Eccentric Disk Research Articles

HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. I. Hydrodynamic simulations

ABSTRACT High-frequency quasi-periodic oscillations (HFQPOs) observed in the emission of black hole X-ray binary systems promise insight into strongly curved spacetime. ‘Discoseismic’ oscillations with frequencies set by the intrinsic properties of the central black hole, in particular ‘trapped inertial waves’ (r modes), offer an attractive explanation for HFQPOs. To produce an observable signature, however, such oscillations must be excited to sufficiently large amplitudes. Turbulence driven by the magnetorotational instability fails to provide the necessary amplification, but r modes may still be excited via interaction with accretion disc warps or eccentricities. We present 3D global hydrodynamic simulations of relativistic accretion discs, which demonstrate for the first time the excitation of trapped inertial waves by an imposed eccentricity in the flow. While the r modes’ saturated state depends on the vertical boundary conditions used in our unstratified, cylindrical framework, their excitation is unambiguous in all runs with eccentricity ≳ 0.005 near the innermost stable circular orbit. These simulations provide a proof of concept, demonstrating the robustness of trapped inertial wave excitation in a non-magnetized context. In a companion paper, we explore the competition between this excitation, and damping by magnetohydrodynamic turbulence.

Associations of prenatal heavy metals exposure with placental characteristics and birth weight in Hangzhou Birth Cohort: Multi-pollutant models based on elastic net regression

BackgroundThe human placenta is vulnerable to environmental pollutants, but the associations between exposure to multiple, correlated metals and placental characteristics have not been studied. MethodsThe current study population was derived from the Hangzhou Birth Cohort Study. Whole blood and urine samples were collected from mothers during 20–28 gestational week. The concentrations of 11 metals in blood and 11 metals in urine were evaluated by inductively coupled plasma mass spectrometry. The data on placental characteristics and birth weight were retrieved from medical records. The elastic net (ENET) model combined with unpenalized regression model was employed to estimate the relationship between levels of metals and placental characteristics (placental weight, chorionic disc area, chorionic disc eccentricity, placental thickness, placental-fetal birth weight ratio) and birth weight. Mediation analysis was performed to explore the mediated effect of placenta on the association of prenatal metals exposure with birth weight. ResultsAmong 512 participants with urine metal levels, the ENET model retained Cadmium (Cd) and Selenium (Se) for placental weight. Further unpenalized regression model including Cd and Se simultaneously showed that one-unite increased natural-logarithm (ln)-transformed urine creatinine corrected (CC) Cd levels was associated with reductions in placental weight of −7.2 g (95% confidence interval (CI): −14.0, −0.4). Among 483 participants with blood metal levels, similarly, blood Cd levels were negatively associated with placental weight (β = −7.5, 95% CI: −17.0, 1.9). Furthermore, mediation analysis demonstrated that urine CC-Cd level was associated with a 21.3 g decrease (95% CI: −42.0, −2.5, p = 0.024) in birth weight through a reduction in placental weight, while blood Cd levels presented a negative association at borderline significance. ConclusionOur findings suggest a mediation effect of the placenta in the relationship between prenatal Cd exposure and lower birth weight. Additional studies with repeated assessment of exposure and more placental parameters are warranted to confirm this relationship.

On the nonlinear dynamics of constant stiffness coefficients 16-pole rotor active magnetic bearings system

The present study is devoted to investigate the oscillatory behaviors of the 16-pole rotor active magnetic bearing system. A controllable electromagnetic force generated via a conventional proportional-derivative controller is utilized to stabilize the system lateral oscillations that excited by the rotating disk eccentricity when the spinning speed (Ω) is close to or equal the system linear natural frequency (ω). The nonlinear dynamical equations governing the controlled system lateral vibrations at constant stiffness coefficients are derived in this article for the first time. Then, four nonlinear autonomous first-order differential equations to describe the considered system oscillation amplitudes and the corresponding phase angles are obtained applying the asymptotic analysis. Bifurcation behavior of the system periodic motions under varying the different control parameters is explored. The main acquired results confirm that the 16-pole rotor-AMB system at constant stiffness coefficients can exhibit one of three oscillatory motions that are periodic, quasiperiodic, or chaotic motions depending on the derivative gain coefficient. Moreover, the system may respond with one-stable solution, bi-stable solutions, tri-stable solutions, or quadri-stable solutions depending on the proportional gain coefficient. Numerical simulations for different system motions are validated via the system time response, Poincare map, orbit plot, and frequency spectrum that are showed an excellent agreement with the obtained analytical results.

Evolution of α Centauri b’s protoplanetary disc

ABSTRACT With hydrodynamical simulations we examine the evolution of a protoplanetary disc around α Centauri B including the effect of the eccentric orbit binary companion α Centauri A. The initially circular orbit disc undergoes two types of eccentricity growth. First, the eccentricity oscillates on the orbital period of the binary, Porb, due to the eccentricity of the binary orbit. Secondly, for a sufficiently small disc aspect ratio, the disc undergoes global forced eccentricity oscillations on a time-scale of around $20\, P_{\rm orb}$. These oscillations damp out through viscous dissipation leaving a quasi-steady eccentricity profile for the disc that oscillates only on the binary orbital period. The time-averaged global eccentricity is in the range 0.05–0.1, with no precession in the steady state. The periastrons of the gas particles are aligned to one another. The higher the disc viscosity, the higher the disc eccentricity. With N-body simulations we examine the evolution of a disc of planetesimals that forms with the orbital properties of the quasi-steady protoplanetary disc. We find that the average magnitude of the eccentricity of particles increases and their periastrons become misaligned to each other once they decouple from the gas disc. The low planetesimal collision velocity required for planet formation suggests that for planet formation to have occurred in a disc of planetesimals formed from a protoplanetary disc around α Centauri B, said disc’s viscosity must be have been small and planet formation must have occurred at orbital radii smaller than about $2.5\, \rm au$. Planet formation may be easier with the presence of gas.

Hydrodynamical turbulence in eccentric circumbinary discs and its impact on the in situ formation of circumbinary planets

ABSTRACT Eccentric gaseous discs are unstable to a parametric instability involving the resonant interaction between inertial-gravity waves and the eccentric mode in the disc. We present three-dimensional global hydrodynamical simulations of inviscid circumbinary discs that form an inner cavity and become eccentric through interaction with the central binary. The parametric instability grows and generates turbulence that transports angular momentum with stress parameter α ∼ 5 × 10−3 at distances ≲ 7 abin, where abin is the binary semimajor axis. Vertical turbulent diffusion occurs at a rate corresponding to αdiff ∼ 1–2 × 10−3. We examine the impact of turbulent diffusion on the vertical settling of pebbles, and on the rate of pebble accretion by embedded planets. In steady state, dust particles with Stokes numbers St ≲ 0.1 form a layer of finite thickness Hd ≳ 0.1H, where H is the gas scale height. Pebble accretion efficiency is then reduced by a factor racc/Hd, where racc is the accretion radius, compared to the rate in a laminar disc. For accreting core masses with mp ≲ 0.1 M⊕, pebble accretion for particles with St ≳ 0.5 is also reduced because of velocity kicks induced by the turbulence. These effects combine to make the time needed by a Ceres mass object to grow to the pebble isolation mass, when significant gas accretion can occur, longer than typical disc lifetimes. Hence, the origins of circumbinary planets orbiting close to their central binary systems, as discovered by the Kepler mission, are difficult to explain using an in situ model that invokes a combination of the streaming instability and pebble accretion.

Numerical and Experimental Analysis of A Vertical-Axis Eccentric-disc Variable-Pitch Turbine (VEVT)

A combined experimental and numerical investigation is carried out to study the performance of a vertical-axis eccentric-disc variable-pitch turbine (VEVT). A scheme of eccentric disc pitch control mechanism based on double-block mechanism is proposed. The eccentric control mechanism and the deflection angle control mechanism in the pitch control structure are designed and optimized according to the functional requirements of the turbine, and the three-dimensional model of the turbine is established. Kinematics analysis of the eccentric disc pitch control mechanism is carried out. Kinematics parameters and kinematics equations which can characterize its motion characteristics are derived. Kinematics analysis and simulation are carried out, and the motion law of the corresponding mechanical system is obtained. By analyzing the force and motion of blade of VEVT, the expressions of the important parameters such as deflection angle, attack angle and energy utilization coefficient are obtained. The lateral induced velocity coefficient is acquired by momentum theorem, the hydrodynamic parameters such as energy utilization coefficient are derived, and the hydrodynamic characteristics of VEVT are also obtained. The experimental results show that the turbine has good energy capture capability at different inflow velocities of different sizes and directions, which verifies that VEVT has good self-startup performance and high energy capture efficiency.

The unexpected narrowness of eccentric debris rings: a sign of eccentricity during the protoplanetary disc phase.

This paper shows that the eccentric debris rings seen around the stars Fomalhaut and HD 202628 are narrower than expected in the standard eccentric planet perturbation scenario (sometimes referred to as ‘pericentre glow’). The standard scenario posits an initially circular and narrow belt of planetesimals at semi-major axis a, whose eccentricity is increased to ef after the gas disc has dispersed by secular perturbations from an eccentric planet, resulting in a belt of width 2aef. In a minor modification of this scenario, narrower belts can arise if the planetesimals are initially eccentric, which could result from earlier planet perturbations during the gas-rich protoplanetary disc phase. However, a primordial eccentricity could alternatively be caused by instabilities that increase the disc eccentricity, without the need for any planets. Whether these scenarios produce detectable eccentric rings within protoplanetary discs is unclear, but they nevertheless predict that narrow eccentric planetesimal rings should exist before the gas in protoplanetary discs is dispersed. PDS 70 is noted as a system hosting an asymmetric protoplanetary disc that may be a progenitor of eccentric debris ring systems.

Sub-Neptune formation: the view from resonant planets

ABSTRACT The orbital period ratios of neighbouring sub-Neptunes are distributed asymmetrically near first-order resonances. There are deficits of systems – ‘troughs’ in the period ratio histogram – just short of commensurability, and excesses – ‘peaks’ – just wide of it. We reproduce quantitatively the strongest peak-trough asymmetries, near the 3:2 and 2:1 resonances, using dissipative interactions between planets and their natal discs. Disc eccentricity damping captures bodies into resonance and clears the trough, and when combined with disc-driven convergent migration, draws planets initially wide of commensurability into the peak. The migration implied by the magnitude of the peak is modest; reductions in orbital period are ∼10 per cent, supporting the view that sub-Neptunes complete their formation more-or-less in situ. Once captured into resonance, sub-Neptunes of typical mass $\sim \,$5–15M⊕ stay captured (contrary to an earlier claim), as they are immune to the overstability that afflicts lower mass planets. Driving the limited, short-scale migration is a gas disc depleted in mass relative to a solar-composition disc by three to five orders of magnitude. Such gas-poor but not gas-empty environments are quantitatively consistent with sub-Neptune core formation by giant impacts (and not, e.g. pebble accretion). While disc-planet interactions at the close of the planet formation era adequately explain the 3:2 and 2:1 asymmetries at periods $\gtrsim \, $5–15 d, subsequent modification by stellar tides appears necessary at shorter periods, particularly for the 2:1.

Vibration analysis of a dual-rotor-bearing-double casing system with pedestal looseness and multi-stage turbine blade-casing rub

Pedestal looseness and rotor-stator rub are two common faults in rotating machines. To increase the thrust-weight ratio and enhance fuel efficiency of aero engines, the structural design of a dual-rotor system has to address these two kinds of common faults. The aim of this paper is to gain insight into the vibration behaviours of a dual-rotor system with pedestal looseness and rotor-stator rub. Firstly, a dual-rotor-bearing-double casing system is modelled. After that, considering the effects of two disc imbalances, and pedestal looseness which exists in high pressure rotor, the rub-impact fault between the multi-stage turbine blades and the multi-layer casings is further introduced to the system. In combination with the distribution of soft and hard coatings, the impact stiffness of the rub-impact model is adjusted accordingly. Then an experimental study is performed on a dual-rotor test rig for verifying the validity of the theoretical model and revealing the dynamic responses at different rotor speed ratio. Finally, taking the stiffness of loosened pedestals, disc eccentricities, speed ratio, and initial gap as the key parameters, the potential effects of pedestal looseness and rub-impact on the dynamic characteristics of the dual-rotor system are investigated in detail.

Nonlinear vibration mitigation of a rotor-casing system subjected to imbalance–looseness–rub coupled fault

Modern industrial requirements are continuously demanding better performances and higher rotational speeds from current aero-engines. Under this circumstance, mitigation of rotor vibration is of considerable importance for safe and efficient functioning of rotating machinery. The main objective of this paper is to investigate the application of nonlinear vibration absorber on vibration suppression of a rotor-casing system having imbalance–looseness–rub coupled fault. Due to large vibration amplitude and pedestal looseness, both the geometrical nonlinearity of the rotor shaft and the support nonlinearity are considered in the system. When dealing with blade-casing rub, the initial gap between them is treated to be in non-uniform distribution because of coating inhomogeneity. Then the equations of motion in the presence and absence of nonlinear vibration absorber are respectively obtained according to the Lagrange’s equation. Through numerical simulation, the vibration mitigation of the rotor-casing system is realized in the different conditions of rotational speed and disc eccentricity. Moreover, from the perspective of vibration displacement and impact force, the effects of the nonlinear vibration absorber on the pedestal looseness and blade-casing rub are further discussed. The numerical results reveal that the nonlinear vibration absorber can effectively suppress the nonlinear vibration of the system and alleviate the detrimental influence of the coupled fault in a wide frequency range.

The Structure of Tidal Disruption Event Host Galaxies on Scales of Tens to Thousands of Parsecs

Abstract We explore the galaxy structure of four tidal disruption event (TDE) host galaxies on 30 pc to kiloparsec scales using Hubble Space Telescope WFC3 multiband imaging. The star formation histories of these hosts are diverse, including one post-starburst galaxy (ASASSN-14li), two hosts with recent weak starbursts (ASASSN-14ae and iPTF15af), and one early-type galaxy (PTF09ge). Compared to early-type galaxies of similar stellar masses, the TDE hosts have higher central surface brightnesses and stellar mass surface densities on 30–100 pc scales. The TDE hosts do not show the large, kiloparsec-scale tidal disruptions seen in some post-starburst galaxies; the hosts have low morphological asymmetries similar to those of early-type galaxies. The lack of strong asymmetries is inconsistent with a recent major (∼1:1 mass) merger, although minor (≲1:3) mergers are possible. Given the time elapsed since the end of the starbursts in the three post-burst TDE hosts and the constraints on the merger mass ratios, it is unlikely that a bound supermassive black hole binary (SMBHB) has had time to coalesce. The TDE hosts have low central (<140 pc) ellipticities compared to early-type galaxies. The low central ellipticities disfavor a strong radial anisotropy as the cause for the enhanced TDE rate, although we cannot rule out eccentric disks at the scale of the black hole gravitational radius of influence (∼1 pc). These observations suggest that the high central stellar densities are a more important driver than SMBHBs or radial anisotropies in increasing the TDE rate in galaxies with recent starbursts.

Mass Segregation in Eccentric Nuclear Disks: Enhanced Tidal Disruption Event Rates for High-mass Stars

Abstract Eccentric nuclear disks (ENDs) are a type of star cluster in which the stars lie on eccentric, apsidally aligned orbits in a disk around a central supermassive black hole. These disks can produce a high rate of tidal disruption events via secular gravitational torques. Previous studies of ENDs have included stars with only one mass. Here, we present the first study of an END with two stellar species. We show that ENDs show radial mass segregation consistent with previous results from other cluster types. Additionally, ENDs show vertical mass segregation by which the heavy stars sink to lower inclinations than light stars. These two effects cause heavy stars to be more susceptible to tidal disruption, which can be seen in the higher fraction of heavy stars that are disrupted compared to light stars.

Radial Versus Cartesian Control Strategies to Stabilize the Nonlinear Whirling Motion of the Six-Pole Rotor-AMBs

Rotor active magnetic bearings system is the most efficient supporting technique of high-speed rotating machinery. This work aims to explore the dynamical behaviors of the 6-pole rotor active magnetic bearings system for the first time. Two different control strategies are introduced to mitigate the considered system lateral vibrations and the corresponding whirling motions. The first control technique (Radial control) is suggested such that the attractive magnetic force in each pole is proportional to both the radial displacement and radial velocity of the rotating disk toward that pole. The second control strategy (Cartesian control) is proposed such that the controlled magnetic force in each pole is designed to be proportional to both the cartesian displacement and cartesian velocity of the rotating disk in two perpendicular directions. Based on the proposed control strategies, two nonlinear dynamical models are derived and then analyzed by applying perturbation methods. Different response-curves and bifurcation diagrams are plotted utilizing the disk spinning-speed and the disk eccentricity as bifurcation control parameters. The main obtained analytical and numerical results illustrated that the considered system can perform a circular forward whirling motion only under the first control technique, while four whirling modes (that are forward whirling, backward whirling, both forward and backward whirling, and oscillation along a straight line) are noticed in the second control method depending on the disk spinning speed. Moreover, it is found that the radial control method is robust against the system instability than the cartesian control one, especially at large disk eccentricity. However, the cartesian control method could exhibit a vibration suppression efficiency higher than the radial control one at small disk eccentricity.

Modeling of the Variable Circumstellar Absorption Features of WD 1145+017

Abstract We present an eccentric precessing gas disk model designed to study the variable circumstellar absorption features detected for WD 1145+017, a metal polluted white dwarf with an actively disintegrating asteroid around it. This model, inspired by one recently proposed by Cauley et al., calculates explicitly the gas opacity for any predetermined physical conditions in the disk, predicting the strength and shape of all absorption features, from the UV to the optical, at any given phase of the precession cycle. The successes and failures of this simple model provide valuable insight on the physical characteristics of the gas surrounding the star, notably its composition, temperature, and density. This eccentric disk model also highlights the need for supplementary components, most likely circular rings, in order to explain the presence of zero velocity absorption as well as highly ionized Si iv lines. We find that a precession period of 4.6 ± 0.3 yr can successfully reproduce the shape of the velocity profile observed at most epochs from 2015 April to 2018 January, although minor discrepancies at certain times indicate that the assumed geometric configuration may not be optimal yet. Finally, we show that our model can quantitatively explain the change in morphology of the circumstellar features during transiting events.

Обрізування книжкових блоків набором ексцентрикових дискових інструментів

Обрізування книжкових блоків набором ексцентрикових дискових інструментів

Вплив розташування ексцентричного дискового ножа на сили обрізування книжкових блоків

Вплив розташування ексцентричного дискового ножа на сили обрізування книжкових блоків

Dynamic analysis and identification of multiple fault parameters in a cracked rotor system equipped with active magnetic bearings: a physical model based approach

This paper proposes a model-based approach for identifying rotordynamic parameters using full spectrum. First, for developing a mathematical model a cracked shaft system with an offset-disc integrated with an active magnetic bearing (AMB) is considered. Moreover, external viscous and internal (rotating) damping is considered in the mathematical model to analyze their effect on the dynamics of the cracked rotor system. Subsequently, an identification algorithm is developed based on the proposed mathematical model to estimate the critical parameters of the model with the help of displacements and AMB currents obtained from full spectrum analysis. Eight parameters, such as the external and internal damping, translational as well as rotational additive crack stiffness, disc eccentricity and its phase, and AMB parameters, are the main parameters affecting the dynamic behaviour of a rotor system estimated. To overcome the practical difficulty in the measurement of rotational displacements during the identification, a gyroscopic dynamic reduction scheme is used to remove the rotational degrees of freedom. The developed algorithm is tested against various random noise in responses and modelling or bias errors in physical parameters to check the sensitiveness and robustness of the model as in the real case.

Accretion Kinematics in the T Tauri Binary TWA 3A: Evidence for Preferential Accretion onto the TWA 3A Primary

Abstract We present time-series, high-resolution optical spectroscopy of the eccentric T Tauri binary TWA 3A. Our analysis focuses on variability in the strength and structure of the accretion-tracing emission lines Hα and He i 5876 Å. We find emission line strengths to display the same orbital phase–dependent behavior found with time-series photometry, namely, bursts of accretion near periastron passages. Such bursts are in good agreement with numerical simulations of young eccentric binaries. During accretion bursts, the emission of He i 5876 Å consistently traces the velocity of the primary star. After removing a model for the system’s chromospheric emission, we find the primary star typically emits ∼70% of the He i accretion flux. We interpret this result as evidence for circumbinary accretion streams that preferentially feed the TWA 3A primary. This finding is in contrast to most numerical simulations, which predict the secondary should be the dominant accretor in a binary system. Our results may be consistent with a model in which the precession of an eccentric circumbinary disk gap alternates between preferentially supplying mass to the primary and secondary.

On the steady-state forward and backward whirling motion of asymmetric nonlinear rotor system

Nonlinear lateral vibrations and the corresponding whirling motions of asymmetric horizontally supported rotor system are investigated within this article. The rotating shaft is modeled as a two-degree-of-freedom nonlinear Jeffcott-rotor system. The nonlinear restoring force of the rotating shaft, asymmetry in both the linear and nonlinear stiffness coefficients, the disk weight, the disk eccentricity, and the eccentricity orientation angle are included in the studied model. The asymptotic analysis is utilized to derive the autonomous amplitude-phase modulating equations that govern the system lateral vibrations in the horizontal and vertical directions. Bifurcation diagrams of both the system vibration amplitudes and the corresponding phase angles are obtained. The main acquired results revealed that the existence of the asymmetry in the rotating shaft stiffness coefficients widens the spinning speed interval at which the system may have more than one stable solution. In addition, increasing the linear asymmetrical stiffness coefficient can eliminate the system backward whirling motion. Finally, numerical confirmations for the obtained analytical results are performed that illustrated their accuracy in the prediction of the system vibration amplitudes and the whirling direction whether forward, backward, or along a straight line.

A simplified model for the secular dynamics of eccentric discs and applications to planet–disc interactions

ABSTRACT We develop a simplified model for studying the long-term evolution of giant planets in protoplanetary discs. The model accounts for the eccentricity evolution of the planets and the dynamics of eccentric discs under the influences of secular planet–disc interactions and internal disc pressure, self-gravity, and viscosity. Adopting the ansatz that the disc precesses coherently with aligned apsides, the eccentricity evolution equations of the planet–disc system reduce to a set of linearized ordinary differential equations, which allows for fast computation of the evolution of planet–disc eccentricities over long time-scales. Applying our model to ‘giant planet + external disc’ systems, we are able to reproduce and explain the secular behaviours found in previously published hydrodynamical simulations. We re-examine the possibility of eccentricity excitation (due to secular resonance) of multiple planets embedded in a dispersing disc, and find that taking into account the dynamics of eccentric discs can significantly affect the evolution of the planets’ eccentricities.