Small Misalignment Angles Research Articles

A Method for SINS Alignment with Large Initial Misalignment Angles Based on Kalman Filter with Parameters Resetting

In the initial alignment process of strapdown inertial navigation system (SINS), large initial misalignment angles always bring nonlinear problem, which causes alignment failure when the classical linear error model and standard Kalman filter are used. In this paper, the problem of large misalignment angles in SINS initial alignment is investigated, and the key reason for alignment failure is given as the state covariance from Kalman filter cannot represent the true one during the steady filtering process. According to the analysis, an alignment method for SINS based on multiresetting the state covariance matrix of Kalman filter is designed to deal with large initial misalignment angles, in which classical linear error model and standard Kalman filter are used, but the state covariance matrix should be multireset before the steady process until large misalignment angles are decreased to small ones. The performance of the proposed method is evaluated by simulation and car test, and the results indicate that the proposed method can fulfill initial alignment with large misalignment angles effectively and the alignment accuracy of the proposed method is as precise as that of alignment with small misalignment angles.

Boundary Between Stable and Unstable Regimes of Accretion

We investigated the boundary between stable and unstable regimes of accretion and its dependence on different parameters. Simulations were performed using a "cubed sphere" code with high grid resolution (244 grid points in the azimuthal direction), which is twice as high as that used in our earlier studies. We chose a very low viscosity value, with alpha-parameter alpha=0.02. We observed from the simulations that the boundary strongly depends on the ratio between magnetospheric radius r_m (where the magnetic stress in the magnetosphere matches the matter stress in the disk) and corotation radius r_cor (where the Keplerian velocity in the disk is equal to the angular velocity of the star). For a small misalignment angle of the dipole field, Theta=5 degrees, accretion is unstable if r_cor/r_m>1.35, and is stable otherwise. In cases of a larger misalignment angle of the dipole, Theta=20 degrees, instability occurs at slightly larger values, r_cor/r_m>1.41.

Analytical hotspot shapes and magnetospheric radius from 3D simulations of magnetospheric accretion

We present an analytical formula for the position and shape of the spots on the surface of accreting magnetized stars in cases where a star has a dipole magnetic field tilted at a small misalignment angle Theta < 30 degrees about the rotational axis, and the magnetosphere is 2.5-5 times the radius of the star. We observed that the azimuthal position of the spots varies significantly when the position of the inner disc varies. In contrast, the polar position of the spots varies only slightly because of the compression of the magnetosphere. The azimuthal width of the spots strongly varies with Theta: spots have the shape of an arc at larger misalignment angles, and resemble a ring at very small misalignment angles. The polar width of the spots varies only slightly with changes in parameters. The motion of the spots in the azimuthal direction can provide phase-shifts in accreting millisecond pulsars, and the "drift" of the period in Classical T Tauri stars. The position and shape of the spots are determined by three parameters: misalignment angle Theta; normalized corotation radius, r_c/R_* and normalized magnetospheric radius, r_m/R_*, where R_* is the stellar radius. We also use our data to check the formula for the Alfv\'en radius, where the main dependencies are r_m \sim (\mu^2/\dot M)^{2/7}, where \mu is the magnetic moment of the star, and \dot M is the accretion rate. We found that the dependence is more gradual, r_m \sim (\mu^2/\dot M)^{1/5}, which can be explained by the compression of the magnetosphere by the disc matter and by the non-dipole shape of the magnetic field lines of the external magnetosphere.

FERMILAT PULSED DETECTION OF PSR J0737–3039A IN THE DOUBLE PULSAR SYSTEM

We report the Fermi Large Area Telescope discovery of gamma-ray pulsations from the 22.7 ms pulsar A in the double pulsar system J0737-3039A/B. This is the first mildly recycled millisecond pulsar (MSP) detected in the GeV domain. The 2.7 s companion object PSR J0737-3039B is not detected in gamma rays. PSR J0737-3039A is a faint gamma-ray emitter, so that its spectral properties are only weakly constrained; however, its measured efficiency is typical of other MSPs. The two peaks of the gamma-ray light curve are separated by roughly half a rotation and are well offset from the radio and X-ray emission, suggesting that the GeV radiation originates in a distinct part of the magnetosphere from the other types of emission. From the modeling of the radio and the gamma-ray emission profiles and the analysis of radio polarization data, we constrain the magnetic inclination $\alpha$ and the viewing angle $\zeta$ to be close to 90$^\circ$, which is consistent with independent studies of the radio emission from PSR J0737-3039A. A small misalignment angle between the pulsar's spin axis and the system's orbital axis is therefore favored, supporting the hypothesis that pulsar B was formed in a nearly symmetric supernova explosion as has been discussed in the literature already.

Thermal leptogenesis and the gravitino problem in the Asaka-Yanagida axion/axino dark matter scenario

A successful implementation of thermal leptogenesis requires the re-heat temperature after inflation TR to exceed ∼ 2 × 109 GeV. Such a high TR value typically leads to an overproduction of gravitinos in the early universe, which will cause conflicts, mainly with BBN constraints. Asaka and Yanagida (AY) have proposed that these two issues can be reconciled in the context of the Peccei-Quinn augmented MSSM (PQMSSM) if one adopts a mass hierarchy m(sparticle) > m(gravitino)>m(axino), with m(axino) ∼ keV. In this case, sparticle decays bypass the gravitino, and decay more quickly to the axino LSP, thus avoiding the BBN constraints. In addition, thermally produced gravitinos decay inertly to axion+axino, also avoiding BBN constraints. We calculate the relic abundance of mixed axion/axino dark matter in the AY scenario, and investigate under what conditions a value of TR sufficient for thermal leptogenesis can be generated. A high value of PQ breaking scale fa is needed to suppress overproduction of axinos, while a small vacuum misalignment angle θi is needed to suppress overproduction of axions. The large value of fa results in late decaying neutralinos. We show that, to avoid BBN constraints, the AY scenario requires a rather low thermal abundance of neutralinos, while higher values of neutralino mass also help. We combine these constraint calculations along with entropy production from late decaying saxions, and find the saxion needs to be typically at least several times heavier than the gravitino. A successful implementation of the AY scenario suggests that LHC should discover a spectrum of SUSY particles consistent with weak scale supergravity; that the apparent neutralino abundance is low; that an axion direct detection signal (probably with ma in the sub-μeV range) may be possible, but no direct or indirect signals for WIMP dark matter should be observed.

BLACK HOLE SPIN–ORBIT MISALIGNMENT IN GALACTIC X-RAY BINARIES

In black hole X-ray binaries, a misalignment between the spin axis of the black hole and the orbital angular momentum can occur during the supernova explosion that forms the compact object. In this letter we present population synthesis models of Galactic black hole X-ray binaries, and study the probability density function of the misalignment angle, and its dependence on our model parameters. In our modeling, we also take into account the evolution of misalignment angle due to accretion of material onto the black hole during the X-ray binary phase. The major factor that sets the misalignment angle for X-ray binaries is the natal kick that the black hole may receive at its formation. However, large kicks tend to disrupt binaries, while small kicks allow the formation of XRBs and naturally select systems with small misalignment angles. Our calculations predict that the majority (>67%) of Galactic field BH XRBs have rather small (>10 degrees) misalignment angles, while some systems may reach misalignment angles as high as ~90 degrees and even higher. This results is robust among all population synthesis models. The assumption of small small misalignment angles is extensively used to observationally estimate black hole spin magnitudes, and for the first time we are able to confirm this assumption using detailed population synthesis calculations.

Director distortions and singularities in inhomogeneous fields

The effect of the electric-field inhomogeneity has been experimentally studied by polarizing microscopy in a homeotropic nematic liquid crystal in confined electrode geometries which may be relevant in display applications. Defects related to tilt inversion have been detected by monitoring the transmitted intensity profile as a function of the applied voltage. The position of the defects could be controlled by an additional magnetic field breaking the symmetry of the original arrangement. The phenomenon has been interpreted via numerical calculation of the director distribution using the continuum theory of nematics. The influence of oblique light incidence and of weak anchoring has also been analyzed. Simulations have provided good qualitative agreement with the observations. The method has turned out to be a sensitive tool to detect small misalignment angles between the magnetic field and the cell plane.

QPO emission from moving hot spots on the surface of neutron stars: a model

We present recent results of 3D magnetohydrodynamic simulations of neutron stars with small misalignment angles, as regards the features in lightcurves produced by regular movements of the hot spots during accretion onto the star. In particular, we show that the variation of position of the hot spot created by the infalling matter, as observed in 3D simulations, can produce high frequency Quasi Periodic Oscillations with frequencies associated with the inner zone of the disk. Previously reported simulations showed that the usual assumption of a fixed hot spot near the polar region is valid only for misalignment angles relatively large. Otherwise, two phenomena challenge the assumption: one is the presence of Rayleigh-Taylor instabilities at the disk-magnetospheric boundary, which produce tongues of accreting matter that can reach the star almost anywhere between the equator and the polar region; the other one is the motion of the hot spot around the magnetic pole during stable accretion. In this paper we start by showing that both phenomena are capable of producing short-term oscillations in the lightcurves. We then use Monte Carlo techniques to produce model lightcurves based on the features of the movements observed, and we show that the main features of kHz QPOs can be reproduced. Finally, we show the behavior of the frequencies of the moving spots as the mass accretion rate changes, and propose a mechanism for the production of double QPO peaks.

Accretion to magnetized stars through the Rayleigh–Taylor instability: global 3D simulations

We present results of 3D simulations of magnetohydrodynamics (MHD) instabilities at the accretion disc‐magnetosphere boundary. The instability is Rayleigh‐Taylor, and develops for a fairly broad range of accretion rates and stellar rotation rates and magnetic fields. It manifests itself in the form of tall, thin tongues of plasma that penetrate the magnetosphere in the equatorial plane. The shape and number of the tongues changes with time on the inner disc dynamical time-scale. In contrast with funnel flows, which deposit matter mainly in the polar region, the tongues deposit matter much closer to the stellar equator. The instability appears for relatively small misalignment angles, � � 30 ◦ , between the star’s rotation and magnetic axes, and is associated with higher accretion rates. The hotspots and light curves during accretion through instability are generally much more chaotic than during stable accretion. The unstable state of accretion has possible implications for quasi-periodic oscillations and intermittent pulsations from accreting systems, as well as planet migration.

A Study of 13 Powerful Classical Double Radio Galaxies

We have carried out an extensive study of a sample of 13 large, powerful Fanaroff-Riley type II radio galaxies with the Very Large Array in multiple configurations at 330 MHz, 1.4, 5 and 8 GHz. We present the total intensity, polarization, spectral index, and rotation measure maps of the sources. On the whole the 13 FRII sources have symmetric structures with arm-length ratios close to unity, small misalignment angles and low values of radio core prominence, suggesting that these radio galaxies lie close to the plane of the sky. We have revisited some well known radio galaxy correlations using a large combined dataset comprising our radio galaxies and others from the literature. We confirm that the hotspot size correlates with the core-hotspot distance. The hotspot spectral index is correlated with, and flatter than the lobe spectral index, consistent with the assumptions of spectral aging models. Both the hotspot and lobe spectral index are correlated with redshift. The depolarization asymmetry in the lobes is not correlated with the radio core prominence or misalignment angle, which are statistical indicators of orientation. The `Liu-Pooley' correlation of lobe depolarization with the lobe spectral index is significant in our radio galaxy sample. Further, the lobe with the steeper spectral index and greater depolarization is shorter and fatter. The arm-length ratio seems to be correlated with the misalignment angle between the two sides of the radio source and strongly anti-correlated with the axial ratio, consistent with environmental effects and/or a change in the outflow direction. In this sample, asymmetries in the local environments and/or motion of the outflow axis are likely to be more important than relativistic beaming effects.

Isocurvature bounds on axions revisited

The axion is one of the best motivated candidates for particle dark matter. We study and update the constraints imposed by the recent CMB and LSS experiments on the mass of axions produced by the misalignment mechanism, as a function of both the inflationary scale and the reheating temperature. Under some particular although not unconventional assumptions, the axion induces isocurvature perturbations with an amplitude too large to be compatible with observations. Specifically, for inflation taking place at intermediate energy scales, we derive some restrictive limits which can only be evaded by assuming an efficient reheating mechanism, with ${T}_{\mathrm{rh}}g{10}^{11}\text{ }\text{ }\mathrm{GeV}$. Chaotic inflation with a quadratic potential is still compatible with the axion scenario, provided that the Peccei-Quinn scale ${f}_{a}$ is close to ${10}^{10}$ or ${10}^{11}\text{ }\text{ }\mathrm{GeV}$. Isocurvature bounds eliminate the possibility of a larger ${f}_{a}$ and a small misalignment angle. We find that isocurvature constraints on the axion scenario must be taken into account whenever the scale of inflation is above ${10}^{12}\text{ }\text{ }\mathrm{GeV}$; below this scale, axionic isocurvature modes are too small to be probed by current observations.

Variability Profiles of Millisecond X‐Ray Pulsars: Results of Pseudo‐Newtonian Three‐dimensional Magnetohydrodynamic Simulations

We model the variability profiles of millisecond-period X-ray pulsars. We performed three-dimensional magneto- hydrodynamic simulations of disk accretion to millisecond-period neutron stars with a misaligned magnetic dipole moment, using the pseudo-Newtonian Paczynski-Wiita potential to model general relativistic effects. We found that the shapes of the resulting funnel streams of accreting matter and the hot spots on the surface of the star are quite similar to those for more slowly rotating stars obtained from earlier simulations using the Newtonian potential. The funnel streams and hot spots rotate approximately with the same angular velocity as the star. The spots are bow- shaped (bar-shaped) for small (large) misalignment angles. We found that the matter falling on the star has a higher Mach number when we use the Paczynski-Wiita potential than in the Newtonian case. Having obtained the surface distribution of the emitted flux, we calculated the variability curves of the star, taking into account general rel- ativistic, Doppler, and light-travel time effects. We found that general relativistic effects decrease the pulse frac- tion (flatten the light curve), while Doppler and light-travel time effects increase it and distort the light curve. We also found that the light curves from our hot spots are reproduced reasonably well by spots with a Gaussian flux distribution centered at the magnetic poles. We also calculated the observed image of the star in a few cases and saw that for certain orientations, both the antipodal hot spots are simultaneously visible, as noted by earlier authors. Subject headingg accretion, accretion disks — pulsars: general — X-rays: stars

INS algorithm using quaternion model for low cost IMU

This paper presents a generic inertial navigation system (INS) error propagation model that does not rely on small misalignment angles assumption. The modelling uses quaternions in the computer frame approach. Based on this model, an INS algorithm is developed for low cost inertial measurement unit (IMU) to solve the initial attitudes uncertainty using in-motion alignment. The distribution approximation filter (DAF) is used to implement the non-linear data fusion algorithm.

Mass-Capture Rate by the Neutron Star in Be/X-Ray Binaries

AbstractWe study the interaction between the Be-star disk and the neutron star in Be/X-ray binaries by three dimensional SPH simulations. We find that, the resonant, truncation of the Be disk works except for systems with extremely high orbital eccentricity or large misalignment angles between the Be disk and the orbital plane. Owing to the truncation, the mass-capture rate by the neutron star is sensitive both to the orbital eccentricity and to the angle of misalignment. It is single-peaked in coplanar systems and in systems with small misalignment angles, whereas it, becomes double-peaked in systems with large misalignment angles.

Spatiotemporal model of the LIGO interferometer

We develop a detailed spatiotemporal model in the adiabatic approximation of the optical response of the Laser Interferometer Gravitational-Wave Observatory (LIGO) optical system to environmental perturbations. We begin by deriving a first-order linear time-dependent evolution equation that models the electromagnetic field as a function of position within a Fabry–Perot interferometer. This model allows both the length of the resonator and the misalignment angles of the end mirrors to vary in time and describes both resonant and nonresonant phenomena. After defining a biorthogonality relation that must be satisfied by general unperturbed spatial eigenfunctions of the Fabry–Perot interferometer, we expand the intracavity field as a linear combination of these functions and convert the spatiotemporal evolution equation into a linear system of coupled time-dependent iteration and/or differential equations. We then calculate the adiabatic connection equations that link the two LIGO Fabry–Perot interferometers through the power recycling cavity, which comprises two mirrors (the power recycling input mirror and the beam splitter) that have the same mechanical degrees of freedom as those in the Fabry–Perot arm cavities. We develop a detailed instance of this model for the evolution of the intracavity field within a resonator with sufficiently small misalignment angles that a Hermite–Gauss basis set can be used. We develop a detailed general approach to signal demodulation for simulation of servo-control systems and describe its implementation in the Hermite–Gauss approximation for Cartesian split-plane detectors. Finally, we demonstrate the use of this small-angle model to simulate the effect of angular misalignment on the longitudinal response function.

A micro-mechanical model for predicting the compressive strength of fibrous composite materials

A micro-mechanical model is proposed for the prediction of the compressive strengths of unidirectional fibrous composite laminates. In these laminates, it is assumed that the fibers have a small misalignment angle which ranges from 1 to 5 ° from the vertical direction. A fiber shear buckling mode is considered in the model formulation which is assumed to cause large shear deformation. A basic energy approach is utilized to determine the critical buckling load. Both fiber and matrix strain energies within the composite and the external work due to applied loads are considered during deformation. The model is tested by using various types of composites: wood/ductile wax, spaghetti/paraffin wax, glass/epoxy and carbon/epoxy. Results of the proposed model are compared with results given by the Rosen and Wisnom micro-models and with available experimental data. It is found that the proposed model yields reasonable results for the composite materials investigated.

Misalignment effects in magnetic resonance

By means of a theoretical approach recently developed by Pegg and Series (1970, 1973), the consequences of misalignment of the rotating field in magnetic resonance are investigated. Three main effects arise: a shift in the resonance frequency, a reduction in power broadening, and the appearance of 'multiple quantum' resonances at integral multiples of the rotating field frequency. For small misalignment angle theta , the misalignment shift is proportional to theta 4 and may be neglected in usual medium-precision experiments. The multiplicity of resonances should be readily detectable in optical pumping experiments.