Individual Orbits Research Articles

Stellar SiO masers in the Galaxy: The Bulge Asymmetries and Dynamic Evolution (BAaDE) survey

AbstractCircumstellar SiO masers can be observed in red giant evolved stars throughout the Galaxy. Since stellar masers are not affected by non-gravitational forces, they serve as point-mass probes of the gravitational potential and form an excellent sample for studies of the Galactic structure and dynamics. Compared to optical studies, the non-obscured masers are in particular valuable when observed close to the highly obscured Galactic Bulge and Plane. Their line-of-sight velocities can easily be obtained with high accuracy, proper motions can be measured and distances can be estimated. Furthermore, when different mass and metallicity effects can be accounted for, such a large sample will highlight asymmetries and evolutionary traces in the sample. In our Bulge Asymmetries and Dynamic Evolution (BAaDE) survey we have searched 20,000 infrared selected evolved stars for 43 GHz SiO masers with the VLA in the northern Bulge and Plane and are in the process of observing another 10,000 stars for 86 GHz SiO masers with ALMA in the southern Bulge. Our instantaneous detection rate in the Bulge is close to 70%, both at 43 and 86 GHz, with occasionally up to 7 simultaneous SiO transitions observed in a single star. Here we will outline the BAaDE survey, its first results and some of the peculiar maser features we have observed. Furthermore we will discuss the prospects for obtaining proper motions and parallaxes for individual maser stars to reconstruct individual stellar orbits.

Average plasma sheet polytropic index as observed by THEMIS

Abstract. Multi-spacecraft data from the years 2008 to 2015 of the THEMIS mission particularly in the near-Earth plasma sheet are used in order to empirically determine the polytropic index in the quiet and active time magnetotail. The results of a number of previous studies in the 1990s can be confirmed. An analysis of the total database, although showing poor correlation, results in an average polytropic index of γ = 1. 72. The active time plasma sheet is well correlated with an average γ = 1. 49. However, the data scattering suggests that the analysis of the data in total is not adequate. In order to reduce the timescales, individual spacecraft orbits are analyzed, giving a broad distribution of polytropic indices throughout the plasma sheet. The major part of the distribution falls in a range between γ = 0. 67 and γ = 2. Our results indicate a variety of thermodynamic processes in the magnetotail and an all-time presence of heat exchange of the plasma. A description of the plasma sheet using an equation of state with a single γ is probably inadequate. This necessitates the application of more sophisticated approaches, such as a parametrization of the heat flux vector in magnetohydrodynamic equations or a superposition of polytropic indices.

Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards.

A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.

Application of Indicators for Chaos in Chaotic Circuit Systems

Lyapunov exponent (LE), fast Lyapunov indicator (FLI), relative finite-time Lyapunov indicator (RLI), smaller alignment index (SALI), and generalized alignment index (GALI) are some of the available methods in most conservative systems. This study focuses on the effects of the above indicators on dissipative chaotic circuit systems such as the Lorenz system and a hyperchaotic model. Numerical experiments show that the performances of the chaos indicators in the hyperchaotic system are almost similar to those in the Lorenz system. These indicators clearly provide transition from chaotic to regular motion. However, FLI, RLI, SALI, and GALI cannot describe transition from chaos to hyperchaos. These indicators are also applied to study a new four-dimensional chaotic circuit system. The basic dynamic behaviors and structures are investigated analytically and numerically. The dynamic qualitative properties of individual orbits are observed using an oscilloscope. Moreover, the entire set of LE about the parameter is found to have three threshold values. Comparisons show that all chaos indicators are able to capture chaotic and periodic motion in chaotic circuit systems, but SALI displays significantly different behavior in several periodic orbits. SALI drops exponentially to zero for “morphologically regular” orbits that are actually unstable and sensitive to perturbation. This conclusion can also be confirmed by GALI.

Ring formation around giant planets by tidal disruption of a single passing large Kuiper belt object

The origin of rings around giant planets remains elusive. Saturn’s rings are massive and made of 90–95% of water ice with a mass of ∼1019 kg. In contrast, the much less massive rings of Uranus and Neptune are dark and likely to have higher rock fraction. According to the so-called “Nice model”, at the time of the Late Heavy Bombardment, giant planets could have experienced a significant number of close encounters with bodies scattered from the primordial Kuiper Belt. This belt could have been massive in the past and may have contained a larger number of big objects (Mbody=1022 kg) than what is currently observed in the Kuiper Belt. Here we investigate, for the first time, the tidal disruption of a passing object, including the subsequent formation of planetary rings. First, we perform SPH simulations of the tidal destruction of big differentiated objects (Mbody=1021 and 1023 kg) that experience close encounters with Saturn or Uranus. We find that about 0.1–10% of the mass of the passing body is gravitationally captured around the planet. However, these fragments are initially big chunks and have highly eccentric orbits around the planet. In order to see their long-term evolution, we perform N-body simulations including the planet’s oblateness up to J4 starting with data obtained from the SPH simulations. Our N-body simulations show that the chunks are tidally destroyed during their next several orbits and become collections of smaller particles. Their individual orbits then start to precess incoherently around the planet’s equator, which enhances their encounter velocities on longer-term evolution, resulting in more destructive impacts. These collisions would damp their eccentricities resulting in a progressive collapse of the debris cloud into a thin equatorial and low-eccentricity ring. These high energy impacts are expected to be catastrophic enough to produce small particles. Our numerical results also show that the mass of formed rings is large enough to explain current rings including inner regular satellites around Saturn and Uranus. In the case of Uranus, a body can go deeper inside the planet’s Roche limit resulting in a more efficient capture of rocky material compared to Saturn’s case in which mostly ice is captured. Thus, our results can naturally explain the compositional difference between the rings of Saturn, Uranus and Neptune.

Nonlinear dynamics of a functionally graded piezoelectric micro-resonator in the vicinity of the primary resonance

This research is on the nonlinear dynamics of a two-sided electrostatically actuated capacitive micro-beam. The micro-resonator is composed of silicon and PZT as a piezoelectric material. PZT is functionally distributed along the height of the micro-beam according to the power law distribution. The micro-resonator is simultaneously subjected to DC piezoelectric and two-sided electrostatic actuations. The DC piezoelectric actuation leads to the generation of an axial force along the length of the micro-beam and this is used as a tuning tool to shift the primary resonance of the micro-resonator. The governing equation of the motion is derived by the minimization of the Hamiltonian and generalized to the viscously damped systems. The periodic solutions in the vicinity of the primary resonance are detected by means of the shooting method and their stability is investigated by determining the so-called Floquet exponents of the perturbed motions. The basins of attraction corresponding to three individual periodic orbits are determined. The results depict that the higher the amplitude of the periodic orbit, the smaller is the area of the attractor.

RICH KOZAI–LIDOV DYNAMICS IN AN INITIALLY THIN AND ECCENTRIC STELLAR DISK AROUND A SUPERMASSIVE BLACK HOLE

ABSTRACT There is growing evidence of star formation in the vicinity of supermassive black holes (SMBHs) in galactic nuclei. A viable scenario for this process assumes infall of a massive gas cloud toward the SMBH and subsequent formation of a dense accretion disk, which gives birth to the young stars. Numerical hydrodynamical models indicate that this star formation process is rather fast and precedes full circularization of the accretion flow, i.e., the new stars are born on elliptic orbits. By means of direct numerical N-body modeling, we show in this paper that the nonzero eccentricity of the stellar disks around the SMBH leads to an onset of various types of the Kozai–Lidov oscillations of a non-negligible subset of individual orbits in the disk, showing a remarkable robustness of this classical mechanism. Among others, we demonstrate that under certain circumstances, the presence of an additional spherical cluster (which is generally known to damp Kozai–Lidov oscillations) may trigger such oscillations as a result of affecting the internal flow of the angular momentum through the disk. We conclude that the Kozai–Lidov oscillations are capable of substantially modifying the initial structure of the disk (its thickness and distribution of eccentricities, in particular).

Early MAVEN Deep Dip campaign reveals thermosphere and ionosphere variability.

The Mars Atmosphere and Volatile Evolution (MAVEN) mission, during the second of its Deep Dip campaigns, made comprehensive measurements of martian thermosphere and ionosphere composition, structure, and variability at altitudes down to ~130 kilometers in the subsolar region. This altitude range contains the diffusively separated upper atmosphere just above the well-mixed atmosphere, the layer of peak extreme ultraviolet heating and primary reservoir for atmospheric escape. In situ measurements of the upper atmosphere reveal previously unmeasured populations of neutral and charged particles, the homopause altitude at approximately 130 kilometers, and an unexpected level of variability both on an orbit-to-orbit basis and within individual orbits. These observations help constrain volatile escape processes controlled by thermosphere and ionosphere structure and variability.

A probabilistic analysis of the implicationsof instrument failures on ESA’s Swarm mission for its individual satellite orbit deployments

On launch, one of Swarm’s absolute scalar magnetometers (ASMs) failed to function, leaving an asymmetrical arrangement of redundant spares on different spacecrafts. A decision was required concerning the deployment of individual satellites into the low-orbit pair or the higher “lonely” orbit. I analyse the probabilities for successful operation of two of the science components of the Swarm mission in terms of a classical probabilistic failure analysis, with a view to concluding a favourable assignment for the satellite with the single working ASM. I concentrate on the following two science aspects: the east-west gradiometer aspect of the lower pair of satellites and the constellation aspect, which requires a working ASM in each of the two orbital planes. I use the so-called “expert solicitation” probabilities for instrument failure solicited from Mission Advisory Group (MAG) members. My conclusion from the analysis is that it is better to have redundancy of ASMs in the lonely satellite orbit. Although the opposite scenario, having redundancy (and thus four ASMs) in the lower orbit, increases the chance of a working gradiometer late in the mission; it does so at the expense of a likely constellation. Although the results are presented based on actual MAG members’ probabilities, the results are rather generic, excepting the case when the probability of individual ASM failure is very small; in this case, any arrangement will ensure a successful mission since there is essentially no failure expected at all. Since the very design of the lower pair is to enable common mode rejection of external signals, it is likely that its work can be successfully achieved during the first 5 years of the mission.

Some improvements of the Katznelson- Tzafriri theorem on Hilbert space

This paper extends two recent improvements in the Hilbert space setting of the well-known Katznelson-Tzafriri theorem by establishing both a version of the result valid for bounded representations of a large class of abelian semigroups and a quantified version for contractive representations. The paper concludes with an outline of an improved version of the Katznelson-Tzafriri theorem for individual orbits, whose validity extends even to certain unbounded representations.

SECULAR EVOLUTION OF THE PULSAR TRIPLE SYSTEM J0337+1715

The pulsar triple system, J0337+1715, is remarkably regular and highly hierarchical. Secular dynamics controls its long term evolution with orbital commensurability having negligible effect. Secular interactions transfer angular momentum between inner and outer orbits unless their apsidal lines are parallel or anti-parallel. These choices correspond, respectively, to orthogonal eigenmodes p and a. Each is characterized by an eccentricity ratio set by the masses and semi-major axes, i.e., $e_{p, 1}/e_{p, 2}\sim a_1/a_2$ while $e_{a, 1}/e_{a, 2}\sim (a_1/a_2)^{-3/2}(m_2/m_1)$. Mode p dominates the system's current state so $e_1/e_2$ always remains close to $e_{p, 1}/e_{p, 2}$. A small contribution by Mode a causes $e_1$ and $e_2$ to oscillate with period $\sim 10^3\,\yr$. Orbital changes should be apparent in a few years. These will reveal the forcing of the apsidal precession of the inner orbit by general relativity (GR), and possibly also the smaller contribution due to the tidal and rotational distortion of the inner white dwarf (WD). Phinney (1992) proposes that the epicyclic energy of a WD-pulsar binary reaches equipartition with the kinetic energy of a single convective eddy when the WD's progenitor fills its Roche lobe. We extend Phinney's theory to apply to modes rather than individual orbits. Thus we predict that Mode p and Mode a achieved equipartition with eddies in the giant envelopes of the progenitors of the outer and inner WD, respectively. The most effective eddies are those with lifetimes closest to the orbit period. These were more energetic in the progenitor of the outer WD. This explains why Mode p overwhelms Mode a, and also why the inner binary's orbit is far more eccentric than other WD-pulsar binaries with similar orbit periods. Mode a's small but finite amplitude places a lower bound of $Q\sim 10^6$ on the tidal quality parameter of the inner WD.

Statistical characteristics of EMIC wave‐driven relativistic electron precipitation with observations of POES satellites: Revisit

AbstractElectromagnetic ion cyclotron (EMIC) waves play an important role in the magnetospheric dynamics and can scatter relativistic electrons in the outer radiation belt into the loss cone leading to the rapid loss of relativistic electrons. In this paper, we present characteristics of EMIC wave‐driven relativistic electron precipitation (REP) with observations of six Polar Orbiting Environmental Satellites (POES). Based on the simultaneity between spikes in the P1 0° (Ep = 30 keV–80 keV) and P6 0° (Ee > 1 MeV) channels, in comparison with the criterion of Carson et al. (2013), we improve the algorithm and make it stricter. A total of 436,286 individual half orbits between 1998 and 2010 are inspected by this algorithm. The majority of selected events are observed at L values within the outer radiation belt (3 < L < 7) and more common in 1800–2200 magnetic local time. The distribution of normalized events follows the location of plasmapause contracting toward lower L value with the decrease of the Dst index, implying a strong link between detected events and the plasmapause. The cluster of normalized events moves to later afternoon sector where the peak occurrence of plasmaspheric plumes is located during geomagnetic storms. It is suggested that there is a connection between plasmaspheric plumes and detected events. Corresponding to the peak of event occurrence in 2003, solar wind dynamic pressure has a same peak. In addition, the minimum values of them are coincident. These results indicate that the increase of the solar wind dynamic pressure enhances the likelihood of EMIC wave‐driven relativistic electron precipitation.

Orbits of radial migrators and non-migrators around a spiral arm in N-body simulations

Recent numerical N-body simulations of spiral galaxies have shown that spiral arms in N-body simulations seem to rotate at a similar speed to the local rotation speed of the stellar disc material. This in turn yields winding, transient and recurrent spiral structure, whose co-rotating nature gives rise to changes in the angular momentum (radial migration) of star particles close to the spiral arm at many radii. From high resolution N-body simulations, we highlight the evolution of strongly migrating star particles (migrators) and star particles that do not migrate (non-migrators) around a spiral arm. We investigate the individual orbit histories of migrators and non-migrators and find that there are several types of migrator and non-migrator, each with unique radial evolution. We contrast each type of orbit to establish the reasons for the differences between them. We find that the positive (negative) migrators sustain a position behind (in front of) the spiral arm, and feel continuous tangential force as long as the spiral arm persists. On the other hand, non-migrators stay close to the spiral arm, and pass or are passed by the spiral arm one or two times. Although they gain or lose the angular momentum when they are behind or in front of the spiral arm, their net angular momentum change becomes close to zero. We discuss also the long term effects of radial migration on the radial metallicity distribution and radial angular momentum and mass profiles. [Abridged]

On the Gravitational Two-Body System and an Infinite Set of Laplace-Runge-Lenz Vectors

The current approach of a system of two bodies that interact through a gravitational force goes beyond the familiar expositions [1-3] and derives some interesting features and laws that are overlooked. A new expression for the angular momentum of a system in terms of the angular momenta of its parts is deduced. It is shown that the characteristics of the relative motion depend on the system’s total mass, whereas the characteristics of the individual motions depend on the masses of the two bodies. The reduced energy and angular momentum densities are constants of motion that do not depend on the distribution of the total mass between the two bodies; whereas the energy may vary in absolute value from an infinitesimal to a maximum value which occurs when the two bodies are of equal masses. In correspondence with infinite possible ways to describe the absolute rotational positioning of a two body system, an infinite set of Laplace-Runge-Lenz vectors (LRL) are constructed, all fixing a unique orientation of the orbit relative to the fixed stars. The common expression of LRV vector is an approximation of the actual one. The conditions for nested and intersecting individual orbits of the two bodies are specified. As far as we know, and apart from the law of periods, the laws of equivalent orbits concerning their associated periods, areal velocities, angular velocities, velocities, energies, as well as, the law of total angular momentum, were never considered before.

The distance to the Galactic Center

AbstractOne of the Milky Way's fundamental parameters is the distance of the Sun from the Galactic Center, R0. This article reviews the various ways of estimating R0, placing special emphasis on methods that have become possible recently. In particular, we focus on the geometric distance estimate made possible thanks to observations of individual stellar orbits around the massive black hole at the center of the Galaxy. The specific issues of concern there are the degeneracies with other parameters, most importantly the mass of the black hole and the definition of the reference frame. The current uncertainty is nevertheless only a few percent, with error bars shrinking every year.

Measuring the stellar luminosity function and spatial density profile of the inner 0.5 pc of the Milky Way nuclear star cluster

We report on measurements of the luminosity function of early (young) and late-type (old) stars in the central 0.5 pc of the Milky Way nuclear star cluster as well as the density profiles of both components. The young (∼ 6 Myr) and old stars (> 1 Gyr) in this region provide different physical probes of the environment around a supermassive black hole; the luminosity function of the young stars offers us a way to measure the initial mass function from star formation in an extreme environment, while the density profile of the old stars offers us a probe of the dynamical interaction of a star cluster with a massive black hole. The two stellar populations are separated through a near-infrared spectroscopic survey using the integral-field spectrograph OSIRIS on Keck II behind the laser guide star adaptive optics system. This spectroscopic survey is able to separate early-type (young) and late-type (old) stars with a completeness of 50% at K' = 15.5. We describe our method of completeness correction using a combination of star planting simulations and Bayesian inference. The completeness corrected luminosity function of the early-type stars contains significantly more young stars at faint magnitudes compared to previous surveys with similar depth. In addition, by using proper motion and radial velocity measurements along with anisotropic spherical Jeans modeling of the cluster, it is possible to measure the spatial density profile of the old stars, which has been difficult to constrain with number counts alone. The most probable model shows that the spatial density profile, n(r) ∝ r−γ, to be shallow with γ = 0.4 ± 0.2, which is much flatter than the dynamically relaxed case of γ = 3/2 to 7/4, but does rule out a 'hole' in the distribution of old stars. We show, for the first time, that the spatial density profile, the black hole mass, and velocity anisotropy can be fit simultaneously to obtain a black hole mass that is consistent with that derived from individual orbits of stars at distances < 1000 AU from the Galactic center.

ORBITS, MASSES, AND EVOLUTION OF MAIN BELT TRIPLE (87) SYLVIA

Sylvia is a triple asteroid system located in the main belt. We report new adaptive optics observations of this system that extend the baseline of existing astrometric observations to a decade. We present the first fully dynamical 3-body model for this system by fitting to all available astrometric measurements. This model simultaneously fits for individual masses, orbits, and primary oblateness. We find that Sylvia is composed of a dominant central mass surrounded by two satellites orbiting at 706.5 +/- 2.5 km and 1357 +/- 4.0 km, i.e., about 5 and nearly 10 primary radii. We derive individual masses of 1.484 -0.014/+0.016 x 10^19 kg for the primary (corresponding to a density of 1.29 +/- 0.39 g cm^-3), 7.33 -2.3/+4.7 x 10^14 kg for the inner satellite, and 9.32 -8.3/+20.7 x 10^14 kg for the outer satellite. The oblateness of the primary induces substantial precession and the J_2 value can be constrained to the range of 0.0985-0.1. The orbits of the satellites are relatively circular with eccentricities less than 0.04. The spin axis of the primary body and the orbital poles of both satellites are all aligned within about two degrees of each other, indicating a nearly coplanar configuration and suggestive of satellite formation in or near the equatorial plane of the primary. We also investigate the past orbital evolution of the system by simulating the effects of a recent passage through 3:1 mean-motion eccentricity-type resonances. In some scenarios this allow us to place constraints on interior structure and past eccentricities.

An extended XMM-Newton observation of the Seyfert galaxy NGC 4051 - III. Fe K emission and absorption

An extended XMM-Newton observation of the Seyfert 1 galaxy NGC 4051 in 2009 detected a photo-ionized outflow with a complex absorption line velocity structure and a broad correlation of velocity with ionization parameter, shown in Pounds et al (2011) to be consistent with a highly ionized, high velocity wind running into the interstellar medium or previous ejecta, losing much of its kinetic energy in the resultant strong shock. In the present paper we examine the Fe K spectral region in more detail and find support for two distinct velocity components in the highly ionized absorber, with values corresponding to the putative fast wind (~ 0.12c) and the post-shock flow (v ~ 5000-7000 km/s). The Fe K absorption line structure is seen to vary on a orbit-to-orbit timescale, apparently responding to both a short term increase in ionizing flux and - perhaps more generally - to changes in the soft X-ray (and simultaneous UV) luminosity. The latter result is particularly interesting in providing independent support for the existence of shocked gas being cooled primarily by Compton scattering of accretion disc photons. The Fe K emission is represented by a narrow fluorescent line from near-neutral matter, with a weak red wing modelled here by a relativistic diskline. The narrow line flux is quasi-constant throughout the 45-day 2009 campaign, but is resolved, with a velocity width consistent with scattering from a component of the post-shock flow. Evidence for a P Cygni profile is seen in several individual orbit spectra for resonance transitions in both Fe XXV and Fe XXVI.

Globally averaged exospheric temperatures derived from CHAMP and GRACE accelerometer measurements

Neutral densities (ρ) inferred from accelerometer measurements on the polar‐orbiting Challenging Minisatellite Payload (CHAMP) and Gravity Recovery and Climate Experiment (GRACE) satellites are used to compile exospheric temperatures (T∞) during extended periods in 2003 and 2004 when their orbital planes were nearly parallel and at quadrature, respectively. Exospheric temperatures were first estimated using ρ‐h‐T∞ relationships implicit within the Jacchia models, then averaged over individual orbits. We found good agreement between the orbital‐averaged T∞ obtained from CHAMP and GRACE accelerometer data as well as with globally averaged exospheric temperatures derived from drag measurements from the constellation of satellites used in the High‐Accuracy Satellite Drag Model. Our analysis corrects a critical conjecture by Burke (2008) that globally averaged T∞ is essentially the same as orbit‐averaged values obtained by polar‐orbiting satellites, independent of the local time of their orbital planes. Unlike the symmetric 0200–1400 LT distribution of T∞ minima and maxima found in early Jacchia models, presented data indicate that the minima are located closer to the dawn meridian. We also demonstrate that the averaging technique used to estimate T∞ affects the outcomes. Statistical analyses provide an empirical basis for improving estimates of the thermosphere's total energy budget.

ANALYSIS OF NEW FOUR-DIMENSIONAL CHAOTIC CIRCUITS WITH EXPERIMENTAL AND NUMERICAL METHODS

Dynamically qualitative properties of individual orbits in a new four-dimensional nonlinear circuit are observed on an oscilloscope. Meanwhile, they are also traced numerically with the help of some methods for finding chaos. Comparisons show that the observed results are consistent with the computed ones to a great extent. In addition, the bifurcation, Lyapunvon spectra, fast Lyapunov indicators and small alignment indexes represent almost the same rules of transitivity to chaos on a control parameter. It is found when the parameter has a threshold value from order to chaos, and the chaos gets stronger and stronger, the parameter is smoothly varied from small to large. In particular, the entire set of Lyapunov exponents can lead to another threshold value of the parameter from chaotic to hyperchaotic behaviors.