Surface Angular Velocity Research Articles

Generalized boundary dilatation flux on a flexible wall

In this paper, by applying theoretical method to the governing equations of compressible viscous flow, we derive the theoretical formula of the boundary dilatation flux (BDF) on a flexible wall, which generalizes the most recent work of Mao et al. (Acta Mechanica Sinica 38 (2022) 321583) for a stationary wall. Different boundary sources of dilatation are explicitly identified, revealing not only the boundary generation mechanisms of vortex sound and entropy sound, but also some additional sources due to the surface vorticity, surface angular velocity, surface acceleration and surface curvature. In particular, the generation mechanism of dilatation at boundary due to the coupled divergence terms is highlighted, namely, the product of the surface velocity divergence (∇∂B·U) and the vorticity-induced skin friction divergence (∇∂B·τω). The former is attributed to the surface flexibility while the latter characterizes the footprints of near-wall coherent structures. Therefore, by properly designing the surface velocity distribution, the dilatation generation at the boundary could be controlled for practical purpose in near-wall compressible viscous flows.

Kinetic joint force in bending/stretching of knee joint; estimated from surface EMG and angular velocity

Kinetic joint force in bending/stretching of knee joint; estimated from surface EMG and angular velocity

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.

Time-series Doppler images and surface differential rotation of the effectively single, rapidly rotating K-giant KU Pegasi

According to most stellar dynamo theories, differential rotation (DR) plays a crucial role for the generation of toroidal magnetic fields. Numerical models predict surface differential rotation to be anti-solar for rapidly-rotating giant stars, i.e., their surface angular velocity could increase with stellar latitude. However, surface differential rotation has been derived only for a handful of individual giant stars to date. The spotted surface of the K-giant KU Pegasi is investigated in order to detect its time evolution and quantify surface differential rotation. We present altogether 11 Doppler images from spectroscopic data collected with the robotic telescope STELLA between 2006--2011. All maps are obtained with the surface reconstruction code iMap. Differential rotation is extracted from these images by detecting systematic (latitude-dependent) spot displacements. We apply a cross-correlation technique to find the best differential rotation law. The surface of KU Peg shows cool spots at all latitudes and one persistent warm spot at high latitude. A small cool polar spot exists for most but not all of the epochs. Re-identification of spots in at least two consecutive maps is mostly possible only at mid and high latitudes and thus restricts the differential-rotation determination mainly to these latitudes. Our cross-correlation analysis reveals solar-like differential rotation with a surface shear of $\alpha=+0.040\pm0.006$, i.e., approximately five times weaker than on the Sun. We also derive a more accurate and consistent set of stellar parameters for KU Peg including a small Li abundance of ten times less than solar.

Rotating models of young solar-type stars

We study the predicted rotational evolution of solar-type stars from the pre-main sequence to the solar age with 1D rotating evolutionary models including physical ingredients. We computed rotating evolution models of solar-type stars including an external stellar wind torque and internal transport of angular momentum following the method of Maeder and Zahn with the code STAREVOL. We explored different formalisms and prescriptions available from the literature. We tested the predictions of the models against recent rotational period data from extensive photometric surveys, lithium abundances of solar-mass stars in young clusters, and the helioseismic rotation profile of the Sun. We find a best-matching combination of prescriptions for both internal transport and surface extraction of angular momentum. This combination provides a very good fit to the observed evolution of rotational periods for solar-type stars from early evolution to the age of the Sun. Additionally, we show that fast rotators experience a stronger coupling between their radiative region and the convective envelope. Regardless of the set of prescriptions, however, we cannot simultaneously reproduce surface angular velocity and the internal profile of the Sun or the evolution of lithium abundance. We confirm the idea that additional transport mechanisms must occur in solar-type stars until they reach the age of the Sun. Whether these processes are the same as those needed to explain recent asteroseismic data in more advanced evolutionary phases is still an open question.

A glimpse inside a magnetar

Hundreds of neutron stars have exhibited 'glitches' in their spin-down rates — an indication of ultra-dense superfluids in their interiors. Now one highly magnetized star has shown a surprising glitch in the 'wrong' direction. See Letter p.591 Hundreds of glitches observed in the emission of radio pulsars and magnetars — strongly magnetic neutron stars emitting X- and γ-rays — have involved a sudden spin-up, or increase in the surface angular velocity. Glitches are thought to arise when angular momentum is transferred between the solid outer crust and the superfluid component of the inner crust. This paper reports the first observation of an 'anti-glitch', a sudden spin-down event, in the magnetar 1E 2259+586. The event coincided with an X-ray flare and X-ray bursts similar to those seen during some previous magnetar spin-up glitches, suggesting an origin in the stellar interior rather than the magnetosphere. Current models of neutron star spin-down do not predict such behaviour.

Populations of rotating stars

B-type stars are known to rotate at various velocities, including very fast rotators near the critical velocity as the Be stars. In this paper, we provide stellar models covering the mass range between 1.7 to 15 Msun, which includes the typical mass of known Be stars, at Z = 0.014, 0.006, and 0.002 and for an extended range of initial velocities on the zero-age main sequence. We used the Geneva stellar-evolution code, including the effects of shellular rotation, with a numerical treatment that has been improved so the code can precisely track the variation in the angular momentum content of the star as it changes under the influence of radiative winds and/or mechanical mass loss. We discuss the impact of the initial rotation rate on the tracks in the Hertzsprung-Russell diagram, the main-sequence (MS) lifetimes, the evolution of the surface rotation and abundances, as well as on the ejected masses of various isotopes. Among the new results obtained from the present grid we find that 1) fast-rotating stars with initial masses around 1.7 Msun present at the beginning of the core hydrogen-burning phase quite small convective cores with respect to their slowly rotating counterparts. This fact may be interesting to keep in mind in the framework of the asteroseismic studies of such stars. 2) The contrast between the core and surface angular velocity is higher in slower rotating stars. The values presently obtained are in agreement with the very few values obtained for B-type stars from asteroseismology. 3) At Z = 0.002, the stars in the mass range of 1.7 to 3 Msun with a mean velocity on the MS of the order of 150 km/s show N/H enhancement superior to 0.2 dex at mid-MS, and superior to 0.4 dex at the end of the MS phase. At solar metallicity the corresponding values are below 0.2 dex at any time in the MS.

Rotational velocities of A-type stars

In previous works of this series, we have shown that late B- and early A-type stars have genuine bimodal distributions of rotational velocities and that late A-type stars lack slow rotators. The distributions of the surface angular velocity ratio \Omega/\Omega_crit (\Omega_crit is the critical angular velocity) have peculiar shapes according to spectral type groups, which can be caused by evolutionary properties. We aim to review the properties of these rotational velocity distributions in some detail as a function of stellar mass and age. We have gathered v sin i for a sample of 2014 B6- to F2-type stars. We have determined the masses and ages for these objects with stellar evolution models. The (Teff, log L/Lsun)-parameters were determined from the uvby-\beta photometry and the HIPPARCOS parallaxes. The velocity distributions show two regimes that depend on the stellar mass. Stars less massive than 2.5 Msun have a unimodal equatorial velocity distribution and show a monotonical acceleration with age on the main sequence (MS). Stars more massive have a bimodal equatorial velocity distribution. Contrarily to theoretical predictions, the equatorial velocities of stars from about 1.7 Msun to 3.2 Msun undergo a strong acceleration in the first third of the MS evolutionary phase, while in the last third of the MS they evolve roughly as if there were no angular momentum redistribution in the external stellar layers. The studied stars might start in the ZAMS not necessarily as rigid rotators, but with a total angular momentum lower than the critical one of rigid rotators. The stars seem to evolve as differential rotators all the way of their MS life span and the variation of the observed rotational velocities proceeds with characteristic time scales \delta(t)\sim 0.2 t_MS, where t_MS is the time spent by a star in the MS.

Differential rotation in rapidly rotating early-type stars

Since the external regions of the envelopes of rapidly rotating early-type stars are unstable to convection, a coupling may exist between the convection and the internal rotation. We explore what can be learned from spectroscopic and interferometric observations about the properties of the rotation law in the external layers of these objects. Using simple relations between the entropy and specific rotational quantities, some of which are found to be efficient at accounting for the solar differential rotation in the convective region, we derived analytical solutions that represent possible differential rotations in the envelope of early-type stars. A surface latitudinal differential rotation may not only be an external imprint of the inner rotation, but induces changes in the stellar geometry, the gravitational darkening, the aspect of spectral line profiles, and the emitted spectral energy distribution. By studying the equation of the surface of stars with non-conservative rotation laws, we conclude that objects undergo geometrical deformations that are a function of the latitudinal differential rotation able to be scrutinized both spectroscopically and by interferometry. The combination of Fourier analysis of spectral lines with model atmospheres provides independent estimates of the surface latitudinal differential rotation and the inclination angle. Models of stars at different evolutionary stages rotating with internal conservative rotation laws were calculated to show that the Roche approximation can be safely used to account for the gravitational potential. The surface temperature gradient in rapid rotators induce an acceleration to the surface angular velocity. A non-zero differential rotation parameter may indicate that the rotation is neither rigid nor shellular underneath the stellar surface.

Internal stellar rotation and orbital period modulation in close binary systems

The orbital period modulation, observed in close binary systems with late-type secondary stars, is considered in the framework of a general model that allows us to test the hypothesis proposed by Applegate. It relates the orbital period variation to the modulation of the gravitational quadrupole moment of their magnetically active secondary stars produced by angular momentum exchanges within their convective envelopes. By considering the case of RS CVn binary systems, it is found that the surface angular velocity variation of the secondary component required by Applegate's hypothesis is between 4 and 12 per cent, i.e. too large to be compatible with the observations and that the kinetic energy dissipated in its convection zone ranges from 4 to 43 times that supplied by the stellar luminosity along one cycle of the orbital period modulation. Similar results are obtained for other classes of close binary systems by applying a scaling relationship based on a simplified internal structure model. The effect of rapid rotation is briefly discussed finding that it is unlikely that the rotational quenching of the turbulent viscosity may solve the discrepancy. Therefore, the hypothesis proposed by Applegate is not adequate to explain the orbital period modulation of close binary systems with a late-type secondary.

Rotation and Properties of Be Stars

The actual characteristic average surface angular velocity ratio of the Be phenomenon may be higher than Ω/Ωc= 0.8 ± 0.1 derived fromvsinivalues not corrected from gravity darkening effects. Late Be Stars need not only higher values of Ω/Ωc, but also larger main sequence age ratios τ/τMSthan early Be Stars to display the Be phenomenon. Galactic field Be Stars appear at any MS phase, but their frequency is higher for τ/τMS≳ 0.5. Be Stars are probably neat differential rotators, i.e. they rotate with energy ratios kinetic/|gravitational| larger than withstood by critical rigid rotators. Initial formation conditions must favor the existence of fast rotators, while only a small fraction of them could be accounted for by mass transfer in close binary systems. Bn stars could perhaps represent a pre-Be phase.

Young Populous Clusters in the Magellanic Clouds

This work examines a sample of young populous clusters in the Magellanic Clouds. The population of these clusters offers insight into the course of stellar evolution for high-mass stars in the 8–20 M, mass range. The clusters of the present study provide a statistically significant sample with which to confront the predictions of stellar evolutionary models. We have paid particular attention to the issue of internal mixing, the consequence of which is extension of the convective core boundary over the classical Schwarzschild limit. We present a quantitative determination of the degree of internal mixing within the convective core overshoot paradigm, which parameterizes the degree of extension to the convective core. The convective core overshoot parameter, Lc, represents the degree of extension that is required to match our observations. The basis of our determination of Lc is Hubble Space Telescope WFPC2 photometry of the clusters NGC 330 (SMC) and NGC 1818, NGC 2004, and NGC 2100 (LMC). Our photometry in visual (F555W), ultraviolet (F160BW), and narrowband Ha (F656N) enabled us to construct the highly temperature sensitive F160BW F555W color and to distinguish the Be star population among the upper main-sequence (MS) population. Infrared photometry in the J and K bands was conducted to obtain accurate temperatures and luminosities for the evolved members. Comparison of the cluster population is made against stellar evolutionary models that incorporate a variable level of core overshoot. The luminosity function of MS stars and the number of evolved stars provide joint constraints on Lc. It is found that models with no convective core overshoot are strongly disfavored by the temperature and luminosity of the MS turnoff of the cluster sample. With a binary fraction of 30% the cluster populations indicate a . L p 0.62 0.22 c This study has established a photometric survey technique for Be stars, a technique that spectroscopic follow-up shows is highly complete. Our study has highlighted the large proportion of Be stars on the upper MS of young Magellanic Cloud clusters. Be stars are characterized by rapid rotation. Our study of the Be star fraction within the cluster and field environs of the LMC and SMC has provided evidence for an evolutionary enhancement of the Be fraction toward the end of the MS. We propose that this enhancement is the consequence of an increase in the ratio of the surface angular velocity to the critical angular velocity toward the end of the MS. In order to verify this scenario and to investigate the dependence of average rotation rates on metallicity, we present the rotational velocities for a sample of B0–B2 V–III stars drawn from the clusters and the field of the LMC. Compared with an equivalent sample of Galactic stars, the LMC cluster stars show faster projected rotational velocities. We discuss this result in the light of emergent evolutionary models that incorporate the effects of rotational mixing.

Perceiving surface slant from deformation of optic flow.

Perceived surface orientation and angular velocity were investigated for orthographic projections of 3-D rotating random-dot planes. It was found that (a) tilt was accurately perceived and (b) slant and angular velocity were systematically misperceived. It was hypothesized that these misperceptions are the product of a heuristic analysis based on the deformation, one of the differential invariants of the first-order optic flow. According to this heuristic, surface attitude and angular velocity are recovered by determining the magnitudes of these parameters that most likely produce the deformation of the velocity field, under the assumption that all slant and angular velocity magnitudes have the same a priori probability. The results of the present investigation support this hypothesis. Residual orientation anisotropies not accounted for by the proposed heuristic were also found.

Differential Rotation and Meridional Flow for Fast‐rotating Solar‐Type Stars

Observations indicate that normalized surface differential rotation decreases for fast-rotating stars, that is, | ΔΩ |/Ω ∝ Ω-0.3. An increase of | ΔΩ |/Ω is provided, however, by the current Reynolds stress theory of differential rotation in stellar convection zones, without the inclusion of meridional flow. We compute both the pole-equator difference of the surface angular velocity and the meridional drift for various Taylor numbers to demonstrate that the inclusion of meridional flow in the computations for fast rotation yields a systematic reduction of the resulting differential rotation. Our model's adiabatic and density-stratified convection zone, with stress-free surfaces and a thickness of 0.3 stellar radii, yields the relation | ΔΩ |/Ω ∝ Ω-(0.15 ... 0.30) for stars with faster rotation than the Sun, in agreement with previous observations. If the Coriolis number rather than the Taylor number is varied, we find a maximum differential rotation of 20%. For stars with fast rotation, exponents of up to n' 0.4 are found. All rotation laws exhibit superrotating equators.

MHD spin-down of a G-type star

Abstract We study MHD time evolution of initially rigidly rotating radiative zone of a G-type star subject to the effect of the magnetic field and of the deceleration of the surface angular velocity. We solve MHD equations of an unsteady axisymmetric Eddington-Vogt-Sweet (EVS)-type flow in the radiative zone, especially with respect to the angular velocity and the toroidal magnetic field, by using the Spectral method of solution. Three kinds of poloidal magnetic configurations (see Figure 1) are examined. We assume (i) that the toroidal magnetic field is induced by the coupling of the poloidal magnetic field with the non-uniform rotation caused by the spin-down process, (ii) that surface angular velocity conforms to the Skumanich law (Skumanich, 1972) of stellar angular velocity and (iii) that the time scale is the Kelvin-Helmholtz (KH)-time and not the EVS-time. Similar to Charbonneau and MacGregor (1992), we can reduce this MHD spin-down problem to the solution of the φ-components [in spherical coordina...

Internal dynamics and magnetism of the Sun

The present internal dynamics and magnetism of the Sun have been determined by the initial conditions in the pre-main sequence age, by the angular momentum loss and its redistribution in the interior, and the interaction of motion with magnetic field.The history of the Sun rotation is traced back by observing the present rotation of stars with the same mass as the Sun at earlier evolutionary stages. The present angular momentum of the Sun, as deduced from its internal rotational behavior derived from helioseismological data, appears to be a small percentage of the original one contained in similar mass stars (T Tauri and α Persei). It is not easy to reconcile the sharp decrease in the surface angular velocity, which follows the α Persei phase, with the subsequent soft decrease, taking place after Pleiades phase, unless some very effective mechanism transfers angular momentum from inner to outer regions, where is lost in the solar wind. Such a mechanism is probably magnetic in origin, since purely hydrodynamic instabilities fail to transfer angular momentum at a rate sufficient to determine the presently observed flat radial gradient of the internal angular velocity.

Evolution of the unsteady Eddington-Vogt-Sweet circulation in the solar radiative zone in response to the solar wind torque - I. A time-similar solution of the basic equations

A time-similar solution of the basic equations of the unsteady axisymmetric Eddington-Vogt-Sweet (EVS)-type flow in the non-viscous radiative interior subject to the solar wind torque is presented. The effect of the solar wind torque is represented by the time decrease of the angular velocity on the outer boundary which coincides with the interface between the outer convective zone and the radiative interior. A special case of a slow decrement, in which the decay time-scale of the surface angular velocity is equal to the EVS time is analysed. Numerical results based on the time-marching method of solution confirm the existence of the time-similar solution in this case.

Rotational evolution of solar-type stars. I - Main-sequence evolution

A simple, parameterized model for the redistribution of angular momentum within the interiors of solar-type stars is presented. By incorporating it with a description of angular momentum loss through the action of a magnetically coupled wind, tracing the rotational histories of low-mass dwarf stars for a variety of initial conditions and parameter specifications is accomplished. The results of calculations are discussed for the rotational evolution of a 1 solar mass star, from the time of its arrival on the zero-age main sequence to the age of the present-day sun. Best agreement is with observational constraints for (1) a surface magnetic field strength which is largely independent of surface angular velocity omega for rapid rotation, and approximately linearly dependent on omega for approximately solar values, and (2), a time scale for angular momentum transfer from the core to the convection zone which remains essentially constant throughout the evolution, with magnitude of a about 10 million yr. This value is approximately equal to the initial wind braking time. These results are discussed in the context of a qualitative description of angluar momentum redistribution by magnetic fields in the radiative interiors of solar-type stars. 48 refs.

Differential rotation and magnetic torques in the interior of the Sun

The frequencies of solar oscillations can be measured with extreme precision and 5-min oscillations reveal the internal structure of the Sun1–5. In particular, measurements of rotational splitting4 have provided the first reliable indications of the variation of angular velocity with radius6, while recent observations5 have yielded information on the variation with depth of latitudinal differential rotation. These results confirm theoretical predictions that the angular velocity decreases inwards in the convective zone7,8 but raise problems for dynamo models of the solar cycle. The suggestion that the core rotates with roughly twice the surface angular velocity has important implications both for the rotational history of the Sun and for other late-type stars, whose magnetic activity is closely correlated with rotation. Such a rapidly rotating core is hard to reconcile with the presence of any significant magnetic field pervading the entire radiative interior. We can only explain it by suggesting that the core contains a fossil field, unaffected by turbulence in the pre-main sequence Hayashi phase, that is decoupled from the rest of the star.

Numerical simulations of stellar convective dynamos. I. the model and method

A numerical model used to simulate global convection and magnetic field generation in stars is described. Nonlinear, three-dimensional, time-dependent solutions of the anelastic magnetohydrodynamic equations are presented for a stratified, rotating, spherical, fluid shell heated from below. The velocity, magnetic field, and thermodynamic perturbations are expanded in spherical harmonics to resolve their horizontal structure and in Chebyshev polynomials to resolve their radial structure. An explicit Adams-Bashforth time integration scheme is used with an implicit Crank-Nicolson treatment of the diffusion terms. Nonlinear terms are computed in physical space; and spatial derivatives are computed in spectral space. The resulting second-order differential equations are solved with a Chebyshev collocation method. Preliminary solutions for a Solar-like model are briefly discussed. Convective motions driven in the upper, superadiabatic part of the zone penetrate into the lower, subadiabatic part of the zone. Differential rotation, induced by the interaction of convection and rotation, is an equatorial acceleration at the surface as observed on the Sun; below the surface angular velocity decreases with depth. The meridional circulation and the equator-pole temperature excess are within Solar observational constraints; however, the giant-cell velocities at the surface are larger than observed. The large-scale magnetic field, induced by the differential rotation and helical motions, peaks in the subadiabatic region below the convection zone; and, near the top of the convection zone, it is concentrated over the downdrafts of giant cells. A systematic drift in latitude of the magnetic field or a field reversal has not yet been seen.