Solar Differential Rotation Research Articles

Comparison of solar horizontal velocity fields from SDO/HMI and Hinode data

The measurement of the Sun's surface motions with a high spatial and temporal resolution is still a challenge. We wish to validate horizontal velocity measurements all over the visible disk of the Sun from Solar Dynamics Observatory/ Helioseismic and Magnetic Imager (SDO/HMI) data. Horizontal velocity fields are measured by following the proper motions of solar granules using a newly developed version of the Coherent Structure Tracking (CST) code. The comparison of the surface flows measured at high spatial resolution (Hinode, 0.1 arcsec) and low resolution (SDO/HMI, 0.5 arcsec) allows us to determine corrections to be applied to the horizontal velocity measured from HMI white light data. We derive horizontal velocity maps with spatial and temporal resolutions of respectively 2.5 Mm and 30 min. From the two components of the horizontal velocity Vx and Vy measured in the sky plane and the simultaneous line of sight component from SDO/HMI dopplergrams v_D, we derive the spherical velocity components (Vr, Vtheta, Vphi). The azimuthal component Vphi gives the solar differential rotation with a high precision (+-0.037km/s) from a temporal sequence of only three hours. By following the proper motions of the solar granules, we can revisit the dynamics of the solar surface at high spatial and temporal resolutions from hours to months and years with the SDO data.

Stellar differential rotation in theory and observation

AbstractStellar differential rotation is intimately related to the stellar magnetic dynamo and, thus, to stellar activity. In recent years, significant progress in the measurement of differential rotation on the basis of Doppler imaging techniques and the availability of space‐based long‐term photometry has been achieved. Similarly, simulations incorporate ever more details of the complexity of convective zones. While some aspects of solar and stellar differential rotation can be explained now, several important questions remain open or controversial. In this splinter session, we discussed the latest observational and theoretical progress in the field of differential rotation. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

太阳较差自转130年(1855~1985)的观测和理论研究史的回顾

本文对太阳较差自转从1855年到1985年130年的观测和理论研究史做了回顾。回顾了天文工作者对太阳较差自转的观测和理论研究结果，其中包括纬向较差自转的表面观测和理论研究，也包括了径向较差自转(内部较差自转)以及产生较差自转的机制，稳定和演化的研究结果。在最后一节中作者还列出了在不同年代一些作者从观测和理论研究给出的太阳的纬向和径向较差自转定律的形式。The history of observational and theoretical research of solar differential rotation is investigated from 1855 to 1985 year for 130 years. The results given by a lot of authors on this topic are reviewed including solar latitudinal and radial differential rotation and its mechanism, evolution and stability. In the last section, the author listed the formation for the law of solar latitudinal and radial differential rotation given by some astronomical workers from observational and theoretical research in the different era.

SIGNATURE OF DIFFERENTIAL ROTATION IN SUN-AS-A-STAR Ca II K MEASUREMENTS

The characterization of solar surface differential rotation (SDR) from disk-integrated chromospheric measurements has important implications for the study of differential rotation and dynamo processes in other stars. Some chromospheric lines, such as Ca II K, are very sensitive to the presence of activity on the disk and are an ideal choice for investigating SDR in Sun-as-a star observations. Past studies indicate that when the activity is low, the determination of Sun's differential rotation from integrated-sunlight measurements becomes uncertain. However, our study shows that using the proper technique, SDR can be detected from these type of measurements even during periods of extended solar minima. This paper describes results from the analysis of the temporal variations of Ca II K line profiles observed by the Integrated Sunlight Spectrometer (ISS) during the declining phase of Cycle 23 and the rising phase of Cycle 24, and discusses the signature of SDR in the power spectra computed from time series of parameters derived from these profiles. The described methodology is quite general, and could be applied to photometric time series of other Main-Sequence stars for detecting differential rotation.

Investigation of the Differential Rotation by Hα Filaments and Long-Lived Magnetic Features for Solar Activity Cycles 20 and 21

For solar activity Cycles 20 and 21 (1966 – 1985) the solar differential rotation has been investigated using Hα filaments and relatively small-scale long-lived magnetic features with negative and positive polarities. We used annual averaged angular velocities of quiescent Hα filaments from Hα photoheliograms of the Abastumani Astrophysical Observatory film collection and selected long-lived magnetic features from the McIntosh atlas (McIntosh, Willock, and Thompson, Atlas of Stackplots, NGDC, 1991). We have determined coefficients of Faye’s formulas for Hα filaments as well as for long-lived magnetic features and have found that for Solar Cycles 20 and 21 the Hα filaments have lower rotation rates and rotated more differentially than the long-lived magnetic features.

Solar differential rotation: hints to reproduce a near-surface shear layer in global simulations

AbstractConvective turbulent motions in the solar interior, as well as the mean flows resulting from them, determine the evolution of the solar magnetic field. With the aim to get a better understanding of these flows we study anelastic rotating convection in a spherical shell whose stratification resembles that of the solar interior. This study is done through numerical simulations performed with the EULAG code. Due to the numerical formulation, these simulations are known as implicit large eddy simulations (ILES), since they intrinsically capture the contribution of, non-resolved, small scales at the same time maximizing the effective Reynolds number. We reproduce some previous results and find a transition between buoyancy and rotation dominated regimes which results in anti-solar or solar like rotation patterns. Even thought the rotation profiles are dominated by Taylor-Proudman columnar rotation, we are able to reproduce the tachocline and a low latitude near-surface shear layer. We find that simulations results depend on the grid resolution as a consequence of a different sub-grid scale contribution.

Solar Convection and Mean Flows

AbstractWe briefly review our current understanding of how the solar differential rotation and meridional circulation are maintained, which has important implications for understanding cyclic magnetic activity in the Sun and stars.

The solar differential rotation in the 18th century

The sunspot drawings of Johann Staudacher of 1749--1799 were used to determine the solar differential rotation in that period. These drawings of the full disk lack any indication of their orientation. We used a Bayesian estimator to obtain the position angles of the drawings, the corresponding heliographic spot positions, a time offset between the drawings and the differential rotation parameter \delta\Omega, assuming the equatorial rotation period is the same as today. The drawings are grouped in pairs, and the resulting marginal distributions for \delta\Omega were multiplied. We obtain \delta\Omega=-0.048 \pm 0.025 d^-1 (-2.75^o/d) for the entire period. There is no significant difference to the value of the present Sun. We find an (insignificant) indication for a change of \delta\Omega throughout the observing period from strong differential rotation, \delta\Omega\approx -0.07 d^-1, to weaker differential rotation, \delta\Omega\approx-0.04 d^-1.

Hydrodynamic model of spatial and temporal variations of poloidal and Toroidal components of three-dimensional solar flows

Numerical simulation results of the global solar flows are presented. The conclusion on the common hydrodynamic nature of the torsional oscillations and spatial-temporal variations of the poloidal flow was made. Both processes were shown to be toroidal and poloidal components of a single hydrodynamic oscillatory flow that is asymmetric about the solar equator. The basis for these processes is the physical mechanism of the loss of stability of the solar differential rotation.

An Exploration of Non-kinematic Effects in Flux Transport Dynamos

Recent global magnetohydrodynamical simulations of solar convection producing a large-scale magnetic field undergoing regular, solar-like polarity reversals also present related cyclic modulations of large-scale flows developing in the convecting layers. Examination of these simulations reveal that the meridional flow, a crucial element in flux transport dynamos, is driven at least in part by the Lorentz force associated with the cycling large-scale magnetic field. This suggests that the backreaction of the field onto the flow may have a pronounced influence on the long-term evolution of the dynamo. We explore some of the associated dynamics using a low-order dynamo model that includes this Lorentz force feedback. We identify several characteristic solutions which include single period cycles, period doubling and chaos. To emulate the role of turbulence in the backreaction process we subject the model to stochastic fluctuations in the parameter that controls the Lorentz force amplitude. We find that short term fluctuations produce long-term modulations of the solar cycle and, in some cases, grand minima episodes where the amplitude of the magnetic field decays to near zero. The chain of events that triggers these quiescent phases is identified. A subsequent analysis of the energy transfer between large-scale fields and flows in the global magnetohydrodynamical simulation of solar convection shows that the magnetic field extracts energy from the solar differential rotation and deposits part of that energy into the meridional flow. The potential consequences of this marked departure from the kinematic regime are discussed in the context of current solar cycle modeling efforts based on flux transport dynamos.

HIGH-LATITUDE SOLAR TORSIONAL OSCILLATIONS DURING PHASES OF CHANGING MAGNETIC CYCLE AMPLITUDE

Torsional oscillations are variations of the solar differential rotation that are strongly linked to the magnetic cycle of the Sun. Helioseismic inversions have revealed significant differences in the high-latitude branch of torsional oscillations between cycle 23 and cycle 24. Here we employ a non-kinematic flux-transport dynamo model that has been used previously to study torsional oscillations and simulate the response of the high-latitude branch to a change in the amplitude of the magnetic cycle. It is found that a reduction of the cycle amplitude leads to an increase in the amplitude of differential rotation that is mostly visible as a drop in the high-latitude rotation rate. Depending on the amplitude of this adjustment the high-latitude torsional oscillation signal can become temporarily hidden due to the unknown changing mean rotation rate that is required to properly define the torsional oscillation signal.

Quasi full-disk maps of solar horizontal velocities using SDO/HMI data

For the first time, the motion of granules (solar plasma on the surface on scales larger than 2.5 Mm) has been followed over the entire visible surface of the Sun, using SDO/HMI white-light data. Horizontal velocity fields are derived from image correlation tracking using a new version of the coherent structure tracking algorithm.The spatial and temporal resolutions of the horizontal velocity map are 2.5 Mm and 30 min respectively . From this reconstruction, using the multi-resolution analysis, one can obtain to the velocity field at different scales with its derivatives such as the horizontal divergence or the vertical component of the vorticity. The intrinsic error on the velocity is ~0.25 km/s for a time sequence of 30 minutes and a mesh size of 2.5 Mm.This is acceptable compared to the granule velocities, which range between 0.3 km/s and 1.8 km/s. A high correlation between velocities computed from Hinode and SDO/HMI has been found (85%). From the data we derive the power spectrum of the supergranulation horizontal velocity field, the solar differential rotation, and the meridional velocity.

Statistical study of the north–south asymmetry of the solar differential rotation based on various solar structures during 1966–1985

The time variation and latitude dependence of the solar rotation are found using observational data on Hα filaments and compact magnetic features with different polarities during solar activity cycles 20 and 21 (1966–1985). Statistical analysis of the observational data shows that there is a north–south asymmetry in the rotation, both for the Hα filaments and for compact magnetic features (structures) with negative and positive polarities. The N-S asymmetry in the differential rotation of the Hα filaments and the compact magnetic features with both polarities shows up quite distinctly in solar activity cycles 20 and 21, but the asymmetry for the compact magnetic features with positive polarity is comparatively lower in cycle 21. The confidence level is lower the compact magnetic features with positive polarity than for the compact magnetic features with negative polarity.

Investigating stellar surface rotation using observations of starspots

AbstractRapid rotation enhances the dynamo operating in stars, and thus also introduces significantly stronger magnetic activity than is seen in slower rotators. Many young cool stars still have the rapid, primordial rotation rates induced by the interstellar molecular cloud from which they were formed. Also older stars in close binary systems are often rapid rotators. These types of stars can show strong magnetic activity and large starspots. In the case of large starspots which cause observable changes in the brightness of the star, and even in the shapes of the spectral line profiles, one can get information on the rotation of the star. At times even information on the spot rotation at different stellar latitudes can be obtained, similarly to the solar surface differential rotation measurements using magnetic features as tracers. Here, I will review investigations of stellar rotation based on starspots. I will discuss what we can obtain from ground-based photometry and how that improves with the uninterrupted, high precision, observations from space. The emphasis will be on how starspots, and even stellar surface differential rotation, can be studied using high resolution spectra.

Effects of differential rotation and meridional circulation in solar oscillations of high degree l

Helioseismic measurements at high degree l are sensitive to mode couplings induced by large-scale flows, with the largest contribution coming from the solar differential rotation. The coupling becomes strong at high degree l, when frequency spacings between interacting modes become small, calling for a more accurate theoretical prediction of the mode-coupling effects in helioseismic data analysis. In this paper, the currently available description based on the quasi-degenerate perturbation theory is developed to a higher order, and extended to include the possible contributing effects of solar meridional circulation. A semi-analytic asymptotic description is developed for effects of the centrifugal forces on the oscillation frequencies of high degree l. Numerical estimates of the corresponding effects in the observational data are discussed.

A relationship between the solar rotation and activity in the period 1998–2006 analysed by tracing small bright coronal structures in SOHO-EIT images

Aims. The study aims to find a relationship between the rotation of the small bright coronal structures (SBCS) described by the solar rotation parameters and indices of solar activity on monthly and yearly temporal scales. Methods. We analyse precise measurements of the solar differential rotation determined by tracing SBCS in SOHO-EIT images and compare the derived solar rotation parameters with the status of solar activity in the period 1998−2006. Full-disc solar images obtained with the Extreme ultraviolet Imaging Telescope (EIT) on board the Solar and Heliospheric Observatory (SOHO) were used to analyse solar differential rotation determined by tracing SBCS. An automatic method to identify and track the SBCS in EIT full-disc images with a six hour cadence is applied. We performed a statistical analysis of the monthly and yearly values of solar sidereal rotation velocity parameters A and B (corresponding to the equatorial rotation velocity and the gradient of the solar differential rotation, respectively) as a function of various solar activity indices. Results. The dependence of the solar rotation on the phase of the solar cycle was found. It is clearly visible for the solar rotation parameter A, whilst the results are not conclusive for parameter B. The relationship between the solar rotation and activity, expressed by the monthly relative sunspot number, the smoothed monthly relative sunspot number, the yearly relative sunspot number, and the interdiurnal variability (IDV) index was investigated. The statistically significant correlation was found for the solar rotation parameter A, whilst a very low and insignificant correlation was obtained for the rotation parameter B. Conclusions. During the maximum of the solar cycle 23 and just after it, the equatorial solar rotation velocity was lower than in other phases of the cycle, when there was less activity. This is consistent with other observational findings, obtained by different tracers and methods.

Quasi 9 and 30–40 days periodicities in the solar differential rotation

Using the daily Mt. Wilson Doppler velocity data during 1986–1994 (solar cycle 22), we studied the short-term variations of the order of a few days to a month timescales in the solar differential rotation. We represent the differential rotation in the form: ω ( λ ) = A ¯ + B ¯ ( 5 sin 2 λ - 1 ) + C ¯ ( 21 sin 4 λ - 14 sin 2 λ + 1 ) , using a set of Gegenbauer polynomials, where ω( λ) is the angular velocity at latitude λ. The coefficients A ¯ , B ¯ , and C ¯ are free of crosstalk. We found that ≈9-day periodicity is statistically highly significant in the variations of C ¯ at the maximum of solar cycle 22. A similar periodicity is found in the variations of B ¯ during the descending phase of the cycle 22 with significant on ⩾99.9% confidence level. At this cycle maximum, a 30–40 day periodicity is found to be dominant among the variations in B ¯ , and this periodicity is found in A ¯ during almost throughout the period 1986–1994. The ≈9-day periodicity in the variation of the differential rotation approximately matches with the known quasi 10-day periodicity in the total solar irradiance (TSI) variability. Hence, we speculate that there exists a relationship between the differential rotation and TSI variability. We suggest that the 9–10 day periodicities of the differential rotation and TSI have a relationship with the production and the emergence rates of the large-scale solar magnetic flux.

Iodine-Cell Spectroscopy Applied to Investigating the Solar Differential Rotation

In an attempt to examine whether the spectroscopic Doppler method with an iodine cell (which is known to be successful for precise radial-velocity determinations in stellar astronomy) could be effective for investigating the solar differential rotation, we carried out intensive observations to collect spectra at a large number of points on the solar disk by using the Domeless Solar Telescope along with the horizontal spectrograph of the Hida Observatory. Having converted the resulting line-of-sight velocity component into the angular rotational rate (ω), we derived a differential rotation law, \(\omega_{\mathrm{sidereal}}\; (\mathrm{deg}\,\mathrm{day}^{-1}) =14.03 (\pm0.06)-1.84 (\pm0.57) \sin^{2}\psi-1.92 (\pm0.85) \sin^{4}\psi\) (ψ: heliographic latitude), which is reasonably consistent with other spectroscopic determinations published so far. Our analysis also revealed several practical points to note for successful application (e.g., exclusion of those data that are not well distant from the meridian; mutual data subtraction/averaging for symmetric counterparts at the eastern and western hemisphere). Considering its easiness and cheapness, this iodine-cell-featured spectroscopic method may be regarded as an effective and practical tool for studying the differential rotation of the Sun.

The rotation rate and its evolution derived from improved mode fitting and inversion methodology

We present inferences of the internal solar rotation rate and its evolution during solar cycle 23. A full solar cycle of MDI observations have been analyzed using an improved fitting methodology and using time series of various lengths, up to a single 4,608 day long epoch (64 times 72 days or 12.6 yr). We used time series of spherical harmonic coefficients computed by the MDI group, including those resulting from using their improved spatial decomposition. This decomposition includes our best estimate of the image plate scale and of the MDI instrumental image distortion. The leakage matrix used in the fitting includes the effect of the distortion of the eigenfunctions by the solar differential rotation, while the undistorted leakage matrix was itself carefully reviewed and independently recomputed. Rotation inversions were carried out for all available mode sets, fitted for that epoch, including the MDI and GONG "pipe-line" values. The improved inversion method uses an iterative methodology based on a least-squares regularization, but with an optimal model grid determined by the actual information in the input set. This method also allows us to use an optimized irregular grid, with a variable number of latitudes at different depths.

Coupling of solar p-modes of high degree l by joint effects of differential rotation and meridional circulation

Perturbational analysis of the p-mode coupling at high degree l, induced by the solar differential rotation [1] is extended to include, into a unified theoretical description, the effects of global meridional circulation. The predicted observational signatures of the meridional circulation in the global p-mode measurements are briefly discussed.