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This article surveys the development of observational understanding of the interior rotation of the Sun and its temporal variation over approximately forty years, starting with the 1960s attempts to determine the solar core rotation from oblateness and proceeding through the development of helioseismology to the detailed modern picture of the internal rotation deduced from continuous helioseismic observations during solar cycle 23. After introducing some basic helioseismic concepts, it covers, in turn, the rotation of the core and radiative interior, the “tachocline” shear layer at the base of the convection zone, the differential rotation in the convection zone, the near-surface shear, the pattern of migrating zonal flows known as the torsional oscillation, and the possible temporal variations at the bottom of the convection zone. For each area, the article also briefly explores the relationship between observations and models.

We describe the defining observations of the solar cycle that provide constraints for the dynamo processes operating within the Sun. Specifically, we report on the following topics: historical sunspot numbers and revisions; active region (AR) flux ranges and lifetimes; bipolar magnetic region tilt angles; Hale and Joy’s law; the impact of rogue ARs on cycle progression and the amplitude of the following cycle; the spatio-temporal emergence of ARs that creates the butterfly diagram; polar fields; large-scale flows including zonal, meridional, and AR in-flows; short-term cycle variability; and helioseismic results including mode parameter changes.

Near-surface flows measured by the ring-diagram technique of local helioseismology show structures that persist over multiple rotations. We examine these phenomena using data from the Global Oscillation Network Group (GONG) and the Helioseismic and Magnetic Imager (HMI) and show that a correlation analysis of the structures can be used to estimate the rotation rate as a function of latitude, giving a result consistent with the near-surface rate from global helioseismology and slightly slower than that obtained from a similar analysis of the surface magnetic field strength. At latitudes of 60 ∘ and above, the HMI flow data reveal a strong signature of a two-sided zonal flow structure. This signature may be related to recent reports of “giant cells” in solar convection.

While the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) provides Doppler-velocity [ V ], continuum-intensity [ I C ], and line-depth [Ld] observations, each of which is sensitive to the five-minute acoustic spectrum, the Atmospheric Imaging Array (AIA) also observes at wavelengths – specifically the 1600 and 1700 Å bands – that are partly formed in the upper photosphere and have good sensitivity to acoustic modes. In this article we consider the characteristics of the spatio–temporal Fourier spectra in AIA and HMI observables for a 15-degree region around NOAA Active Region 11072. We map the spatio–temporal-power distribution for the different observables and the HMI Line Core [ I L ], or Continuum minus Line Depth, and the phase and coherence functions for selected observable pairs, as a function of position and frequency. Five-minute oscillation power in all observables is suppressed in the sunspot and also in plage areas. Above the acoustic cut-off frequency, the behaviour is more complicated: power in HMI I C is still suppressed in the presence of surface magnetic fields, while power in HMI I L and the AIA bands is suppressed in areas of surface field but enhanced in an extended area around the active region, and power in HMI  V is enhanced in a narrow zone around strong-field concentrations and suppressed in a wider surrounding area. The relative phases of the observables and their cross-coherence functions are also altered around the active region. These effects may help us to understand the interaction of waves and magnetic fields in the different layers of the photosphere and will need to be taken into account in multi-wavelength local-helioseismic analysis of active regions.

We study temporal variations in the amplitudes and widths of high-degree acoustic modes by applying the ring-diagram technique to the GONG+, MDI and HMI Dopplergrams during the declining phase of cycle 23 and rising phase of cycle 24. The mode parameters from all three instruments respond similarly to the varying magnetic activity. The mode amplitudes and widths show consistently lower variation due to smaller magnetic activity in cycle 24 as compared to the previous solar cycle.

Sleep is the brain state when cortical activity decreases and memory consolidates. However, in human epileptic patients, including genetic epileptic seizures such as Dravet syndrome, sleep is the preferential period when epileptic spike-wave discharges (SWDs) appear, with more severe epileptic symptoms in female patients than male patients, which influencing patient sleep quality and memory. Currently, seizure onset mechanisms during sleep period still remain unknown. Our previous work has shown that the sleep-like state-dependent synaptic potentiation mechanism can trigger epileptic SWDs (Zhang et al., 2021). In this study, using one heterozygous (het) knock-in (KI) transgenic mice (GABAA receptor γ2 subunit Gabrg2Q390X mutation) and an optogenetic method, we hypothesized that slow-wave oscillations (SWOs) themselves in vivo could trigger epileptic seizures. We found that epileptic SWDs in het Gabrg2+/Q390X KI mice exhibited preferential incidence during NREM sleep period, accompanied by motor immobility/ facial myoclonus/vibrissal twitching, with more frequent incidence in female het KI mice than male het KI mice. Optogenetic induced SWOs in vivo significantly increased epileptic seizure incidence in het Gabrg2+/Q390X KI mice with increased duration of NREM sleep or quiet-wakeful states. Furthermore, suppression of SWO-related homeostatic synaptic potentiation by 4-(diethylamino)-benzaldehyde (DEAB) injection (i.p.) greatly decreased seizure incidence in het KI mice, suggesting that SWOs did trigger seizure activity in het KI mice. In addition, EEG delta-frequency (0.1-4 Hz) power spectral density during NREM sleep was significantly larger in female het Gabrg2+/Q390X KI mice than male het Gabrg2+/Q390X KI mice, which likely contributes to the gender difference in seizure incidence during NREM sleep/quiet-wake as that in human patients. Competing Interest Statement The authors have declared no competing interest.

We study the relation between the vorticty of solar subsurface flows and surface magnetic activity, analyzing more than five years of GONG+ data with ring-diagram analysis. We focus on the enstrophy, defined as the square of vorticity, and the kinetic helicity density, defined as the scalar product of velocity and vorticity, and derive them from the surface to a depth of about 16 Mm. We find that enstrophy and helicity density of subsurface flows are rather constant at low flux values (less than about 10 G), while at higher flux values there is a linear relation between flux and the logarithm of enstrophy or unsigned helicity. In addition, we analyze the temporal variation of thirteen emerging active regions. At the locations of these active regions, there is little enstrophy or helicity before the regions emerge, while after flux emergence the vorticity and helicity values are large. The crosscorrelation in time between flux and enstrophy shows that they are correlated and that shallow layers lag behind deeper layers. This signal might be a hint of the emergence of active regions.

We study temporal variations in the amplitudes and widths of high-degree acoustic modes in the quiet and active Sun by applying ring-diagram technique to the GONG+ and MDI Dopplergrams during the declining phase of cycle 23. The increase in amplitudes and decrease in line-widths in the declining phase of the solar activity is in agreement with previous studies. A similar solar cycle trend in the mode parameters is also seen in the quiet-Sun regions but with a reduced magnitude. Moreover, the amplitudes obtained from GONG+ data show long-term variations on top of the solar cycle trend.

Non-Joy oriented active regions (ARs) are a challenge for solar magnetic field modelers. Although significant deviations from Joy's law are relatively rare for simple bipolar ARs, understanding the causes of their particularity could be critical for the big picture of the solar dynamo. We explore the possibility of the sub-surface local dynamics being responsible for the significant rotation of these ARs. We apply the ring-diagram technique, a local helioseismology method, to infer the flows under and surrounding a non-Joy oriented AR and present the results of a case study in this paper.