results from the theory of random fields provide powerful tools which may be used to alleviate this difficulty, in a wide range of applications. We review those results and discuss their implementation, with a detailed example applied for neutrino point source analysis in the IceCube experiment.     

On the Dynamics of a Deformable Satellite in the Gravitational Field of a Spherical Rigid Body

In this paper, a model is developed for the dynamics of a system of two bodies whose material points are under the influence of a central gravitational force. One of the bodies is assumed to be rigid and spherically symmetric, while the other is assumed to be deformable. To develop a tractable model for the system, the deformable body is modeled using Cohen and Muncaster's theory of a pseudo-rigid body. The resulting model of the system has several of the features, such as angular momentum conservation, exhibited by more restrictive models. We also show how the self-gravitation of the deformable body can be accommodated using appropriate constitutive equations for a force tensor. This enables our model to subsume many existing models of ellipsoidal figures of equilibrium. After the model and its conservations have been discussed, attention is restricted to steady motions of the system. Several results, which generalize recent works on rigid satellites, are established for these motions. For a specific choice of constitutive equations for the pseudo-rigid body, we determine the steady motions with the aid of a numerical continuation method. These results can also be considered as generalizations of earlier works on Roche's ellipsoids of equilibrium.     

Motion of a satellite in the equatorial plane of a spheroid

An exact, closed-form solution of the problem of the motion of a satellite in the equatorial plane of an oblate body is obtained. It is shown that the classic formula for the motion of the perihelion is a first order approximation to the exact formula.     

Refinement of the phase of a spherical planet located at a small distance from the Sun

Formulas for refining the phase of a spherical planet located a small distance from the Sun are derived. Finite heliocentric distance of the planet results in the formation on its visible disk of the geometric terminator, which is not coincident with the orthographic terminator. The visible disk is assumed to be observed from Earth in orthographic projection. We suggest introducing linear and surface phases for the geometric terminator in accordance with two existing definitions of the phase of a planet. Linear and surface phases of a planet are shown to be given by different sets of formulas. An example of the computation of the phase of Mercury is given.     

The Skewness of a Solar Cycle as a Precursor of the Amplitude of the Next

As a precursor for predicting the maximum amplitude of the coming solar cycle, the skewness of the previous cycle proposed by Ramaswamy (1977) is revisited. The reliability of the prediction method is improved by separating odd and even cycles. A first method is proposed on the basis of calculated skewness. In that case, the prediction is available at the end of the previous cycle. A possibility to anticipate the availability of the skewness by about one year is pointed out. A second method, adding prediction of the skewness itself is studied. The statistical reliability is lower than in the first case, but the prediction of a cycle maximum is available at the maximum of the previous cycle.     

Stability of a finite disc under the influence of a spherical halo

We have studied the stability of finite gaseous discs, against large-scale perturbations, under the influence of spherical, massive haloes. A surface-density distribution consistent with the observed spiral-tracer profiles in disc galaxies is considered for the disc. We find that growing eigenmodes with both ‘trailing’ and ‘leading’ spirals exist in ‘cold’ discs for a wide range of values of the halo mass and its radius. The amplification rates of the unstable modes reduce as the ratio of the mass of the halo to the mass of the disc is increased. A uniform halo is not very effective towards stabilizing the disc against these modes. The results from the present study are consideredvis-a-vis previous studies on the global modes of self-gravitating discs.     

Larmor radius effects on the instability of a rotating layer of a self-gravitating plasma

The instability of a stratified layer of a self-gravitating plasma has been studied to include jointly the effects of viscosity, Coriolis forces and the finite Larmor radius (FLR). For a plasma permeated by a uniform horizontal magnetic field, the stability analysis has been carried out for a transverse mode of wave propagation. The solution has been obtained through variational methods for the case when the direction of axis of rotation is along the magnetic field. The analysis for the case when the direction of rotation is transverse to the magnetic field has also been considered and the solutions for this case have been obtained through integral approach. The dispersion relations have been derived in both the cases and solved numerically. It is found that both the viscous and FLR effects have a stabilizing influence on the growth rate of the unstable mode of disturbance. Coriolis forces are found to have stabilizing influence for small wave numbers and destabilizing for large wave numbers.     

Libration points and the general case in the problem of the motion of a star inside a layered inhomogeneous elliptical galaxy with a variable mass

We have found libration points and investigated their Lyapunov stability in the problem of the motion of a star inside a layered inhomogeneous rotating elliptical galaxy with a variable mass. We have constructed the surfaces of zero velocity and obtained stability conditions for unsteady motion in the first approximation. We analyze general case where the densities of the galactic nucleus and layers vary with time according to different laws.     

Determining the minimum sum of the component masses for a binary with a known parallax from observations of a short arc of its apparent motion

An inequality that allows the minimum sum of the component masses for a binary, M₀, to be determined was derived from simple geometric considerations. This quantity satisfies the observed orbital motion according to Newton's law with a known parallax. The M₀ value can be calculated if the apparent-motion parameters for the components, including the curvature of the observed short orbital arc, were determined from observations. We estimated M₀ for 14 Pulkovo program stars for which the apparent orbital arc covered with observations was no less than 10°. We compare M₀ with the masses estimated from the mass-luminosity relation. A significant mass excess was found for the star ADS 10329.     

About the Influence of a Magnetic Field on the Model Atmosphere of a Magnetic Star

A quasi-static magnetic field similar to that of a large single sunspot is assumed to be embedded in a photospheric model of an Ao star. The differences of the model atmosphere within the magnetic spot relative to the photosphere are calculated by means of the equations of hydromagnetics. The differences are small for τ ≧ I but increase towards smaller τ. The spot model is more transparent in its high layers. In equal geometrical depth the thermodynamic parameters are reduced by the magnetic field. While a small spot is darker than its photospheric surroundings, a large spot appears brighter; the wavelength dependence of its excess in brightness coincides with observations. Compared with the photosphere, the Balmer lines show narrower and deeper cores in the large spot, these differences increase towards larger quantum numbers. Also these features are qualitatively confirmed by observations. An outline is given how to extend and generalize the present model calculations.     

Quasi-Tangency Points on the Orbits of a Small Body and a Planet at the Low-Velocity Encounter

We propose a method for selecting a low-velocity encounter of a small body with a planet from the evolution of the orbital elements. Polar orbital coordinates of the quasi-tangency point on the orbit of a small body are determined. Rectangular heliocentric coordinates of the quasi-tangency point on the orbit of a planet are determined. An algorithm to search for low-velocity encounters in the evolution of the orbital elements of small bodies is described. The low-velocity encounter of comet 39P/Oterma with Jupiter is considered as an example.     

Dynamical friction and the escape of a compact supermassive object shot from the center of a galaxy

A numerical study has been made of the motion of a compact object consisting of a supermassive black hole with a dense cluster of stars around through a galaxy which has recoiled from the center of the latter as a result of anisotropic emission of gravitational radiation or asymmetrical plasma emission. We find that the effect of dynamical friction on its motion through the galaxy (mass10¹¹ M ) estimated using the impulsive approximation technique, is minimal for an object mass 10⁹ M and for recoil taking place at a velocity larger than that of escape. A velocity 1.1 times the escape velocity is needed for the object to escape from the galaxy, whereas for velocities of recoil less than this critical velocity, damped oscillatory motion ensures. The energy exchange of the object with the galaxy is not large enough to cause appreciable change in the internal energy of the latter.     

Exact solution of a problem in a stellar atmosphere using the Laplace transform and the Wiener-Hopf technique

The general equation for radiative transfer of line scattering intensity — including the effects of scattering, absorption and thermal emission — in the Milne-Eddington model is considered here. The scattering function is assumed to be quadratically anisotropic in the cosine of the scattering angle, and Planck's intensity function is assumed for thermal emission. The exact solutions for emergent intensity from the bounding face and the intensity at any optical depth are obtained by the method of the Laplace transform in combination with the Wiener-Hopf technique.     

Non-linear equations for the rotation of a viscoelastic planet taking into account the influence of a liquid core

Non-linear equations governing the temporal evolution of the vector of instantaneous rotation are developed for an Earth with a homogeneous mantle having a viscoelastic Maxwell rheology and with a homogeneous inviscid fluid core.This general theory is investigated using the angular momentum theorem applied to the coupled core-mantle system. It allows to study the influence upon the planetary rotation of a quasi-rigid rotational motion in the liquid core. It also enables to investigate the consequences of excitation sources (e.g. pressure), located at the core-mantle interface. Especially, the influence of viscoelastic variations in the inertia tensors resulting from the rotation itself or from various excitation sources are detailed with the help of a Love number formalism. The equations of the linear theory for an elastic Earth with a liquid core, and the non-linear theory for a viscous planet with a quasi-fluid behavior are shown to be particular cases of our generalized system of equations. Some planetological applications may be derived from the quasi-fluid approximation.     

Effect of a helical magnetic field on the stability of a gravitating cylinder

The effect of a helical magnetic field on the stability of an infinitely conducting, inviscid, incompressible and infinitely long self-gravitating cylinder is studied for axisymmetric perturbations. The effect of helicity is also examined.     

Molecular band variations as a probe of the vertical structure of a Jovian atmosphere

A variational technique is used to compute synthetic spectra for models of cloudy Jovian planetary atmospheres which incorporate abrupt changes in their vertical structure. The dependence of the center-to-limb variations in equivalent widths of molecular bands upon the properties of the various scattering layers in the model is examined. A range of theoretical models are delineated on the basis of their ability to reproduce observational results for the specific case of Jupiter.     

Dynamics of the Interstellar Gas in the Vicinity of a Bar

A numerical simulation of the disk dynamics of a flat stellar-gaseous galaxy is presented. This simulation is based on N-body modelling for a stellar disk, together with integration of the two-dimensional hydrodynamic equations for a gaseous disk. The existence of a quasi-periodic regime of disk evolution found earlier in a purely hydrodynamic simulation is confirmed. Intense gas flows in the central area of the disk due to the saddle point of the bar potential can support the active galactic nuclei in Seyfert galaxies and form double nuclei.     

Perspectives of a visible instrument on the VLTI

In this paper we present the most promising science cases for a new generation visible instrument on the VLTI and the conceptual idea for the instrumental configuration. We also present a statistical study of the potential targets that may be accessible for the different classes of objects and for the required spectral resolutions.