Constant Angular Momentum Research Articles

Stability of the celestial body orbits under the influence of Yukawa potential

The famous Yukawa-type potential was very often used for explaining a great variety of recent observed astronomical phenomena which range from the solar-system scale to cosmological distances. In this paper we tackle the two-body problem in the Yukawa post-Newtonian field from the particular standpoint of orbits stability. Starting from the equations of motion and first integrals written in standard polar coordinates, we apply McGehee-type transformations of the second kind. Then we depict the phase-space structure considering the foliations by the energy constant and the angular momentum constant. Various stability regions are found for each case. The problem presents interesting features, such as: cases when all trajectories (maybe except for a separatrix) are stable; cases when there exist totally different types of orbits, both stable and unstable, for the same values of the energy constant and the angular momentum constant; the existence of stable motion for nonnegative energy levels; positive Lebesgue measure for initial data leading to quasiperiodic and noncircular periodic orbits; the key role of the angular momentum.

Underactuated Spacecraft Switching Law for Two Reaction Wheels and Constant Angular Momentum

This paper develops a switching feedback controller for the attitude of an underactuated spacecraft that exploits two internal control torques provided by reaction wheels. The problem is challenging; for example, even in the zero total angular momentum case, no smooth or even continuous time-invariant feedback law for stabilizing a desired orientation exists. The method introduced here exploits the separation of the system states into inner-loop base variables and outer-loop fiber variables. The base variables track periodic reference trajectories, the amplitude of which is governed by parameters that are adjusted to induce an appropriate change in the fiber variables. Under suitable assumptions on the total angular momentum, this controller stabilizes an equilibrium that corresponds to a desired inertially fixed orientation. If the desired attitude violates the assumption on angular momentum, then controlled oscillations in a neighborhood around the target orientation are induced by the switching controller. The control scheme is based on several approximations and is designed for relatively small maneuvers close to the desired attitude in a vicinity which may be achieved by thruster-based control schemes. Simulation results demonstrate that the switching feedback law provides good performance in controlling the attitude of an underactuated spacecraft.

Charged perfect fluid tori in strong central gravitational and dipolar magnetic fields

We study electrically charged perfect fluid toroidal structures encircling a spherically symmetric gravitating object with Schwarzschild spacetime geometry and endowed with a dipole magnetic field. The work represents a direct continuation of our previous general-relativistic studies of electrically charged fluid in the approximation of zero conductivity, which formed tori around a Reissner-Nordstr\om black hole or a Schwarzschild black hole equipped with a test electric charge and immersed in an asymptotically uniform magnetic field. After a general introduction of the zero-conductivity charged fluid model, we discuss a variety of possible topologies of the toroidal fluid configurations. Along with the charged equatorial tori forming interesting coupled configurations, we demonstrate the existence of the off-equatorial tori, for which the dipole type of magnetic field seems to be necessary. We focus on orbiting structures with constant specific angular momentum and on those in permanent rigid rotation. We stress that the general analytical treatment developed in our previous works is enriched here by the integrated form of the pressure equations. To put our work into an astrophysical context, we identify the central object with an idealization of a nonrotating magnetic neutron star. Constraining ranges of its parameters and also parameters of the circling fluid, we discuss a possible relevance of the studied toroidal structures, presenting along with their topology also pressure, density, temperature and charge profiles.

Turbulent Taylor–Couette flow with stationary inner cylinder

A series of direct numerical simulations were performed of Taylor–Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed. Three cases were considered, where the Reynolds number of the outer cylinder was $Re_{o}=5.5\times 10^{4}$, $Re_{o}=1.1\times 10^{5}$ and $Re_{o}=2.2\times 10^{5}$. The ratio of radii ${\it\eta}=r_{i}/r_{o}$ was fixed to ${\it\eta}=0.909$ to mitigate the effects of curvature. Axially periodic boundary conditions were used, with the aspect ratio of vertical periodicity ${\it\Gamma}$ fixed to ${\it\Gamma}=2.09$. Being linearly stable, TC flow with outer cylinder rotation is known to have very different behaviour than TC flow with pure inner cylinder rotation. Here, we find that the flow nonetheless becomes turbulent, but the torque required to drive the cylinders and level of velocity fluctuations was found to be smaller than those for pure inner cylinder rotation at comparable Reynolds numbers. The mean angular momentum profiles showed a large gradient in the bulk, instead of the constant angular momentum profiles of pure inner cylinder rotation. The near-wall mean and fluctuation velocity profiles were found to coincide only very close to the wall, showing large deviations from both pure inner cylinder rotation profiles and the classic von Karman law of the wall elsewhere. Finally, transport of angular velocity was found to occur mainly through intermittent bursts, and not through wall-attached large-scale structures as is the case for pure inner cylinder rotation.

Phase-space structure of the Buckingham’s two-body problem

In this paper, we study the global flow for the two-body problem associated to the Buckingham potential. For this, using McGehee-type transformations, we write the regularized equations of motion. Then, reducing the 4-dimensional phase space to a 2-dimension one, the global flow in the phase plane is described for all possible values of the parameters of the potential and those of the energy and angular momentum constants. Every phase trajectory is interpreted in terms of physical motion, our problem being depicted both geometrically and physically.

Numerical relativity simulations of thick accretion disks around tilted Kerr black holes

In this work we present 3D numerical relativity simulations of thick accretion disks around tilted Kerr BH. We investigate the evolution of three different initial disk models with a range of initial black hole spin magnitudes and tilt angles. For all the disk-to-black hole mass ratios considered (0.044-0.16) we observe significant black hole precession and nutation during the evolution. This indicates that for such mass ratios, neglecting the self-gravity of the disks by evolving them in a fixed background black hole spacetime is not justified. We find that the two more massive models are unstable against the Papaloizou-Pringle (PP) instability and that those PP-unstable models remain unstable for all initial spins and tilt angles considered, showing that the development of the instability is a very robust feature of such PP-unstable disks. Our lightest model, which is the most astrophysically favorable outcome of mergers of binary compact objects, is stable. The tilt between the black hole spin and the disk is strongly modulated during the growth of the PP instability, causing a partial global realignment of black hole spin and disk angular momentum in the most massive model with constant specific angular momentum l. For the model with non-constant l-profile we observe a long-lived m=1 non-axisymmetric structure which shows strong oscillations of the tilt angle in the inner regions of the disk. This effect might be connected to the development of Kozai-Lidov oscillations. Our simulations also confirm earlier findings that the development of the PP instability causes the long-term emission of large amplitude gravitational waves, predominantly for the l=m=2 multipole mode. The imprint of the BH precession on the gravitational waves from tilted BH-torus systems remains an interesting open issue that would require significantly longer simulations than those presented in this work.

Stellar models simulating the disk-locking mechanism and the evolutionary history of the Orion Nebula cluster and NGC 2264

Rotational evolution in young stars is described by pMS evolutionary tracks including rotation, conservation of angular momentum (AM), and simulations of disk-locking (DL). By assuming that DL is the regulation mechanism for the stellar angular velocity during the early stages of pMS, we use our models and observational data to constrain disk lifetimes (Tdisk) of a sample of low-mass stars in the ONC and NGC2264. The period distributions of the ONC and NGC2264 are bimodal and depend on the stellar mass. To follow the rotational evolution of these two clusters' stars, we generated some sets of evolutionary tracks. We assumed that the evolution of fast rotators can be modeled by considering conservation of AM during all stages and of moderate rotators by considering conservation of angular velocity during the first stages of evolution. With these models we estimate a mass and an age for all stars. For the ONC, we assume that the secondary peak in the period distribution is due to high-mass objects locked in their disks, with a locking period (Plock) of ~8 days. For NGC2264 we make two hypotheses: (1) the stars in the secondary peak are locked with Plock=5 days, and (2) NGC2264 is in a later stage in the rotational evolution (this implies in a DL scenario with Plock=8 days, a Tdisk of 1 Myr and, after that, constant AM evolution). We simulated the period distribution of NGC2264 when its mean age was 1 Myr. Dichotomy and bimodality appear in the simulated distribution, presenting one peak at 2 days and another one at 5-7 days, indicating that the assumption of Plock=8 days is plausible. Our hypotheses are compared with observational disk diagnoses available in the literature. DL models with Plock=8 days and 0.2 Myr<=Tdisk<=3 Myr are consistent with observed periods of moderate rotators of the ONC. For NGC2264, hyphotesis 2 is the more promising explanation for its period distribution.

Effect of Inlet Clearance on the Aerodynamic Performance of a Centrifugal Blower

AbstractThe present work reports the effect of inlet clearance on the performance of a centrifugal blower, with parallel wall volute, over its full operating range. For a particular impeller configuration, four volutes based on constant angular momentum principle, have been designed and analysed numerically for varying inlet clearances ranging from 0 mm (ideal clearance) to 5 mm. The computational methodology is validated using experimental data. The results indicate that as the clearance increases, the impeller performance in terms of both static and total pressure rise deteriorate. Further, the stage performances deteriorate in terms of efficiency and specific work for all mass flow rates. However, the performance of volute improves at lower mass flow rates compared to the Best Efficiency Point (BEP). A set of correlations have been developed to predict the change in stage performance as a function of clearance ratio. The non-dimensional values of change in specific work, isentropic efficiency and static pressure are found to be same irrespective of the shape of the volute.

Circular geodesics and thick tori around rotating boson stars

Accretion disks play an important role in the evolution of their relativistic inner compact objects. The emergence of a new generation of interferometers will allow us to resolve these accretion disks and provide more information about the properties of the central gravitating object. Due to this instrumental leap forward it is crucial to investigate the accretion disk physics near various types of inner compact objects now to deduce later constraints on the central objects from observations. A possible candidate for the inner object is the boson star. Here, we will try to analyze the differences between accretion structures surrounding boson stars and black holes. We aim at analysing the physics of circular geodesics around boson stars and study simple thick accretion tori (so-called Polish doughnuts) in the vicinity of these stars. We realize a detailed study of the properties of circular geodesics around boson stars. We then perform a parameter study of thick tori with constant angular momentum surrounding boson stars. This is done using the boson star models computed by a code constructed with the spectral solver library KADATH. We demonstrate that all the circular stable orbits are bound. In the case of a constant angular momentum torus, a cusp in the torus surface exists only for boson stars with a strong gravitational scalar field. Moreover, for each inner radius of the disk, the allowed specific angular momentum values lie within a constrained range which depends on the boson star considered. We show that the accretion tori around boson stars have different characteristics than in the vicinity of a black hole. With future instruments it could be possible to use these differences to constrain the nature of compact objects.

THE HELIOCENTRIC DISTANCE WHERE THE DEFLECTIONS AND ROTATIONS OF SOLAR CORONAL MASS EJECTIONS OCCUR

Understanding the trajectory of a coronal mass ejection (CME), including any deflection from a radial path, and the orientation of its magnetic field is essential for space weather predictions. Kay et al. (2015b) developed a model, Forecasting a CME's Altered Trajectory (ForeCAT), of CME deflections and rotation due to magnetic forces, not including the effects of reconnection. ForeCAT is able to reproduce the deflection of observed CMEs (Kay et al. 2015a). The deflecting CMEs tend to show a rapid increase of their angular momentum close to the Sun, followed by little to no increase at farther distances. Here we quantify the distance at which the CME deflection is "determined," which we define as the distance after which the background solar wind has negligible influence on the total deflection. We consider a wide range in CME masses and radial speeds and determine that the deflection and rotation of these CMEs can be well-described by assuming they propagate with constant angular momentum beyond 10 Rs. The assumption of constant angular momentum beyond 10 Rs yields underestimates of the total deflection at 1 AU of only 1% to 5% and underestimates of the rotation of 10%. Since the deflection from magnetic forces is determined by 10 Rs, non-magnetic forces must be responsible for any observed interplanetary deflections or rotations where the CME has increasing angular momentum.

Testing SgrA* with the spectrum of its accretion structure

SgrA* is the supermassive black hole candidate at the center of the Galaxy and an ideal laboratory to test general relativity. Following previous work by other authors, we use the Polish doughnut model to describe an optically thin and constant angular momentum ion torus in hydrodynamical equilibrium and model the accretion structure around SgrA*. The radiation mechanisms are bremsstrahlung, synchrotron emission, and inverse Compton scattering. We compute the spectrum as seen by a distant observer in Kerr and non-Kerr spacetimes and we study how an accurate measurement can constrain possible deviations form the Kerr solution. As in the case of emission from a thin accretion disk, we find a substantial degeneracy between the determination of the spin and of possible deviations from the Kerr geometry, even when the parameters of the ion torus are fixed. This means that this technique cannot independently test the nature of SgrA* even in the presence of good data and with the systematics under control. However, it might do it in combination with other measurements (black hole shadow, radio pulsar, etc.).

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.

Two-dimensional models of early-type fast rotating stars: the ESTER project

AbstractIn this talk I present the latest results of the ESTER project that has taken up the challenge of building two dimensional (axisymmetric) models of stars rotating at any rotation rate. In particular, I focus on main sequence massive and intermediate mass stars. I show what should be expected in such stars as far as the differential rotation and the associated meridional circulation are concerned, notably the emergence of a Stewartson layer along the tangent cylinder of the core. I also indicate what may be inferred about the evolution of an intermediate-mass star at constant angular momentum and how Be stars may form. I finally give some comparisons between models and observations of the gravity darkening on some nearby fast rotators as it has been derived from interferometric observations. In passing, I also discuss how 2D models can help to recover the fundamental parameters of a star.

Magneto-rotational instability with the effect of cosmic rays

AbstractCosmic ray (CR) is an important component of the interstellar medium. It interacts with plasma via embedded magnetic irregularities. We study the magneto-rotational instability (MRI) in the presence of CRs. We analyse the effect of CRs including their diffusion using both linear stability analysis and MHD simulations. Two models are studied. (1) In the shearing box model, uniform initial state is adopted. Linear analysis shows that the growth rate of MRI is not sensitive to the value of CR diffusion coefficient. (2) In the differentially rotating cylinder model, the initial state is taken as a constant angular momentum polytropic disk threaded by weak uniform vertical magnetic field. Linear analysis shows that the growth rate of MRI becomes larger if the CR diffusion coefficient is larger. Both linear results are confirmed by MHD simulations.

Azimuthal velocity profiles in Rayleigh-stable Taylor–Couette flow and implied axial angular momentum transport

We present azimuthal velocity profiles measured in a Taylor–Couette apparatus, which has been used as a model of stellar and planetary accretion disks. The apparatus has a cylinder radius ratio of ${\it\eta}=0.716$, an aspect ratio of ${\it\Gamma}=11.74$, and the plates closing the cylinders in the axial direction are attached to the outer cylinder. We investigate angular momentum transport and Ekman pumping in the Rayleigh-stable regime. This regime is linearly stable and is characterized by radially increasing specific angular momentum. We present several Rayleigh-stable profiles for shear Reynolds numbers $\mathit{Re}_{S}\sim O(10^{5})$, for both ${\it\Omega}_{i}&gt;{\it\Omega}_{o}&gt;0$ (quasi-Keplerian regime) and ${\it\Omega}_{o}&gt;{\it\Omega}_{i}&gt;0$ (sub-rotating regime), where ${\it\Omega}_{i,o}$ is the inner/outer cylinder rotation rate. None of the velocity profiles match the non-vortical laminar Taylor–Couette profile. The deviation from that profile increases as solid-body rotation is approached at fixed $\mathit{Re}_{S}$. Flow super-rotation, an angular velocity greater than those of both cylinders, is observed in the sub-rotating regime. The velocity profiles give lower bounds for the torques required to rotate the inner cylinder that are larger than the torques for the case of laminar Taylor–Couette flow. The quasi-Keplerian profiles are composed of a well-mixed inner region, having approximately constant angular momentum, connected to an outer region in solid-body rotation with the outer cylinder and attached axial boundaries. These regions suggest that the angular momentum is transported axially to the axial boundaries. Therefore, Taylor–Couette flow with closing plates attached to the outer cylinder is an imperfect model for accretion disk flows, especially with regard to their stability.

Investigating the rotational evolution of young, low-mass stars using Monte Carlo simulations

We investigate the rotational evolution of young stars through Monte Carlo simulations. We simulate 280,000 stars, each of which is assigned a mass, a rotational period, and a mass accretion rate. The mass accretion rate depends on mass and time, following power-laws indices 1.4 and -1.5, respectively. A mass-dependent accretion threshold is defined below which a star is considered as diskless, which results in a distribution of disk lifetimes that matches observations. Stars are evolved at constant angular spin rate while accreting and at constant angular momentum when they become diskless. We recover the bimodal period distribution seen in several young clusters. The short period peak consists mostly of diskless stars and the long period one is mainly populated by accreting stars. Both distributions present a long tail towards long periods and a population of slowly rotating diskless stars is observed at all ages. We reproduce the observed correlations between disk fraction and spin rate, as well as between IR excess and rotational period. The period-mass relation we derive from the simulations exhibits the same global trend as observed in young clusters only if we release the disk locking assumption for the lowest mass stars. We find that the time evolution of median specific angular momentum follows a power law index of -0.65 for accreting stars and of -0.53 for diskless stars, a shallower slope that results from a wide distribution of disk lifetimes. Using observationally-documented distributions of disk lifetimes, mass accretion rates, and initial rotation periods, and evolving an initial population from 1 to 12 Myr, we reproduce the main characteristics of pre-main sequence angular momentum evolution, which supports the disk locking hypothesis. (abridged)

Instability in stratified accretion flows under primary and secondary perturbations.

We consider horizontal linear shear flow (shear rate denoted by Λ) under vertical uniform rotation (ambient rotation rate denoted by Ω(0)) and vertical stratification (buoyancy frequency denoted by N) in unbounded domain. We show that, under a primary vertical velocity perturbation and a radial density perturbation consisting of a one-dimensional standing wave with frequency N and amplitude proportional to w(0)sin(ɛNx/w(0))≈ɛNx(≪1), where x denotes the radial coordinate and ɛ a small parameter, a parametric instability can develop in the flow, provided N(2)>8Ω(0)(2Ω(0)-Λ). For astrophysical accretion flows and under the shearing sheet approximation, this implies N(2)>8Ω(0)(2)(2-q), where q=Λ/Ω(0) is the local shear gradient. In the case of a stratified constant angular momentum disk, q=2, there is a parametric instability with the maximal growth rate (σ(m)/ɛ)=3√[3]/16 for any positive value of the buoyancy frequency N. In contrast, for a stratified Keplerian disk, q=1.5, the parametric instability appears only for N>2Ω(0) with a maximal growth rate that depends on the ratio Ω(0)/N and approaches (3√[3]/16)ɛ for large values of N.

Effects of Volute Curvature on Performance of a Low Specific-Speed Centrifugal Pump at Design and Off-Design Conditions

The effects of the volute geometry on the head, efficiency, and radial force of a low specific-speed centrifugal pump were investigated focusing on off-design conditions. This paper is divided into three parts. In the first part, the three-dimensional flow inside the pump with rectangular volute was simulated using three well-known turbulence models. Simulation results were compared with the available experimental data, and an acceptable agreement was obtained. In the second part, two volute design methods, namely, the constant velocity and the constant angular momentum were investigated. Obtained results showed that in general the constant velocity method gives more satisfactory performance. In the third part, three volutes with different cross section and diffuser shape were designed. In general, it was found that circular cross section volute with radial diffuser provides higher head and efficiency. Moreover, the minimum radial force occurs at higher flowrate in circular volute geometry comparing to rectangular cross section volute.

An energy‐entropy‐consistent time stepping scheme for nonlinear thermo‐viscoelastic continua

This paper deals with an energy‐entropy‐consistent time integration of a thermo‐viscoelastic continuum in Poissonian variables. The four differential evolution equations of first‐order are transformed by a new General Equation for Non‐Equilibrium Reversible‐Irreversible Coupling (GENERIC) format into a matrix‐vector notation. Since the entropy is a primary variable, we include thermal constraints to affect the temperatures at the boundary of the body. This enhanced GENERIC format with thermal constraints yields with the related degeneracy conditions structure preservation properties for a system with thermal constraints. The properties of an isolated system are in addition to a constant total linear and angular momentum, the constant total energy, an increasing total entropy and a decreasing Lyapunov function. The last one is a stability criterion for thermo‐viscoelastic systems and also for unisolated systems without loads valid. The discretization in time is done with a new TC (Thermodynamically Consistent) integrator. This ETC integrator is constructed such, that the algorithmic structural properties after the space‐time discretization reflect the underlying enhanced GENERIC format with thermal constraints. As discretization in space the finite element method is used. A projection of the test function of the thermal evolution equation is necessary for an energy‐consistent discretization in space. The enhanced GENERIC format with thermal constraints, which is here given in the strong evolution equations, contains the external loads. The consistency properties are discussed for representative numerical examples with different boundary conditions. The coupled mechanical system is solved with a multi‐level Newton‐Raphson method based on a consistent linearization.

Critical review on complete dynamic balancing of mechanisms and parallel robots

When mechanisms and parallel manipulators move, due to the fact that the centre of mass is not fixed and angular momentum is not constant, they often produce vibrations in the base. Shaking force balancing can be achieved by making the centre of mass of mechanism be fixed, i.e. linear momentum is constant; shaking moment balancing can be achieved by making the angular momentum constant. There are generally two main ways for shaking force balancing and shaking moment balancing, i.e. 'balancing before kinematic synthesis' and 'balancing at the end of the design process'. Under the category of balancing at the end of design process, add counterweights and counter-rotations, add ADBU and add auxiliary links are mostly used principles; here a new method is proposed, i.e. balancing through reconfiguration, which can reduce the addition of mass and inertia. Fisher's method belongs to the method of balancing before kinematic synthesis. In this paper, we will discuss the advances and problems on dynamic balancing of mechanisms in detail under the above two main categories. Two main contributions of the paper can be concluded as follows: new reactionless parallel manipulators are derived and dynamic balancing through reconfiguration concept is proposed in first time.