Eccentric Disk Research Articles

Advanced disc degeneration, bi-planar instability and pathways of peri-discal gas suffusion contribute to pathogenesis of intradiscal vacuum phenomenon.

Intradiscal vacuum phenomenon (IDVP), despite being ubiquitous, is poorly understood. The dynamic passage of peri-discal gases into the degenerated disc is a commonly accepted theory. But the reasons behind its selective appearance in some discs are unevaluated. 721 patients with chronic low back pain ± radiculopathy, were evaluated with AP and flexion-extension lateral radiographs and MRI. IDVP was classified based on its morphology and location. Radiographic parameters including sagittal translation, sagittal angulation, lateral listhesis, eccentric disc collapse, Pfirrmann's grade, disc height, Modic changes, anterior longitudinal ligament status, and primary spinal disease at the level of IDVP was analyzed. IDVP was present in 342 patients, and theyhad a higher mean age (57.2 ± 12.5years) than controls (p < 0.001). Eccentric disc space narrowing (26.5% vs 1.3%, p < 0.01), coronal listhesis (7.83% vs 1.1%, p < 0.001), sagittal angular motion difference (11.3 ± 4.6°, p < 0.001), higher mean disc degeneration (4.36 ± 0.69, p < 0.001), ALL disruption (30.3% vs 2.2%, p < 0.001) and Modic changes (88.6% vs 17.5%, p < 0.001) were significantly higher in IDVP discs (vs. non-IDVP). Binary logistic regression analysis indicated sagittal angular motion difference was the most predictive factor. IDVP was classified into three types-dense type (47.5%), linear (29.5%), dot type (23%). Dense type matched radiological correlations of IDVP while dot types behaved like non-IDVP discs. Modic disc-endplate contacts, ALL disruption and coronal translation could be pathways for the passage of peri-discal gases into the degenerated disc. In the pathogenesis of IDVP, advanced disc degeneration, the presence of pathways of gas transfer and angular/coronal instability seem to play complementary roles.

Electrified eccentric circular disk situated in an infinite hollow cylinder

We investigate the distribution of electric potential in a circular cylinder containing a circular disk whose center is not on that of the cylinder. By satisfying the boundary conditions on the disk and the surface of the cylinder, an integral equation is obtained for the solution of the problem. It is shown that this integral equation reduces to the known Fredholm integral equation of the second kind when the disk is coaxial with the cylinder.

Eccentric Dust-ring Formation in Kozai–Lidov Gas Disks

Abstract A highly misaligned gas disk around one component of a binary star system can undergo global Kozai–Lidov (KL) oscillations for which the disk inclination and eccentricity are exchanged. With hydrodynamical simulations of a gas and dust disk we explore the effects of these oscillations on the dust density distribution. For dust that is marginally coupled to the gas (St ≈ 1), we find that the dust undergoes dynamical behavior similar to that of the gas disk but the radial distribution of dust may be very different from that of the gas. The inward radial drift of the dust is faster in an eccentric disk leading to a smaller outer dust disk radius. The dust breaks into multiple narrow eccentric rings during the highly eccentric disk phase. Eccentric dust-ring formation may have significant implications for the formation of planets in misaligned disks. We suggest that multiple dust rings may generally occur within gas disks that have sufficiently strong eccentricity peaks at intermediate radii.

Eccentric debris disc morphologies – I. Exploring the origin of apocentre and pericentre glows in face-on debris discs

ABSTRACT The location of surface brightness maxima (e.g. apocentre and pericentre glow) in eccentric debris discs are often used to infer the underlying orbits of the dust and planetesimals that comprise the disc. However, there is a misconception that eccentric discs have higher surface densities at apocentre and thus necessarily exhibit apocentre glow at long wavelengths. This arises from the expectation that the slower velocities at apocentre lead to a ‘pile up’ of dust, which fails to account for the greater area over which dust is spread at apocentre. Instead we show with theory and by modelling three different regimes that the morphology and surface brightness distributions of face-on debris discs are strongly dependent on their eccentricity profile (i.e. whether this is constant, rising, or falling with distance). We demonstrate that at shorter wavelengths the classical pericentre glow effect remains true, whereas at longer wavelengths discs can either demonstrate apocentre glow or pericentre glow. We additionally show that at long wavelengths the same disc morphology can produce either apocentre glow or pericentre glow depending on the observational resolution. Finally, we show that the classical approach of interpreting eccentric debris discs using line densities is only valid under an extremely limited set of circumstances, which are unlikely to be met as debris disc observations become increasingly better resolved.

Misaligned disks induced by infall

Arc- and tail-like structures associated with disks around Herbig stars can be a consequence of infall events occurring after the initial collapse phase of a forming star, consistent with the observation of luminosity bursts. An encounter event of gas with an existing star can lead to the formation of a second-generation disk significantly after the initial protostellar collapse phase. Additionally, observations of shadows in disks can be well described by a configuration of a misaligned inner and outer disk, such that the inner disk casts a shadow on the outer disk. Carrying out altogether eleven 3D hydrodynamical models with the moving mesh code AREPO, we tested whether a late encounter of an existing star–disk system with a cloudlet of gas can lead to the formation of an outer disk that is misaligned with respect to the primordial inner disk. Our models demonstrate that a second-generation disk with a large misalignment with respect to an existing primordial disk can easily form if the infall angle is large. The second-generation outer disk is more eccentric, though the asymmetric infall also triggers eccentricity of the inner disk of e ≈ 0.05 to 0.1. Retrograde infall can lead to the formation of counter-rotating disks and enhanced accretion. As the angular momentum of the inner disk is reduced, the inner disk shrinks and a gap forms between the two disks. The resulting misaligned disk system can survive for ~100 kyr or longer without aligning with each other even for low primordial disk masses given an infall mass of ~10−4 M⊙. A synthetic image for one of our models reveals shadows in the outer disk similar to the ones observed in multiple transition disks that are caused by the misaligned inner disk. We conclude that late infall onto an existing star–disk system leads to the formation of a misaligned outer disk for infall that is inclined with respect to the orientation of the inner disk. Infall might therefore be responsible for observations of shadows in at least some transition disks.

Eccentric Neutron Star Disk Driven Type II Outburst Pairs in Be/X-ray Binaries

Abstract Be star X-ray binaries are transient systems that show two different types of outbursts. Type I outbursts occur each orbital period while type II outbursts have a period and duration that are not related to any periodicity of the binary system. Type II outbursts may be caused by mass transfer to the neutron star from a highly eccentric Be star disk. A sufficiently misaligned Be star decretion disk undergoes secular Von Zeipel–Lidov–Kozai (ZLK) oscillations of eccentricity and inclination. Observations show that in some systems the type II outbursts come in pairs with the second being of lower luminosity. We use numerical hydrodynamical simulations to explore the dynamics of the highly misaligned disk that forms around the neutron star as a consequence of mass transfer from the Be star disk. We show that the neutron star disk may also be ZLK unstable and that the eccentricity growth leads to an enhancement in the accretion rate onto the neutron star that lasts for several orbital periods, resembling a type II outburst. We suggest that in a type II outburst pair, the first outburst is caused by mass transfer from the eccentric Be star disk while the second and smaller outburst is caused by the eccentric neutron star disk. We find that the timescale between outbursts in a pair may be compatible with the observed estimates.

On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System

The performance of a nonlinear position-velocity controller in stabilising the lateral vibrations of a rotor-active magnetic-bearings system (RAMBS) is investigated. Cubic nonlinear position-velocity and linear position-velocity controllers are introduced to stabilise RAMBS lateral oscillations. According to the proposed control law, the nonlinear system model is established and then investigated with perturbation analysis. Nonlinear algebraic equations that govern the steady-state oscillation amplitudes and the corresponding phases are derived. Depending on the obtained algebraic equations, the different frequency response curves and bifurcation diagrams are plotted for the studied model. Sensitivity analysis for the linear and nonlinear controllers’ gains is explored. Obtained analytical results demonstrated that the studied model had symmetric bifurcation behaviours in both the horizontal and vertical directions. In addition, the integration of the cubic position controller made the control algorithm more flexible to reshape system dynamical behaviours from the hardening spring characteristic to the softening spring characteristic (or vice versa) to avoid resonance conditions. Moreover, the optimal design of the cubic position gain and/or cubic velocity gain could stabilise the unstable motion and eliminate the nonlinear effects of the system even at large disc eccentricities. Lastly, numerical validations for all acquired results are performed, where the presented simulations show accurate correspondence between numerical and analytical investigations.

Handling dilatant isocyanates

One of the most hard-to-handle liquids is dilatant isocyanates as it is both sensitive and hazardous. This article examines why eccentric disc pumps have become popular for the production and handling of these and other classes of dilatant fluids.

On the Formation of an Eccentric Nuclear Disk following the Gravitational Recoil Kick of a Supermassive Black Hole

Abstract The anisotropic emission of gravitational waves during the merger of two supermassive black holes can result in a recoil kick of the merged remnant. We show here that eccentric nuclear disks—stellar disks of eccentric, apse-aligned orbits—can directly form as a result. An initially circular disk of stars will align orthogonal to the black hole kick direction with a distinctive “tick-mark” eccentricity distribution and a spiral pattern in mean anomaly.

The circumbinary rings of GG Carinae: indications of disc eccentricity growth in the B[e] supergiant’s atomic emission lines

ABSTRACT B[e] supergiants have unusual circumstellar environments which may include thin, concentric rings displaying atomic line emission. GG Carinae is a B[e] supergiant binary which exhibits such a geometry in its circumbinary environment. We study atomic emission lines arising from GG Carinae’s circumbinary disc in FEROS spectra collected between 1998 and 2015. We find that semiforbidden Fe ii] and permitted Ca ii emission are formed in the same thin circumbinary ring previously reported to have forbidden [O i] and [Ca ii] emission. We find that there are two circumbinary rings orbiting with projected velocities of 84.6 ± 1.0 and 27.3 ± 0.6 $\rm km\, s^{-1}$. Deprojecting these velocities from the line of sight, and using updated binary masses presented by Porter et al. (2021a), we find that the radii of the circumbinary rings are $2.8^{+0.9}_{-1.1}$ and $27^{+9}_{-10}$ au for the inner ring and outer ring, respectively. We find evidence of subtle dynamical change in the inner circumbinary ring over the 17 yr spanned by the data, manifesting in variability in the ratio of the intensity of the blueshifted peak to the redshifted peak of its emission lines and the central velocity becoming more blueshifted. We perform smoothed-particle hydrodynamic simulations of the system which suggest that these observed changes are consistent with pumping of the eccentricity of a radially thin circumbinary ring by the inner binary. We find a systemic velocity of the GG Carinae system of −23.2 ± 0.4 $\rm km\, s^{-1}$.

A road-map to white dwarf pollution: Tidal disruption, eccentric grind-down, and dust accretion

Abstract A significant fraction of white dwarfs show metal lines indicative of pollution with planetary material but the accretion process remains poorly understood. The main aim of this paper is to produce a road-map illustrating several potential routes for white dwarf pollution and to link these paths to observational outcomes. Our proposed main road begins with the tidal disruption of a scattered asteroid and the formation of a highly eccentric tidal disc with a wide range of fragment sizes. Accretion of these fragments by Poynting-Robertson (PR) drag alone is too slow to explain the observed rates. Instead, in the second stage, several processes including differential apsidal precession cause high-velocity collisions between the eccentric fragments. Large asteroids produce more fragments when they disrupt, causing rapid grind-down and generating short and intense bursts of dust production, whereas smaller asteroids grind down over longer periods of time. In the final stage, the collisionally produced dust circularises and accretes onto the white dwarf via drag forces. We show that optically thin dust accretion by PR drag produces large infrared (IR) excesses when the accretion rate exceeds 107 g/s. We hypothesise that around white dwarfs accreting at a high rate, but with no detected infrared excess, dust circularisation requires enhanced drag - for instance due to the presence of gas near the disc’s pericentre.

The eccentric disk and its eccentric behavior

Providing example problems that stimulate curiosity and cultivate intuition among students is a prominent responsibility for physics educators. A concept that can be particularly challenging for students to grasp and educators to convey is the relationship between frictional and normal forces in rolling motion. A system that may be a useful tool to exhibit a rich interplay between these forces is a rolling eccentric disk. An eccentric disk has a non-constant normal force and therefore has four distinct phases of motion: oscillations about a stable equilibrium, roll without slip, roll with slip, and hop. Thus, this paper examines the eccentric disk rolling down an incline as a valuable teaching medium and explores its peculiar behavior. The rolling system is analytically modeled using an augmented Lagrangian formulation, solved with numerical integration, and experimentally realized. Then, the results are presented and discussed in detail.

Photometry and Kinematics of Self-gravitating Eccentric Nuclear Disks

Abstract The Andromeda galaxy hosts an elongated nucleus with (at least) two distinct brightness peaks. The double nucleus can be explained by the projection of a thick, apsidally aligned eccentric nuclear disk of stars in orbit about the central black hole. Several nearby early-type galaxies have similar asymmetric nuclear features, indicating the possible presence of eccentric nuclear disks. We create simulated photometric (surface density) and kinematic (line-of-sight velocity) maps of eccentric nuclear disks using N-body simulations. We image our simulations from various lines of sight in order to classify them as double nuclei, offset nuclei, and centered nuclei. We explore the effects of mass segregation on the photometric maps, finding that heavier stars are concentrated in the brighter peak. The average line-of-sight velocity values are lower in an eccentric nuclear disk than for a circular ring about the supermassive black hole. The velocity dispersion values are higher and peak at the position of the supermassive black hole, which does not typically match the peak in photometry.

The Impact of Shocks on the Vertical Structure of Eccentric Disks

Abstract Accretion disks whose matter follows eccentric orbits can arise in multiple astrophysical situations. Unlike circular orbit disks, the vertical gravity in eccentric disks varies around the orbit. In this paper, we investigate some of the dynamical effects of this varying gravity on the vertical structure using 1D hydrodynamics simulations of individual gas columns assumed to be mutually noninteracting. We find that time-dependent gravitational pumping generically creates shocks near pericenter; the energy dissipated in the shocks is taken from the orbital energy. Because the kinetic energy per unit mass in vertical motion near pericenter can be large compared to the net orbital energy, the shocked gas can be heated to nearly the virial temperature, and some of it becomes unbound. These shocks affect larger fractions of the disk mass for larger eccentricity and/or disk aspect ratio. If the orbit can be maintained despite orbital energy loss, diverse initial structures evolve in only a few orbits so that they follow a limit cycle characterized by a low-entropy midplane and a much higher entropy outer layer. In favorable cases (such as the tidal disruption of stars by supermassive black holes), these effects could be a potentially important energy dissipation and mass-loss mechanism.

Disks in close binary stars

Context. Close binaries (abin ≤ 20 au) are known to harbor planets, yet planet formation is unlikely to succeed in such systems. Studying the dynamics of disks in close binaries can help to understand how those planets could have formed. Aims. We study the impact that numerical and physical parameters have on the dynamics of disks in close binaries. We use the γ-Cephei system as an example and focus on disk quantities such as disk eccentricity and the precession rate as indicators for the dynamical state of the disks. Methods. We simulate disks in close binaries by performing two-dimensional radiative hydrodynamical simulations using a modified version of the FARGO code. First, we perform a parameter study for different numerical parameters to confirm that our results are robust. In the second part, we study the effects of different masses and different viscosities on the disks’ dynamics. Results. Previous studies on radiative disks in close binaries used too low resolutions and too small simulation domains, which impacted the disk’s dynamics. We find that radiative disks in close binaries, after an initialization phase, become eccentric with mean eccentricities between 0.06 and 0.27 and display a slow retrograde precession with periods ranging from 4−40Tbin which depends quadratically on the disk’s mean aspect ratio. In general, the disks show a coherent, rigid precession which can be broken, however, by changes in the opacity law reducing the overall eccentricity of the disk.

Outward Migration of Super-Jupiters

Abstract Recent simulations show that giant planets of about 1 M J migrate inward at a rate that differs from the type II prediction. Here we show that at higher masses, planets migrate outward. Our result differs from previous ones because of our longer simulation times, lower viscosity, and boundary conditions that allow the disk to reach a viscous steady state. We show that, for planets on circular orbits, the transition from inward to outward migration coincides with the known transition from circular to eccentric disks that occurs for planets more massive than a few Jupiters. In an eccentric disk, the torque on the outer disk weakens due to two effects: the planet launches weaker waves, and those waves travel further before damping. As a result, the torque on the inner disk dominates, and the planet pushes itself outward. Our results suggest that the many super-Jupiters observed by direct imaging at large distances from the star may have gotten there by outward migration.

Angle-of-arrival and time-of-arrival statistics of multipaths arising from scatterers on an elliptical disc with conic spatial density around the mobile

This paper presents the angle-of-arrival (AOA) and time-of-arrival (TOA) statistics of multipaths arriving from scatterers with conic spatial density and located on an elliptical disc around the mobile. For simplification of analysis, a common practice in geometric channel modeling of macrocell networks in the open literature is to assume the scatterers to be located on a circular disc around the mobile for non-uniform scatterers’ spatial densities. This paper extends the analysis for scatterers with conic spatial density on a circular disc around the mobile to that on an elliptical disc around the mobile. The AOA-TOA joint probability densities and AOA marginal probability densities from the base station and mobile station sides were derived analytically in closed form. The TOA marginal probability densities for both the base-station and mobile-station sides were also studied. The effect of the eccentricity of the elliptical disc on the derived probability densities was discussed. In most cases, increase in the eccentricity results to reduction in the AOA support region.

Investigation on mixed-mode II-III fracture of the sandstone by using eccentric cracked disk

Most of the fractures in deep rock mass are in compression condition. The deep rock failure is complex and different modes of failure play important roles. In this study, the central cracked circular disk specimen was improved by deviating from the distance between the crack on the circular surface and the center of the circle, and a new mixed-mode II-III fracture specimen called the eccentric crack disk (ECD) specimen was proposed. The ECD specimen was a simple structure and easy to machining with low cost. In addition, it could be tested in conventional loading machines without extra fixtures. The finite element was used to calculate mode I, mode II and mode III stress intensity factors for different loading angles and crack deviation distances. The critical loading angles of mixed-mode II-III fracture under different crack deviation distances were obtained. And the mixed-mode II-III fracture experiments were carried out with sandstone. The experimental results clearly revealed that the crack initiation started from the middle of the crack. The experimental data also conformed to the effective stress intensity factor criterion of mixed-mode II-III mode fracture from the literature.

Planet formation in stellar binaries: global simulations of planetesimal growth

Planet formation around one component of a tight, eccentric binary system such as γ Cephei (with semimajor axis around 20 AU) is theoretically challenging because of destructive high-velocity collisions between planetesimals. Despite this fragmentation barrier, planets are known to exist in such (so-called S-type) orbital configurations. Here we present a novel numerical framework for carrying out multi-annulus coagulation-fragmentation calculations of planetesimal growth, which fully accounts for the specifics of planetesimal dynamics in binaries, details of planetesimal collision outcomes, and the radial transport of solids in the disk due to the gas drag-driven inspiral. Our dynamical inputs properly incorporate the gravitational effects of both the eccentric stellar companion and the massive non-axisymmetric protoplanetary disk in which planetesimals reside, as well as gas drag. We identify a set of disk parameters that lead to successful planetesimal growth in systems such as γ Cephei or α Centauri starting from 1 to 10 km size objects. We identify the apsidal alignment of a protoplanetary disk with the binary orbit as one of the critical conditions for successful planetesimal growth: It naturally leads to the emergence of a dynamically quiet location in the disk (as long as the disk eccentricity is of order several percent), where favorable conditions for planetesimal growth exist. Accounting for the gravitational effect of a protoplanetary disk plays a key role in arriving at this conclusion, in agreement with our previous results. These findings lend support to the streaming instability as the mechanism of planetesimal formation. They provide important insights for theories of planet formation around both binary and single stars, as well as for the hydrodynamic simulations of protoplanetary disks in binaries (for which we identify a set of key diagnostics to verify).

Model reduction of the tippedisk: a path to the full analysis

The tippedisk is a mechanical-mathematical archetype for friction-induced instability phenomena that exhibits an interesting inversion phenomenon when spun rapidly. The inversion phenomenon of the tippedisk can be modeled by a rigid eccentric disk in permanent contact with a flat support, and the dynamics of the system can therefore be formulated as a set of ordinary differential equations. The qualitative behavior of the nonlinear system can be analyzed, leading to slow–fast dynamics. Since even a freely rotating rigid body with six degrees of freedom already leads to highly nonlinear system equations, a general analysis for the full system equations is not feasible. In a first step the full system equations are linearized around the inverted spinning solution with the aim to obtain a local stability analysis. However, it turns out that the linear dynamics of the full system cannot properly describe the qualitative behavior of the tippedisk. Therefore, we simplify the equations of motion of the tippedisk in such a way that the qualitative dynamics are preserved in order to obtain a reduced model that will serve as the basis for a following nonlinear stability analysis. The reduced equations are presented here in full detail and are compared numerically with the full model. Furthermore, using the reduced equations we give approximate closed form results for the critical spinning speed of the tippedisk.