Average Rotation Rate Research Articles

Differential Rotation for Different-sized Sunspot Groups Early Observed by the OGAUC

Solar differential rotation is an important ingredient of the solar dynamo model, not only because the solar rotation profile is one of the key inputs in a solar dynamo model, but also because it imposes constraints for the solar dynamo model. In this study, we use the sunspot group catalog published by the Coimbra Astronomical Observatory for the period 1929–1941 to analyze solar rotation profiles of different-sized sunspot groups and the dependence of their annual average of the absolute latitude and annual average rotation rate on the solar cycle. The following main results are obtained: (1) smaller sunspot groups (with an area <100 millionths of the solar hemisphere (msh)) rotate faster than larger ones (with an area >500 msh); (2) different-sized sunspot groups drift toward the equator at different velocities of latitudinal drift, reflecting that they are rooted at different anchoring depths; (3) the rotation rate reaches a maximum during the minimum of the solar cycle, which seems to be independent of the size of sunspot groups. The possible mechanisms for the above results are discussed, and we infer that the differences may be due to the different anchoring depths at which flux tubes of different-sized sunspot groups are rooted, their different ages, and the different ways in which sunspot group coordinates are determined.

Non-LTE Monte Carlo radiative transfer – III. The thermal properties of tilted and warped Be star discs

ABSTRACT We use the three-dimensional Monte Carlo radiative transfer code hdust to model Be stars where the disc is tilted from the equatorial plane of the star. We compute 128 models across four spectral types, B0, B2, B5, and B8, tilting the disc by 0, 10○, 20○, and 40○, respectively, while varying disc density according to spectral type. We also compute every model for an average and high stellar rotation rate. We first discuss non-tilted disc temperatures and show its nonlinear dependence on stellar and disc parameters. We find that tilting the disc minimally affects the density-weighted average disc temperature, but tilting does create a temperature asymmetry in disc cross-sections, which is more pronounced for a faster rotation rate. We also investigate the effect tilting has on V-band magnitude, polarization, and the H$\rm \alpha$ line. Tilting the disc does affect these observables, but the changes are entirely dependent on the position of the observer relative to the direction of tilt. We find the observables that distinguish tilting from a change in density or geometry are the H$\rm \alpha$ line shapes, where it can transition between single-peaked and double-peaked, and the polarization position angle, whose value is dependent on the projected major elongation axis of the disc on the sky. We also present one early- and one late-type model with warped discs. We find their temperature structure varies a small amount from the uniformly tilted models, and the different observables correspond to different tilt angles, consistent with their expected volume of origin within the disc.

Rotational Characteristics of the Solar Transition Region Using SDO/AIA 304 Å Images

To date, the rotational characteristics of the solar transition region remain unclear. In this work, by applying the flux modulation method to the images derived from the Solar Dynamics Observatory/Atmospheric Imaging Assembly between 2011 and 2022 at 304 Å wavelength, we have studied the rotation of the solar transition region, and the results obtained are as follows. The solar transition region rotates differentially, while, from the perspective of the entire time interval, the rotation coefficients A and B are 14.39 (±0.08) and −1.61 (±0.15), respectively, and we find no prominent asymmetry in the average rotation rate of the northern and southern hemispheres. The solar transition region rotates fastest during the solar cycle maximum, and the average rotation rate follows the overall trend of solar activity. Both the equatorial rotation rate (represented by coefficient A) and the latitudinal gradient (represented by coefficient B) of the solar transition region are smaller than that of the solar chromosphere and the corona, indicating the solar transition region rotates more slowly and more rigidly than the other two layers, and we speculate that the solar chromosphere and corona seem to restrain the rotation of the solar transition region at the same time.

Rotation of a Long-Lived Coronal Hole in Solar Cycle 24

This paper discusses the results of a statistical study of the rotation characteristics of a long-livedgiant coronal hole. The study is based on observation data obtained by the Atmospheric Imaging Assemblyin the Fe XII 19.3 nm line aboard the Solar Dynamics Observatory spacecraft during the period from June2015 to March 2017; this was 24 Carrington revolutions. Four stages of the development of a coronal hole areconsidered separately: formation, two phases of a developed coronal hole, and the final phase. It has beenfound that the average rotation rate at a latitude of 40° is close to the standard speed at the beginning(12.75°/day) and in the first phase of maximum development (13°/day); it is lower in the second phase ofmaximum development (11.7°/day) and at the end of its existence (12.5°/day). A slight increase in velocity atthe final stage is associated with the restructuring of the coronal hole. According to modern theories, the rotationof the solar corona reflects the rotation of the subphotospheric layers. The higher layers of the coronareflect the rotation of the deeper layers of the Sun. The results obtained in our work show that the rotationrate of a giant coronal hole in the maximum phase of its development is greater than the rotation rate of thesolar disk. Perhaps this indicates that coronal holes can be associated with deep solar layers through the configurationof the global magnetic field and that the source of coronal hole formation is deeper than the sourceof the background field.

Rotational properties of solar EUV corona using SDO/AIA-19.3-nm observations

ABSTRACT In this article, we present the differential rotational profile of extreme ultraviolet (EUV) corona. For this purpose, we used observations with high resolution obtained from SDO/AIA at 19.3-nm wavelength from years 2011 to 2021. We found the higher rotation rate of the equatorial segment (14.8 deg d−1) which drops about 13.5 deg d−1 on both sides of the poles. The average rotation rate (i.e. from 2011 to 2021) of the equatorial region of EUV corona is found to be higher than that of the photosphere, chromosphere, transition region, and corona. Furthermore, the average rotational gradient (as a function of latitude) of the EUV corona is lower than that of the photosphere and transition region. Interestingly, we found a significant correlation of the hemispheric rotational asymmetry with the solar activity indicator (SSNs) and EUV emission. The cross-correlation analysis indicates that the hemispheric rotational asymmetry leads the solar activity indicator (SSN) and EUV emission by about 1.5 months.

On the rotation of melting ice disks

This investigation was inspired by the work of Dorbolo et al. (Phys Rev E 93(3):15, 2016), which was the first to study, at a laboratory scale, the phenomenon observed in the natural world of floating disks of ice rotating. They conclude that, in controlled conditions, ice disks are able to induce their own rotation. Whilst their work successfully exposes multiple aspects of the kinematics of such disks, and the buoyancy-driven flow generated beneath them as they melt, the mechanism by which rotation is triggered remains unsubstantiated. We therefore return in this work to the study of floating ice disks, focusing specifically on the importance of experimental technique in obtaining reliable measurements of disk behaviour. Our investigation reveals that the motion of ice disks placed on a nominally quiescent body of fresh water is unpredictable, with some disks remaining motionless, and others rotating clockwise or anticlockwise. For those in motion, the average rate of rotation observed was less than half of that recorded by Dorbolo et al., a discrepancy possibly explained by residual background motions in the nominally quiescent surrounding body of water. However, given our observation that non-melting disks of high-density polyethylene (HDPE) cooled to the same temperature as the ice (comparable HDPE and ice disks differing by only sim 4% in mass) consistently rotated at rates less than those made of ice, it is hypothesised that, within the confines of the freshwater environment, the motion of the turbulent meltwater plume that forms beneath an ice disk amplifies the effect of residual background motions. From our observations, it is concluded that residual motions are an underlying physical trigger for disk rotation.

Finite element simulations for slip flow and heat transfer phenomenon through a cosine-based wavy channel

The objective of current communication is to study heat transfer phenomenon for slip flow of viscous fluid due to wavy channel with general cosine function boundaries and fixed amplitude. The walls along with slip boundary constraints are kept at different temperatures. The flow is incompressible and Newtonian with AIS as a predicting material being used to check the fluids and thermal properties. The Navier–Stokes expressions with 2D flow regime subject to heat transfer due to convection are used to develop the simulations. A parametric theoretical assumptions analysis is performed for specified range of Reynolds number (100–1000) with upper and lower surface vibration periods of 1 to 6. The results are displayed with graphs, surface and contours plots and first, ever a novel work was done to represent the percentage change in velocity magnitude and local Nusselt number as surface plots and contours, respectively. The results are authentic due to mesh independent study and verification with the experimental correlation. A periodic flow at the lower wall was deducted. The maximum and average rotation rates attain a linear relationship with Reynolds number and their correlation was found. The simulations show the strict relationship of Reynolds number and the geometry of the channel with shear rate. The pressure gradient in [Formula: see text]-direction was found minimum in trough and maximum in the crest region. It has been observed that the boundary friction is reduced due to periodic variation of walls surface.

Inner Core Rotation Captured by Earthquake Doublets and Twin Stations

AbstractThe Earth's solid inner core (IC) is generally believed to rotate relative to the mantle, but the proposal remains controversial. Here we use seven waveform doublets in the South Sandwich Islands region with time lapses of 5.8–17.0 years that are recorded by two close stations in Kyrgyzstan with virtually the same epicentral distance. The fortuitous geometry allows precise measurements of the IC temporal changes and the underlying local structure at the same time. The remarkable observations in waveforms and spatial‐temporal measurements show unequivocally that the IC must have shifted (rotated) eastward in 1991–2010 and help determine accurately the average rotation rate as 0.127 ± 0.006°/yr at 95% confidence level during the time span.

In situ EBSD/DIC-based investigation of deformation and fracture mechanism in FCC- and L12-structured FeCoNiV high-entropy alloys

This study investigated the plastic deformation behavior of a polycrystalline L12-structured FeCoNiV high-entropy alloy (HEA) using in situ electron backscatter diffraction (EBSD) and digital image correlation (DIC) methods. The different deformation mechanisms in two HEAs, which affected their mechanical performance, were explored using a face-centered cubic (FCC)-structured sample for comparison. Using slip traces and lattice rotation path analysis, {111}<110> slip systems were found to be activated in the L12-structured FeCoNiV HEA. In addition, a lower average lattice rotation rate was estimated for this sample compared to that of the FCC specimen; this macroscopically verified the existence of additional obstacles to dislocation slip caused by the ordered structure during plastic deformation, and was found to contribute to the high strength of the L12-structured FeCoNiV HEA. Furthermore, these additional obstacles blocked the formation of deformed substructures in the L12-structured sample and aggravated the intergranular incompatibility, which enabled crack initiation at the grain boundaries. These findings are important for understanding the deformation behavior and fracture mechanism in L12-structured HEAs and for designing new high-performance ordered HEAs.

Effect of Differential Rotation on the Magnetic Braking of Low-mass and Solar-like Stars: A Proof-of-concept Study

Abstract On the main sequence, low-mass and solar-like stars are observed to spin down over time, and magnetized stellar winds are thought to be predominantly responsible for this significant angular momentum loss. Previous studies have demonstrated that the wind torque can be predicted via formulations dependent on stellar properties, such as magnetic field strength and geometry, stellar radius and mass, wind mass-loss rate, and stellar rotation rate. Although these stars are observed to experience surface differential rotation, torque formulations so far have assumed solid-body rotation. Surface differential rotation is expected to affect the rotation of the wind and thus the angular momentum loss. To investigate how differential rotation affects the torque, we use the PLUTO code to perform 2.5D magnetohydrodynamic, axisymmetric simulations of stellar winds, using a colatitude-dependent surface differential rotation profile that is solar-like (i.e., rotation is slower at the poles than the equator). We demonstrate that the torque is determined by the average rotation rate in the wind so that the net torque is less than that predicted by assuming solid-body rotation at the equatorial rate. The magnitude of the effect is essentially proportional to the magnitude of the surface differential rotation, for example, resulting in a torque for the Sun that is ∼20% smaller than predicted by the solid-body assumption. We derive and fit a semianalytic formulation that predicts the torque as a function of the equatorial spin rate, magnitude of differential rotation, and wind magnetization (depending on the dipolar magnetic field strength and mass-loss rate, combined).

Abel inversion of soft x-ray fluctuations associated with fast particle-driven fishbone instabilities in MAST plasmas

A set of soft x-ray cameras provided measurements of high frequency instabilities as well as steady-state emission in the Mega Amp Spherical Tokamak (MAST). It is shown that Abel inversion can be readily applied to fluctuating soft x-ray emission from the MAST midplane associated with fast particle-driven ‘fishbone’ instabilities, characterised by toroidal mode number n = 1. Each fishbone burst had an early phase in which high amplitude fluctuating soft x-ray signals from the plasma core were close to being in phase with each other, and there was a region close to the outboard plasma edge in which the fluctuations were relatively weak and in antiphase with those in the core. The major radius of the ‘phase axis’ at which the mode amplitude changed sign R p was initially outboard of the tokamak magnetic axis at R 0, but moved inboard during the burst, eventually becoming close to R 0, at which time the oscillations were of similar amplitude inboard and outboard of R p . The fishbone radial structure early in the burst can be understood in part by recognising that the mode is supported by energetic ions with a high average toroidal rotation rate: in a co-rotating frame, the effective magnetic axis is shifted outboard by a distance that is comparable to the difference between the major radii of the phase axis early in the burst and the laboratory frame magnetic axis. It is conjectured that the transition to a mode with R p ≃ R 0 occurred because most of the energetic ions were expelled from the plasma core region where the mode amplitude peaked, so that the instability could no longer be characterised as an energetic particle mode. Abel inversion of fishbone soft x-ray emission thus provides useful insights into the nature of energetic particle modes in tokamak plasmas and their relationship with MHD modes.

Strain distribution and lattice rotations during in-situ tension of aluminum with a transmodal grain structure

Samples of aluminum were prepared using spark plasma sintering from a mixture of coarse (average particle size of 6 μm) and fine (average particle size of 1 μm) powders to achieve a heterogeneous transmodal grain size distribution covering a range of grain sizes from ≈1 to 10 μm. By careful choice of surface markers both electron back-scatter diffraction (EBSD) data, to track crystal rotations, and digital image correlation (DIC) data, to track local plastic deformation, were collected from the same region during in-situ tensile deformation up to a strain of εt = 0.126. A heterogeneous pattern of crystal rotation is observed for all grain sizes, although in some smaller grains (defined as those <4 μm diameter) no clear grain sub-division was identified. Plastic strain was more concentrated in the larger grains, but the average rotation rate of the smaller grains was found to be higher than that of larger grains, showing also a much wider spread in rotation rate. Based on the change in average orientation, a clear orientation dependence in the tensile axis rotation direction was observed for many larger grains, in agreement with previously reported data for aluminum with average grain size of 75 μm, whereas the smaller grains showed a more complex rotation behavior, with more of these grains showing unexpected tensile axis rotations. The combination of both EBSD and DIC during in-situ experiments provides a rich data set for analysis of plastic deformation in samples with a heterogeneous microstructure.

Differential rotation of the solar transition region from STEREO/EUVI 30.4-nm images

ABSTRACT The solar photosphere, chromosphere, and corona are known to rotate differentially as a function of latitude. To date, it is unclear whether the solar transition region also rotates differentially. In this work, we investigate the differential rotational profile of the solar transition region as a function of latitude, using solar full-disc (SFD) images at 30.4-nm wavelength recorded by the Extreme Ultraviolet Imager (EUVI) on board the Solar Terrestrial Relations Observatory(STEREO) space mission for the period from 2008–2018 (Solar Cycle 24). Our investigations show that the solar transition region rotates differentially. The sidereal rotation rate obtained in the ${\pm}5{^\circ }$ equatorial band is quite high (∼14.7 deg day−1), dropping to ∼13.6 deg day−1 towards both polar regions. We also find that rotational differentiality is low during the period of high solar activity (the rotation rate varies from 14.86–14.27 deg day−1), while it increases during the ascending and descending phases of the 24th solar cycle (the rotation rate varies from 14.56 to ∼13.56 deg day−1 in 2008 and 14.6–13.1 deg day−1 in 2018). The average sidereal rotation rate (over SFD) follows the trend of solar activity (maximum ∼14.97 deg day−1 during the peak phase of solar activity, slowly decreasing to a minimum ∼13.9 deg day−1 during ascending and descending phases of the 24th solar cycle). We also observe that the solar transition region rotates less differentially than the corona.

Dynamo action between two rotating discs

Dynamo action is considered in the region between two differentially rotating infinite discs. The boundaries may be insulating, perfectly conducting or ferromagnetic. In the absence of a magnetic field, various well-known self-similar flows arise, generalising that of von Kármán. Magnetic field instabilities with the same similarity structure are sought. The kinematic eigenvalue problem is found to have growing modes for . The growth rate is real for the perfectly conducting and ferromagnetic cases, but may be complex for insulating boundaries. As it is shown that the dynamo can be fast or slow, depending on the flow structure. In the slow case, the growth rate is governed by a magnetic boundary layer on one of the discs. The growing field saturates in a solution to the nonlinear dynamo problem. The bifurcation is found to be subcritical and nonlinear dynamos are found for . Finally, the flux of magnetic energy to large r is examined, to determine which solutions might generalise to dynamos between finite discs. It is found that the fast dynamos tend to have inward energy flux, and so are unlikely to be realised in practice. Slow dynamos with outward flux are found. It is suggested that the average rotation rate should be non-zero in practice.

Optical rotation detection method based on acousto-optic modulation in an atomic spin co-magnetometer

A new concept for probe light intensity stability control and high-frequency modulation based on an acousto-optic modulation in a K-Rb-21Ne co-magnetometer is reported. The structure and optical path are ingeniously designed to avoid the interference of zero-order diffraction light. The average rotation rate sensitivity of is achieved under the light intensity closed-loop control condition and the bias instability calculated by the Allan deviation is improved from 0.13 deg h−1 to 0.06 deg h−1 comparing with open-loop scheme. A square wave modulation with a wide range of frequencies is applied to the probe light intensity and the appropriate modulation frequency for the co-magnetometer is tested to be 10 kHz to 300 kHz and megahertz scale. Finally, the closed-loop control of light intensity has been combined with the high-frequency modulation, which could suppress the low-frequency noise contained in the probe system and improve the long-term stability of the angular velocity measurement.

The rotation rate of solar active and ephemeral regions – I. Dependence on morphology and peak magnetic flux

ABSTRACT Using magnetic field maps acquired by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, we measured rotation rates of 864 active and 322 ephemeral regions observed between 2010 and 2016. We found smaller magnetic tracers to show a tendency to rotate faster as compared to larger ones. Thus, ephemeral regions exhibit on average the fastest rotation rate. We further divided active regions into three classes. Class A comprised magnetic bipoles obeying Hale’s polarity law, Joy’s law, and exhibiting more coherent leading polarity in comparison with the following one. The second class B included active regions violating at least one of the aforementioned empirical laws. The third class U comprised unipolar active regions. We found no significant difference between the rotation rates of active regions of classes A and B. In contrast, unipolar active regions exhibited on average lower rotation rate and narrower distribution of the rotation rate differences. Assuming the rotation rate to indicate the anchoring depth of the magnetic structure within the convection zone, we supposed that active regions of classes A and B might be anchored throughout the entire convective envelope while unipolar active regions a rooted within a thin layer located either near the base of the convection zone or at a shallow near-surface depth.

3D DEM analysis of soil excavation test on lunar regolith simulant

To validate the application of three-dimensional (3D) discrete element method (DEM) on modeling the excavation process, a discrete analogue of lunar regolith simulant is excavated under terrestrial conditions using DEM and the results were compared with the previous experimental data using TJ-1 lunar soil simulant. The soil failure mechanism is first described at different scales, with detailed DEM studies of excavation force, earth pressure, soil heap, void ratio changes, APR (average micro-pure rotation rate) field, particle displacements and velocities. Following these, the effects of cutting depth, cutting angle, blade width on the excavation force and size of the affected zone are analyzed and compared with the experimental data. The results illustrate that a “real-time” affected zone can be identified from the APR field and particle velocities which fluctuate significantly in a similar tendency to the excavation force at the post-peak stage. In contract, a “cumulative” affected zone can be identified from the void ratio and particle displacements, which remain increasing gradually at the post-peak stage and invariable when the excavation displacement is large enough to allow a stable soil heap to form. In addition, the simulation results can capture the effects of cutting depth, cutting angle and blade width, which reveals the validity of the numerical modeling approach and thus further studies on the effects of lunar environments on soil excavation can be carried out using DEM.

Depletion forces in athermally sheared mixtures of frictionless disks and rods in two dimensions.

We carry out numerical simulations to study the behavior of an athermal mixture of frictionless circular disks and elongated rods in two dimensions, under three different types of global linear deformation at a finite strain rate: (i) simple shearing, (ii) pure shearing, and (iii) isotropic compression. We find that the fluctuations induced by such deformations lead to depletion forces that cause rods to group in parallel oriented clusters for the cases of simple and pure shear, but not for isotropic compression. For simple shearing, we find that as the fraction of rods increases, this clustering increases, leading to an increase in the average rate of rotation of the rods, and a decrease in the magnitude of their nematic ordering.

Seismic evidence for near solid-body rotation in two Kepler subgiants and implications for angular momentum transport

Context. Asteroseismic measurements of the internal rotation of subgiants and red giants all show the need for invoking a more efficient transport of angular momentum than theoretically predicted. Constraints on the core rotation rate are available starting from the base of the red giant branch (RGB) and we are still lacking information on the internal rotation of less evolved subgiants. Aims. We identify two young Kepler subgiants, KIC 8524425 and KIC 5955122, whose mixed modes are clearly split by rotation. We aim to probe their internal rotation profile and assess the efficiency of the angular momentum transport during this phase of the evolution. Methods. Using the full Kepler data set, we extracted the mode frequencies and rotational splittings for the two stars using a Bayesian approach. We then performed a detailed seismic modeling of both targets and used the rotational kernels to invert their internal rotation profiles using the MOLA inversion method. We thus obtained estimates of the average rotation rates in the g-mode cavity (⟨Ω⟩g) and in the p-mode cavity (⟨Ω⟩p). Results. We found that both stars are rotating nearly as solid bodies, with core-envelope contrasts of ⟨Ω⟩g/⟨Ω⟩p = 0.68 ± 0.47 for KIC 8524425 and ⟨Ω⟩g/⟨Ω⟩p = 0.72 ± 0.37 for KIC 5955122. This result shows that the internal transport of angular momentum has to occur faster than the timescale at which differential rotation is forced in these stars (between 300 Myr and 600 Myr). By modeling the additional transport of angular momentum as a diffusive process with a constant viscosity νadd, we found that values of νadd &gt; 5 × 104 cm2 s−1 are required to account for the internal rotation of KIC 8524425, and νadd &gt; 1.5 × 105 cm2 s−1 for KIC 5955122. These values are lower than or comparable to the efficiency of the core-envelope coupling during the main sequence, as given by the surface rotation of stars in open clusters. On the other hand, they are higher than the viscosity needed to reproduce the rotation of subgiants near the base of the RGB. Conclusions. Our results yield further evidence that the efficiency of the internal redistribution of angular momentum decreases during the subgiant phase. We thus bring new constraints that will need to be accounted for by mechanisms that are proposed as candidates for angular momentum transport in subgiants and red giants.

The rotation problem

Any reasonable form of quantum gravity can explain (by phase interference) why on a large scale, inertial frames seem not to rotate relative to the average matter distribution in the universe without the need for absolute space, finely tuned initial conditions, or without giving up independent degrees of freedom for the gravitational field. A simple saddlepoint approximation to a path-integral calculation for a perfect fluid cosmology shows that only cosmologies with an average present relative rotation rate smaller than about $T^*H^2 \approx 10^{-71}$ radians per year could contribute significantly to a measurement of relative rotation rate in our universe, where $T^*\approx 10^{-51}$ years is the Planck time and $H \approx 10^{-10}$ yr$^{-1}$ is the present value of the Hubble parameter. A more detailed calculation (taking into account that with vorticity, flow lines are not normal to surfaces of constant global time, and approximating the action to second order in the mean square vorticity) shows that the saddlepoint at zero vorticity is isolated and that only cosmologies with an average present relative rotation rate smaller than about $T^*H^2 a_1^{1/2} \approx 10^{-73}$ radians per year could contribute significantly to a measurement of relative rotation rate in our universe, where $a_1 \approx 10^{-4}$ is the value of the cosmological scale factor at the time when matter became more significant than radiation in the cosmological expansion. This is consistent with measurements indicating a present relative rotation rate less than about $10^{-20}$ radians per year. The observed lack of relative rotation may be evidence for the existence of quantum gravity.