We present a nonlinear mean-field model of the solar interior dynamics and dynamo, which reproduces the observed cyclic variations of the global magnetic field of the Sun, as well as the differential rotation and meridional circulation. Using this model, we explain, for the first time, the extended 22-year pattern of the solar torsional oscillations, observed as propagation of zonal variations of the angular velocity from high latitudes to the equator during the time equal to the full dynamo cycle. In the literature, this effect is usually attributed to the so-called "extended solar cycle". In agreement with the commonly accepted idea our model shows that the torsional oscillations can be driven by a combinations of magnetic field effects acting on turbulent angular momentum transport, and the large-scale Lorentz force. We find that the 22-year pattern of the torsional oscillations can result from a combined effect of an overlap of subsequent magnetic cycles and magnetic quenching of the convective heat transport. The latter effect results in cyclic variations of the meridional circulation in the sunspot formation zone, in agreement with helioseismology results. The variations of the meridional circulation together with other drivers of the torsional oscillations maintain their migration to the equator during the 22-year magnetic cycle, resulting in the observed extended pattern of the torsional oscillations.
Temporal variations in the Suns internal velocity field with a periodicity of about 11 years have been observed over the last four decades. The period of these torsional oscillations and their latitudinal propagation roughly coincides with the period and equatorward propagation of sunspots which originate from a magnetohydrodynamic dynamo mechanism operating in the Suns interior. While the solar differential rotation plays an important role in this dynamo mechanism by inducting the toroidal component of magnetic field, the impact of torsional oscillations on the dynamo mechanism and hence the …
Selfsimilarity relations for torsional oscillation frequencies of neutron star crust are discussed. For any neutron star model, the frequencies of fundamental torsional oscillations (with no nodes of radial wave function, i.e. at n=0, and at all possible angular wave numbers l >= 2) is determined by a single constant. Frequencies of ordinary torsional oscillations (at any n>0 with l >= 2) are determined by two constants. These constants are easily calculated through radial integrals over the neutron star crust, giving the simplest method to determine full oscillation spectrum. All constants fo…
Using a nonlinear mean-field solar dynamo model, we study relationships between the amplitude of the `extended' mode of migrating zonal flows (`torsional oscillations') and magnetic cycles, and investigate whether properties the torsional oscillations in subsurface layers and in the deep convection zone can provide information about the future solar cycles. We consider two types of dynamo models: models with regular variations of the alpha-effect, and models with stochastic fluctuations, simulating `long'- and 'short-memory' types of magnetic activity variations. It is found that torsional osc…
Assuming that the torsional oscillation is driven by the Lorentz force of the magnetic field associated with the sunspot cycle, we use a flux transport dynamo to model it and explain its initiation at a high latitude before the beginning of the sunspot cycle.
Solar torsional oscillations are migrating bands of slower- and faster-than-average rotation, which are strongly related to the Sun's magnetic cycle. We perform a long-term study (16 yr) of hemispherical asymmetry in solar torsional oscillation velocity using helioseismic data for the first time. We study the north-south asymmetry in the velocity using the zonal flow velocities obtained by ring diagram analysis of the Global Oscillation Network Group (GONG) Doppler images. We find significant hemispherical asymmetry in the torsional oscillation velocity and explore its variation with respect t…
Torsional Alfvén waves are promising candidates for transport of energy across different layers of the solar atmosphere and have been theoretically predicted for decades. Previous detections of Alfvén waves so far have however mostly relied on indirect signatures. We present a first direct observational evidence of a fully resolved torsional Alfvén oscillation of a large-scale structure occurring at coronal heights. We analyse IRIS imaging and spectral observation of a surge resulting from magnetic reconnection between active region prominence threads and surrounding magnetic fieldlines. The I…
In this work we seek evidence for global torsional oscillations in alpha sunspots. We have used long time series of continuum intensity and magnetic field vector maps from the Helioseismic and Magnetic Imager (HMI) instrument on board the Solar Dynamics Observatory (SDO) spacecraft. The time series analysed here span the total disk passage of 25 isolated sunspots. We found no evidence of global long-term periodic oscillations in the azimuthal angle of the sunspot magnetic field within $\sim$ 1 degree. This study could help us to understand the sunspot dynamics and its internal structure.
Rotation of the leading sunspot of active region NOAA 10421 was investigated using magnetograms and Dopplergrams from the MDI instrument of the Solar and Heliospheric Observatory (SOHO), and white-light images from the Transition Region and Coronal Explorer (TRACE). The vertical, radial, and azimuthal axisymmetrical components of both magnetic and velocity field vectors were reconstructed for the sunspot umbra and penumbra. All three components of both vectors in the umbra and penumbra show torsional oscillations with the same rotational period of about 3.8 days. The TRACE white-light data als…
We report the discovery of torsional Alfvénic oscillations in solar flares, which modulate the time evolution of the magnetic free energy $E_f(t)$, while the magnetic potential energy $E_p(t)$ is uncorrelated, and the nonpotential energy varies as $E_{np}(t) = E_p + E_f(t)$. The mean observed time period of the torsional oscillations is $P_{obs}=15.1 \pm 3.9$ min, the mean field line length is $L=135\pm35$ Mm, and the mean phase speed is $v_{phase} =315 \pm 120$ km s$^{-1}$, which we interpret as torsional Alfvénic waves in flare loops with enhanced electron densities. Most of the torsional os…
We show here a component of the meridional circulation developing at medium-high latitudes (40-50 degrees) before the new solar cycle starts. Like the torsional oscillation of the zonal flows, this extra circulation seems to precede the onset of magnetic activity at the solar surface and move slowly towards lower latitudes. However, the behavior of this component differs from that of the torsional oscillation regarding location and convergence towards the equator at the end of the cycle. The observation of this component before the magnetic regions appear at the solar surface has only been pos…
We characterize and analyze rotational torsional oscillations developing in a large-eddy magnetohydrodynamical simulation of solar convection (Ghizaru, Charbonneau, and Smolarkiewicz, Astrophys. J. Lett., 715, L133 (2010); Racine et al., Astrophys. J., 735, 46 (2011)) producing an axisymmetric large-scale magnetic field undergoing periodic polarity reversals. Motivated by the many solar-like features exhibited by these oscillations, we carry out an analysis of the large-scale zonal dynamics. We demonstrate that simulated torsional oscillations are not driven primarily by the periodically-varyi…
Although the Sun's torsional oscillation is believed to be driven by the Lorentz force associated with the sunspot cycle, this oscillation begins 2--3 yr before the sunspot cycle. We provide a theoretical explanation of this with the help of a solar dynamo model having a meridional circulation penetrating slightly below the bottom of the convection zone, because only in such dynamo models the strong toroidal field forms a few years before the sunspot cycle and at a higher latitude.
Some chemically peculiar stars in the upper main sequence show rotational period variations of unknown origin. We propose these variations are a consequence of the propagation of internal waves in magnetic rotating stars that lead to the torsional oscillations of the star. We simulate the magnetohydrodynamic waves and calculate resonant frequencies for two stars that show rotational variations: CU Vir and HD 37776. We provide updated analyses of rotational period variations in these stars and compare our results with numerical models. For CU Vir, the length of the observed rotational-period cy…
Torsional oscillations represent bands of fast and slow zonal flows around the Sun, which extend deep into the convection zone and migrate during solar cycles towards the equator following the sunspot butterfly diagram. Analysis of helioseismology data obtained in 1996-2018 for almost two solar cycles reveals zones of deceleration of the torsional oscillations inside the Sun due to dynamo-generated magnetic field. The zonal deceleration originates near the bottom of the convection zone at high latitudes, and migrates to the surface revealing patterns of magnetic dynamo waves predicted by the P…
We examine the evolution of the zonal flow pattern in the upper solar convection zone during the current extended solar minimum, and compare it with that during the previous minimum. The results suggest that a configuration matching that at the previous minimum was reached during 2008, but that the flow band corresponding to the new cycle has been moving more slowly towards the equator than was observed in the previous cycle, resulting in a gradual increase in the apparent length of the cycle during the 2007 -- 2008 period. The current position of the lower-latitude fast-rotating belt correspo…
The periodically varying Lorentz force of the periodic solar magnetic field generated by the solar dynamo can induce two kinds of motions: torsional oscillations and periodic variations in the meridional circulation. Observational evidence now exists for both these kinds of motions. We discuss our ongoing effort in theoretically studying the variations of the meridional circulation. Then we present our theoretical model of torsional oscillations, which addresses the question why these oscillations start before sunspot cycles at latitudes higher than where sunspots are seen.
The effects of both density stratification and magnetic field expansion on torsional Alfven waves in solar spicules are studied. Also, their eigenfrequencies, eigenfunctions, and the period ratio P_1/P_2 are obtained with a novel mathematical method. We showed that under some circumstances this ratio can approach its observational value even though it departs from its canonical value of $2$. Moreover, Eigenfunction height variations show that the oscillations amplitude are increasing towards higher heights which is in agreement with the observations. This means that with a little increase in h…
The phenomenon of solar "torsional oscillations" (TO) represents migratory zonal flows associated with the solar cycle. These flows are observed on the solar surface and, according to helioseismology, extend through the convection zone. We study the origin of the TO using results from a global MHD simulation of the solar interior that reproduces several of the observed characteristics of the mean-flows and magnetic fields. Our results indicate that the magnetic tension (MT) in the tachocline region is a key factor for the periodic changes in the angular momentum transport that causes the TO. T…
Strange stars are one of the possible compact stellar objects that can be formed after a supernova collapse. We consider a model of strange star having an inner core in the color-flavor locked phase surmounted by a crystalline color superconducting layer. These two phases constitute the {\it quarksphere}, which we assume to be the largest and heaviest part of the strange star. The next layer consists of standard nuclear matter forming a ionic crust, hovering on the top of the quarksphere and prevented from falling by a strong dipolar electric field. The dipolar electric field arises because qu…
Registering periodic variations of spectral line widths serves as the main method for observing torsional Alfvén waves. Theoretically, the method seems valid, yet it entails a number of caveats when applied to data. For instance, the amplitudes of these observations should vary with changes of the location on the disk, and they should be associated with no intensity oscillations. We analyze extensive observational material of periodic non-thermal variations of line widths in coronal holes and facular regions in a number of spectral lines: Hα, He I 10830 Å, Ca II 8542 Å, Ba II 4554 Å. In most c…
The torsional oscillation is a well established observational fact and there are theoretical attempts for its description but no final solution has yet been accepted. One of the possible candidates for its cause is the presence of sunspots modifying the streaming conditions. The present work focuses on the temporally varying latitudinal distribution of several sunspot features, such as the spot sizes and spot numbers. These features are different faces of the butterfly diagram. In fact some weak spatial correlations can be recognized.
The striking similarity between the cyclic equatorward migration of the torsional oscillation belts and the sunspot activity latitudes inspired several attempts to seek an explanation of the torsional phenomenon in terms of interactions between flux ropes and plasma motions. The aim of the present work is to examine the spatial and temporal coincidences of the torsional waves and the emergence of sunspot magnetic fields. The locations of the shearing latitudes have been compared with the distributions of certain sunspot parameters by using sunspot data of more than two cycles. The bulges of th…
The solar dynamo and the solar Global internal Magnetic Structure (GMS) appear to be a thin ($\sim$2 Mm thick) structure near ($\sim$1 Mm below) the solar surface. Evidence for these properties are found from the amplitude of the torsional oscillations and in their velocity contours relationship to solar magnetogram; the power to the chromosphere; power to the corona and the solar wind; the current in the helio-current-sheet measured at the radius of the orbit of Earth; the calculated size ($\sim$1 Mm) of the expanding polar flux when it enters the photosphere; and from the observation that so…
We propose a scenario for the quasi-periodic oscillations observed in magnetar flares wherein a tangled component of the stellar magnetic field introduces nearly isotropic stress that gives the fluid core of the star an effective shear modulus. In a simple, illustrative model of constant density, the tangled field eliminates the problematic Alfvén continuum that would exist in the stellar core for an organized field. For a tangled field energy density comparable to that inferred from the measured dipole fields of $\sim 10^{15}$ G in SGRs 1806-20 and 1900+14, torsional modes exist with fundamen…
Motivated by stability considerations and observational evidence, we argue that magnetars possess highly-tangled internal magnetic fields. We propose that the quasi-periodic oscillations (QPOs) seen to accompany giant flares can be explained as torsional modes supported by a tangled magnetic field, and we present a simple model that supports this hypothesis for SGR 1900+14. Taking the strength of the tangle as a free parameter, we find that the magnetic energy in the tangle must dominate that in the dipolar component by a factor of $\sim 14$ to accommodate the observed 28 Hz QPO. Our simple mo…
We extend a general-relativistic ideal magneto-hydrodynamical code to include the effects of elasticity. Using this numerical tool we analyse the magneto-elastic oscillations of highly magnetised neutron stars (magnetars). In simulations without magnetic field we are able to recover the purely crustal shear oscillations within an accuracy of about a few per cent. For dipole magnetic fields between 5 x 10^13 and 10^15 G the Alfvén oscillations become modified substantially by the presence of the crust. Those quasi-periodic oscillations (QPOs) split into three families: Lower QPOs near the equat…
Stars are self-gravitating fluids in which pressure, buoyancy, rotation and magnetic fields provide the restoring forces for global modes of oscillation. Pressure and buoyancy energetically dominate, while rotation and magnetism are generally assumed to be weak perturbations and often ignored. However, observations of anomalously weak dipole mode amplitudes in red giant stars suggest that a substantial fraction of these are subject to an additional source of damping localised to their core region, with indirect evidence pointing to the role of a deeply buried magnetic field. It is also known t…
A quantitative study of the observable radio signatures of the sausage, kink, and torsional MHD oscillation modes in flaring coronal loops is performed. Considering first non-zero order effect of these various MHD oscillation modes on the radio source parameters such as magnetic field, line of sight, plasma density and temperature, electron distribution function, and the source dimensions, we compute time dependent radio emission (spectra and light curves). The radio light curves (of both flux density and degree of polarization) at all considered radio frequencies are than quantified in both t…
We report the detection of oscillatory phenomena associated with a large bright-point group that is 430,000 square kilometers in area and located near the solar disk center. Wavelet analysis reveals full-width half-maximum oscillations with periodicities ranging from 126 to 700 seconds originating above the bright point and significance levels exceeding 99%. These oscillations, 2.6 kilometers per second in amplitude, are coupled with chromospheric line-of-sight Doppler velocities with an average blue shift of 23 kilometers per second. A lack of cospatial intensity oscillations and transversal …
Torsional Alfven Oscillation in the Regime of Firehose Instability as a Mechanism of Plasma Stratification in a Laboratory Experiment on Modeling a Coronal Arch
A. V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences（俄罗斯科学院阿·瓦·加蓬诺夫-格列霍夫应用物理研究所）；Lobachevsky University（罗巴切夫斯基大学）
Solar subsurface zonal and meridional-flow profiles during the rising phase of solar cycle 24 are studied using time-distance helioseismology technique. The faster zonal bands in the torsional-oscillation pattern show strong hemispheric asymmetries and temporal variations in both width and speed. The faster band in the northern hemisphere is located closer to the equator than the band in the southern hemisphere, and migrates past the equator when the magnetic activity in the southern hemisphere is reaching maximum. The meridional-flow speed decreases substantially with the increase of magnetic…
The Sun's axisymmetric flows, differential rotation and meridional flow, govern the dynamics of the solar magnetic cycle and variety of methods are used to measure these flows, each with its own strengths and weaknesses. Flow measurements based on cross-correlating images of the surface magnetic field have been made since the 1970s which require advanced numerical techniques that are capable of detecting movements of less than the pixel size in images of the Sun. We have identified several systematic errors in addition to the center-to-limb effect that influence previous measurements of these …
The parameters of the p-mode oscillations vary with solar activity. Such temporal variations provide insights for the study of the structural and dynamical changes occurring in the Sun's interior throughout the solar cycle. We present here a complete picture of the temporal variations of the global p-mode parameters (excitation, damping, frequency, peak asymmetry, and rotational splitting) over the entire solar cycle 23 and the beginning of cycle 24 as observed by the space-based, Sun-as-a-star helioseismic GOLF and VIRGO instruments onboard SoHO.
Magneto-solid-mechanical model of two-component, core-crust, paramagnetic neutron star responding to quake-induced perturbation by differentially rotational, torsional, oscillations of crustal electron-nuclear solid-state plasma about axis of magnetic field frozen in the immobile paramagnetic core is developed. Particular attention is given to the node-free torsional crust-against-core vibrations under combined action of Lorentz magnetic and Hooke's elastic forces; the damping is attributed to Newtonian force of shear viscose stresses in crustal solid-state plasma. The spectral formulae for th…
The pattern of migrating zonal flow bands associated with the solar cycle, known as the torsional oscillation, has been monitored with continuous global helioseismic observations by the Global Oscillations Network Group, together with those made by the Michelson Doppler Imager onboard the Solar and Heliosepheric Observatory and its successor the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory, since 1995, giving us nearly two full solar cycles of observations. We report that the flows now show traces of the mid-latitude acceleration that is expected to become the main e…
The evolution of the solar activity comprises, apart from the well-known 11-year cycle, various temporal scales ranging from months up to the secondary cycles known as mid-term oscillations. Its nature deserves a physical explanation. In this work, we consider the 5-to-6 year oscillations as derived both from sunspot and from solar magnetic dipole time series. Using the solar dynamo model, we deduced that these variations may be a manifestation of the dynamo nonlinearities and non-harmonic shape of the solar activity cycles. We conclude that the observed mid-term oscillations are related to th…
Recent observations have revealed that MHD waves and oscillations are ubiquitous in the solar atmosphere, with a wide range of periods. We give a brief review of some aspects of MHD waves and coronal seismology which have recently been the focus of intense debate or are newly emerging. In particular, we focus on four topics: (i) the current controversy surrounding propagating intensity perturbations along coronal loops, (ii) the interpretation of propagating transverse loop oscillations, (iii) the ongoing search for coronal (torsional) Alfven waves and (iv) the rapidly developing topic of quas…
We performed a multi-wave study of the oscillation dynamic in short-lived facula regions during their lifetime. We studied oscillations in five regions, three of which belonged to the beginning of the current solar activity cycle, and two of them existed at the end of the previous cycle. We found that in the facula regions of the current cycle, low-frequency 1-2 mHz oscillation dominated at the early stages of the faculae formation, while in the regions of the previous cycle, five-minute oscillations dominated at this stage. At the maximal development phase of all the facula regions, the locat…
Recent years have seen an increased interest in the question of whether the gravitational action of planets could have an influence on the solar dynamo. Without discussing the observational validity of the claimed correlations, we ask for a possible physical mechanism that might link the weak planetary forces with solar dynamo action. We focus on the helicity oscillations that were recently found in simulations of the current-driven, kink-type Tayler instability, which is characterized by an m=1 azimuthal dependence. We show how these helicity oscillations can be resonantly excited by some m=2…
The solar-activity-cycle minimum observed between Cycles 23 and 24 is generally regarded as being unusually deep and long. That minimum is being followed by one of the smallest amplitude cycles in recent history. We perform an in-depth analysis of this minimum with helioseismology. We use Global Oscillation Network Group (GONG) data to demonstrate that the frequencies of helioseismic oscillations are a sensitive probe of the Sun's magnetic field: The frequencies of the helioseismic oscillations were found to be systematically lower in the minimum following Cycle 23 than in the minimum precedin…
The latitudinal distributions of the yearly mean rotation rates measured respectively by Suzuki in 1998 and 2012 and Pulkkinen $\&$ Tuominen in 1998 are utilized to investigate internal-cycle variation of solar differential rotation. The rotation rate at the solar Equator seems to decrease since cycle 10 onwards. The coefficient $B$ of solar differential rotation, which represents the latitudinal gradient of rotation, is found smaller in the several years after the minimum of a solar cycle than in the several years after the maximum time of the cycle, and it peaks several years after the maxim…
We investigate the variation in the mode parameters obtained from time series of length 9, 36, 72 and 108 days to understand the changes occurring on different time-scales. The regression analysis between frequency shifts and activity proxies indicates that the correlation and slopes are correlated and both increase in going from time series of 9 to 108 days. We also observe that the energy of the mode is anti-correlated with solar activity while the rate at which the energy is supplied remains constant over the solar cycle.
The crystalline color superconducting phase is believed to be the ground state of deconfined quark matter for sufficiently large values of the strange quark mass. This phase has the remarkable property of being more rigid than any known material. It can therefore sustain large shear stresses, supporting torsional oscillations of large amplitude. The torsional oscillations could lead to observable electromagnetic signals if strange stars have a crystalline color superconducting crust. Indeed, considering a simple model of strange star with a bare quark matter surface, it turns out that a positi…
Spatio-temporal analysis of helioseismic quasi-biennial oscillations
Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick（华威大学物理与天体物理融合空间与天文研究中心）；Engineering Research Institute “Ventspils International Radio Astronomy Centre (VIRAC)”, Ventspils University of Applied Sciences（文茨皮尔斯应用科学大学文茨皮尔斯国际射电天文中心（VIRAC）工程研究所）
Rotation of the large scale solar magnetic field has a great importance for the understanding of solar dynamic, for the search of longitidinal structure and for the study of solar-terrestrial relations. 30-year long observations taken at the Wilcox Solar Observatory (USA) in 21-23 cycles have been analysed carefully to deduce magnetic field rotation rate at different latitudes in both hemispheres and its variability in time. The WSO data appear to indicate that additionally to the differential rotation along the latitudes there are running waves of fast rotation of the magnetic field. These to…
