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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]

Differential rotation is one of the basic characteristics of the Sun, and it plays an important role in generating the magnetic fields and its activities. We investigated rotation rate using chromospheric features such as plages, enhanced network (EN), active network (AN), and quiet network (QN) separately (for the first time). The digitized Ca-K images from Kodaikanal Observatory for 1907–1996 are used to study rotation over 0°–80° latitudes at an interval of 10°. We find that plages and all types of networks exhibit the differential rotation of the chromosphere. Furthermore, the rotation rate shows a decreasing pattern as one move from the equator to the higher polar latitudes for all the features used in the study. At the equator the rotation rate (rotation period) is obtained to be ∼13.98° day−1 (25.74 days), ∼13.91° day−1 (25.88 days), ∼13.99° day−1 (25.74 days), and ∼14.11° day−1 (25.51 days) for plage, EN, AN, and QN areas, respectively. By analyzing how the area of chromospheric features varies over time, we can effectively map the Sun's rotation rate at all latitudes, including the polar regions. Interestingly, both plages and small-scale networks exhibit a similar differential rotation rate. This suggests these features likely rooted at the same layer below the visible surface of the Sun. Therefore, the long-term Ca-K data is very useful for studying the solar rotation rate at all latitudes including the polar regions. [ABSTRACT FROM AUTHOR]

We present a new iterative rotation inversion technique based on the Simultaneous Algebraic Reconstruction Technique developed for image reconstruction. We describe in detail our algorithmic implementation and compare it to the classical inversion techniques like the Regularized Least Squares (RLS) and the Optimally Localized Averages (OLA) methods. In our implementation, we are able to estimate the formal uncertainty on the inferred solution using standard error propagation, and derive the averaging kernels without recourse to any Monte-Carlo simulation. We present the potential of this new technique using simulated rotational frequency splittings. We use noiseless sets that cover the range of observed modes and associate to these artificial splittings observational uncertainties. We also add random noise to present the noise magnification immunity of the method. Since the technique is iterative we also show its potential when using an a priori solution. With the correct regularization, this new method can outperform our RLS implementation in precision, scope, and resolution. Since it results in very different averaging kernels where the solution is poorly constrained, this technique infers different values. Adding such a technique to our compendium of inversion methods will allow us to improve the robustness of our inferences when inverting real observations and better understand where they might be biased and/or unreliable, as we push our techniques to maximize the diagnostic potential of our observations. [ABSTRACT FROM AUTHOR]

We perform a data-constrained simulation with the zero- β assumption to study the mechanisms of strong rotation and failed eruption of a filament in active region 11474 on 2012 May 5 observed by Solar Dynamics Observatory and Solar Terrestrial Relations Observatory. The initial magnetic field is provided by nonlinear force-free field extrapolation, which is reconstructed by the regularized Biot–Savart laws and magnetofrictional method. Our simulation reproduces most observational features very well, e.g., the filament large-angle rotation of about 130°, the confined eruption, and the flare ribbons, allowing us to analyze the underlying physical processes behind observations. We discover two flux ropes in the sigmoid system, an upper flux rope (MFR1) and a lower flux rope (MFR2), which correspond to the filament and hot channel in observations, respectively. Both flux ropes undergo confined eruptions. MFR2 grows by tether-cutting reconnection during the eruption. The rotation of MFR1 is related to the shear-field component along the axis. The toroidal field tension force and the nonaxisymmetry forces confine the eruption of MFR1. We also suggest that the mutual interaction between MFR1 and MFR2 contributes to the large-angle rotation and the eruption failure. In addition, we calculate the temporal evolution of the twist and writhe of MFR1, which is a hint of probable reversal rotation. [ABSTRACT FROM AUTHOR]

Solar differential rotation exhibits a prominent feature: its cyclic variations over the solar cycle, referred to as zonal flows or torsional oscillations, are observed throughout the convection zone. Given the challenge of measuring magnetic fields in subsurface layers, understanding deep torsional oscillations becomes pivotal in deciphering the underlying solar dynamo mechanism. In this study, we address the critical question of identifying specific signatures within helioseismic frequency-splitting data associated with the torsional oscillations. To achieve this, a comprehensive forward modeling approach is employed to simulate the helioseismic data for a dynamo model that, to some extent, reproduces solar-cycle variations of magnetic fields and flows. We provide a comprehensive derivation of the forward modeling process utilizing generalized spherical harmonics, as it involves intricate algebraic computations. All estimated frequency-splitting coefficients from the model display an 11 yr periodicity. Using the simulated splitting coefficients and realistic noise, we show that it is possible to identify the dynamo wave signal present in the solar zonal flow from the tachocline to the solar surface. By analyzing observed data, we find similar dynamo wave patterns in the observational data from the Michelson Doppler Imager, Helioseismic Magnetic Imager, and Global Oscillation Network Group. This validates the earlier detection of dynamo waves and holds potential implications for the solar dynamo theory models.

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.

Differential rotation plays a crucial role in the dynamics of the Sun. We study the solar rotation and its correlation with solar activity by applying a modified machine learning algorithm to identify and track coronal bright points (CBPs) from the Solar Dynamics Observatory/Atmospheric Imaging Assembly observations at 193 Å during cycle 24. For more than 321,440 CBPs, the sidereal and meridional velocities are computed. We find the occurring height of CBPs to be about 5627 km above the photosphere. We obtain a rotational map for the corona by tracking CBPs at the formation height of Fe xii (193 Å) emissions. The equatorial rotation (14.°40 to 14.°54 day ^−1 ) and latitudinal gradient of rotation (−3.°0 to −2.°64 day ^−1 ) show very slightly positive and negative trends with solar activity (sunspots and flares), respectively. For cycle 24, our investigations show that the northern hemisphere has more differential rotation than the southern hemisphere, confirmed by the asymmetry of the midlatitude rotation parameter. The asymmetry (ranked) of the latitudinal gradient of the rotation parameter is concordant with the sunspot numbers for 7 yr within the 9 yr of the cycle; however, for only 3 yr, it is concordant with the flare index. The minimum horizontal Reynolds stress changes from about −2500 m ^2 s ^−2 (corresponding to high activity) in 2012 and 2014 to −100 m ^2 s ^−2 (corresponding to low activity) in 2019 over 5° to 35° latitudes within cycle 24. We conclude that the negative horizontal Reynolds stress (momentum transfer toward the Sun’s equator) is a helpful indication of solar activity.

The ratio of metal abundance to hydrogen abundance of the solar photosphere, ( Z / X ) _s , has been revised several times. Standard solar models, based on these revised solar abundances, are in disagreement with seismically inferred results. Recently, Magg et al. introduced a new value for ( Z / X ) _s , which is still under debate in the community. The solar abundance problem or solar modeling problem remains a topic of ongoing debate. We constructed rotating solar models in accordance with various abundance scales where the effects of convection overshoot and enhanced diffusion were included. Among these models, those utilizing Magg’s abundance scale exhibit superior sound speed and density profiles compared to models using other abundance scales. Additionally, they reproduce the observed frequency separation ratios r _02 and r _13 . These models also match the seismically inferred surface helium abundance and convection zone depth within the 1 σ level. Furthermore, the calculated neutrino fluxes from these models agree with detected ones at the level of 1 σ . We found that neutrino fluxes and density profile are influenced by nuclear reactions, allowing us to use the combination of detected neutrino fluxes and seismically inferred density for diagnosing astrophysical S -factors. This diagnostic approach shows that S _11 may be underestimated by 2%, while S _33 may be overestimated by about 3% in previous determinations. The S -factors favored by updated neutrino fluxes and helioseismic results can lead to significant improvements in solar models.

Differential rotation is one of the basic characteristics of the Sun, and it plays an important role in generating the magnetic fields and its activities. We investigated rotation rate using chromospheric features such as plages, enhanced network (EN), active network (AN), and quiet network (QN) separately (for the first time). The digitized Ca-K images from Kodaikanal Observatory for 1907–1996 are used to study rotation over 0°–80° latitudes at an interval of 10°. We find that plages and all types of networks exhibit the differential rotation of the chromosphere. Furthermore, the rotation rate shows a decreasing pattern as one move from the equator to the higher polar latitudes for all the features used in the study. At the equator the rotation rate (rotation period) is obtained to be ∼13.98° day ^−1 (25.74 days), ∼13.91° day ^−1 (25.88 days), ∼13.99° day ^−1 (25.74 days), and ∼14.11° day ^−1 (25.51 days) for plage, EN, AN, and QN areas, respectively. By analyzing how the area of chromospheric features varies over time, we can effectively map the Sun’s rotation rate at all latitudes, including the polar regions. Interestingly, both plages and small-scale networks exhibit a similar differential rotation rate. This suggests these features likely rooted at the same layer below the visible surface of the Sun. Therefore, the long-term Ca-K data is very useful for studying the solar rotation rate at all latitudes including the polar regions.

The gradient of rotation in the near-surface shear layer (NSSL) of the Sun provides valuable insights into the dynamics associated with the solar activity cycle and the dynamo. Results obtained with global oscillation mode splittings lack resolution near the surface, prompting the use of the local helioseismic ring-diagram method. While the Helioseismic and Magnetic Imager ring-analysis pipeline has been used previously for analyzing this layer, default pipeline parameters limit the accuracy of the near-surface gradients. To address these challenges, we fitted the flow parameters to power spectra averaged over one-year periods at each location, followed by additional averaging over 12 yr. We find that the NSSL can be divided into three fairly distinct regions: a deeper, larger region with a small shear, steepening toward the surface; a narrow middle layer with a strong shear, with a gradient approximately 3 times larger; and a layer very close to the surface, where the logarithmic gradient is close to zero but becomes steeper again toward the surface. The middle layer appears to be centered at 3 Mm, but the poor resolution in these layers implies that it is potentially located closer to the surface, around 1.5 Mm deep. While our analysis primarily focused on regions along the central meridian, we also investigated systematic errors at longitudes off the center. The east–west antisymmetric component of the gradient reveals a layer of substantial differences between the east and west longitude of around 1.7 Mm, and the amplitude of the differences increases with the longitude.

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.

Rotational periods derived from autocorrelation function (ACF) techniques on stars photometrically similar to the Sun in Kepler data have proven difficult to reliably determine. We investigate various instrumental and astrophysical factors affecting the accuracy of these measurements, including the effects of observational windows and noise, stellar activity and inclination, spectral passbands, and the separate normalization of contiguous segments. We validate that the flux variations due to faculae are very periodic, but starspots are the dominant source of bolometric and visible differential variability in Sun-like stars on rotational timescales. We quantify how much stronger the relative contribution of faculae would have to be to render Sun-like light curves periodic enough to reliably measure with autocorrelation methods. We also quantify how long starspot lifetimes need to be to render pure spot light curves periodic enough. In general, longer observational windows yield more accurate ACF measurements, even when faculae are not present. Due to the enhancement of the relative contribution of faculae, observing stars with intermediate inclinations, during activity minima, and/or through bluer passbands has the effect of strengthening the periodicity of the light curve. We search for other manifestations of faculae in broadband photometry of Sun-like stars and conclude that without absolute flux measurements or restriction to shorter-wavelength passbands, differential light curves are uninformative about faculae.

We perform a data-constrained simulation with the zero- β assumption to study the mechanisms of strong rotation and failed eruption of a filament in active region 11474 on 2012 May 5 observed by Solar Dynamics Observatory and Solar Terrestrial Relations Observatory. The initial magnetic field is provided by nonlinear force-free field extrapolation, which is reconstructed by the regularized Biot–Savart laws and magnetofrictional method. Our simulation reproduces most observational features very well, e.g., the filament large-angle rotation of about 130°, the confined eruption, and the flare ribbons, allowing us to analyze the underlying physical processes behind observations. We discover two flux ropes in the sigmoid system, an upper flux rope (MFR1) and a lower flux rope (MFR2), which correspond to the filament and hot channel in observations, respectively. Both flux ropes undergo confined eruptions. MFR2 grows by tether-cutting reconnection during the eruption. The rotation of MFR1 is related to the shear-field component along the axis. The toroidal field tension force and the nonaxisymmetry forces confine the eruption of MFR1. We also suggest that the mutual interaction between MFR1 and MFR2 contributes to the large-angle rotation and the eruption failure. In addition, we calculate the temporal evolution of the twist and writhe of MFR1, which is a hint of probable reversal rotation.

Chromospheric differential rotation is a key component in comprehending the atmospheric coupling between the chromosphere and the photosphere at different phases of the solar cycle. In this study, we therefore utilize the newly calibrated multidecadal Ca ii K spectroheliograms (1907–2007) from the Kodaikanal Solar Observatory (KoSO) to investigate the differential rotation of the solar chromosphere using the technique of image cross-correlation. Our analysis yields the chromospheric differential rotation rate Ω( θ ) = (14.61 ± 0.04–2.18 ± 0.37 ${\sin }^{2}\theta -1.10\pm 0.61{\sin }^{4}\theta )^\circ $ day ^−1 . These results suggest the chromospheric plages exhibit an equatorial rotation rate 1.59% faster than the photosphere when compared with the differential rotation rate measured using sunspots and also a smaller latitudinal gradient compared to the same. To compare our results to those from other observatories, we have applied our method on a small sample of Ca ii K data from Rome, Meudon, and Mount Wilson observatories, which support our findings from KoSO data. Additionally, we have not found any significant north–south asymmetry or any systematic variation in chromospheric differential rotation over the last century.