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We estimate the contributions to the solar-cycle variation of solar meridional and zonal flows near the surface expected solely from local magnetic regions. Maps of flows near magnetic regions are obtained using helioseismic holography and averaged over ensembles of such regions with similar magnetic flux. These averaged flows are assigned to the positions and times of all magnetic regions identified from daily magnetograms over an 11 yr period. Residuals are obtained after averaging both meridional and zonal-flow components over longitude for each Carrington rotation and subtracting the temporal mean at each latitude. Results indicate that magnetic regions produce solar-cycle variations of both components in the active latitude range with peak amplitudes of about 1 m s−1, which represents only a fraction of the known variations in either the residual zonal or meridional flow with amplitudes around 3 and 5 m s−1, respectively. Thus it is unlikely that active regions, and compact magnetic concentrations in general, are the primary source of the 11 yr variation in these global flows. A threshold magnetic flux of 5 × 1020 Mx, below which no significant flows are observed, is identified as a check on the completeness of the set of magnetic regions. We also find that inflows around most magnetic regions are confined to within 10°–12° of their centers, in contrast with recent evidence of more extended inflows. [ABSTRACT FROM AUTHOR]

We estimate the contributions to the solar-cycle variation of solar meridional and zonal flows near the surface expected solely from local magnetic regions. Maps of flows near magnetic regions are obtained using helioseismic holography and averaged over ensembles of such regions with similar magnetic flux. These averaged flows are assigned to the positions and times of all magnetic regions identified from daily magnetograms over an 11 yr period. Residuals are obtained after averaging both meridional and zonal-flow components over longitude for each Carrington rotation and subtracting the temporal mean at each latitude. Results indicate that magnetic regions produce solar-cycle variations of both components in the active latitude range with peak amplitudes of about 1 m s ^−1 , which represents only a fraction of the known variations in either the residual zonal or meridional flow with amplitudes around 3 and 5 m s ^−1 , respectively. Thus it is unlikely that active regions, and compact magnetic concentrations in general, are the primary source of the 11 yr variation in these global flows. A threshold magnetic flux of 5 × 10 ^20 Mx, below which no significant flows are observed, is identified as a check on the completeness of the set of magnetic regions. We also find that inflows around most magnetic regions are confined to within 10°–12° of their centers, in contrast with recent evidence of more extended inflows.

We have carried out inversions of travel times as measured by Gizon et al. to infer the internal profile of the solar meridional circulation (MC). A linear inverse problem has been solved by the regularized least-squares method with a constraint that the angular momentum (AM) transport by MC should be equatorward (HK21-type constraint). Our motivation for using this constraint is based on the result by Hotta & Kusano (hereafter HK21), where the solar equator-fast rotation was reproduced successfully without any manipulation. The inversion result indicates that the MC profile is a double-cell structure if the so-called HK21 regime, in which AM transported by MC sustains the equator-fast rotation, correctly describes the physics inside the solar convective zone. The sum of the squared residuals computed with the inferred double-cell MC profile is comparable to that computed with the single-cell MC profile obtained when we exclude the HK21-type constraint, showing that both profiles can explain the data more or less at the same level. However, we also find that adding the HK21-type constraint degrades the resolution of the averaging kernels. Although it is difficult for us to determine the large-scale morphology of the solar MC at the moment, our attempt highlights the relevance of investigating the solar MC profile from both theoretical and observational perspectives.

The propagation of meridional circulation below the base of the convection zone (CZ) of low-mass stars may play a crucial role in the transport of angular momentum and also significantly contribute to the transport of chemical species and magnetic fields within their stable radiative zone (RZ). We systematically study these large-scale mean flows by performing three-dimensional global numerical simulations in a spherical shell that consists of a convective region overlying a stably stratified region. We find that the meridional flows can penetrate distances as large as ∼0.21 r _o (where r _o is the outer radius) below the base of the CZ, provided that the Eddington–Sweet timescale t _ES is much shorter than the viscous timescale t _ν , as measured by the parameter $\sigma ={({t}_{\mathrm{ES}}/{t}_{\nu })}^{1/2}$ . In the solar-like regime, where σ ≲ 1 in the upper RZ, we find that the angular momentum transport in the deep RZ is determined primarily by the action of the Coriolis force on meridional flows. In contrast, in models run in the σ > 1 regime, the meridional flows become weaker and the viscous effects dominate. We find that the penetration lengthscale δ _MC of these mean flows when σ ≲ 1 is proportional to σ ^−0.22 . Our findings may provide a better understanding of the role of the meridional flows in the dynamics of the solar interior and inform future numerical studies that are focused on capturing solar-like dynamics self-consistently.

Meridional circulation regulates the Sun’s interior dynamics and magnetism. While it is well accepted that meridional flows are poleward at the Sun’s surface, helioseismic observations have yet to provide a definitive answer for the depth at which those flows return to the equator, or the number of circulation cells in depth. Here, we explore the observability of multiple circulation cells stacked in radius. Specifically, we examine the seismic signature of several meridional flow profiles by convolving time–distance averaging kernels with mean flows obtained from a suite of 3D hydrodynamic simulations. At mid and high latitudes, we find that weak flow structures in the deep convection zone can be obscured by signals from the much stronger surface flows. This contamination of 1–2 m s ^−1 is caused by extended side lobes in the averaging kernels, which produce a spurious equatorward signal with flow speeds that are 1 order of magnitude stronger than the original flow speeds in the simulations. At low latitudes, the flows in the deep layers of the simulations are stronger (>2 m s ^−1 ) and multiple cells across the convection zone can produce a sufficiently strong signal to survive the convolution process. Now that meridional flows can be measured over two decades of data, the uncertainties arising from convective noise have fallen to a level where they are comparable in magnitude to the systematic biases caused by nonlocal features in the averaging kernels. Hence, these systematic errors are beginning to influence current helioseismic deductions and need broader consideration.

Using time–distance local helioseismology flow maps within 1 Mm of the solar photosphere, we detect inflows toward activity belts that contribute to solar-cycle scale variations in the near-surface meridional flow. These inflows stretch out as far as 30° away from the active region centroids. If active region neighborhoods are excluded, the solar-cycle-scale variation in the background meridional flow diminishes to below 2 m s−1, but still shows systematic variations in the absence of active regions between sunspot cycles 24 and 25. We therefore propose that the near-surface meridional flow is a three-component flow made up of a constant baseline flow profile that can be derived from quiet-Sun regions, variations due to inflows around active regions, and solar-cycle-scale variation of about 2 m s−1. Torsional oscillation, on the other hand, is found to be a global phenomenon, i.e., exclusion of active region neighborhoods does not significantly affect its magnitude or phase. This nonvariation in torsional oscillation with distance away from active regions and the three-component breakdown of the near-surface meridional flow serve as vital constraints for solar dynamo models and surface flux-transport simulations. [ABSTRACT FROM AUTHOR]

We present evidence of hitherto undiscovered global-scale oscillations in the near-surface shear layer of the Sun. These oscillations are seen as large-scale variations of radial shear in both the zonal and meridional flows relative to their mean values. The variations cover all or most of a visible hemisphere, and reverse with a timescale on the order of a solar rotation. A large annual variation in the meridional shear anomaly is understandable in terms of the tilt of the rotation axis, but the rapid oscillations of the shear anomalies in both zonal and the meridional directions appear to be modulated in a more complex, not-quite-annual way, although the latter are also strongly modulated by the projected rotational axis angle. Small-scale anomalies in the neighborhood of active regions lend support to their solar origin and physical interpretation. These results were obtained by analyzing ring-diagram fits of low-order modes in high-resolution Doppler data from the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory.

Solar meridional circulation is an axisymmetric flow system, extending from the equator to the poles (∼ 20 m/s at the surface, ≈ 1% of the mean solar rotation rate), plunging inwards and subsequently completing the circuit in the interior through an equatorward return flow and a radially outward flow back up to the surface. This article reviews the profound role that meridional circulation plays in maintaining global dynamics and regulating large-scale solar magnetism. Because it is relatively weak in comparison to differential rotation (∼ 300 m/s, ≈ 7% of the mean solar rotation rate) and owing to numerous systematical errors, accurate surface measurements were only first made in 1978 and initial inferences of interior meridional circulation were obtained using helioseismology two decades later. However, systematical biases have made it very challenging to reliably recover flow in the deep interior. Despite numerous advances that have served to improve the accuracy of inferences, the location of the return flow and the full extent of the circulation are still open problems. This article follows the historical developments and summarises contemporary advances that have led to modern inferences of surface and interior meridional flow. [ABSTRACT FROM AUTHOR]

Mapping the large-scale subsurface plasma flow profile within the Sun has been attempted using various methods for several decades. One such flow in particular is the meridional circulation, for which numerous studies have been published. However, such studies often show disagreement in structure. In an effort to constrain the flow profile from the data, a Bayesian Markov chain Monte Carlo framework has been developed to take advantage of the advances in computing power that allow for the efficient exploration of high-dimensional parameter spaces. This study utilizes helioseismic travel-time difference data covering a span of 21 years and a parameterized model of the meridional circulation to find the most likely flow profiles. Tests were carried out on artificial data to determine the ability of this method to recover expected solar-like flow profiles, as well as a few extreme cases. We find that this method is capable of recovering the input flows of both single- and double-cell flow structures. Some inversion results indicate potential differences in meridional circulation between the two solar cycles in terms of both magnitude and morphology, in particular in the mid-convection zone. Of these, the most likely solutions show that solar cycle 23 has a large single-celled profile, while cycle 24 shows weaker flows in general and hints toward a double-celled structure.

Using time–distance local helioseismology flow maps within 1 Mm of the solar photosphere, we detect inflows toward activity belts that contribute to solar-cycle scale variations in the near-surface meridional flow. These inflows stretch out as far as 30° away from the active region centroids. If active region neighborhoods are excluded, the solar-cycle-scale variation in the background meridional flow diminishes to below 2 m s ^−1 , but still shows systematic variations in the absence of active regions between sunspot cycles 24 and 25. We therefore propose that the near-surface meridional flow is a three-component flow made up of a constant baseline flow profile that can be derived from quiet-Sun regions, variations due to inflows around active regions, and solar-cycle-scale variation of about 2 m s ^−1 . Torsional oscillation, on the other hand, is found to be a global phenomenon, i.e., exclusion of active region neighborhoods does not significantly affect its magnitude or phase. This nonvariation in torsional oscillation with distance away from active regions and the three-component breakdown of the near-surface meridional flow serve as vital constraints for solar dynamo models and surface flux-transport simulations.

We solve the inverse problem in the Kuramoto model with three nonidentical oscillators and a phase lag. The model represents a three-cell-in-depth radial profile of the solar meridional circulation in each solar hemisphere and describes the synchronization between the two components (toroidal and poloidal) of the solar magnetic field. We reconstruct natural frequencies of the top and the bottom oscillators from the evolution of their phases when the oscillators are phase-locked. The phase-locking allows to solve the inverse problem when the phase of the middle oscillator is not available. We present the exact solution and investigate its stability. The model reveals a crucial role of the phase lag in the inverse problem solution. We apply the model to the reconstruction of the deep meridional circulation of the Sun and discuss peculiarities of its evolution in terms of solar dynamo. [ABSTRACT FROM AUTHOR]

Abstract: The correlation between geomagnetic activity and the sunspot number in the 11-year solar cycle exhibits long-term variations due to the varying time lag between the sunspot-related and non-sunspot related geomagnetic activity, and the varying relative amplitude of the respective geomagnetic activity peaks. As the sunspot-related and non-sunspot related geomagnetic activity peaks are caused by different solar agents, related to the solar toroidal and poloidal fields, respectively, we use their variations to derive the parameters of the solar dynamo transforming the poloidal field into toroidal field and back. We find that in the last 12 cycles the solar surface meridional circulation varied between 5 and 20m/s (averaged over latitude and over the sunspot cycle), the deep circulation varied between 2.5 and 5.5m/s, and the diffusivity in the whole of the convection zone was ∼108 m2/s. In the last 12 cycles solar dynamo has been operating in moderately diffusion dominated regime in the bulk of the convection zone. This means that a part of the poloidal field generated at the surface is advected by the meridional circulation all the way to the poles, down to the tachocline and equatorward to sunspot latitudes, while another part is diffused directly to the tachocline at midlatitudes, “short-circuiting” the meridional circulation. The sunspot maximum is the superposition of the two surges of toroidal field generated by these two parts of the poloidal field, which is the explanation of the double peaks and the Gnevyshev gap in sunspot maximum. Near the tachocline, dynamo has been operating in diffusion dominated regime in which diffusion is more important than advection, so with increasing speed of the deep circulation the time for diffusive decay of the poloidal field decreases, and more toroidal field is generated leading to a higher sunspot maximum. During the Maunder minimum the dynamo was operating in advection dominated regime near the tachocline, with the transition from diffusion dominated to advection dominated regime caused by a sharp drop in the surface meridional circulation which is in general the most important factor modulating the amplitude of the sunspot cycle. [Copyright &y& Elsevier]