Rotational Evolution Research Articles

On the Rotation of a Spacecraft Carrying a Deformable Antenna in the Gravitational Field of Force

The problem of motion, relative to the center of mass, of a satellite rotating around the center of gravity over an elliptical orbit, is studied. The satellite consists of axisymmetric solid and viscoelastic sections, with the viscoelastic section being a hemispherical antenna. It is shown that the evolution of satellite rotations can be subdivided into two stages; fast, caused by deformations under an effect of inertia forces, and slow, or the dissipative stage. It is shown that the fast evolution stage consists in the fact that the angular momentum vector is located along the satellite’s axis of symmetry (in this case, the axial moment of inertia is greater than the equatorial), and in the equatorial plane of the ellipsoid of inertia (if the equatorial moment of inertia is greater than the axial). The slow evolution stage was considered for the case where the axial moment of inertia is greater than the equatorial. It is found that slow evolution consists in decelerating the axial rotation and in the angular momentum vector inclining to the orbital plane.

Slingshot prominence evolution for a solar-like star

Although the present-day Sun rotates too slowly to exhibit centrifugally-supported 'slingshot prominences', at some time during its past it may have formed these clouds of cool gas and ejected them into the interplanetary medium. We determine the time period for this behaviour by using a rotation evolution code to derive the properties of the formation and ejection of slingshot prominences during the lifetime of a star similar to our Sun. The mass, mass loss rate and rate of ejection of these prominences are calculated using the analytical expression derived in our previous work. We find that for stars with an initial rotation rate larger than $4.6\, \Omega_\odot$, about half of all solar mass stars, slingshot prominences will be present even after the star reaches the main sequence phase. In a fast rotator, this means that prominences can form until the star reaches $\sim 800$ Myr old. Our results also indicate that the mass and lifetime of this type of prominence have maximum values when the star reaches the ZAMS at an age of $\sim 40$ Myr for a solar mass star.

Slowing the spins of stellar cores

ABSTRACT The angular momentum (AM) evolution of stellar interiors, along with the resulting rotation rates of stellar remnants, remains poorly understood. Asteroseismic measurements of red giant stars reveal that their cores rotate much faster than their surfaces, but much slower than theoretically predicted, indicating an unidentified source of AM transport operates in their radiative cores. Motivated by this, we investigate the magnetic Tayler instability and argue that it saturates when turbulent dissipation of the perturbed magnetic field energy is equal to magnetic energy generation via winding. This leads to larger magnetic field amplitudes, more efficient AM transport, and smaller shears than predicted by the classic Tayler–Spruit dynamo. We provide prescriptions for the effective AM diffusivity and incorporate them into numerical stellar models, finding they largely reproduce (1) the nearly rigid rotation of the Sun and main sequence stars, (2) the core rotation rates of low-mass red giants during hydrogen shell and helium burning, and (3) the rotation rates of white dwarfs. We discuss implications for stellar rotational evolution, internal rotation profiles, rotational mixing, and the spins of compact objects.

Tiangong-1\u2019s accelerated self-spin before reentry

The detection and study of the rotational motion of space debris, which is affected by environmental factors, is a popular topic. However, relevant research in extremely low-orbit regions cannot be conducted due to a lack of observational data. Here, we fill in the gaps to present the rotational evolution of Tiangong-1 in the 5 months prior to reentry. Derived from the changes in the relative distance of its two corner cube reflectors from satellite laser ranging data, the angular momentum of Tiangong-1, which is relatively stable during observation, deviates from its maximum principal axis of inertia and precesses around the normal direction of the orbital plane due to gravity gradient torque at an angle of 23.1^circ pm,2.5^circ. Requiring consistency with the relationship between the angular momentum and precession rate leads to a solution for the rotation rate, which is thus found to increase. This result cannot be explained by any previously developed torque models. Hence, an atmospheric density gradient torque (ADGT) model that considers the torque generated by the change in atmospheric density with orbital altitude at the satellite scale is proposed to explain the rotational acceleration mechanism of extremely low-orbit objects. The numerical results show that the ADGT model provides a non-negligible ability to explain, but cannot fully describe, the acceleration effect. The data on the rotational evolution of Tiangong-1 can provide an important basis for aerodynamic model improvement by addressing minor factors omitted in previous models.

Long-Term Evolution of the Deviatoric Background Stress in the Focal Region of the 2011 Tohoku-Oki Earthquake

On 11 March 2011, a giant interplate earthquake of magnitude Mw 9.1 struck Tohoku-Oki area in eastern Japan. The earthquake is acknowledged to have permanently altered the stress field in and around the focal region. To capture the temporal change of the overall stress field, I examined 1251 focal mechanisms, from the NIED MT catalog, that occurred before and after the Tohoku-Oki earthquake from January, 2006 to January, 2017 in the focal region near the subducting slab. The examined observations were grouped into six periods, and based on the selected NIED MT catalog, the stress regime in each period was obtained by using the damped stress tensor inversion method. Based on the temporal evolution of stress rotation, the corresponding deviatoric stress level was estimated using a simplified 2D model. Results of the 10-year seismic stress cycle show that several years before the Tohoku-Oki earthquake, the stress accumulation level seems to have experienced an acceleration process. Studies suggest that this increasingly critically stress state combined with the sufficiently reduced coupling rate off the Tohoku area finally resulted in the unprecedented megathrust event. The coseismic process was violent and released almost all of the deviatoric stress that presented before the main shock. The resultant stress state even reached frictional overshoot. Thus, the postseismic stress pattern in the source region was reshaped significantly, especially for the upper plate and updip portion of the lower plate. After the main shock near the rupture surface, a surprisingly rapid and high-level stress reloading occurred within several postseismic years. To reconcile the classical subduction zone earthquake generation cycle model, the event may be described as an instantaneously decoupled stress state between the upper and inner plates.

On tidal theories and the rotation of viscous bodies

Celestial bodies are complex systems with the ability to get deformed by tides. Modelling accurately this process is a difficult task even for the planets of our own solar system. This is why tidal theories applied to exoplanets are often reduced to a simple formula accounting for our lack of knowledge. In this work, we identify the three minimal assumptions leading to this level of simplification. We then compare different rheologies compatible with these hypotheses and discuss their qualitative behaviour. Finally, we apply the viscous model to close-in planets and describe their rotation evolution, emphasising the apparition of spin-orbit resonances as the viscous timescale increases.

Effect of the rotation, tidal dissipation history and metallicity of stars on the evolution of close-in planets

Since 1995, numerous close-in planets have been discovered around low-mass stars (M to A-type stars). These systems are susceptible to be tidally evolving, in particular the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and also shape the orbital architecture of the surrounding planetary system. Recent theoretical studies have shown that the amplitude of the stellar dissipation can vary over several orders of magnitude as the star evolves, and that it also depends on the stellar mass and rotation. We present here one of the first studies of the dynamics of close-in planets orbiting low-mass stars (from 0.6 M☉ to 1.2 M☉) where we compute the simultaneous evolution of the star’s structure, rotation and tidal dissipation in its external convective envelope. We demonstrate that tidal friction due to the stellar dynamical tide, i.e. tidal inertial waves (their restoring force is the Coriolis acceleration) excited in the convection zone, can be larger by several orders of magnitude than the one of the equilibrium tide currently used in celestial mechanics. This is particularly true during the Pre Main Sequence (PMS) phase and to a lesser extent during the Sub Giant (SG) phase. Numerical simulations show that only the high dissipation occurring during the PMS phase has a visible effect on the semi-major axis of close-in planets. We also investigate the effect of the metallicity of the star on the tidal evolution of planets. We find that the higher the metallicity of the star, the higher the dissipation and the larger the tidally-induced migration of the planet.

Evolution of star–planet systems under magnetic braking and tidal interaction

Context.With the discovery over the last two decades of a large diversity of exoplanetary systems, it is now of prime importance to characterize star–planet interactions and how such systems evolve.Aims.We address this question by studying systems formed by a solar-like star and a close-in planet. We focus on the stellar wind spinning down the star along its main-sequence phase and tidal interaction causing orbital evolution of the systems. Despite recent significant advances in these fields, all current models use parametric descriptions to study at least one of these effects. Our objective is to introduce ab initio prescriptions of the tidal and braking torques simultaneously, so as to improve our understanding of the underlying physics.Methods.We develop a one-dimensional (1D) numerical model of coplanar circular star–planet systems taking into account stellar structural changes, wind braking, and tidal interaction and implement it in a code called ESPEM. We follow the secular evolution of the stellar rotation and of the semi-major axis of the orbit, assuming a bilayer internal structure for the former. After comparing our predictions to recent observations and models, we perform tests to emphasize the contribution of ab initio prescriptions. Finally, we isolate four significant characteristics of star–planet systems: stellar mass, initial stellar rotation period, planetary mass and initial semi-major axis; and browse the parameter space to investigate the influence of each of them on the fate of the system.Results.Our secular model of stellar wind braking accurately reproduces the recent observations of stellar rotation in open clusters. Our results show that a planet can affect the rotation of its host star and that the resulting spin-up or spin-down depends on the orbital semi-major axis and on the joint influence of magnetic and tidal effects. The ab initio prescription for tidal dissipation that we used predicts fast outward migration of massive planets orbiting fast-rotating young stars. Finally, we provide the reader with a criterion based on the characteristics of the system that allows us to assess whether or not the planet will undergo orbital decay due to tidal interaction.

Three-dimensional numerical assessment of axial and torsional interface shear behaviour

Interfaces between geo-materials and soils play a critical role in a wide spectrum of geotechnical structures and soil/site characterization techniques in geotechnical engineering. Consequently, understanding the mechanics of interface shear behaviour at different scales can benefit both soil characterization and the design of geotechnical systems. This paper presents a series of numerical simulations that utilize the 3D discrete element modelling (DEM) technique and compares the results with those obtained from laboratory counterpart tests under axial and torsional axisymmetric interface shear. The difference observed in macro- and meso-scale responses under these loading conditions, such as shear strength, volumetric change, and shear zone characteristics are evaluated. In addition, responses at microscale including particle displacement trajectory, particles rotation, and local void ratio evolution are assessed allowing for links to the results obtained at larger spatial scales. These 3D numerical model studies expand the micromechanical processes under different shearing conditions previously presented by the authors from 2D to 3D space.

Separatrix Crossing in Rotation of a Body with Changing Geometry of Masses

We consider free rotation of a body whose parts move slowly with respect to each other under the action of internal forces. This problem can be considered as a perturbation of the Euler--Poinsot problem. The dynamics has an approximate conservation law---an adiabatic invariant. This allows us to describe the evolution of rotation in the adiabatic approximation. The evolution leads to an overturn in the rotation of the body: the vector of angular velocity crosses the separatrix of the Euler--Poinsot problem. This crossing leads to a quasirandom scattering in body's dynamics. We obtain formulas for probabilities of capture into different domains in the phase space at separatrix crossings.

Ultrafast electron and spin dynamics of strongly correlated NdNiO3

Electron and spin dynamics of strongly correlated NdNiO3 are investigated across the metal–insulator transition with ultrafast optical spectroscopy at different temperatures, pump laser fluences, and laser polarizations. Transient differential reflectivity measurements on the insulating phase NdNiO3 show two characteristic electronic decay processes. The slow decay process, strongly dependent on coherent phonon excitation, is attributed to the electron–phonon interaction, while the fast decay process, to the electron-spin interaction. The temporal evolution of Kerr rotation reveals that net spin polarization can be induced by circularly polarized light in insulating NdNiO3 via electron excitation from the Ni t to e orbital, and two net spin polarizations with opposite directions are observed given the antiferromagnetic ordering in insulating NdNiO3. At the insulator-to-metal transition, the transient differential reflectivity reverses its sign; the metallic phase NdNiO3 also shows two characteristic electronic decay processes, a typical metallic decay processes and a slow decay process; the slow decay process is attributed to the interaction between electrons and the low frequency coherent phonons (2.45 THz). Our experiments demonstrate that the phase transition involves several processes upon continuous heating: the electron-spin interaction disappears at 9 K below the transition temperature; at the transition temperature, NdNiO3 transitions into the metallic phase and the antiferromagnetic ordering transitions into the paramagnetic ordering; at the transition temperature, the structure of NdNiO3 changes from a monoclinic structure () to a high temperature orthorhombic () structure. Such a structure change results in the change in phonon vibrations, and subsequently, leads to the disappearance of the electron–phonon interactions due to the insulating phase NdNiO3 and the emergence of other types of electron–phonon interactions due to the metallic phase.

Anisotropic turbulent transport in stably stratified rotating stellar radiation zones

Context. Rotation is one of the key physical mechanisms that deeply impact the evolution of stars. Helio- and asteroseismology reveal a strong extraction of angular momentum from stellar radiation zones over the whole Hertzsprung–Russell diagram. Aims. Turbulent transport in differentially rotating, stably stratified stellar radiation zones should be carefully modelled and its strength evaluated. Stratification and rotation imply that this turbulent transport is anisotropic. So far only phenomenological prescriptions have been proposed for the transport in the horizontal direction. This, however, constitutes a cornerstone in current theoretical formalisms for stellar hydrodynamics in evolution codes. We aim to improve its modelling. Methods. We derived a new theoretical prescription for the anisotropy of the turbulent transport in radiation zones using a spectral formalism for turbulence that takes simultaneously stable stratification, rotation, and a radial shear into account. Then, the horizontal turbulent transport resulting from 3D turbulent motions sustained by the instability of the radial differential rotation is derived. We implemented this framework in the stellar evolution code STAREVOL and quantified its impact on the rotational and structural evolution of solar metallicity low-mass stars from the pre-main-sequence to the red giant branch. Results. The anisotropy of the turbulent transport scales as N4τ2/(2Ω2), N and Ω being the buoyancy and rotation frequencies respectively and τ a time characterizing the source of turbulence. This leads to a horizontal turbulent transport of similar strength in average that those obtained with previously proposed prescriptions even if it can be locally larger below the convective envelope. Hence the models computed with the new formalism still build up too steep internal rotation gradients compared to helioseismic and asteroseismic constraints. As a consequence, a complementary transport mechanism such as internal gravity waves or magnetic fields is still needed to explain the observed strong transport of angular momentum along stellar evolution. Conclusions. The new prescription links for the first time the anisotropy of the turbulent transport in radiation zones to their stratification and rotation. This constitutes important theoretical progress and demonstrates how turbulent closure models should be improved to get firm conclusions on the potential importance of other processes that transport angular momentum and chemicals inside stars along their evolution.

Monitoring of Space Debris Rotation Based on Photometry

The number of spacecraft and space debris (SD) in orbit has become so great that there is a real threat to flight safety. The task of precision calculation of the upcoming positions of any space objects (SO) in orbit in order to predict dangerous mutual approaches and to solve practical tasks has become topical. For the development of a modern orbit propagation model and the associated unified forecast of the evolution of orientation and rotation of an uncontrolled satellite, it is necessary to rely on long-term series of high-quality measurements and their analysis. At present, the direction of research on determining the state of SO rotation around a center of mass has become more and more developed. In our work, we analyze the results of photometric observations of several large objects of space debris obtained at the Astronomical Observatory of Odessa University using the KT-50 telescope during the last six years or more. The results of the evolution of the rotation rate and orientation of the Topex/Poseidon, Envisat, Oicets, Cosmos-2487 (Kondor-E) and Sich-2 satellites are presented.

The Rotational Evolution of Young, Binary M Dwarfs

Abstract We have analyzed K2 light curves for more than 3000 low-mass stars in the ∼8 Myr old Upper Sco association, the ∼125 Myr age Pleiades open cluster, and the ∼700 Myr old Hyades and Praesepe open clusters to determine stellar rotation rates. Many of these K2 targets show two distinct periods, and for the lowest-mass stars in these clusters, virtually all of these systems with two periods are photometric binaries. The most likely explanation is that we are detecting the rotation periods for both components of these binaries. We explore the evolution of the rotation rate in both components of photometric binaries relative to one another and to nonphotometric binary stars. In Upper Sco and the Pleiades, these low-mass binary stars have periods that are much shorter on average and much closer to each other than would be true if drawn at random from the M dwarf single stars. In Upper Sco, this difference correlates strongly with the presence or absence of infrared excesses due to primordial circumstellar disks—the single-star population includes many stars with disks, and their rotation periods are distinctively longer on average than their binary star cousins of the same mass. By Praesepe age, the significance of the difference in rotation rate between the single and binary low-mass M dwarf stars is much less, suggesting that angular momentum loss from winds for fully convective zero-age main-sequence stars erases memory of the rotation rate dichotomy for binary and single very low mass stars at later ages.

Planetary tidal interactions and the rotational evolution of low-mass stars

Context. The surface angular velocity evolution of low-mass stars is now globally understood and the main physical mechanisms involved in it are observationally quite constrained. However, while the general behaviour of these mechanisms is grasped, their theoretical description is still under ongoing work. This is the case, for instance, about the description of the physical process that extracts angular momentum from the radiative core, which could be described by several theoretical candidates. Additionally, recent observations showed anomalies in the rotation period distribution of open cluster, main sequence, early K-type stars that cannot be reproduced by current angular momentum evolution models. Aims. In this work, we study the parameter space of star-planet system’s configurations to investigate if including the tidal star-planet interaction in angular momentum evolution models could reproduce the anomalies of this rotation period distribution. Methods. To study this effect, we use a parametric angular momentum evolution model that allows for core-envelope decoupling and angular momentum extraction by magnetized stellar wind that we coupled to an orbital evolution code where we take into account the torque due to the tides raised on the star by the planet. We explore different stellar and planetary configurations (stellar mass from 0.5 to 1.0 M⊙ and planetary mass from 10 M⊕ to 13 Mjup) to study their effect on the planetary orbital and stellar rotational evolution. Results. The stellar angular momentum is the most impacted by the star-planet interaction when the planet is engulfed during the early main sequence phase. Thus, if a close-in Jupiter-mass planet is initially located at around 50% of the stellar corotation radius, a kink in the rotational period distribution opens around late and early K-type stars during the early main sequence phase. Conclusions. Tidal star-planet interactions can create a kink in the rotation period distribution of low-mass stars, which could possibly account for unexpected scatter seen in the rotational period distribution of young stellar clusters.

An ultrasonic-based method for longwall top-coal cavability assessment

Longwall top-coal caving (LTCC) is widely employed in the underground mining of thick coal seams. The technique divides a thick coal seam into a lower and an upper section. The bottom coal is sheared by a cutting head and transported by a conveyor in front of the support while the top coal fails and caves under mining pressure, transported by a conveyor at the rear of the support. In an LTCC panel, accurate assessment of top-coal cavability is critical to the design of mining parameters required to achieve continuous caving of top coal. In the present paper, an integrated detection system in which fracture development and ultrasonic wave velocity are used to characterize top-coal cavability is introduced. The cavability is predicted conveniently due to ease of access of the ultrasonic wave velocity in the top coal. Accordingly, an ultrasonic model is established and coupled to the mechanical model previously proposed by the authors to simulate the evolution of the wave velocity in stressed coal. The mechanical-ultrasonic coupling model is validated by comparison against experimental data and further extended to evaluate top-coal cavability in Dongzhouyao mine with a finite difference type code. The predictions, including the excavation-damaged zone, roof weighting interval, stress distribution, stress rotation and ultrasonic wave velocity evolution, are consistent with the field measurements. With the proposed model, the influence provided by hydraulic fracturing on top-coal cavability is investigated by conducting the finite difference type modeling.

Slingshot prominences: nature’s wind gauges

Mass loss rates for the tenuous, hot winds of cool stars are extremely difficult to measure, yet they are a crucial ingredient in the stars' rotational evolution. We present a new method for measuring these mass loss rates in young, rapidly-rotating stars. These stars are known to support systems of "slingshot prominences" fed by hot wind material flowing up from the stellar surface into the summits of closed magnetic loop structures. The material gathers and cools near the co-rotation radius until its density becomes large enough that it is visible as a transient absorption feature in the hydrogen Balmer lines and strong resonance lines such as Ca II H \&\ K. Here we present the key insight that the sonic point usually lies well below the condensation region. The flow at the wind base is therefore unaffected by the presence of an overlying prominence, so we can use the observed masses and recurrence times of the condensations to estimate the mass flux in the wind. These measurements extend the relationship between mass loss rate per unit surface area and X-ray flux to span 5 orders of magnitude. They demonstrate no evidence of the suspected weakening of stellar mass loss rates at high X-ray flux levels.

The Effect of Magnetic Variability on Stellar Angular Momentum Loss. I. The Solar Wind Torque during Sunspot Cycles 23 and 24

Abstract The rotational evolution of cool stars is governed by magnetized stellar winds that slow the stellar rotation during their main sequence lifetimes. Magnetic variability is commonly observed in Sun-like stars, and the changing strength and topology of the global field is expected to affect the torque exerted by the stellar wind. We present three different methods for computing the angular momentum loss in the solar wind. Two are based on MHD simulations from Finley & Matt (2018), with one using the open flux measured in the solar wind, and the other using remotely observed surface magnetograms. Both methods agree in the variation of the solar torque seen through the solar cycle and show a 30%–40% decrease from cycles 23 to 24. The two methods calculate different average values, 2.9 × 1030 erg (open flux) and 0.35 × 1030 erg (surface field). This discrepancy results from the already well-known difficulty of reconciling the magnetograms with the observed open flux, which is currently not understood, leading to an inability to discriminate between these two calculated torques. The third method is based on the observed spin rates of Sun-like stars, which decrease with age, directly probing the average angular momentum loss. This method gives 6.2 × 1030 erg for the solar torque, larger than the other methods. This may be indicative of further variability in the solar torque on timescales much longer than the magnetic cycle. We discuss the implications for applying the formula to other Sun-like stars, where only surface field measurements are available, and where the magnetic variations are ill-constrained.

Rocky Planet Rotation, Thermal Tide Resonances, and the Influence of Biological Activity.

It has been established theoretically that atmospheric thermal tides on rocky planets can lead to significant modifications of rotational evolution, both close to synchronous rotation and at faster rotations if certain resonant conditions are met. Here it is demonstrated that the normally considered dissipative gravitational tidal evolution of rocky planet rotation could, in principle, be “stalled” by thermal tide resonances for Earth-analog worlds in the liquid–water orbital zone of stars more massive than nsim 0.3{M_ odot }n. The possibility of feedback effects between a planetary biosphere and the planetary rotational evolution is examined. Building on earlier studies, it is suggested that atmospheric oxygenation and ozone production could play a key role in planetary rotational evolution, and therefore represents a surprising but potent form of biological imprint on astronomically accessible planetary characteristics.

Further Investigation of Changes in Cometary Rotation

Abstract Samarasinha & Mueller related changes of cometary rotation to other physical parameters for four Jupiter-family comets defining a parameter X, which is approximately constant within a factor of two irrespective of the active fraction of a comet. In this paper two additional comets are added to the original sample, and the claim of a nearly constant parameter X for these six comets is confirmed, albeit with a larger scatter. Taking the geometric mean of X for all of the comets above excluding 2P/Encke (as X for each comet was determined with respect to that of 2P/Encke), the expected changes in the rotation periods for a sample of 24 periodic comets are derived. From this sample we identify the comets that are most likely to show observationally detectable changes in their rotation periods. Using these 24 comets and including the six comets used to determine X, we find a correlation between the parameter ζ (i.e., the total water production per unit surface area per orbit approximated by that inside of 4 au) and the perihelion distance q; specifically, we derive ζ ∝ q −0.8 and provide a theoretical basis for this in the Appendix. This relationship between ζ and q enables ready comparisons of activity due to insolation between comets. Additionally, a relationship between the nuclear radius R and the rotation period P is found. We find that on average smaller nuclei have smaller rotation periods compared to the rotation periods of larger nuclei. This is consistent with expectations for the rotational evolution and spin-up of comet nuclei, providing strong observational evidence for sublimation-driven rotational changes in comets.