Tachocline Region Research Articles

A Synchronized Two-Dimensional alpha –Omega Model of the Solar Dynamo

We consider a conventional alpha –Omega -dynamo model with meridional circulation that exhibits typical features of the solar dynamo, including a Hale-cycle period of around 20 years and a reasonable shape of the butterfly diagram. With regard to recent ideas of a tidal synchronization of the solar cycle, we complement this model by an additional time-periodic alpha -term that is localized in the tachocline region. It is shown that amplitudes of some decimeters per second are sufficient for this alpha -term to become capable of entraining the underlying dynamo. We argue that such amplitudes of alpha may indeed be realistic, since velocities in the range of m s−1 are reachable, e.g., for tidally excited magneto–Rossby waves.

Statistical properties of coronal hole rotation rates: Are they linked to the solar interior?

The present paper discusses results of a statistical study of the characteristics of coronal hole (CH) rotation in order to find connections to the internal rotation of the Sun. The goal is to measure CH rotation rates and study their distribution over latitude and their area sizes. In addition, the CH rotation rates are compared with the solar photospheric and inner layer rotational profiles. We study coronal holes observed within $\pm 60$ latitude and longitude degrees from the solar disc centre during the time span from the 1 January 2013 to 20 April 2015, which includes the extended peak of solar cycle 24.We used data created by the Spatial Possibilistic Clustering Algorithm (SPoCA), which provides the exact location and characterisation of solar coronal holes using SDO=AIA 193 {\AA} channel images. The CH rotation rates are measured with four-hour cadence data to track variable positions of the CH geometric centre. North-south asymmetry was found in the distribution of coronal holes: about 60 percent were observed in the northern hemisphere and 40 percent were observed in the southern hemisphere. The smallest and largest CHs were present only at high latitudes. The average sidereal rotation rate for 540 examined CHs is $13:86 (\pm 0:05)$ degrees/d. Conclusions. The latitudinal characteristics of CH rotation do not match any known photospheric rotation profile. The CH angular velocities exceed the photospheric angular velocities at latitudes higher than 35-40 degrees. According to our results, the CH rotation profile perfectly coincides with tachocline and the lower layers of convection zone at around 0.71 $R_{\odot}$; this indicates that CHs may be linked to the solar global magnetic field, which originates in the tachocline region.

UNDERSTANDING SOLAR TORSIONAL OSCILLATIONS FROM GLOBAL DYNAMO MODELS

ABSTRACT 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. The torque induced by the MT at the base of the convection zone is positive at the poles and negative at the equator. A rising MT torque at higher latitudes causes the poles to speed up, whereas a declining negative MT torque at the lower latitudes causes the equator to slow-down. These changes in the zonal flows propagate through the convection zone up to the surface. Additionally, our results suggest that it is the magnetic field at the tachocline that modulates the amplitude of the surface meridional flow rather than the opposite as assumed by flux-transport dynamo models of the solar cycle.

EXPLAINING THE COEXISTENCE OF LARGE-SCALE AND SMALL-SCALE MAGNETIC FIELDS IN FULLY CONVECTIVE STARS

Despite the lack of a shear-rich tachocline region low-mass fully convective stars are capable of generating strong magnetic fields, indicating that a dynamo mechanism fundamentally different from the solar dynamo is at work in these objects. We present a self-consistent three dimensional model of magnetic field generation in low-mass fully convective stars. The model utilizes the anelastic magnetohydrodynamic equations to simulate compressible convection in a rotating sphere. A distributed dynamo working in the model spontaneously produces a dipole-dominated surface magnetic field of the observed strength. The interaction of this field with the turbulent convection in outer layers shreds it, producing small-scale fields that carry most of the magnetic flux. The Zeeman-Doppler-Imaging technique applied to synthetic spectropolarimetric data based on our model recovers most of the large-scale field. Our model simultaneously reproduces the morphology and magnitude of the large-scale field as well as the magnitude of the small-scale field observed on low-mass fully convective stars.

Double-diffusive magnetic buoyancy instability in a quasi-two-dimensional Cartesian geometry

Magnetic buoyancy, believed to occur in the solar tachocline, is both an important part of large-scale solar dynamo models and the picture of how sunspots are formed. Given that in the tachocline region the ratio of magnetic diffusivity to thermal diffusivity is small it is important, for both the dynamo and sunspot formation pictures, to understand magnetic buoyancy in this regime. Furthermore, the tachocline is a region of strong shear and such investigations must involve structures that become buoyant in the double-diffusive regime which are generated entirely from a shear flow. In a previous study, we have illustrated that shear-generated doublediffusive magnetic buoyancy instability is possible in the tachocline. However, this study was severely limited due to the computational requirements of running three-dimensional magnetohydrodynamic simulations over diffusive time-scales. A more comprehensive investigation is required to fully understand the double-diffusive magnetic buoyancy instability and its dependency on a number of key parameters; such an investigation requires the consideration of a reduced model. Here we consider a quasi-two-dimensional model where all gradients in the x direction are set to zero. We show how the instability is sensitive to changes in the thermal diffusivity and also show how different initial configurations of the forced shear flow affect the behaviour of the instability. Finally, we conclude that if the tachocline is thinner than currently stated then the double-diffusive magnetic buoyancy instability can more easily occur.

IMPACT OF A REALISTIC DENSITY STRATIFICATION ON A SIMPLE SOLAR DYNAMO CALCULATION

In our Sun, the magnetic cycle is driven by the dynamo action occurring inside the convection zone, beneath the surface. Rotation couples with plasma turbulent motions to produce organized magnetic fields that erupt at the surface and undergo relatively regular cycles of polarity reversal. Among others, the axisymmetric dynamo models have been proved to be a quite useful tool to understand the dynamical processes responsible for the evolution of the solar magnetic cycle and the formation of the sunspots. Here, we discuss the role played by the radial density stratification on the critical layers of the Sun on the solar dynamo. The current view is that a polytropic description of the density stratification from beneath the tachocline region up to the Sun's surface is sufficient for the current precision of axisymmetric dynamo models. In this work, by using an up-to-date density profile obtained from a standard solar model, which is itself consistent with helioseismic data, we show that the detailed peculiarities of the density in critical regions of the Sun's interior, such as the tachocline, the base of the convection zone, the layers of partial ionization of hydrogen and helium, and the super-adiabatic layer, play a non-negligible role on the evolution of the solar magnetic cycle. Furthermore, we found that the chemical composition of the solar model plays a minor role in the formation and evolution of the solar magnetic cycle.

BIPOLAR MAGNETIC REGIONS ON THE SUN: GLOBAL ANALYSIS OF THESOHO/MDI DATA SET

The magnetic flux that is generated by dynamo inside the Sun emerges in the form of bipolar magnetic regions. We have analyzed the whole set of solar magnetograms obtained with the SOHO/MDI instrument in 1995-2011, and automatically identified 160,079 bipolar magnetic regions that span a range of scale sizes across nearly four orders of magnitude. Their properties have been statistically analyzed, in particular with respect to the polarity orientations of the bipolar regions, including their tilt angle distributions. The latitude variation of the average tilt angles (with respect to the E-W direction), known as Joy's law, is found to closely follow the relation 32.1*sin(latitude)[deg]. There is no indication of a dependence on region size that one may expect if the tilts were produced by the Coriolis force during the buoyant rise of flux loops from the tachocline region. A few percent of all regions have orientations that violate Hale's polarity law. We show examples, from different phases of the solar cycle, where well defined medium-size bipolar regions with opposite polarity orientations occur side by side in the same latitude zone. Such oppositely oriented large bipolar regions cannot be part of the same toroidal flux system, but different flux systems must coexist in the same latitude zones. These examples are incompatible with the paradigm of coherent, subsurface toroidal flux ropes as the source of sunspots, and instead show that fluctuations must play a major role at all scales for the turbulent dynamo. We see no observational support for a separation of scales or a division between a global and a local dynamo, since also the smallest scales in the data set retain a non-random component that significantly contributes to the accumulated emergence of a N-S dipole moment that leads to the replacement of the old global poloidal field with a new one that has the opposite orientation.

Seismic study of magnetic field in the solar interior

Magnetic field in the solar interior contributes to the even order splitting coefficients, but it is not possible to separate the effect of magnetic field from those due to other deviations from spherical symmetry. Results obtained using GONG and MDI data are discussed. Limits on possible magnetic field in the solar core and in the tachocline region are obtained. There is some signal from possible magnetic field in the convection zone, but evidence of possible temporal variation in the solar interior is only marginal.

Structure and stability of the magnetic solar tachocline

Rather weak fossil magnetic fields in the radiative core can produce the solar tachocline if the field is almost horizontal in the tachocline region, i.e. if the field is confined within the core. This particular field geometry is shown to result from a shallow penetration of the meridional flow existing in the convection zone into the radiative core. Two conditions are thus crucial for a magnetic tachocline theory: (i) the presence of meridional flow of a few metres per second at the base of the convection zone, and (ii) a magnetic diffusivity inside the tachocline smaller than 108 cm2 s−1. Numerical solutions for the confined poloidal fields and the resulting tachocline structures are presented. We find that the tachocline thickness runs as Bp−1/2 with the poloidal field amplitude falling below 5% of the solar radius for Bp > 5 mG. The resulting toroidal field amplitude inside the tachocline of about 100 G does not depend on the Bp. The hydromagnetic stability of the tachocline is only briefly discussed. For the hydrodynamic stability of latitudinal differential rotation we found that the critical 29% of the 2D theory of Watson (1981 Geophys. Astrophys. Fluid Dyn.16 285) are reduced to only 21% in 3D for marginal modes of about 6 Mm radial scale.

Searching for mid-term variations in different aspects of solar activity - looking for probable common origins and studying temporal variations of magnetic polarities

Several studies have examined the temporal variability of the solar activity, and many variations are reported in the literature. We also (re)analyse the statistical properties of the following kinds of data series of solar activity phenomena: magnetic synoptic charts, hemispherical relative sunspot numbers, solar flare index, coronal index, solar radio flux, interplanetary magnetic field and proton speed in the solar wind, in order to find common mid-term periods during solar cycles 21–23. As a new approach, we focus on the magnetic polarity relations and we define new quantities (e.g. magnetic positive–negative polarity asymmetry) to explore the connections between several aspects of the solar activity from different points of view. According to our survey, the mid-term periodicities (1–2 yr) are manifest in almost all data with the exception of the coronal index and the 10.7-cm solar flux data. In the case of these latter two we note that these surveys produce global data on the solar corona, so the Sun is studied on these bandwidths as a star. Besides these, with the accumulation of helioseismic data over the last 10 yr, it has become possible to study the temporal variation in the rotational rate residuals in tachocline region. In addition, we examine possible common origins of different activity markers and/or possible connections to differential rotation.

Magnetic field confinement by meridional flow and the solar tachocline

We show that the MHD theory that explains the solar tachocline by an effect of the magnetic field can work with the decay modes of a fossil field in the solar interior if the meridional flow of the convection zone penetrates slightly the radiative zone beneath. An equatorward flow of about 10 m/s penetrating to a maximum depth of 1000 km below the convection zone is able to generate almost horizontal field lines in the tachocline region so that the internal field is almost totally confined to the radiative zone. The theory of differential solar rotation indeed provides meridional flows of about 10 m/s and a penetration depth of <1000 km for viscosity values

Large-Scale Dynamics of the Convection Zone and Tachocline

The past few decades have seen dramatic progress in our understanding of solar interior dynamics, prompted by the relatively new science of helioseismology and increasingly sophisticated numerical models. As the ultimate driver of solar variability and space weather, global-scale convective motions are of particular interest from a practical as well as a theoretical perspective. Turbulent convection under the influence of rotation and stratification redistributes momentum and energy, generating differential rotation, meridional circulation, and magnetic fields through hydromagnetic dynamo processes. In the solar tachocline near the base of the convection zone, strong angular velocity shear further amplifies fields which subsequently rise to the surface to form active regions. Penetrative convection, instabilities, stratified turbulence, and waves all add to the dynamical richness of the tachocline region and pose particular modeling challenges. In this article we review observational, theoretical, and computational investigations of global-scale dynamics in the solar interior. Particular emphasis is placed on high-resolution global simulations of solar convection, highlighting what we have learned from them and how they may be improved.

Global‐Scale Turbulent Convection and Magnetic Dynamo Action in the Solar Envelope

The operation of the solar global dynamo appears to involve many dynamical elements, including the generation of fields by the intense turbulence of the deep convection zone, the transport of these fields into the tachocline region near the base of the convection zone, the storage and amplification of toroidal fields in the tachocline by differential rotation, and the destabilization and emergence of such fields due to magnetic buoyancy. Self-consistent magnetohydrodynamic (MHD) simulations that realistically incorporate all of these processes are not yet computationally feasible, although some elements can now be studied with reasonable fidelity. Here we consider the manner in which turbulent compressible convection within the bulk of the solar convection zone can generate large-scale magnetic fields through dynamo action. We accomplish this through a series of three-dimensional numerical simulations of MHD convection within rotating spherical shells using our anelastic spherical harmonic (ASH) code on massively parallel supercomputers. Since differential rotation is a key ingredient in all dynamo models, we also examine here the nature of the rotation profiles that can be sustained within the deep convection zone as strong magnetic fields are built and maintained. We find that the convection is able to maintain a solar-like angular velocity profile despite the influence of Maxwell stresses, which tend to oppose Reynolds stresses and thus reduce the latitudinal angular velocity contrast throughout the convection zone. The dynamo-generated magnetic fields exhibit a complex structure and evolution, with radial fields concentrated in downflow lanes and toroidal fields organized into twisted ribbons that are extended in longitude and achieve field strengths of up to 5000 G. The flows and fields exhibit substantial kinetic and magnetic helicity although systematic hemispherical patterns are only apparent in the former. Fluctuating fields dominate the magnetic energy and account for most of the back-reaction on the flow via Lorentz forces. Mean fields are relatively weak and do not exhibit systematic latitudinal propagation or periodic polarity reversals as in the Sun. This may be attributed to the absence of a tachocline, i.e., a penetrative boundary layer between the convection zone and the deeper radiative interior possessing strong rotational shear. The influence of such a layer will await subsequent studies.

Updated Toulouse solar models including the diffusion-circulation coupling and the effect of μ-gradients

New solar models are presented, which have been computed with the most recent physical inputs (nuclear reaction rates, equation of state, opacities, microscopic diffusion). Rotation-induced mixing has been introduced in a way which includes the feed-back effect of the μ-gradient induced by helium settling. A parametrization of the tachocline region below the convective zone has also been added in the computations. The sound velocities have been computed in the models and compared to the seismic Sun. Our best model is described in some detail. Besides the new physical inputs, the most important improvement concerns the computations of μ-gradients during the solar evolution and their influence in slowing down rotation-induced mixing. This process can explain why lithium is depleted in the present Sun while beryllium is not, and meanwhile why 3He has not increased at the solar surface for at least 3 Gyrs.

Changes in Solar Dynamics from 1995 to 2002

Data obtained by the GONG and MDI instruments over the last 7 years are used to study how solar dynamics—both rotation and other large scale flows—has changed with time. In addition to the well-known phenomenon of bands of faster and slower rotation moving toward the equator and pole, we find that the zonal flow pattern rises upward with time. Like the zonal flows, the meridional flows also show distinct solar activity–related changes. In particular, the antisymmetric component of the meridional flow shows a decrease in speed with activity. We do not see any significant temporal variations in the dynamics of the tachocline region where the solar dynamo is believed to be operating. Subject headings: Sun: helioseismology — Sun: interior — Sun: oscillations — Sun: rotation

A study of possible temporal and latitudinal variations in the properties of the solar tachocline

Temporal variations of the structure and the rotation rate of the solar tachocline region are studied using helioseismic data from the Global Oscillation Network Group (GONG) and the Michelson Doppler Imager (MDI) obtained during the period 1995-2000. We do not find any significant temporal variation in the depth of the convection zone, the position of the tachocline or the extent of overshoot below the convection zone. No systematic variation in any other properties of the tachocline, like width, etc., is found either. The possibility of periodic variations in these properties is also investigated. Time-averaged results show that the tachocline is prolate with a variation of about 0.02 R ⊙ in its position. Neither the depth of the convection zone nor the extent of overshoot shows any significant variation with latitude.