Retrograde Precession Research Articles

A New Puzzling Periodic Signal in GeV Energies of the γ-Ray Binary LS I+61°303

LS I+61°303 is a high-mass X-ray binary system comprising a massive Be star and a rapidly rotating neutron star. Its spectral energy distribution across multiwavelengths categorizes it as a γ-ray binary system. In our analysis of LS I+61°303 using Fermi Large Area Telescope observations, we not only confirmed the three previously discussed periodicities of orbital, superorbital, and orbital–superorbital beat periods observed in multiwavelength observations, but also identified an additional periodic signal. This newly discovered signal exhibits a period of ∼26.3 days at a ∼7σ confidence level. Moreover, the power spectrum peak of the new signal gradually decreases as the energy increases across the energy ranges of 0.1–0.3, 0.3–1.0, and 1.0–500.0 GeV. Interestingly, a potential signal with a similar period was found in data obtained from the Owens Valley Radio Observatory 40 m telescope. We suggest that the newly discovered periodic signal may originate from a coupling between the orbital period and the retrograde stellar precession period.

A parametric study of precession driven dynamos inside a sphere

The dynamo actions of an electrically conducting fluid in a precessing sphere are investigated over a wide range of parameters by direct numerical simulation using a Galerkin spectral method. The focus of this work is to identify the most promising parameter regimes for the dynamo action and to investigate the characteristics of the magnetic field generated by precession. The influence of different nutation angles (30°,60°,90°) and different precession ratios on the ability to drive dynamo action are investigated. The optimal angle for dynamo actions is found at 90°, followed by 60° with retrograde precession. A moderate precession ratio around 0.3 is shown to be more feasible for dynamo actions. A rich set of self-sustained dynamo solutions are obtained in the parameter space we explored, including steady, periodic, quasi-periodic, and turbulent dynamos. The structure of the generated magnetic fields is analyzed by using helical wave decomposition. None of the precession driven dynamos we obtained produce a predominantly dipolar field, contrary to the convection driven dynamos. The long-time evolution of the magnetic dipole moment is investigated and different types of polarity reversals are observed.

On precession of Lagrange’s top

The article describes the results obtained for the upper and lower bounds (estimates) for the apsidal angle (precession angle) in the theory of the motion of the heavy symmetrical solid body about fixed point (Lagrange’s case) for arbitrary initial conditions and parameters of the body. All regions of initial conditions is divided into two sets. In the first set there is a direct precession of the top, in the second set there is a retrograde precession of the top.

Mergers of black hole binaries driven by misaligned circumbinary discs

ABSTRACT With hydrodynamical simulations we examine the evolution of a highly misaligned circumbinary disc around a black hole binary including the effects of general relativity. We show that a disc mass of just a few per cent of the binary mass can significantly increase the binary eccentricity through von-Zeipel–Kozai–Lidov (ZKL) like oscillations provided that the disc lifetime is longer than the ZKL oscillation time-scale. The disc begins as a relatively narrow ring of material far from the binary and spreads radially. When the binary becomes highly eccentric, disc breaking forms an inner disc ring that quickly aligns to polar. The polar ring drives fast retrograde apsidal precession of the binary that weakens the ZKL effect. This allows the binary eccentricity to remain at a high level and may significantly shorten the black hole merger time. The mechanism requires the initial disc inclination relative to the binary to be closer to retrograde than to prograde.

Nonlinear regimes of inertial wave attractors generated by a precessing lid: Zonal flows and Rossby waves

Fluid flow excited by inertial waves in a rotating annulus with a trapezoidal cross section is experimentally investigated. The forcing is introduced by the precession of a flat annular lid bounding the cavity. Such a setup allows to investigate interactions between inertial waves and zonal flows in the presence of equivalent topographic beta-effect, and its dynamic behavior under weak and strong forcing is experimentally studied for the first time. Due to the specific dispersion relation of inertial waves, a cavity shape supports wave attractors that appear only for retrograde lid precession. At a relatively low wave intensity, a zonal flow is generated in the vicinity of a “virtual” axial cylinder, the radius of which coincides with the radius of the focusing reflection from the conical bottom. A succession of non-linear regimes is observed as forcing increases, starting with a clearly identifiable case of triadic resonance. Further, the frequency spectrum is progressively enriched by emergence of additional discrete components, gradually reaching the state of “overheated” wave turbulence with a significant continuous background of the frequency spectrum. Finally, a strong low-frequency component develops in the frequency spectrum, and the continuous background of the spectrum decreases dramatically. The low-frequency component corresponds to azimuthally periodic structures identified as Rossby waves. In the case of strong forcing, a long-term variability of zonal-flow velocity at the timescale of tens of forcing periods is observed, which is likely a consequence of the interaction of azimuthal structures corresponding to a rich wave number set.

A twisted and precessing Cepheid warp in the outer Milky Way disc

ABSTRACT We examine the Galactic warp in a sample of all classical Cepheids with Gaia Data Release 3 radial velocity. In each radial bin, we determine (1) the inclined plane normal to the mean orbital angular momentum of the stars and (2) that best fitting their positions. We find no warping inside $R\approx 11\,$kpc; for larger R, the disc is increasingly inclined, reaching i ∼ 3° at $R\ge 14\,$kpc. With larger R, the azimuth of the warp’s ascending node shifts from φlon ≈ −15° at 11 kpc by about 14° kpc−1 in the direction of Galactic rotation, implying a leading spiral of nodes, the general behaviour of warped galaxies. From the method of fitting planes to the positions, we also obtain ${\dot{\varphi }}_{\mathrm{lon}}$ and find prograde precession of ${\dot{\varphi }}_{\mathrm{lon}}\sim 12\, \rm{km{}\,s^{-1}{}\,kpc^{-1}}$ at 12 kpc decreasing to ${\sim}\,6\, \rm{km{}\,s^{-1}{}\,kpc^{-1}}$ at 14 kpc and beyond. This would unwind the leading spiral of nodes in ${\sim}\,100\,$Myr, suggesting that our instantaneous measurements of ${\dot{\varphi }}_{\mathrm{lon}}$ reflect transient behaviour. This is consistent with existing simulations, which show oscillations in ${\dot{\varphi }}_{\mathrm{lon}}$ overlaying a long-term retrograde differential precession that generates the leading spiral of nodes.

Gravitational-wave imprints of compact and galactic-scale environments in extreme-mass-ratio binaries

Circumambient and galactic-scale environments are intermittently present around black holes that reside in active galactic nuclei. As supermassive black holes impart energy on their host galaxy, so the galactic environment affects the dynamics of solar-mass objects around black holes and the gravitational waves emitted from non-vacuum asymmetric binaries. Only recently an exact general-relativistic solution has been found that describes a Schwarzschild black hole immersed in a dark matter halo of the Hernquist type. We perform an extensive analysis of generic geodesics delving in such non-vacuum spacetimes and compare our results with those obtained in Schwarzschild, as well as calculate their gravitational-wave emission. Our findings indicate that the radial and polar oscillation frequency ratios descend deeper into the strong gravity region as the compactness of the halo increases. This translates to a redshift of non-vacuum geodesics and their resulting waveforms with respect to the vacuum ones. We calculate the overlap between waveforms resulting from Schwarzschild and non-vacuum geometries and find that it decreases as the halo compactness grows, meaning that dark matter environments should be distinguishable by space-borne detectors. For compact environments, we find that the apsidal precession is strongly affected due to the gravitational pull of dark matter; the orbit's axis can rotate in the opposite direction as that of the orbital motion, leading to a retrograde precession drift that depends on the halo mass, as opposed to the typical prograde precession transpiring in galactic-scale environments. Gravitational waves in retrograde-to-prograde alterations demonstrate transient frequency phenomena around critical non-precessing turning points, thus they may serve as `smoking guns' for the presence of compact dark matter environments around supermassive black holes.

The effect of nutation angle on the flow inside a precessing cylinder and its dynamo action

The effect of the nutation angle on the flow inside a precessing cylinder is experimentally explored and compared with numerical simulations. The focus is laid on the typical breakdown of the directly forced m = 1 Kelvin mode for increasing precession ratio (Poincaré number) and the accompanying transition between laminar and turbulent flows. Compared to the reference case with a 90° nutation angle, prograde rotation leads to an earlier breakdown, while in the retrograde case, the forced mode continues to exist also for higher Poincaré numbers. Depending largely on the occurrence and intensity of an axisymmetric double-roll mode, a kinematic dynamo study reveals a sensitive dependence of the self-excitation condition on the nutation angle and the Poincaré number. Optimal dynamo conditions are found for 90° angle which, however, might shift to slightly retrograde precession for higher Reynolds numbers.

Behavior of hydrodynamic and magnetohydrodynamic turbulence in a rotating sphere with precession and dynamo action

The effect of precession in a rotating sphere filled with fluid was studied with direct numerical simulations, both in the incompressible hydrodynamics (HD) and magnetohydrodynamics (MHD) scenarios. In both cases the asymptotic state and its dependence with both rotating and precession frequency was analyzed. For the MHD case no self-sustaining dynamos were found for the prograde precession case, whereas on the other hand a critical retrograde precession frequency was found above which dynamo action is self-sustained. It was also found that these correspond to small-scale dynamos with a developed turbulent regime. Furthermore, it is observed the presence of reversals of the magnetic dipole moment with greater waiting times between reversals for smaller precession frequencies.

Prograde and retrograde precession of a fluid-filled cylinder

We numerically study precession driven flows in a cylindrical container whose nutation angle varies between 60 and 90 degrees for prograde and retrograde precession. For prograde precession we observe sharp transitions between a laminar and a turbulent flow state with low and high geostrophic axisymmetric flow components related with a centrifugal instability, while for retrograde precession a rather smooth transition between a low state and a high state occurs. At the same time prograde and perpendicular precession shows an abrupt breakdown of the flow directly excited by the forcing mechanism, which is not the case for retrograde motion. We characterize the corresponding flow states in terms of the directly driven, non-axisymmetric Kelvin mode, the axisymmetric geostrophic mode, and an axisymmetric poloidal flow which is promising for precession-driven dynamo action. The latter issue is discussed with particular view on an optimal parameter choice for the DRESDYN dynamo project.

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.

Influence of bulk mass distribution on orbital precession of S2 star in Yukawa gravity

In this study we investigate possible applications of observed S2 orbit around Galactic Center for constraining the Yukawa gravity at scales in the range between several tens and several thousands astronomical units (AU) to obtain graviton mass constraints. In our model we suppose that bulk distribution of matter (includes stellar cluster, interstellar gas distribution and dark matter) exists near Supermassive Black Hole (SMBH) in our Galactic Center. We obtain the values of orbital precession angle for different values of mass density of matter and we require that the value of orbital precession is the same like in General Relativity (GR). From that request we determine gravity parameter $\lambda$ and the upper value for graviton mass. We found that in the cases where the density of extended mass is higher, the maximum allowed value for parameter $\lambda$ is smaller and the upper limit for graviton mass is higher. It is due to the fact that the extended mass causes the retrograde orbital precession. We believe that this study is a very efficient tool to evaluate a gravitational potential at the Galactic Center, parameter $\lambda$ of the Yukawa gravity model, and to constrain the graviton mass.

Null and Timelike Geodesics near the Throats of Phantom Scalar Field Wormholes

We study geodesic motion near the throats of asymptotically flat, static, spherically symmetric traversable wormholes supported by a self-gravitating minimally coupled phantom scalar field with an arbitrary self-interaction potential. We assume that any such wormhole possesses the reflection symmetry with respect to the throat, and consider only its observable “right half”. It turns out that the main features of bound orbits and photon trajectories close to the throats of such wormholes are very different from those near the horizons of black holes. We distinguish between wormholes of two types, the first and second ones, depending on whether the redshift metric function has a minimum or maximum at the throat. First, it turns out that orbits located near the centre of a wormhole of any type exhibit retrograde precession, that is, the angle of pericentre precession is negative. Second, in the case of high accretion activity, wormholes of the first type have the innermost stable circular orbit at the throat while those of the second type have the resting-state stable circular orbit in which test particles are at rest at all times. In our study, we have in mind the possibility that the strongly gravitating objects in the centres of galaxies are wormholes, which can be regarded as an alternative to black holes, and the scalar field can be regarded as a realistic model of dark matter surrounding galactic centres. In this connection, we discuss qualitatively some observational aspects of results obtained in this article.

Secular Evolution of Rings around Rotating Triaxial Gravitating Bodies

The problem of the secular evolution of a thin ring around a rapidly rotating triaxial celestial body is formulated and solved. The technology for calculating secular perturbations is based on two formulas: the azimuthally averaged force field of the central body and the mutual energy $${{W}_{{{\text{mut}}}}}$$ of this body and a Gaussian ring. With $${{W}_{{{\text{mut}}}}}$$ instead of the usual perturbing function, a system of differential equations for the osculating elements of the ring is obtained. An equation is obtained that allows one to find the coefficients of the zonal harmonics of the azimuthally averaged potential of an inhomogeneous ellipsoid using a unified scheme. The method is applied to dwarf planet Haumea with refined masses of the rocky core and the ice shell and the coefficients $${{C}_{{20}}}$$ and $${{C}_{{40}}}$$ of the po-tential’s zonal harmonics. According to new data, the ring around Haumea has a slight obliquity and must precess. It was established that the period of the retrograde nodal precession of the Haumea’s ring (without regard to self-gravity) is $${{T}_{\Omega }} = 12.9 \pm 0.7$$ days and the period of the forward of the apside line precession is $${{T}_{\omega }} \approx 8.{\text{08}}\;{\text{days}}$$ . It is proven that the 3:1 orbital resonance for the particles of the Haumea’s ring is fulfilled only approximately and the averaging time of additional perturbations at a nonsharp resonance turned out to be an order of magnitude smaller than $${{T}_{\Omega }}$$ . This confirms the adequacy of the method.

Experimental and theoretical research of continuous motion of rotor on anisotropic gapped elastic support

Kinematic and dynamic features of flexible rotor rolling of an unlubricated uneven-stiffness gapped support are shown with the help of a theoretical model and full-scale tests. A combination of original approaches and well-known analytical and experimental methods is used. In particular, the motion equations are Lagrangian, derived in complex and complex-conjugate coordinates, and their solutions are sought in the exponential form, by excluding contact forces from consideration and by introducing a small parameter. Vibration measurements are not made on the rig frame using accelerometers, but at the source of vibration, i.e. by direct tracking of the rotor axle by a pair of eddy-current contactless displacement sensors installed in a XY configuration. Hence, the preciseness of the experimental data does not depend on the mechanical conductivity of the parts between the source rotor and the receiver sensors. As a result, the frequency, amplitude and existence domain of retrograde precession are reliably determined, and a conclusion is drawn that rolling under a certain combination of parameters is impossible in principle.

Experimental study of the convection in a rotating tangent cylinder

This paper experimentally investigates the convection in a rapidly rotating tangent cylinder (TC), for Ekman numbers down to $E=3.36\times 10^{-6}$. The apparatus consists of a hemispherical fluid vessel heated in its centre by a protruding heating element of cylindrical shape. The resulting convection that develops above the heater, i.e. within the TC, is shown to set in for critical Rayleigh numbers and wavenumbers respectively scaling as $Ra_{c}\sim E^{-4/3}$ and $a_{c}\sim E^{-1/3}$ with the Ekman number $E$. Although exhibiting the same exponents as for plane rotating convection, these laws reflect much larger convective plumes at onset. The structure and dynamics of supercritical plumes are in fact closer to those found in solid rotating cylinders heated from below, suggesting that the confinement within the TC induced by the Taylor–Proudman constraint influences convection in a similar way as solid walls would do. There is a further similarity in that the critical modes in the TC all exhibit a slow retrograde precession at onset. In supercritical regimes, the precession evolves into a thermal wind with a complex structure featuring retrograde rotation at high latitude and either prograde or retrograde rotation at low latitude (close to the heater), depending on the criticality and the Ekman number. The intensity of the thermal wind measured by the Rossby number $Ro$ scales as $Ro\simeq 5.33(Ra_{q}^{\ast })^{0.51}$ with the Rayleigh number based on the heat flux $Ra_{q}^{\ast }\in [10^{-9},10^{-6}]$. This scaling is in agreement with heuristic predictions and previous experiments where the thermal wind is determined by the azimuthal curl of the balance between the Coriolis force and buoyancy. Within the range $Ra\in [2\times 10^{7},10^{9}]$ which we explored, we also observe a transition in the heat transfer through the TC from a diffusivity-free regime where $Nu\simeq 0.38E^{2}Ra^{1.58}$ to a rotation-independent regime where $Nu\simeq 0.2Ra^{0.33}$.

Patterns of the Rotor-over-Stator Rolling under Change in the Damping Components

As experimental studies show, the rubbing of the rotor against the structure usually excites harmonics of different frequencies. In high-frequency regions, the power of the vibration signal appears to be considerable. The rotor—supports—stator system is in an unstable equilibrium state during the contact interaction between the rotor and the stator. The forces exerted on the rotor facilitate the excitation of the asynchronous rolling and its damping. The forces have been determined that facilitate the excitation of the progressive and retrograde rotor precession. The consideration of these forces in the algorithm for modeling the rotor-over-stator rolling development allows investigation of the impact of the components of the above forces on the behavior of the rotor system. The initial excitation—disturbance of the normal operation—of the rotor and subsequent unsteady oscillations of it result from sudden imbalance in the second span. The results of numerical modeling of the rubbing in the second span and the rotor-over-stator rolling upon change in the damping components of secondary (gyroscopic) components b ij (i ≠ j) of the damping matrix are presented for the rotor on three bearing-supports considering the synergetic effect of the forces of various types exerted on the rotor. It is shown that change in one of the parameters of the excitation forces leads to ambiguity of the pattern (manifestation form) of the asynchronous rotor-over-stator rolling and proves the existence of more than one states towards which the rotor—supports—stator system tends. In addition to the rolling with a constant rotor—stator contact, oscillations of the rotor develop in the direction perpendicular to the common trajectory of the precession motion of the rotor’s center with transition to the vibro-impact motion mode. The oscillations of the rotor tend towards the symmetry center of the system (the stator bore center). The reason is the components of the stiffness and damping forces that act in the direction transverse to the rotor’s motion trajectory. Recommendations are given for eliminating dangerous consequences of the development of the asynchronous rolling fraught with great financial losses.

Probabilistic eccentricity bifurcation for stars around shrinking massive black hole binaries

Based on the secular theory, we discuss the orbital evolution of stars in a nuclear star cluster to which a secondary massive black hole is infalling with vanishing eccentricity. We find that the eccentricities of the stars could show sharp transitions, depending strongly on their initial conditions. By examining the phase-space structure of an associated Hamiltonian, we show that these characteristic behaviours are partly due to a probabilistic bifurcation at a separatrix crossing, resulting from the retrograde apsidal precession by the cluster potential. We also show that separatrix crossings are closely related to realization of a large eccentricity and could be important for astrophysical phenomena such as tidal disruption events or gravitational wave emissions.

A 16-yr photometric campaign on the eclipsing novalike variable DW Ursae Majoris

We present an analysis of photometric observations of the eclipsing novalike variable DW UMa made by the CBA consortium between 1999 and 2015. Analysis of 372 new and 260 previously published eclipse timings reveals a 13.6 year period or quasi-period in the times of minimum light. The seasonal light curves show a complex spectrum of periodic signals: both positive and negative superhumps, likely arising from a prograde apsidal precession and a retrograde nodal precession of the accretion disc. These signals appear most prominently and famously as sidebands of the orbital frequency but the precession frequencies themselves, at 0.40 and 0.22 cycles per day, are also seen directly in the power spectrum. The superhumps are sometimes seen together and sometimes separately. The depth, width and skew of eclipses are all modulated in phase with both nodal and apsidal precession of the tilted and eccentric accretion disc. The superhumps, or more correctly the precessional motions which produce them, may be essential to understanding the mysterious SW Sextantis syndrome. Disc wobble and eccentricity can both produce Doppler signatures inconsistent with the true dynamical motions in the binary, and disc wobble might boost the mass-transfer rate by enabling the hot white dwarf to directly irradiate the secondary star.

Analysis of rolling with slip of flexible rotor inside stator

The interaction of a rotor with a stator without separation is considered during their plane-parallel motion and under assumption of constant rotor speed. In contrast to known papers devoted to the problem of the possibility of rolling in the rotor system, it is shown that the retrograde precession frequency is always lower than the inherent one, which corresponds to a zero-clearance flexible–mobile stator system.