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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]

This paper uses wavelet transforms to look for the rotational frequencies of the Sun's mean line-of-sight magnetic field. For a sufficiently high wavelet frequency, the spectra of the dipole, quadrupole, and hexapole field components each show a time-dependent fine structure with periods in the range of 26.5–30 days and their harmonics. These maps confirm that a large enhancement of power at 30 days occurred in the dipole field during 1989–1990, as recorded previously using Fourier techniques. In addition, during some years the maps show power at 26.5 days (or its harmonics), which is clearly distinguishable from the rotation period of 26.9–27.0 days at the Sun's equator. In at least one case, the 26.5-day period was a wave phenomenon caused by the systematic eruption of active regions at progressively more western locations in the Carrington coordinate system, as if the flux were emerging from a fixed longitude in a faster-rotating subsurface layer. Based on previous studies of the mean field, I conclude that the enhanced wavelet patterns in this paper are regions where magnetic flux is emerging in configurations that strengthen the Sun's horizontal dipole, quadrupole, and hexapole fields, and (in the case of the more slowly rotating patterns) where this flux is being transported to midlatitudes whose rotation periods are in the range of 28–30 days. [ABSTRACT FROM AUTHOR]

In 1777 Ruđer Bošković observed sunspots, determined their positions and the solar rotation elements by his own methods briefly described here. We repeat his calculations of the mean solar time, sunspot positions, and solar rotation elements using both the Bošković's original equations and equations adapted for modern computers. We repeat the calculations using two values of the obliquity of the ecliptic, Bošković's, and an interpolated one. Using his 1777 observations, Bošković obtained the solar equator's inclination, ecliptic longitude of the ascending node, and sidereal and synodic rotation periods. We analyzed and compared these original Bošković results with our repeated calculations. Our results confirm the validity of Bošković's methods and the precision of his calculations. Additionally, the paper presents the solar differential rotation determination using all 1777 observations by Ruđer Bošković. [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.

The responses of Earth's and Mars' thermospheric densities to quasi‐periodic (∼27‐day) solar rotation variations in flux were measured contemporaneously by the Mars Atmosphere and Volatile EvolutioN, Geostationary Operational Environmental Satellites, and Swarm‐C satellites. While large solar rotation variability is found in both planetary thermospheres, correlation analyses performed on over 6 years of observations reveal that, independently of extreme ultraviolet flux level, Earth's daytime density response is about 10%–50% larger than Mars' at a similar density level. Important altitude dependencies in the density sensitivity to the solar rotation in solar flux are found in the Martian thermosphere, while the terrestrial thermosphere is shown to exhibit only small (±5%) day/night and latitude variations in the response. Detailed analyses focused on correlative periods in 2015–2016 and 2020 indicate important solar cycle effects in the sensitivities of both planetary thermospheres, with increased slopes under low solar flux conditions. These results provide important new insights into processes relevant to the interpretation of the sources of short‐term density variability in Mars' and Earth's thermospheres associated with solar drivers and point to the need for targeted modeling efforts along with dedicated data analyses to help resolve current unknowns in thermal balance processes. Plain Language Summary: The quasi‐periodic change in solar extreme ultraviolet (EUV) radiation from active regions on the Sun rotating with a period of about 27 days is one of the largest sources of short‐term variability in the upper atmospheres of both Mars and Earth. This work investigates the response of total mass densities in the upper atmospheres of Mars (∼160–260 km altitude) and Earth (∼450–480 km altitude) to the solar rotation variation in EUV flux, as a tracer of short‐term solar‐driven impacts on neutral densities. We use simultaneous density and solar flux observations from the Mars Atmosphere and Volatile EvolutioN, Swarm‐C, and Geostationary Operational Environmental Satellites from 2014 through 2021. Earth's daytime densities in the middle thermosphere are found to be about 10%–50% more responsive than Mars' for an equivalent altitude. Important dependencies on height are found at Mars, while small day/night and latitude dependencies are found at Earth. Correlation analyses also suggest strong solar cycle effects on the sensitivities, with significantly higher sensitivities during solar minimum. The results of this study can help to better constrain comparative planetary thermosphere simulations and resolve unknowns in thermal balance processes but also suggest the need for additional data‐ and modeling‐driven studies. Key Points: Solar rotation effects on Earth's and Mars' thermospheric densities are quantified in over 6 years of simultaneous satellite observationsEarth's middle thermospheric daytime density is 30%–50% (10%–30%) more responsive than Mars' during solar maximum (minimum) conditionsDensity sensitivities to solar rotation variability in extreme ultraviolet flux show clear dependencies on altitude and solar cycle at both planets [ABSTRACT FROM AUTHOR]

The temporal variations of solar rotation in the photosphere, chromosphere, and corona have been widely investigated, whereas the rotation of the solar transition region is rarely studied. Here, we perform a primary study about the long-term variation of the rotation in the transition region using Ly α irradiance from 1947 February 14 to 2023 February 20. Correlation techniques are used, and the main results are as follows. (1) The sidereal rotation period of the solar transition region varies between 22.24 and 31.49 days, and the mean sidereal rotation period is 25.50 days for the studied time interval 1947–2022. (2) The rotation period of the transition region exhibits a clear downward trend during 1947–2022, which might be caused by the reduced heliospheric pressure and the weaker solar global magnetic fields. (3) Significant periodic signal of the quasi-Schwabe cycle is found in the rotation periods of the transition region. (4) The cross-correlation between the rotation periods of the solar transition region and sunspot activity corroborates a strong correlation with the Schwabe cycle. Possible mechanisms responsible for these results are discussed.

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.

There has been scientific debate about speculations that 'neutrino-induced' radioactive decay causes apparent violations of the exponential-decay law. Sturrock and others repeatedly publish papers asserting influences by solar and cosmic neutrinos on radioactive decay measurements and therefrom draw conclusions about space science that are highly speculative. Recurrent themes in their work are claims that the solar neutrino flux reveals oscillations at a monthly rate which can be linked to solar rotation, that annual and monthly oscillations occur in radioactive decay rates or directionality of emitted radiation which can be linked to variations in solar and cosmic neutrino flux hitting Earth's surface, and that unstable radioactivity measurements can be used as a source of information about the interior of the Sun and dark matter. Radionuclide metrologists have extensively investigated and refuted their arguments. Metrological evidence shows that radioactive decay does not violate the exponential-decay law and is not a probe for variations in solar neutrino flux. In this review paper, the main arguments of Sturrock are listed and counterarguments are presented. Reference is made to earlier published work in which the evidence has been scrutinised in detail. [ABSTRACT FROM AUTHOR]

We study the radial gradient of the solar rotation rate in the near-surface shear layer (NSSL) from about .950 R⊙ to the solar surface and its variation during Solar Cycles 23 and 24 with ring-diagram analysis applied to Global Oscillation Network Group (GONG) and Helioseismic and Magnetic Imager (HMI) Dopplergrams. The average radial gradient is ∂ log Ω/∂ log r = − 1.0 ± .1 at .990 R⊙ in agreement with previous studies. The average radial gradient is ∂ log Ω/∂ log r = − .11 ± .01 at the base of the NSSL at .950R⊙, while it is steeper than −1 closer to the surface between .990R⊙ and .997R⊙. The average radial gradient is rather flat within ±40° latitude from about .970 R⊙ to the solar surface. The radial gradient of the solar rotation rate varies with the solar cycle. At locations of high magnetic activity, the radial gradient is more negative than average from about .970 R⊙ to .990 R⊙, while in quiet regions the radial gradient is less negative than average at these depths. Close to the surface at .997 R⊙, this relationship appears to be reversed. Prominent features of the solar-cycle variation of large-scale flows, such as poleward branches or precursor flows, are not obviously present. The variation of the radial gradient thus more likely indicates the presence or absence of magnetic flux above a certain threshold. The temporal variations derived from the different HMI and GONG data sets agree within one error bar at most depths and latitudes, while their amplitudes might be different.

The solar filaments obtained from the daily Ca ii K3 observations at the Coimbra Astronomical Observatory, which is now called the Geophysical and Astronomical Observatory of the University of Coimbra (OGAUC), for the period 1929 – 1941 have been digitized and validated, and they are confirmed to be reliable for solar activity studies. We use these filament data to investigate the rotation and differential degree of the solar high chromosphere. The main results are as follows: (1) the rotation profile of filaments is somewhat steeper than the rotation profile for long-lived Hα filaments; (2) the high chromosphere filaments rotate faster than sunspots, the photosphere, and the medium-low chromosphere at middle-low latitudes; (3) solar filaments rotate at a higher rotation rate in the descending phase of the solar cycle than in the ascending phase, and their rotation velocities are relatively faster around the year of solar maximum. The possible explanation for the above results is given. [ABSTRACT FROM AUTHOR]

This paper uses wavelet transforms to look for the rotational frequencies of the Sun’s mean line-of-sight magnetic field. For a sufficiently high wavelet frequency, the spectra of the dipole, quadrupole, and hexapole field components each show a time-dependent fine structure with periods in the range of 26.5–30 days and their harmonics. These maps confirm that a large enhancement of power at 30 days occurred in the dipole field during 1989–1990, as recorded previously using Fourier techniques. In addition, during some years the maps show power at 26.5 days (or its harmonics), which is clearly distinguishable from the rotation period of 26.9–27.0 days at the Sun’s equator. In at least one case, the 26.5-day period was a wave phenomenon caused by the systematic eruption of active regions at progressively more western locations in the Carrington coordinate system, as if the flux were emerging from a fixed longitude in a faster-rotating subsurface layer. Based on previous studies of the mean field, I conclude that the enhanced wavelet patterns in this paper are regions where magnetic flux is emerging in configurations that strengthen the Sun’s horizontal dipole, quadrupole, and hexapole fields, and (in the case of the more slowly rotating patterns) where this flux is being transported to midlatitudes whose rotation periods are in the range of 28–30 days.

Solar differential rotation is an important ingredient of the solar dynamo model, not only because the solar rotation profile is one of the key inputs in a solar dynamo model, but also because it imposes constraints for the solar dynamo model. In this study, we use the sunspot group catalog published by the Coimbra Astronomical Observatory for the period 1929–1941 to analyze solar rotation profiles of different-sized sunspot groups and the dependence of their annual average of the absolute latitude and annual average rotation rate on the solar cycle. The following main results are obtained: (1) smaller sunspot groups (with an area 500 msh); (2) different-sized sunspot groups drift toward the equator at different velocities of latitudinal drift, reflecting that they are rooted at different anchoring depths; (3) the rotation rate reaches a maximum during the minimum of the solar cycle, which seems to be independent of the size of sunspot groups. The possible mechanisms for the above results are discussed, and we infer that the differences may be due to the different anchoring depths at which flux tubes of different-sized sunspot groups are rooted, their different ages, and the different ways in which sunspot group coordinates are determined.

To date, the rotational characteristics of the solar transition region remain unclear. In this work, by applying the flux modulation method to the images derived from the Solar Dynamics Observatory/Atmospheric Imaging Assembly between 2011 and 2022 at 304 Å wavelength, we have studied the rotation of the solar transition region, and the results obtained are as follows. The solar transition region rotates differentially, while, from the perspective of the entire time interval, the rotation coefficients A and B are 14.39 (±0.08) and −1.61 (±0.15), respectively, and we find no prominent asymmetry in the average rotation rate of the northern and southern hemispheres. The solar transition region rotates fastest during the solar cycle maximum, and the average rotation rate follows the overall trend of solar activity. Both the equatorial rotation rate (represented by coefficient A ) and the latitudinal gradient (represented by coefficient B ) of the solar transition region are smaller than that of the solar chromosphere and the corona, indicating the solar transition region rotates more slowly and more rigidly than the other two layers, and we speculate that the solar chromosphere and corona seem to restrain the rotation of the solar transition region at the same time.

Recently, Rozelot & Eren pointed out that the first solar gravitational moment ( J _2 ) might exhibit a temporal variation. The suggested explanation is through the temporal variation of the solar rotation with latitude. This issue is deeper developed due to an accurate knowledge of the long-term variations in solar differential rotation regarding solar activity. Here we analyze solar cycles 12–24, investigating the long-term temporal variations in solar differential rotation. It is shown that J _2 exhibits a net modulation over the 13 studied cycles of ≈(89.6 ± 0.1) yr, with a peak-to-peak amplitude of ≈0.1 × 10 ^−7 for a reference value of 2.07 × 10 ^−7 ). Moreover, J _2 exhibits a positive linear trend in the period of minima solar activity (sunspot number up to around 40) and a marked declining trend in the period of maxima (sunspot number above 50). In absolute magnitude, the mean value of J _2 is more significant during periods of minimum than in periods of maximum. These findings are based on observational results that are not free of errors and can be refined further by considering torsional oscillations for example. They are comforted by identifying a periodic variation of the J _2 term evidenced through the analysis of the perihelion precession of planetary orbits either deduced from ephemerides or computed in the solar equatorial coordinate system instead of the ecliptic coordinate one usually used.

Along with a butterfly diagram of sunspots, combined observational studies of ephemeral active regions, X-ray and EUV bright points, plage, filaments, faculae, and prominences demonstrate a pattern, which is known as the Extended Solar Cycle. This pattern indicates that the wings of the sunspot butterfly could be extended to much higher latitudes (up to ∼60°), to an earlier time than the start of a sunspot cycle, hence yielding a strong overlap between cycles. Thus, during the ongoing cycle’s activity near 30° latitude in each hemisphere, the next cycle kicks off at around 60°. By representing these epochs of overlaps by oppositely directed double magnetic bands in each hemisphere, we compute the unstable eigenmodes for MHD Rossby waves at the base of the convection zone and study how the properties of these energetically active Rossby waves change as these band pairs migrate equatorward. We find that in each hemisphere the low-latitude band interacts with the high-latitude band and drives the MHD instability as the solar activity progresses from 35°–15° latitude, which is essentially the rising phase. When the activity proceeds further equatorward from 15°, the interaction between low- and high-latitude bands weakens, and the cross-equatorial interaction between two low-latitude bands in each hemisphere starts. The eigenmodes in the latitude-longitude plane also reflect such changes in their pattern as the bend of the active cycle moves below 15° latitude.

The traditional method considers the Sun as a rigid sphere and diffuse radiator, and neglects the solar characteristics. However, this leads to high bias in the measurement model. In this study, to build a more realistic bias model and a statistical model of noise, the authors consider three solar characteristics, including the solar differential rotation, Lambert radiator and small‐scale solar activities. After mathematical derivation, the bias model of the solar Doppler difference measurement considering the solar differential rotation and Lambert radiator is built. Simulation results demonstrate that the difference between the proposed bias model and the traditional one is on the order of 0.1–1 m/s, which is slowly‐varying and non‐ignorable. Therefore, the bias model considering the solar differential rotation and Lambert radiator is meaningful. After mathematical analysis, they also find that small‐scale solar activities cause an extremely low error in the solar Doppler difference measurement. Moreover, the noise of the Doppler difference is within 2 m/s. Due to the randomness of small‐scale solar activities, the extremely low errors caused by activities can be regarded as noises. These results provide a reference for the measurement modelling of the solar Doppler difference velocimetry navigation. [ABSTRACT FROM AUTHOR]

Galactic cosmic rays as observed by the Hermanus and Jungfraujoch Neutron Monitors between 1960 and 2018 have been analysed using various spectral analysis techniques. Daily mean neutron monitor measurements are used to identify how several harmonics of the roughly 27-day synodic rotation period change during each of these years. Spectral analysis using Lomb-Scargle and Morlet wavelet techniques of Hermanus and Jungfraujoch data revealed in particular that the fourth harmonic (∼7-day) of the solar rotation period is exceptionally strong during the minima of solar cycles when A < 0 (solar dipole pointing south) in comparison to the minima of cycles when A > 0 (solar dipole pointing north). The power spectrum results obtained in this investigation showed that galactic cosmic rays at both Hermanus and Jungfraujoch exhibit peculiar short-term periodicity behaviour as a result of solar polarity dependent magnetic drifts during negative minima. [ABSTRACT FROM AUTHOR]

Accurate measurements of the solar differential rotation parameters are necessary for understanding the solar dynamo mechanism. We use the orthogonalization process to estimate these parameters. The advantage of the orthogonalization of the data in the tracer motion statistical analysis is outlined. The differential rotation is represented in terms of various types of polynomials. We compare the quality of a set of models of the solar differential rotation using the Akaike information criterion and choose the best one. Applying the proposed method, we studied the solar differential rotation and its North-South asymmetry using observations of coronal holes. A statistical analysis of observations from the Atmospheric Imaging Assembly (AIA) on Solar Dynamics Observatory (SDO) reveals the differential rotation pattern of coronal holes and its North-South asymmetry. [ABSTRACT FROM AUTHOR]

In this study, we are investigating the solar flare events during each Carrington rotation in the period 2002–2017. We studied the relationship between solar flare event location and solar cycle progress (phases). The solar flare events are tending to accumulate around a specific latitude line in the southern and northern hemispheres of the solar disk, which we call the "eruptive latitude". The eruptive latitude is migrating towards the solar equator during the declining phase and away from the solar equator during the ascending phase. The eruptive latitude is consistent with the sunspot butterfly diagram. We found the suitable equation describing the relationship between the eruptive latitude φ and the Carrington rotation number CR using sinusoidal summation function. [ABSTRACT FROM AUTHOR]

In this study, the National Center for Atmospheric Research Thermosphere Ionosphere Electrodynamic General Circulation Model is used to explore the physical mechanisms of the time delay of daytime thermospheric temperature response to the 27‐day solar extreme ultraviolet (EUV) flux variation. The contributions from different physical processes to the time delay of thermospheric temperature response, the peak perturbation of the thermospheric temperature with respect to the peak of 27‐day solar EUV flux variation, were examined by diagnostically analyzing the thermospheric energy equation in a fixed local time frame. It was found that the time delay of the thermospheric temperature response to the 27‐day solar EUV flux variation corresponds to the time needed for the total heating and cooling rates to be balanced. This time is slightly later than the times of the peaks of both the heating and cooling rates. Furthermore, the global circulation in the upper atmosphere plays a significant role in the delayed response of thermospheric temperature to solar EUV flux variations. Our simulation results show that the time delay of thermospheric temperature response to the 27‐day solar EUV flux variation is about 0.5–0.8 day, depending on the amplitude of solar EUV flux variations. Key Points: The time delay of daytime thermospheric temperature response to 27‐day EUV flux variations is 0.5–0.8 dayThe time delay of thermospheric temperature response corresponds to the time needed for the heating rate and the cooling rate to be balancedThe time delay of thermospheric temperature response to 27‐day EUV flux variations is modulated by the thermospheric circulation [ABSTRACT FROM AUTHOR]

This paper presents the first analysis of Van Allen Probes measurements of the cold plasma density and electric field in the inner magnetosphere to show that intervals of strong modulation at the solar rotation period occur in the locations of the outer plasmasphere and plasmapause (~0.7 RE peak‐to‐peak), in the large‐scale electric field (~0.24 mV/m peak‐to‐peak), and in the cold plasma density (~250 to ~70 cm−3 peak‐to‐peak). Solar rotation modulation of the inner magnetosphere is more apparent in the declining phase of the solar cycle than near solar maximum. The periodicities in these parameters are compared to solar extreme ultraviolet irradiance, solar wind dawn‐dusk electric field, and Kp. The variations in the plasmapause location at the solar rotation period anticorrelate with solar wind electric field, magnetospheric electric field, and Kp, but not with extreme ultraviolet irradiance, indicating that convective erosion is the dominant physical process controlling the plasmapause at these timescales. Plain Language Summary: As the Sun rotates with a 27‐day period, it also emits winds of ionized gas. In some places these winds are leaving at faster speeds than in other places. These winds flow out to the Earth and beyond, and because the Sun rotates, the Earth is hit with each stream of fast wind every 27 days. A region of cooler ionized gas in space surrounding Earth, called the plasmasphere, shrinks when the effects of the fast wind on Earth's magnetic field cause the removal of the outer part of the plasmasphere. When the wind speeds decrease, the plasmasphere grows in size again. The result is that the plasmasphere breathes in and out at the solar rotation period. We use the Van Allen Probe‐B satellite to measure the size and density of the plasmasphere and to show for the first time with direct measurements the 27‐day variation in the plasmasphere and its connection to the fast winds from the Sun. This result is important, as the behavior of the plasmasphere affects various kinds of waves that can exist in space around Earth, some of which are responsible for the creation and loss of energetic electrons that can damage spacecraft. Key Points: The dawn‐dusk electric field, plasmaspheric density, and plasmapause L value are driven at near the solar rotation period, ~27 daysThe solar rotation periodicity in plasmaspheric densities and plasmapause L value is due to magnetospheric convectionConvective driving of the inner magnetosphere at the solar rotation period is more dominant in the declining phase of the solar cycle [ABSTRACT FROM AUTHOR]

Highlights • Reply to rebuttal and new papers by Sturrock et al. which repeat old claims. • The radon experiment at GSI is susceptible to sunshine and rainfall. • There is no evidence that solar or cosmic neutrinos induce radioactive decay. • There is no relationship between radioactive decay and solar rotation. Abstract Sturrock et al. have published a "rebuttal" to a paper by Pommé et al. who refuted their claim that variations in a radon decay experiment at the Geological Survey of Israel (GSI) can be associated with solar rotation. Sturrock et al. misinterpret the variability of the decay rates in the gamma counter to assert influences by solar and cosmic neutrinos on beta decay and draw unsubstantiated conclusions about solar dynamics. Evidence suggests that the radon measurements were susceptible to solar irradiance and rainfall, whereas there is no indication that radioactive decay is influenced by the solar neutrino flux. In this reply to the rebuttal, the arguments raised by Sturrock et al. are scrutinised. [ABSTRACT FROM AUTHOR]

To investigate the differential rotation of sunspot groups using the Greenwich data, we propose an approach based on a statistical analysis of the histograms of particular longitudinal velocities in different latitude intervals. The general statistical velocity distributions for all such intervals are shown to be described by two rather than one normal distribution, so that two fundamental rotation modes exist simultaneously: fast and slow. The differentiality of rotation for the modes is the same: the coefficient at sin2 in Faye’s law is 2.87-2.88 deg/day, while the equatorial rotation rates differ significantly, 0.27 deg/day. On the other hand, an analysis of the longitudinal velocities for the previously revealed two differing populations of sunspot groups has shown that small short-lived groups (SSGs) are associated with the fast rotation mode, while large long-lived groups (LLGs) are associated with both fast and slow modes. The results obtained not only suggest a real physical difference between the two populations of sunspots but also give new empirical data for the development of a dynamo theory, in particular, for the theory of a spatially distributed dynamo. [ABSTRACT FROM AUTHOR]

Claims were made by Sturrock et al. that radioactive decay can be induced by interaction of the nucleus with solar neutrinos and that cyclic modulations in decay rates are indicative of the dynamics of the solar interior. They analysed a series of measurements of gamma radiation associated with the emanation and decay of radon in a sealed container at the Geological Survey of Israel (GSI) laboratory. The integral count rates in the NaI detector showed strong variations in time of year and time of day. From time-series analysis, Sturrock et al. claim the presence of small oscillations at frequencies in a range between 7.4 a −1 and 12.5 a −1 , which they speculatively associated with rotational influence on the solar neutrino flux. In this work, it is argued that the GSI radon measurements are unsuited for studying the variability of decay constants, because the data are strongly influenced by environmental conditions, such as solar irradiance and rainfall. At the JRC and PTB, decay rate measurements of the radon decay chain were performed with ionisation chambers, gamma-ray spectrometers and an alpha spectrometer. No deviation from the exponential-decay law was observed. The existence of cyclic variations in the decay constants is refuted, as well as the concept of measuring solar rotation through radioactive decay. [ABSTRACT FROM AUTHOR]

Abstract: It is well known that the time variations of the diverse solar wind variables at 1 AU (e.g., solar wind speed, density, proton temperature, electron temperature, magnetic field strength, specific entropy, heavy‐ion charge‐state densities, and electron strahl intensity) are highly intercorrelated with each other. In correlation studies of the driving of the Earth's magnetosphere‐ionosphere‐thermosphere system by the solar wind, these solar wind intercorrelations make determining cause and effect very difficult. In this report analyses of solar wind spacecraft measurements and compressible‐fluid computer simulations are used to study the origins of the solar wind intercorrelations. Two causes are found: (1) synchronized changes in the values of the solar wind variables as the plasma types of the solar wind are switched by solar rotation and (2) dynamic interactions (compressions and rarefactions) in the solar wind between the Sun and the Earth. These findings provide an incremental increase in the understanding of how the Sun‐Earth system operates. [ABSTRACT FROM AUTHOR]