The effects of the satellite position on the spatial occurrence of angular scintillations

Phase interferometry, based on longitudinal (north-south) and transverse (east-west) antenna systems, was used to record scintillations in the angle-of-arrival of satellite beacon transmissions at a frequency of 136.410 MHz. It was found that the enhancement region of angular scintillations was equatorwards of the recording stations, and coincided with small angles (denoted as aspect angles) between the ray-path and magnetic field. Ninety per cent of the night-time passes, recorded at the azimuth angles 170–190°, were associated with the occurrence of scintillations; the number of scintillations decreased for satellite passes removed east or west of the plane of the station's meridian. Horizontal extents of scintillations were considerably larger east or west, than directly south of the station. Finally, no transverse angular scintillations were recorded whenever the aspect angle reached its minimum value for each satellite pass; simultaneously longitudinal scintillations were enhanced. It is suggested that the above effects are associated with a specific satellite position in relation to the recording station.     

Corrections stemming from the non-osculating character of the Andoyer variables used in the description of rotation of the elastic Earth

We explore the evolution of the angular velocity of an elastic Earth model, within the Hamiltonian formalism. The evolution of the rotation state of the Earth is caused by the tidal deformation exerted by the Moon and the Sun. It can be demonstrated that the tidal perturbation to spin depends not only upon the instantaneous orientation of the Earth, but also upon its instantaneous angular velocity. Parameterizing the orientation of the Earth figure axis with the three Euler angles, and introducing the canonical momenta conjugated to these, one can then show that the tidal perturbation depends both upon the angles and the momenta. This circumstance complicates the integration of the rotational motion. Specifically, when the integration is carried out in terms of the canonical Andoyer variables (which are the rotational analogues to the orbital Delaunay variables), one should keep in mind the following subtlety: under the said kind of perturbations, the functional dependence of the angular velocity upon the Andoyer elements differs from the unperturbed dependence (Efroimsky in Proceedings of Journées 2004: Systèmes de référence spatio-temporels. l’Observatoire de Paris, pp 74–81, 2005; Efroimsky and Escapa in Celest. Mech. Dyn. Astron. 98:251–283, 2007). This happens because, under angular velocity dependent perturbations, the requirement for the Andoyer elements to be canonical comes into a contradiction with the requirement for these elements to be osculating, a situation that parallels a similar antinomy in orbital dynamics. Under the said perturbations, the expression for the angular velocity acquires an additional contribution, the so called convective term. Hence, the time variation induced on the angular velocity by the tidal deformation contains two parts. The first one comes from the direct terms, caused by the action of the elastic perturbation on the torque-free expressions of the angular velocity. The second one arises from the convective terms. We compute the variations of the angular velocity through the approach developed in Getino and Ferrándiz (Celest. Mech. Dyn. Astron. 61:117–180, 1995), but considering the contribution of the convective terms. Specifically, we derive analytical formulas that determine the elastic perturbations of the directional angles of the angular velocity with respect to a non-rotating reference system, and also of its Cartesian components relative to the Tisserand reference system of the Earth. The perturbation of the directional angles of the angular velocity turns out to be different from the evolution law found in Kubo (Celest. Mech. Dyn. Astron. 105:261–274, 2009), where it was stated that the evolution of the angular velocity vector mimics that of the figure axis. We investigate comprehensively the source of this discrepancy, concluding that the difference between our results and those obtained in Ibid. stems from an oversimplification made by Kubo when computing the direct terms. Namely, in his computations Kubo disregarded the motion of the tide raising bodies with respect to a non-rotating reference system when compared with the Earth rotational motion. We demonstrate that, from a numerical perspective, the convective part provides the principal contribution to the variation of the directional angles and of length of day. In the case of the x and y components in the Tisserand system, the convective contribution is of the same order of magnitude as the direct one. Finally, we show that the approximation employed in Kubo (Ibid.) leads to significant numerical differences at the level of a hundred micro-arcsecond.     

A tidal hypothesis about the origin of planetary rotation

We assume that the solar tidal action on accreting protoplanets forced them to corotation. If this is true, and assuming a subsequent conservation of spin angular momentum, we can easily get a rough explanation of: (1) the actual rotation periods of the planets, (2) the trend toward small inclination angles for the rotation axes, (3) the existence of a relation between rotational angular momenta and planetary masses similar to the empirical ones due to McDonald (1964). Hartmann and Larson (1967) and Fish (1967).     

Statistical distribution of gravitational-lensing excursion angles: winding ways to us from the deep Universe

We investigate statistical distributions of differences in gravitational-lensing deflections between two light rays, the so-called lensing excursion angles. A probability distribution function of the lensing excursion angles, which plays a key role in estimates of lensing effects on angular clustering of objects (such as galaxies, quasi-stellar objects and also the cosmic microwave background temperature map), is known to consist of two components: a Gaussian core and an exponential tail. We use numerical gravitational-lensing experiments in a ΛCDM cosmology for quantifying these two components. We especially focus on the physical processes responsible for generating these two components. We develop a simple empirical model for the exponential tail which allows us to explore its origin. We find that the tail is generated by the coherent lensing scatter by massive haloes with   M > 10¹⁴  h ⁻¹ M_⊙  at   z < 1  and that its exponential shape arises due to the exponential cut-off of the halo mass function at that mass range. On scales larger than 1 arcmin, the tail does not have a practical influence on the lensing effects on the angular clustering. Our model predicts that the coherent scatter may have non-negligible effects on angular clustering at subarcminute scales.     

Statistics of weak lensing at small angular scales: analytical predictions for lower order moments

Weak lensing surveys are expected to provide direct measurements of the statistics of the projected dark matter distribution. Most analytical studies of weak lensing statistics have been limited to quasi-linear scales as they relied on perturbative calculations. On the other hand, observational surveys are likely to probe angular scales less than 10 arcmin, for which the relevant physical length-scales are in the non-linear regime of gravitational clustering. We use the hierarchical ansatz to compute the multipoint statistics of the weak lensing convergence for these small smoothing angles. We predict the multipoint cumulants and cumulant correlators up to fourth order and compare our results with high-resolution ray-tracing simulations. Averaging over a large number of simulation realizations for four different cosmological models, we find close agreement with the analytical calculations. In combination with our work on the probability distribution function, these results provide accurate analytical models for the full range of weak lensing statistics. The models allow for a detailed exploration of cosmological parameter space and of the dependence on angular scale and the redshift distribution of source galaxies. We compute the dependence of the higher moments of the convergence on the parameters Ω and Λ.     

The use of angles and angular rates

MIT's Lincoln Laboratory has developed a computer driven, rapidly slewing (4° s^–1), electro-optical (3 resolution) telescope. This enables the rapid measurement of angles and instantaneous angular rates for artificial satellites. The simultaneous acquisition of angles and angular rates constitutes a new initial orbit problem which has been solved. Three different methods of solution are presented including an exact, analytical one. Numerical tests on six widely different satellite orbits indicate that the topocentric distance can be determined to better than 1% (and usually as well as 0.1%) for most satellites after a 5–10 min observation interval.The views and conclusion contained in this document are those of the contractor and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the United States Government.This work was sponsored by the Department of the Air Force.     

Dynamical model of binary asteroid systems using binary octahedrons

We used binary octahedrons to investigate the dynamical behaviors of binary asteroid systems. The mutual potential of the binary polyhedron method is derived from the fourth order to the sixth order. The irregular shapes, relative orbits, attitude angles, as well as the angular velocities of the binary asteroid system are included in the model. We investigated the relative trajectory of the secondary relative to the primary, the total angular momentum and total energy of the system, the three-axis attitude angular velocity of the binary system, as well as the angular momentum of the two components. The relative errors of the total angular momentum and the total energy indicate that the calculation has a high precision. It is found that the influence of the orbital and attitude motion of the primary from the gravitational force of the secondary is obvious. This study is useful in understanding the complicated dynamical behaviors of the binary asteroid systems discovered in our Solar system.     

Active region magnetic fields

The tilt angles of sunspot groups are defined, using the Mount Wilson data set. It is shown that groups with tilt angles greater than or less than the average value (&amp;#x2248; 5 deg) show different latitude dependences. This effect is also seen in synoptic magnetic field data defining plages. The fraction of the total sunspot group area that is found in the leading spots is discussed as a parameter that can be useful in studying the dynamics of sunspot groups. This parameter is larger for low tilt angles, and small for extreme tilt angles in either direction. The daily variations of sunspot group tilt angles are discussed. The result that sunspot tilt angles tend to rotate toward the average value is reviewed. It is suggested that at some depth, perhaps 50 Mm, there is a flow relative to the surface that results from a rotation rate faster than the surface rate by about 60 m/sec and a meridional drift that is slower than the surface rate by about 5 m/sec. This results in a slanted relative flow at that depth that is in the direction of the average tilt angle and may be responsible for the tendency for sunspot groups (and plages) to rotate their magnetic axes in the direction of the average tilt angle.     

On the Balmer: Paschen ratio in prominences

Vidicon data for the intensities of Balmer and Paschen lines for n = 11 to 18 indicate a line ratio within 1σ of the theoretical value of 3.27, calculated with the assumptions of an optically thin atmosphere and angular momentum substates populated according to their statistical weights. The observed value is not consistent with the value of 8 reported in some early work, or with the model that higher angular momentum states have low populations.     

Observations of lensed relativistic jets as a tool for constraining lens galaxy parameters

The possibility of using lensed relativistic jets on very small angular scales to construct proper models of spiral lens galaxies and to independently determine the Hubble constant is considered. The system B0218+357 is used as an example to illustrate that there exists a great choice of model parameters adequately reproducing its observed large-scale properties but leading to a significant spread in the Hubble constant. The jet image position angle is suggested as an additional parameter that allows the range of models under consideration to be limited. It is shown that themodels for which the jet image position angles differ by at least 40° can be distinguished between themselves during observations on very small angular scales. The possibility of observing the geometric properties of lensed relativistic jets and measuring the superluminal velocities of knot images on time scales of several months with very long baseline space interferometers is discussed.     

The influence of non-uniform solar wind expansion on the angular momentum loss from the Sun

The influence on the rate of angular momentum loss from the Sun of magnetic geometries which are not spherically symmetric is estimated. Departures from spherical symmetry are expected to influence significantly the loss rate by two effects - the presence of closed magnetic field regions with no loss and also the variability in the radial distance to the Alfvénic point, as stressed by Mestel (1968).The loss rate is calculated for an MHD solar wind model with a solar magnetic field whose normal component at the surface is that of a north-south dipole. In contrast to Mestel's work, where the field was assumed dipolar within a certain surface and radial outside, the coupling between the solar wind and magnetic field is here taken into account exactly. For equivalent boundary conditions at the surface, the resulting field configuration yields an angular momentum loss rate which is only 15% of that for the monopole field normally used in angular momentum loss estimates. If, instead of equating boundary conditions at the Sun, one equates the two losses at the equator to that observed at 1 AU by spacecraft, then the ratio of the total loss for the distended dipole to that for the monopole is about 40%.On Leave from the Department of Applied Mathematics, The University, St. Andrews, Scotland.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Spectrum,angular distribution and polarization of auroral hard X-rays

The angular variations of elastic and inelastic scattering cross-sections have been calculated accounting for Hartree-Fock atomic model. Using these cross-sections the evolution of electron energy and angular distributions at different heights in the ionosphere have been computed with the help of Monte Carlo technique. Mono-energetic, power law and exponential electron spectra with isotropic and mono-directional incidence starting at an altitude of 300 km have been taken to obtain the angular and energy distribution at certain height intervals. It is found that isotropic distribution incident at the top of the ionosphere becomes anisotropic due to collisions at lower heights. Using Sauter bremsstrahlung cross-section and the calculated electron flux we have computed the spectrum, angular distribution and polarization of bremsstrahlung X-rays at different heights.The emission is found to be peaked at lower angles at higher heights and becomes isotropic with depth of penetration. Polarization is considerable at higher altitudes for mono-directional beams and becomes significant at lower heights for isotropic incidence. It is argued that the study of angular distribution and polarization can yield information about the nature of precipitating electron flux and hence about the acceleration mechanism operating during electron precipitation.     

Numerical study of the statistical properties of the lensing excursion angles

We present ray tracing simulations combined with sets of large N -body simulations. Experiments were performed to explore, for the first time, the statistical properties of fluctuations in angular separation of nearby light-ray pairs (the so-called lensing excursion angle) induced by weak lensing by large-scale structures. We found that the probability distribution function (PDF) of the lensing excursion angles is not simply Gaussian, but has an exponential tail. It is found, however, that the tail, or more generally the non-Gaussian nature of the PDF has no significant impact on the weak lensing of the cosmic microwave background (CMB). Moreover, we found that the variance in the lensing excursion angles predicted by the power spectrum approach is in good agreement with our numerical results. These results demonstrate the validity of using the power spectrum approach to compute lensing effects on the CMB.     

Inverting the angular correlation function

The two point angular correlation function is an excellent measure of structure in the Universe. To extract from it the three-dimensional power spectrum, one must invert Limber's equation. Here we perform this inversion using a Bayesian prior constraining the smoothness of the power spectrum. Among other virtues, this technique allows for the possibility that the estimates of the angular correlation function are correlated from bin to bin. The outputs of this technique are estimators for the binned power spectrum and a full covariance matrix. Angular correlations mix small and large scales but after the inversion, small-scale data can be trivially eliminated, thereby allowing for realistic constraints on theories of large-scale structure. We analyse the automated plate measurement (APM) catalogue as an example, comparing our results with previous results. As a by-product of these tests, we find – in rough agreement with previous work – that APM places stringent constraints on cold dark matter inspired models, with the shape parameter constrained to be 0.25±0.04 (using data with wavenumber k ≤0.1  h  Mpc⁻¹). This range of allowed values uses the full power spectrum covariance matrix, but assumes negligible covariance in the off-diagonal angular correlation error matrix, which is estimated with a large angular resolution of 0.5° (in the range 0.5° and 20°).     

on the role of nonthermal electrons in EUV and X-ray line emissions from solar flares

The energy and angular distribution of electrons as a function of column densities initially for monoenergetic and monodirectional electron beams and incidence angles of 0‡, 30‡ and 60‡ have been studied by combining small angle scattering using analytical treatment with large angle collisions using Monte Carlo calculations. Using these distributions, X-ray and EUV-line flux have been studied as a function of column density. It is observed that the line flux increases with the increase in column density, becoming significant at intermediate column densities where the electron energies and angular distributions have a non-Maxwellian nature.     

Angular momenta in the solar system

A statistical study of the orbital parameters of comets, asteroids and meteor streams shows that the vectors representing their angular momenta per mass unit (or the average angular momentum for meteor streams) are not arbitrarily distributed in the space: They are clustered around determinated values of angles . This synthesizes the eccentricities and inclinations of the orbital planes in a unique parameter adequated for the statistical purposes of the present work being defined by cos = cos (arc sin e) cos i.The discreteness of the obtained distribution N() and its relation with the components of the angular momenta per mass unit is analysed having this distribution common features for objects of different nature and located in different places in the solar potential well. Some hypotheses concerning to these effects are discussed.     

Properties of New Coordinates for the General Three-Body Problem

This is an analysis of the features of the new coordinate system given by the principal axes of inertia, as determined by Euler angles, and twodistances related to the inertia principal moments and an auxiliar angleas coordinates, for studying the general three-body problem, interactingthrough gravitational forces.The reduction of order is performed in these new coordinates by using the angular velocity vector or the Euler angles.The Eulerian case of collinear motion is revisited from our own perspective.The value of the auxiliar angle is computed for the Sun–Earth–Moon system.     

Axial tilt angles of active regions

Separate Mount Wilson plage and sunspot group data sets are analyzed in this review to illustrate several interesting aspects of active region axial tilt angles. (1) The distribution of tilt angles differs between plages and sunspot groups in the sense that plages have slightly higher tilt angles, on average, than do spot groups. (2) The distributions of average plage total magnetic flux, or sunspot group area, with tilt angle show a consistent effect: those groups with tilt angles nearest the average values are larger (or have a greater total flux) on average than those farther from the average values. Moreover, the average tilt angles on which these size or flux distributions are centered differ for the two types of objects, and represent closely the actual different average tilt angles for these two features. (3) The polarity separation distances of plages and sunspot groups show a clear relationship to average tilt angles. In the case of each feature, smaller polarity separations are correlated with smaller tilt angles. (4) The dynamics of regions also show a clear relationship with region tilt angles. The spot groups with tilt angles nearest the average value (or perhaps 0-deg tilt angle) have on average a faster rotation rate than those groups with extreme tilt angles.All of these tilt-angle characteristics may be assumed to be related to the physical forces that affect the magnetic flux loop that forms the region. These aspects are discussed in this brief review within the context of our current view of the formation of active region magnetic flux at the solar surface.Dedicated to Cornelis de JagerOperated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

Multidimensional simulations of radiative transfer in Type Ia supernovae

A three-dimensional Monte Carlo code for modelling radiation transport in Type Ia supernovae is described. In addition to tracking Monte Carlo quanta to follow the emission, scattering and deposition of radiative energy, a scheme involving volume-based Monte Carlo estimators is used to allow properties of the emergent radiation field to be extracted for specific viewing angles in a multidimensional structure. This eliminates the need to compute spectra or light curves by angular binning of emergent quanta. The code is applied to two test problems to illustrate consequences of multidimensional structure on the modelling of light curves. First, elliptical models are used to quantify how large-scale asphericity can introduce angular dependence to light curves. Secondly, a model which incorporates complex structural inhomogeneity, as predicted by modern explosion models, is used to investigate how such structure may affect light-curve properties.