Wide Range Of Inclinations Research Articles

The orbital architecture and stability of the μ Arae planetary system

ABSTRACT We re-analyse the global orbital architecture and dynamical stability of the HD 160691 planetary system. We have updated the best-fitting elements and minimal masses of the planets based on literature precision radial velocity (RV) measurements, now spanning 17.3 yr. This is twice the RVs interval used for the first characterization of the system in 2006. It consists of a Saturn- and two Jupiter-mass planets in low-eccentric orbits resembling the Earth–Mars–Jupiter configuration in the Solar system, as well as the close-in warm Neptune with a mass of ≃14 Earth masses. Here, we constrain this early solution with the outermost period to be accurate to one month. The best-fitting Newtonian model is characterized by moderate eccentricities of the most massive planets below 0.1 with small uncertainties ≃0.02. It is close but meaningfully separated from the 2e:1b mean motion resonance of the Saturn–Jupiter-like pair, but may be close to weak three-body MMRs. The system appears rigorously stable over a wide region of parameter space covering uncertainties of several σ. The system stability is robust to a five-fold increase in the minimal masses, consistent with a wide range of inclinations, from ≃20° to 90°. This means that all planetary masses are safely below the brown dwarf mass limit. We found a weak statistical indication of the likely system inclination $I \simeq \, 20^{\circ }$–30°. Given the well-constrained orbital solution, we also investigate the structure of hypothetical debris discs, which are analogues of the Main Belt and Kuiper Belt, and may naturally occur in this system.

Gait Speed Modulations Are Proportional to Grades of Virtual Visual Slopes-A Virtual Reality Study.

Gait is a complex mechanism relying on integration of several sensory inputs such as vestibular, proprioceptive, and visual cues to maintain stability while walking. Often humans adapt their gait to changes in surface inclinations, and this is typically achieved by modulating walking speed according to the inclination in order to counteract the gravitational forces, either uphill (exertion effect) or downhill (braking effect). The contribution of vision to these speed modulations is not fully understood. Here we assessed gait speed effects by parametrically manipulating the discrepancy between virtual visual inclination and the actual surface inclination (aka visual incongruence). Fifteen healthy participants walked in a large-scale virtual reality (VR) system on a self-paced treadmill synchronized with projected visual scenes. During walking they were randomly exposed to varying degrees of physical-visual incongruence inclinations (e.g., treadmill leveled & visual scene uphill) in a wide range of inclinations (−15° to +15°). We observed an approximately linear relation between the relative change in gait speed and the anticipated gravitational forces associated with the virtual inclinations. Mean relative gait speed increase of ~7%, ~11%, and ~17% were measured for virtual inclinations of +5°, +10°, and +15°, respectively (anticipated decelerating forces were proportional to sin[5°], sin[10°], sin[15°]). The same pattern was seen for downhill virtual inclinations with relative gait speed modulations of ~-10%, ~-16%, and ~-24% for inclinations of −5°, −10°, and −15°, respectively (in anticipation of accelerating forces). Furthermore, we observed that the magnitude of speed modulation following virtual inclination at ±10° was associated with subjective visual verticality misperception. In conclusion, visual cues modulate gait speed when surface inclinations change proportional to the anticipated effect of the gravitational force associated the inclinations. Our results emphasize the contribution of vision to locomotion in a dynamic environment and may enhance personalized rehabilitation strategies for gait speed modulations in neurological patients with gait impairments.

On the Structure and Kinematics of an Algerian Eddy in the Southwestern Mediterranean Sea

An Algerian Eddy, anticyclonic vortex generated by the instability of the Algerian Current in the southwestern Mediterranean Sea, is studied using data provided by drifters (surface currents), Argo floats (temperature and salinity profiles), environmental satellites (absolute dynamic topography maps and ocean color images) and operational oceanography products. The eddy was generated in May 2018 and lasted as an isolated vortex until November 2018. Its morphology and kinematics are described in June–July 2018 when drifters were trapped in its core. During that period, the eddy was slowly moving to the NE (~2 km/day), with an overall diameter of about 200 km (slowly growing with time) and maximal surface swirl velocity of ~50 cm/s at a radius of ~50 km. Geostrophic currents derived from satellite altimetry data compare well with low-pass filtered drifter velocities, with only a slight overestimation, which is expected as its maximum vorticity corresponds to a small Rossby number of ~0.6. Satellite ocean color images and some drifters show that the eddy has an elliptical spiral structure. The looping tracks of the drifters trapped in the eddy were analyzed using two statistical methods: least-squares ellipse fitting and wavelet ridge analysis, revealing a typical eccentricity of about 0.5, a wide range of inclination and a rotation period between 3 and 10 days. Clusters of drifters on the northeastern limb of the eddy were also considered to estimate divergence and vorticity. The results indicate convergence (divergence) and downwelling (upwelling) at scales of 20–50 km near the northeastern (northwestern) edge of the eddy, in agreement with the quasi-geostrophic theory. Vertically, the eddy extends mostly down to 250 m depth, with a warm, low-salinity and low-density signature and with geostrophic currents near 50 cm/s in the top layer (down to ~80 m) reducing to less than 10 cm/s near 250 m. Near the surface, colder water is advected into it.

The Eccentric Kozai-Lidov Effect and Its Applications

The hierarchical triple-body approximation has useful applications to a variety of systems from planetary and stellar scales to supermassive black holes. In this approximation, the energy of each orbit is separately conserved, and therefore the two semimajor axes are constants. On timescales much larger than the orbital periods, the orbits exchange angular momentum, which leads to eccentricity and orientation (i.e., inclination) oscillations. The orbits' eccentricity can reach extreme values, leading to a nearly radial motion, which can further evolve into short orbit periods and merging binaries. Furthermore, the orbits' mutual inclinations may change dramatically from pure prograde to pure retrograde, leading to misalignment and a wide range of inclinations. This dynamical behavior is coined the “eccentric Kozai-Lidov mechanism.” The behavior of such a system is exciting, rich, and chaotic in nature. Furthermore, these dynamics are accessible from a large part of the triple-body parameter space and can be applied to a diverse range of astrophysical settings and used to gain insights into many puzzles.

Twin peak high-frequency quasi-periodic oscillations as a spectral imprint of dual oscillation modes of accretion tori

High frequency (millisecond) quasi-periodic oscillations (HF QPOs) are observed in the X-ray power-density spectra of several microquasars and low mass X-ray binaries. Two distinct QPO peaks, so-called twin peak QPOs, are often detected simultaneously exhibiting their frequency ratio close or equal to 3/2. Following the analytic theory and previous studies of observable spectral signatures, we aim to model the twin peak QPOs as a spectral imprint of specific dual oscillation regime defined by a combination of the lowest radial and vertical oscillation mode of optically thick slender tori with constant specific angular momentum. We examined power spectra and fluorescent K$\alpha$ iron line profiles for two different simulation setups with the mode frequency relations corresponding to the epicyclic resonance HF QPOs model and modified relativistic precession QPOs model. We use relativistic ray-tracing implemented in parallel simulation code LSDplus. In the background of the Kerr spacetime geometry, we analyze the influence of the distant observer inclination and the spin of the central compact object. Relativistic optical projection of the oscillating slender torus is illustrated by images in false colours related to the frequency shift. We show that performed simulations yield power spectra with the pair of dominant peaks corresponding to the frequencies of radial and vertical oscillation modes with the proper ratio equal to 3/2 on a wide range of inclinations and spin values. We also discuss exceptional cases of a very small and very high inclination as well as unstable high spin relativistic precession-like configuration predicting constant frequency ratio equal to 1/2. We demonstrate signifiant dependency of broadened K$\alpha$ iron line profiles on the inclination of the distant observer.

Secular Resonances in the Dynamic Evolution of Near-Earth Space Objects on Prolate Orbits

Results are presented of a study of the effect of secular resonances on the dynamic evolution of objects moving along prolate orbits over a wide range of inclinations and with semimajor axes up to 55,000 km. It is shown that the most important effect on the orbital evolution of such space objects is the inclination of their orbits. For objects starting in orbits with large eccentricities and inclinations 55–65, the process of catastrophic orbital evolution goes faster in time than for objects on almost circular orbits.

CO bandhead emission of massive young stellar objects: determining disc properties★

Massive stars play an important role in many areas of astrophysics, but numerous details regarding their formation remain unclear. In this paper we present and analyse high resolution (R ~ 30,000) near-infrared 2.3 micron spectra of 20 massive young stellar objects from the RMS database, in the largest such study of CO first overtone bandhead emission to date. We fit the emission under the assumption it originates from a circumstellar disc in Keplerian rotation. We explore three approaches to modelling the physical conditions within the disc - a disc heated mainly via irradiation from the central star, a disc heated mainly via viscosity, and a disc in which the temperature and density are described analytically. We find that the models described by heating mechanisms are inappropriate because they do not provide good fits to the CO emission spectra. We therefore restrict our analysis to the analytic model, and obtain good fits to all objects that possess sufficiently strong CO emission, suggesting circumstellar discs are the source of this emission. On average, the temperature and density structure of the discs correspond to geometrically thin discs, spread across a wide range of inclinations. Essentially all the discs are located within the dust sublimation radius, providing strong evidence that the CO emission originates close to the central protostar, on astronomical unit scales. In addition, we show that the objects in our sample appear no different to the general population of MYSOs in the RMS database, based on their near- and mid-infrared colours. The combination of observations of a large sample of MYSOs with CO bandhead emission and our detailed modelling provide compelling evidence of the presence of small scale gaseous discs around such objects, supporting the scenario in which massive stars form via disc accretion.

A new approach to the modeling of oblique cutting processes

A new upper-bound model that incorporates force equilibrium parallel to the cutting edge is proposed for oblique cutting operations. The energy approach is framed in terms of the normal shear angle and two new fundamental variables that characterize the energy requirements of the oblique cutting process. SLIP is a kinematic variable and is defined as the ratio of the shear velocity imparted to the chip on the shear plane parallel to the cutting edge, to the incoming velocity in the same direction. RATIO is a force-based variable and is defined as the ratio of the friction force on the rake face to the resultant shear force in the shear plane. Calibration of the model for either real time identification purposes or for process planning/optimization requires experimental force data but no shear angle data, making it very suitable for the analysis of cutting operations with non-straight cutting edges. The relationships between SLIP, chip flow angle, and RATIO are shown to be remarkably consistent over a very wide range of inclination and normal rake angles. Finally, the authors demonstrate the success of the model using existing experimental data.

ITAL]Hubble Space Telescope[/ITAL] Observations of the Old Nova [CLC]DI[/CLC] Lacertae

We have carried out a synthetic spectral analysis of a Hubble Space Telescope Space Telescope Imaging Spectrograph observation of the old nova DI Lacertae (Nova Lacerta 1910). The spectrum, obtained with the E140M disperser, reveals a rising continuum shortward of 1560 A, a C IV P Cygni profile indicative of wind outflow associated with disk accretion, a deep Lyα profile, and strong N V (1238 and 1242 A) and O V (1371 A) wind/coronal absorption lines. Numerous sharp interstellar resonance lines are also present. A grid of accretion disk models, spanning a wide range of inclinations, accretion rates, and white dwarf masses, was compared with three sets of dereddened data. From the three best fits, we conclude that the most likely parameters characterizing the far-UV spectrum of DI Lac are an inclination below 18°, a white dwarf mass between 0.6 and 0.8 M⊙, and an accretion rate between 10-9.0 and 10-9.5 M⊙ yr-1. The scale factors for the three best-fit disk models indicate distances between 2 and 2.5 kpc. The extreme weakness or absence of silicon features in the observed spectrum corresponds to a silicon underabundance of 10-4 times solar. The best-fitting high-gravity photosphere model has log g = 8, Teff = 27,000 K, V sin i = 200 km s-1, and a scale factor distance (for a 0.7 M⊙ white dwarf) of only 76 pc. Thus, a white dwarf photosphere cannot be contributing appreciably to the far-UV spectrum.

Dust on the Outskirts of the Jovian System

The outer region of the jovian system between ∼50 and 300 jovian radii from the planet is found to be the host of a previously unknown dust population. We used the data from the dust detector aboard the Galileo spacecraft collected from December 1995 to April 2001 during Galileo's numerous traverses of the outer jovian system. Analyzing the ion amplitudes, calibrated masses and speeds of grains, and impact directions, we found about 100 individual events fully compatible with impacts of grains moving around Jupiter in bound orbits. These grains have moderate eccentricities and a wide range of inclinations—from prograde to retrograde ones. The radial number density profile of the micrometer-sized dust is nearly flat between about 50 and 300 jovian radii. The absolute number density level (∼10 km−3 with a factor of 2 or 3 uncertainty) surpasses by an order of magnitude that of the interplanetary background. We identify the sources of the bound grains with outer irregular satellites of Jupiter. Six outer tiny moons are orbiting the planet in prograde and fourteen in retrograde orbits. These moons are subject to continuous bombardment by interplanetary micrometeoroids. Hypervelocity impacts create ejecta, nearly all of which get injected into circumjovian space. Our analytic and numerical study of the ejecta dynamics shows that micrometer-sized particles from both satellite families, although strongly perturbed by solar tidal gravity and radiation pressure, would stay in bound orbits for hundreds of thousands of years as do a fraction of smaller grains, several tenths of a micrometer in radius, ejected from the prograde moons. Different-sized ejecta remain confined to spheroidal clouds embracing the orbits of the parent moons, with appreciable asymmetries created by the radiation pressure and solar gravity perturbations. Spatial location of the impacts, mass distribution, speeds, orbital inclinations, and number density of dust derived from the data are all consistent with the dynamical model.

Geopotential harmonics of orders 15 and 30

The Earth's gravitational potential is usually expressed as a double infinite series of spherical harmonics. In recent models1–3, derived from photographic, radio and laser observations of satellites, gravimetry and satellite altimetry, the harmonics have been evaluated up to a degree and an order of 36 or more, so that there are 1,296 or more coefficients to be evaluated. The geoid surfaces derived from such models have errors of approximately 1 m, but much better accuracy is required to take advantage of satellite altimeter measurements accurate to 10 cm or better. So there is a continuing demand to improve the models. The accuracy of the individual coefficients is questionable, and difficult to estimate4. The most precise technique for determining coefficients of a particular order is by analysis of satellite orbits which experience resonance with the Earth's gravitational field. We have recently5 re-evaluated individual harmonic coefficients of orders 15 and 30 from analyses of 24 orbits having a wide range of inclinations to the Equator. These coefficients have standard deviations equivalent to an accuracy in geoid height of 1 cm, for degree up to 23, and are valuable as a standard against which the comprehensive gravity field models can be tested.

Strain-Stress Relations and Failure of Anisotropic Clays

Different degrees of anisotropy were induced in two kaolinitic clays and one illitic clay by one-dimensional consolidation of thin hollow circular cylinders in a specially designed cell. For each degree of anisotropy, a pneumatic analog computer was used to subject the clay specimens to 16 different stress paths corresponding to a wide range of inclinations of the principal stresses on the axis of symmetry of the material. The computer was programmed to maintain this inclination constant for the duration of each test. The results show that the incremental strain-stress relations which are presented are valid for the three clays at their various degrees of anisotropy. The failure criterion of Goldenblat and Kopnov which takes into account anisotropy as well as the difference in behavior between extension and compression, is found to be extremely satisfactory in the range of stresses covered.

Commensurable eccentric orbits near critical inclination

Artificial satellites whose mean motion is commensurable with the rotation of the Earth are subject to resonance effects arising from the slight longitude-dependence of the geopotential. Previous papers have discussed this problem where one or other of the eccentricity or inclination is sufficiently small that it can be considered to be zero. The situation for orbits which are both inclined and eccentric is in general more complicated, but again becomes relatively simple near the critical inclination since the argument of perigee is approximately constant. The particular example of 12-hr orbits is discussed in some detail; it is of special interest since the U.S.S.R. has now launched twelve Molniya 1 satellites in highly eccentric 12-hr orbits at about 65o inclination, and eight of these have had at least partially stabilished ground tracks. It is shown that the gravity coefficientJ 2, 2 becomes dominant whene exceeds ∼ 0.05, taking over fromJ 3, 2 which is in control fore=0. The appropriate resonant variable is of the novel form∏ 1,2=M + 2 (Ω−not) which does not seem capable of physical or geometrical interpretation. This description is valid over a wide range of eccentricity (e>0.15) and a fairly wide range of inclination (50o<I<90o) and is illustrated by the behaviour of Molniyas 1J and 1K.

A Reflectance Spectrometer/Environmental Chamber for Frosts

As part of a study of frost spectral properties, a low incident energy, near ir reflectance spectrometer has been designed and built as an integral part of an environmental chamber. The total incident energy on the sample from the monochromater and cooled chamber, 4 x 10(-3) W cm(-2), is one to two orders of magnitude less than in previous ir spectral measurements of frosts and avoids thermal metamorphism of the sample. All supports, connections, and windows are mounted in the chamber lid allowing very simple, readily interchangeable chambers to be used. This permits growth of samples under a variety of controlled conditions and allows spectral measurements over a wide range of inclinations. The apparatus allowed photography and access to the sample so that sample density, thickness, grain size, and composition of H(2)O-CO(2) frosts could be determined.

A Theoretical Approach to the Radiation Dose-rate Distribution from Combined X- or γ-ray Beams with special reference to Wedge-filtered Beams

An analytical treatment is developed which allows prediction of the clinically important features of the resultant field when two similar wedge fields are superposed. An extensive analysis of the results obtained using a number of different wedge sizes with cobalt γ-rays, shows that the predicted values agree with those obtained by the conventional graphical method of summation over a wide range of inclinations and linear separations of the two fields.It is shown that using information obtained from the isodose charts of single wedge fields, the clinical data required for planning treatments using superposed fields may be simply computed. This data, together with a knowledge of the effect of varying any of the physical parameters, eliminates the need to issue to the radiotherapist full isodose charts covering all possible clinical arrangements.The various mathematical relationships obtained are used to deduce the practical limitations that are imposed on the physical parameters of the system when the principles governing radiotherapeutic practice are applied.It is also shown that the magnitude of the ` hot spot ' found near the port of entry of each field is simply related to an attenuation coefficient and to the wedge angle.The function of an additional plain field is also discussed.The conditions under which the method would be applicable to the superposition of plain fields are described.