Differential Rotation Research Articles

Helioseismic Properties of Dynamo Waves in the Variation of Solar Differential Rotation

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.

Measuring stellar surface rotation and activity with the PLATO mission

The Planetary Transits and Oscillations of stars mission (PLATO) will allow us to measure surface rotation and monitor photometric activity of tens of thousands of main sequence solar-type and subgiant stars. This paper is the first of a series dedicated to the preparation of the analysis of stellar surface rotation and photospheric activity with the near-future PLATO data. We describe in this work the strategy that will be implemented in the PLATO pipeline to measure stellar surface rotation, photometric activity, and long-term modulations. The algorithms are applied on both noise-free and noisy simulations of solar-type stars, which include activity cycles, latitudinal differential rotation, and spot evolution. PLATO simulated systematics are included in the noisy light curves. We show that surface rotation periods can be recovered with confidence for most of the stars with only six months of observations and that the recovery rate of the analysis significantly improves as additional observations are collected. This means that the first PLATO data release will already provide a substantial set of measurements for this quantity, with a significant refinement on their quality as the instrument obtains longer light curves. Measuring the Schwabe-like magnetic activity cycle during the mission will require that the same field be observed over a significant timescale (more than four years). Nevertheless, PLATO will provide a vast and robust sample of solar-type stars with constraints on the activity-cycle length. Such a sample is lacking from previous missions dedicated to space photometry.

Differential Rotation of CoRoT Stars and a Kepler Binary Star from Starspot Transit Mapping

Abstract While direct magnetic field measurements are rare for slowly rotating stars, spots observed during planetary transits provide a potential indicator of magnetic activity on stellar surfaces. Moreover, the rotation of the stellar surface can be probed by monitoring the spots’ position with time in subsequent transits. This study investigates the dynamic interplay of rotational shear and stellar rotation rate in six stars of spectral types F to M, all hosting exoplanets observed by the CoRoT space mission, except for one binary star from Kepler. The analysis, facilitated by the ECLIPSE code, unveils the physical properties of stellar spots, including radius, intensity, temperature, and position. The five CoRoT stars exhibit spot characteristics consistent with those observed in solar type stars. The determination of a spot longitude during different transits allows for the inference of the star’s differential rotation profile, revealing a decreasing trend of rotational shear with the mean stellar rotation period, given by Δ Ω ∝ P ¯ − 0.9 . This implies that, at least for slow rotators (mean rotation period >5 days), as stars age, their differential rotation decreases. Additionally, the six stars analyzed here seem to fall into two categories, according to their spot flux deficit: those with ΔF spot > 0.005 and those with ΔF spot < 0.002.

Metallicity Dependence of Pressure-regulated Feedback-modulated Star Formation in the TIGRESS-NCR Simulation Suite

We present a new suite of numerical simulations of the star-forming interstellar medium (ISM) in galactic disks using the TIGRESS-NCR framework. Distinctive aspects of our simulation suite are (1) sophisticated and comprehensive numerical treatments of essential physical processes including magnetohydrodynamics, self-gravity, and galactic differential rotation, as well as photochemistry, cooling, and heating coupled with direct ray-tracing UV radiation transfer and resolved supernova feedback and (2) wide parameter coverage including the variation in metallicity over Z′≡Z/Z⊙∼0.1-3 , gas surface density Σgas ∼ 5–150 M ⊙ pc−2, and stellar surface density Σstar ∼ 1–50 M ⊙ pc−2. The range of emergent star formation rate surface density is ΣSFR ∼ 10−4–0.5 M ⊙ kpc−2 yr−1, and ISM total midplane pressure is P tot/k B = 103–106 cm−3 K, with P tot equal to the ISM weight W . For given Σgas and Σstar, we find ΣSFR∝Z′0.3 . We provide an interpretation based on the pressure-regulated feedback-modulated (PRFM) star formation theory. The total midplane pressure consists of thermal, turbulent, and magnetic stresses. We characterize feedback modulation in terms of the yield ϒ, defined as the ratio of each stress to ΣSFR. The thermal feedback yield varies sensitively with both weight and metallicity as ϒth∝W−0.46Z′−0.53 , while the combined turbulent and magnetic feedback yield shows weaker dependence ϒturb+mag∝W−0.22Z′−0.18 . The reduction in ΣSFR at low metallicity is due mainly to enhanced thermal feedback yield, resulting from reduced attenuation of UV radiation. With the metallicity-dependent calibrations we provide, PRFM theory can be used for a new subgrid star formation prescription in cosmological simulations where the ISM is unresolved.

Solar Rotation and Activity for Cycle 24 from SDO/AIA Observations

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 m2 s−2 (corresponding to high activity) in 2012 and 2014 to −100 m2 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.

Solar differential rotation coefficients fitted from synoptic magnetic maps

ABSTRACT Based on the consecutive synoptic magnetic maps, we devise a new method to calculate the solar differential rotation coefficients. This method is very easy to implement and has a high accuracy. Firstly, based on the two-term or three-term differential rotation formula, we simulate a synoptic map CR$_{n}$ evolves one Carrington Rotation (CR) time only under the effect of the differential rotation, and thereby a stretched synoptic map CR$_{n*}$ is obtained. Then, through searching the maximum covariance between the maps CR$_{n*}$ and CR$_{n+1}$ by the grid search method, the rotation coefficients can be determined. Based on the synoptic maps of CRs 1625 to 2278 (during the years 1975–2023), the two-term coefficients A and B for latitude region between $\pm 40^{\circ }$ are calculated. The rotation coefficient B shows an obvious 11-yr period. From the time series of B, we find that the Sun usually rotates more differentially in the rising phases of the sunspot cycles than in the falling phases. Moreover, the strong magnetic field corresponds to an increasing of B (note that B has a negative sign) or decreasing of differential. The evolutionary trend of B also indicates that there are several years until the maximum value of B will be reached in solar cycle 25, and the coefficient B will be still in the rising phase in the few coming years. The two-term rotation coefficients for the two hemispheres are also calculated separately, and in the studied time-scale, the largest N–S asymmetry of the rotation rate appeared in October 2007.

Asteroseismic measurement of core and envelope rotation rates for 2006 red giant branch stars

Context. Tens of thousands of red giant stars in the Kepler data exhibit solar-like oscillations. The mixed-mode characteristics of their oscillations enable us to study the internal physics from the core to the surface, such as differential rotation. However, envelope rotation rates have only been measured for about a dozen red giant branch (RGB) stars so far. This limited the theoretical interpretation of angular momentum transport in post-main sequence phases. Aims. We report the measurements of g-mode properties and differential rotation in the largest sample of Kepler RGB stars. Methods. We applied a new approach to calculate the asymptotic frequencies of mixed modes, which accounts for so-called near-degeneracy effects (NDEs) and leads to improved measurements of envelope rotation rates. By fitting these asymptotic expressions to the observations, we obtained measurements of the properties of g modes (period spacing, ΔΠ1, coupling factor, q, g-mode offset term, εg, small separation, δν01) and the internal rotation (mean core, Ωcore, and envelope, Ωenv, rotation rates). Results. Among 2495 stars with clear mixed-mode patterns, we found that 800 show doublets and 1206 show triplets, while the remaining stars do not show any rotational splittings. We measured core rotation rates for 2006 red giants, doubling the size of pre-existing catalogues. This led us to discover an over-density of stars that are narrowly distributed around a well-defined ridge in the plane, showing core rotation rate versus evolution along the RGB. These stars could experience a different angular momentum transport compared to other red giants. With this work, we also increased the sample of stars with measured envelope rotation rates by two orders of magnitude. We found a decreasing trend between envelope rotation rates and evolution, implying that the envelopes slow down with expansion, as expected. We found 243 stars whose envelope rotation rates are significantly larger than zero. For these stars, the core-to-envelope rotation ratios are around Ωcore/Ωenv ∼ 20 and show a large spread with evolution. Several stars show extremely mild differential rotations, with core-to-surface ratios between 1 and 2. These stars also have very slow core rotation rates, suggesting that they go through a peculiar rotational evolution. We also discovered more stars located below the ΔΠ1–Δν degeneracy sequence, which presents an opportunity to study the history of plausible stellar mergers.

OO Leo: An Active Contact Binary with Possible Solar-like Differential Rotation

With Transiting Exoplanet Survey Satellite (TESS) high-precision photometry and Large Sky Area Multi-object Fiber Spectroscopic Telescope medium-resolution spectra, we present the first light and radial velocity curve analyses for the eclipsing binary OO Leo. The simultaneous solution suggests that OO Leo is a W-subtype contact binary with a relatively low mass ratio (1/q = 0.173) and a moderate degree of contact (f = 28.1%). The asymmetry and continuous changes observed in the TESS light curve were properly modeled by one retrograde cool spot on its secondary surface. A detailed investigation of the Hα line also confirmed that the secondary star had a high level of magnetic activity. The retrograde longitudinal motion of the spot can be explained by a solar-like differential rotation in the secondary component. The orbital period investigation revealed that OO Leo is undergoing a secular decrease and a cyclic variation in its orbital period. The secular decrease may be mainly caused by mass transfer from the more massive secondary star to the less massive primary star. The cyclic period variation can be explained by the light–time effect of an invisible third body or the cyclic magnetic activity of the secondary star. The long-lived spot migration in the longitudinal direction makes OO Leo an excellent target for investigating the differential rotations of contact binaries.

Meridional circulation streamlined

Time-dependent meridional circulation and differential rotation in radiative zones are central open issues in stellar evolution theory. We streamline this challenging problem using the “downward control principle” of atmospheric science, under a geostrophic f-plane approximation. We recover the known stellar physics result that the steady-state meridional circulation decays on the length scale proportional to N / f × Pr , assuming molecular viscosity is the dominant drag mechanism. Prior to steady-state, the meridional circulation and the zonal wind (= differential rotation) spread together via radiative diffusion, under thermal wind balance. The corresponding (fourth-order) hyperdiffusion process is reasonably well approximated by regular (second-order) diffusion on scales of order a pressure scale-height. We derive an inhomogeneous diffusion (equiv. advection-diffusion) equation for the zonal flow which admits closed-form time-dependent solutions in a finite depth domain, allowing for rapid prototyping of differential rotation profiles. In the weak drag limit, we find that the time to rotational steady-state can be longer than the Eddington-Sweet time and be instead determined by the longer drag time. Unless strong enough drag operates, the internal rotation of main-sequence stars may thus never reach a steady-state. Streamlined meridional circulation solutions provide leading-order internal rotation profiles for studying the role of fluid/MHD instabilities (or waves) in redistributing angular momentum in the radiative zones of stars. Despite clear geometrical limitations and simplifying assumptions, one might expect our thin-layer geostrophic approach to offer qualitatively useful results to understand deep meridional circulation in stars.

Long-term stellar activity of M dwarfs

Studies of the rotation and activity of M type stars are essential in order to enhance our understanding of stellar dynamos and angular momentum evolution. Using the outstanding photometric capabilities of space telescopes, even those rotation signals with low amplitudes can now be investigated in previously unrivaled detail. By combining data of K2 and the TESS prime mission, the star spot activity of M dwarfs can be monitored over a timescale of half a decade. In the framework of our study on the rotation–activity relation for bright and nearby M dwarfs, we also aim to investigate their long-term activity. While K2 was observing fields distributed around the ecliptic plane, the TESS prime mission was oriented along a line of ecliptic longitude, with one camera centered on an ecliptic pole. Due to these different observing strategies, the overlap between K2 and the TESS prime mission is marginal. However, 45 stars from our sample were observed with both missions, and of these, two early M-type stars that fulfill our selection criteria, EPIC 202059229 and EPIC 245919787, were analyzed in more detail. We find that, for both stars, the rotation period did not change, while the rotational phase did change for EPIC 245919787 by ∼0.2. The amplitude of the spot-induced variability changed for both stars but more significantly for EPIC 245919787. By comparing the cumulative flare frequency distributions, we find that the flare activity for EPIC 202059229 is unchanged, while it slightly changes for EPIC 245919787 between the K2 and TESS epochs. Using a combination of light curves from K2 and TESS that span a baseline of up to 4.5 yr, we are able to measure significant differential rotation for EPIC 245919787. Furthermore, we show that combining missions like K2 and TESS is a promising method for detecting stellar activity cycles.

The Coherent Magnetic Field of the Milky Way

We present a suite of models of the coherent magnetic field of the Galaxy based on new divergence-free parametric functions describing the global structure of the field. The model parameters are fit to the latest full-sky Faraday rotation measures (RMs) of extragalactic sources and polarized synchrotron intensity (PI) maps from the Wilkinson Microwave Anisotropy Probe and Planck. We employ multiple models for the density of thermal and cosmic-ray electrons in the Galaxy, needed to predict the sky maps of RMs and PI for a given Galactic magnetic field (GMF) model. The robustness of the inferred properties of the GMF is gauged by studying many combinations of parametric field models and electron density models. We determine the pitch angle of the local magnetic field (11° ± 1°), explore the evidence for a grand-design spiral coherent magnetic field (inconclusive), determine the strength of the toroidal and poloidal magnetic halo fields below and above the disk (magnitudes the same for both hemispheres within ≈10%), set constraints on the half-height of the cosmic-ray diffusion volume (≥2.9 kpc), investigate the compatibility of RM- and PI-derived magnetic field strengths (compatible under certain assumptions), and check if the toroidal halo field could be created by the shear of the poloidal halo field due to the differential rotation of the Galaxy (possibly). A set of eight models is identified to help quantify the present uncertainties in the coherent GMF spanning different functional forms, data products, and auxiliary input. We present the corresponding sky maps of rates for axion–photon conversion in the Galaxy and deflections of ultrahigh-energy cosmic rays.

Measurement of Solar Differential Rotation by Absolutely Calibrated Iodine-Cell Spectroscopy

Measurement of Solar Differential Rotation by Absolutely Calibrated Iodine-Cell Spectroscopy

Realistic models of general-relativistic differentially rotating stars

ABSTRACT General-relativistic equilibria of differentially rotating stars are expected in a number of astrophysical scenarios, from core-collapse supernovae to the remnant of binary neutron-star mergers. The latter, in particular, have been the subject of extensive studies where they were modelled with a variety of laws of differential rotation with varying degree of realism. Starting from accurate and fully general-relativistic simulations of binary neutron-star mergers with various equations of state and mass ratios, we establish the time when the merger remnant has reached a quasi-stationary equilibrium and extract in this way realistic profiles of differential rotation. This allows us to explore how well traditional laws reproduce such differential-rotation properties and to derive new laws of differential rotation that better match the numerical data in the low-density Keplerian regions of the remnant. In this way, we have obtained a novel and somewhat surprising result: the dynamical stability line to quasi-radial oscillations computed from the turning-point criterion can have a slope that is not necessarily negative with respect to the central rest-mass density, as previously found with traditional differential-rotation laws. Indeed, for stellar models reproducing well the properties of the merger remnants, the slope is actually positive, thus reflecting remnants with angular momentum at large distances from the rotation axis, and hence with cores having higher central rest-mass densities and slower rotation rates.

HIP 65426 is a High-frequency Delta Scuti Pulsator in Plausible Spin–Orbit Alignment with its Directly Imaged Exoplanet

HIP 65426 hosts a young giant planet that has become the first exoplanet directly imaged with JWST. Using time-series photometry from the Transiting Exoplanet Survey Satellite (TESS), we classify HIP 65426 as a high-frequency δ Scuti pulsator with a possible large-frequency separation of Δν = 7.23 ± 0.02 cycles day−1. We check the TESS data for pulsation-timing variations and use the nondetection to estimate a 95% dynamical mass upper limit of 12.8 M Jup for HIP 65426 b. We also identify a low-frequency region of signal that we interpret as stellar latitudinal differential rotation with two rapid periods of 7.85 ± 0.08 hr and 6.67 ± 0.04 hr. We use our TESS rotation periods together with published values of radius and vsini to jointly measure the inclination of HIP 65426 to i⋆=107−11+12 °. Our stellar inclination is consistent with the orbital inclination of HIP 65426 b ( 108−3+6 °) at the 68% percent level based on our orbit fit using published relative astrometry. The lack of significant evidence for spin–orbit misalignment in the HIP 65426 system supports an emerging trend consistent with preferential alignment between imaged long-period giant planets and their host stars.

Evolution of Stellar Rotation in Open Clusters

Understanding stellar rotation and the role of magnetic braking remains a major outstanding problem in astrophysics. In this paper, stellar rotation of the young open cluster Blanco 1 is investigated and compared with other clusters with ages ranging from ∼35 Myr to ∼950 Myr and star masses in the range 0.2 < M⊙ < 1.4. It is proposed that rotation rates of stars in young open clusters are determined by the early angular momentum acquired during formation and not by magnetic braking effects, which operate on longer time scales. On the convective C Sequence, for lighter stars, the early angular velocity is related directly to the moment of inertia. However, for the interface or I Sequence, differential rotation exists and observed rotation rates are essentially the rotation rates of the outer convection zone. It is estimated that the convection zone can rotate at over 10× the rate of the inner radiative zone for heavier stars. This differential rotation process can drive saturated interface dynamos that lead to large rotational mass dependences which can be described by a simple energy transfer model. Comparing with clusters of different ages magnetic braking outlines the evolution of older clusters from young clusters. For old clusters such as Praesepe the majority of stars have experienced spin down, that can be described by a simple model based on an additional momentum loss proportional to the angular momentum of the early cluster, which for the I Sequence is consistent with the well known Skumanich relation.

Partial tidal disruption events: the elixir of life

ABSTRACT In our Galactic Centre, about $10\,000$ to $100\,000$ stars are estimated to have survived tidal disruption events, resulting in partially disrupted remnants. These events occur when a supermassive black hole (SMBH) tidally interacts with a star, but not enough to completely disrupt the star. We use the 1D stellar evolution code Kepler and the 3D smoothed particle hydrodynamics code Phantom to model the tidal disruption of 1, 3, and $10\, \mathrm{M}_\odot$ stars at zero-age main sequence (ZAMS), middle-age main sequence (MAMS), and terminal-age main sequence (TAMS). We map the disruption remnants into Kepler in order to understand their post-distribution evolution. We find distinct characteristics in the remnants, including increased radius, rapid core rotation, and differential rotation in the envelope. The remnants undergo composition mixing that affects their stellar evolution. Although the remnants formed by disruption of ZAMS models evolve similarly to unperturbed models of the same mass, for MAMS and TAMS stars, the remnants have higher luminosity and effective temperature. Potential observational signatures include peculiarities in nitrogen and carbon abundances, higher luminosity, rapid rotation, faster evolution, and unique tracks in the Hertzsprung–Russell diagram.

Equator to Pole Solar Chromospheric Differential Rotation Using Ca-K Features Derived from Kodaikanal Data

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.

Modeling the effects of starspots on stellar magnetic cycles

Context. Observations show that faster rotating stars tend to have stronger magnetic activity and shorter magnetic cycles. The cyclical magnetic activity of the Sun and stars is believed to be driven by the dynamo process. The success of the Babcock-Leighton (BL) dynamo in explaining the solar cycle suggests that starspots could play an important role in stellar magnetic cycles. Aims. We aim to extend the BL mechanism to solar-mass stars with various rotation rates and explore the effects of emergence properties of starspots in latitudes and tilt angles on stellar magnetic cycles. Methods. We adopt a kinematic BL-type dynamo model operating in the bulk of the convection zone. The profiles of the large-scale flow fields are from the mean-field hydrodynamical model for various rotators. The BL source term in the model is constructed based on the rotation dependence of starspot emergence; that is, faster rotators have starspots at higher latitudes with larger tilt angles. Results. Faster rotators have poloidal flux appearing closer to about ±55° latitudes, where the toroidal field generation efficiency is the strongest because of the peak in the strength of the latitudinal differential rotation there. It takes a shorter time for faster rotators to transport the surface poloidal field from their emergence latitude to the ±55° latitudes of efficient Ω-effect, which shortens their magnetic cycles. The faster rotators operate in a more supercritical regime because of a stronger BL α-effect relating to the tilt angles, which leads to stronger saturated magnetic fields and makes the coupling of the poloidal field between two hemispheres more difficult. The magnetic field parity therefore shifts from the hemispherically asymmetric mixed mode to quadrupole, and further to dipole when a star spins down. Conclusions. The emergence of starspots plays an essential role in the large-scale stellar dynamo.

The solar dynamo begins near the surface

The magnetic dynamo cycle of the Sun features a distinct pattern: a propagating region of sunspot emergence appears around 30° latitude and vanishes near the equator every 11 years (ref. 1). Moreover, longitudinal flows called torsional oscillations closely shadow sunspot migration, undoubtedly sharing a common cause2. Contrary to theories suggesting deep origins of these phenomena, helioseismology pinpoints low-latitude torsional oscillations to the outer 5–10% of the Sun, the near-surface shear layer3,4. Within this zone, inwardly increasing differential rotation coupled with a poloidal magnetic field strongly implicates the magneto-rotational instability5,6, prominent in accretion-disk theory and observed in laboratory experiments7. Together, these two facts prompt the general question: whether the solar dynamo is possibly a near-surface instability. Here we report strong affirmative evidence in stark contrast to traditional models8 focusing on the deeper tachocline. Simple analytic estimates show that the near-surface magneto-rotational instability better explains the spatiotemporal scales of the torsional oscillations and inferred subsurface magnetic field amplitudes9. State-of-the-art numerical simulations corroborate these estimates and reproduce hemispherical magnetic current helicity laws10. The dynamo resulting from a well-understood near-surface phenomenon improves prospects for accurate predictions of full magnetic cycles and space weather, affecting the electromagnetic infrastructure of Earth.

Multi-year crop rotation and quicklime application promote stable peanut yield and high nutrient-use efficiency by regulating soil nutrient availability and bacterial/fungal community.

Diversifying cultivation management, including different crop rotation patterns and soil amendment, are effective strategies for alleviating the obstacles of continuous cropping in peanut (Arachis hypogaea L.). However, the peanut yield enhancement effect and temporal changes in soil chemical properties and microbial activities in response to differential multi-year crop rotation patterns and soil amendment remain unclear. In the present study, a multi-year localization experiment with the consecutive application of five different cultivation managements (including rotation with different crops under the presence or absence of external quicklime as soil amendment) was conducted to investigate the dynamic changes in peanut nutrient uptake and yield status, soil chemical property, microbial community composition and function. Peanut continuous cropping led to a reduction in peanut yield, while green manure-peanut rotation and wheat-maize-peanut rotation increased peanut yield by 40.59 and 81.95%, respectively. A combination of quicklime application increased yield by a further 28.76 and 24.34%. Alterations in cultivation management also strongly affected the soil pH, nutrient content, and composition and function of the microbial community. The fungal community was more sensitive than the bacterial community to cultivation pattern shift. Variation in bacterial community was mainly attributed to soil organic carbon, pH and calcium content, while variation in fungal community was more closely related to soil phosphorus content. Wheat-maize-peanut rotation combined with quicklime application effectively modifies the soil acidification environment, improves the soil fertility, reshapes the composition of beneficial and harmful microbial communities, thereby improving soil health, promoting peanut development, and alleviating peanut continuous cropping obstacles. We concluded that wheat-maize-peanut rotation in combination with quicklime application was the effective practice to improve the soil fertility and change the composition of potentially beneficial and pathogenic microbial communities in the soil, which is strongly beneficial for building a healthy soil micro-ecology, promoting the growth and development of peanut, and reducing the harm caused by continuous cropping obstacles to peanut.