Differential Rotation Research Articles

Time-dependent Dynamics of the Corona

We present in this Letter the first global comparison between traditional line-tied steady-state magnetohydrodynamic models and a new, fully time-dependent thermodynamic magnetohydrodynamic simulation of the global corona. To approximate surface magnetic field distributions and magnitudes around solar minimum, we use the Lockheed Evolving Surface-Flux Assimilation Model to obtain input maps that incorporate flux emergence and surface flows over a full solar rotation, including differential rotation and meridional flows. Each time step evolves the previous state of the plasma with a new magnetic field input boundary condition, mimicking photospheric driving on the Sun. We find that this method produces a qualitatively different corona compared to steady-state models. The magnetic energy levels are higher in the time-dependent model, and coronal holes evolve more along the following edge than they do in steady-state models. Coronal changes, as illustrated with forward-modeled emission maps, evolve on longer timescales with time-dependent driving. We discuss implications for active and quiet Sun scenarios, solar wind formation, and widely used steady-state assumptions like potential field source surface calculations.

Pre-selection of solar analogues with differential rotation signature

The light curve of a star allows studying the variation of its brightness over time, being suitable for determining rotation periods, detecting planets, studying binary systems and differential rotation. The light curve analysis can be performed with the autocorrelation function (ACF), a robust mathematical tool in the detection of the stellar rotation period, by finding patterns in the photometric data. In this work, a sample of stars from the CoRoT mission is analyzed. The analysis is carried out with the ACF to carry out a pre-selection of stars that show signs of rotational modulation, a determining characteristic for the study of differential rotation. 17 stars were selected by visual inspection of the curves and by the ACF function. It was found that three stars have an excellent profile of autocorrelation function and rotational modulation, three have a good profile and the remaining eleven have inappropriate profiles for the study of differential rotation. The photometric time series analyzes show that the autocorrelation function method is very suitable as a previous criterion for the selection of candidate stars for the study of differential rotation, when they present exponential decay of the oscillation peaks of the light curve.

Dynamical Analysis of the Maclaurin Disk with Velocity Dispersion and Its Influence on the Formation of the Bar

We investigate the influence of Toomre’s Q parameter on the bar-forming dynamics of the Maclaurin disk using N-body simulations. According to Toomre’s criterion, the local velocity dispersion parametrized by Q ≥ 1 is required to suppress the local axisymmetric instability but, in turn, it deviates particle orbits from a nearly circular limit in which particle natural frequencies are calculated. We resolve this by including the effect of velocity dispersion, as the pressure potential, into the effective potential with the gravitational potential. With this formulation, a circular orbit approximation is retrieved. The effective potential hypothesis can describe the Q dependence of angular and epicyclic motions of the processes of the formation of a bar and the established bars reasonably well provided that Q ≥ 1. This indicates the influence of the initial Q imprinted on the entire disk dynamics and not only that Q serves as the indicator of stability. In addition, we perform a stability test for the disk-in-halo systems. With the presence of a halo, disks are more susceptible to the formation of a bar as seen by the elevated critical Q than that for the isolated disk. This is attributed to the differential rotation that builds the unstable non-axisymmetric spiral modes more efficiently, which are the ingredients of the bar instability.

Single-shot vector magnetic measurements using synchronous coherent population trapping resonance in a feedback compensation system

We demonstrate a real-time, single-shot vector magnetic measurement technique using synchronous coherent population trapping (SCPT) in an apparatus consisting of a small rubidium vapor cell. Vector modality of our magnetometer is enabled by designing a feedback system based on performing a peak-lock on a particularly strong 2ΩL magnetic resonance produced in the SCPT spectrum and compensating the external magnetic field via a three-axis field coil. With its current design, this magnetometer exhibits high sensitivities of approximately 155, 129, and 57pT/Hz in measuring the magnetic field vector components along the (x,y,z) axes. Sensitivities closer to the shot-noise limit can be achieved in the future by reducing the technical noise of our equipment and by employing a differential detection and polarization rotation measurement scheme in our system.

A Wall Effects and Means of Controlling the Evolution of Swirling Flows with Vortex Breakdown

This paper investigates numerically the bubble-type vortex breakdown apparition in the case of closed rotating flows of a viscous, axisymmetric, and incompressible fluid. First, a truncated conical/cylindrical cavity of spherical end disks is used to simulate and analyze the vortex structure under rigid surface conditions. The geometric effects of the enclosure are also studied. Vortex breakdown is demonstrated beyond the lower disk rotation rate threshold by introducing the no-slip condition imposed on the upper wall. The objective is to explore ways of controlling the evolution of this physical event by modifying the confinement conditions upstream of the vortex rupture. Particular attention is also paid to the effective kinematic viscosity, thermal diffusivity and geometric control of recirculation zones on the axis of rotation (axial bubble type). The second geometry consists of a spherical annulus formed by two concentric hemispheres in differential rotation under plat-free surface conditions. The results show that rotation of the inner hemisphere induces a vortex bubble on the polar axis. In contrast, the outer hemisphere rotation induces a toroidal vortex on the equator.

MHD in a Cylindrical Shearing Box. II. Intermittent Bursts and Substructures in MRI Turbulence

By performing ideal magnetohydrodynamical (MHD) simulations with weak vertical magnetic fields in unstratified cylindrical shearing boxes with modified boundary treatment, we investigate MHD turbulence excited by magnetorotational instability. The cylindrical simulation exhibits extremely large temporal variation in the magnetic activity compared with the simulation in a normal Cartesian shearing box, although the time-averaged field strengths are comparable in the cylindrical and Cartesian setups. Detailed analysis of the terms describing magnetic energy evolution with “triangle diagrams” surprisingly reveals that in the cylindrical simulation the compression of toroidal magnetic field is unexpectedly as important as the winding due to differential rotation in amplifying magnetic fields and triggering intermittent magnetic bursts, which are not seen in the Cartesian simulation. The importance of the compressible amplification is also true for a cylindrical simulation with tiny curvature; the evolution of magnetic fields in the nearly Cartesian shearing box simulation is fundamentally different from that in the exact Cartesian counterpart. The radial gradient of epicyclic frequency, κ, which cannot be considered in the normal Cartesian shearing box model, is the cause of this fundamental difference. An additional consequence of the spatial variation of κ is continuous and ubiquitous formation of narrow high-density (low-density) and weak-field (strong-field) localized structures; seeds of these ring gap structures are created by the compressible effect and subsequently amplified and maintained under the marginally unstable condition regarding “viscous-type” instability.

Geometry and formation mechanism of tension gashes and their implication on the hydrocarbon accumulation in the deep-seated strata of sedimentary basin: A case from Shunnan area of Tarim Basin

With the theoretical and technological developments related to cratonic strike-slip faults, the Shuntuoguole Low Uplift in the Tarim Basin has attracted considerable attention recently. Affected by multi-stage tectonic movements, the strike-slip faults have controlled the distribution of hydrocarbon resources owing to the special fault characteristics and fault-related structures. In contrast, the kinematics and formation mechanism of strike-slip faults in buried sedimentary basins are difficult to investigate, limiting the discussion of these faults and hydrocarbon accumulation. In this study, we identified the characteristics of massive sigmoidal tension gashes (STGs) that formed in the Shunnan area of the Tarim Basin. High-resolution three-dimensional seismic data and attribute analyses were used to investigate their geometric and kinematic characteristics. Then, the stress state of each point of the STGs was calculated using seismic curvature attributes. Finally, the formation mechanism of the STGs and their roles in controlling hydrocarbon migration and accumulation were discussed. The results suggest that: (1) the STGs developed in the Shunnan area have a wide distribution, with a tensile fault arranged in an en échelon pattern, showing an S-shaped bending. These STGs formed in multiple stages, and differential rotation occurred along the direction of strike-slip stress during formation. (2) Near the principal displacement zone of the strike-slip faults, the stress value of the STGs was higher, gradually decreasing at both ends. The shallow layer deformation was greater than the deep layer deformation. (3) STGs are critical for connecting source rocks, migrating oil and gas, sealing horizontally, and developing efficient reservoirs. This study not only provides seismic evidence for the formation and evolution of super large STGs, but also provides certain guidance for oil and gas exploration in this area.

Differential Rotation in Convecting Spherical Shells with Non-Uniform Viscosity and Entropy Diffusivity

Contemporary three-dimensional physics-based simulations of the solar convection zone disagree with observations. They feature differential rotation substantially different from the true rotation inferred by solar helioseismology and exhibit a conveyor belt of convective “Busse” columns not found in observations. To help unravel this so-called “convection conundrum”, we use a three-dimensional pseudospectral simulation code to investigate how radially non-uniform viscosity and entropy diffusivity affect differential rotation and convective flow patterns in density-stratified rotating spherical fluid shells. We find that radial non-uniformity in fluid properties enhances polar convection, which, in turn, induces non-negligible lateral entropy gradients that lead to large deviations from differential rotation geostrophy due to thermal wind balance. We report simulations wherein this mechanism maintains differential rotation patterns very similar to the true solar profile outside the tangent cylinder, although discrepancies remain at high latitudes. This is significant because differential rotation plays a key role in sustaining solar-like cyclic dipolar dynamos.

Monitoring the young planet host V1298 Tau with SPIRou: planetary system and evolving large-scale magnetic field

ABSTRACT We report results of a spectropolarimetric monitoring of the young Sun-like star V1298 Tau based on data collected with the near-infrared spectropolarimeter SPIRou at the Canada–France–Hawaii Telescope between late 2019 and early 2023. Using Zeeman–Doppler Imaging and the Time-dependent Imaging of Magnetic Stars methods on circularly polarized spectra, we reconstructed the large-scale magnetic topology of the star (and its temporal evolution), found to be mainly poloidal and axisymmetric with an average strength varying from 90 to 170 G over the ∼3.5 yr of monitoring. The magnetic field features a dipole whose strength evolves from 85 to 245 G, and whose inclination with respect to the stellar rotation axis remains stable until 2023 where we observe a sudden change, suggesting that the field may undergo a polarity reversal, potentially similar to those periodically experienced by the Sun. Our data suggest that the differential rotation shearing the surface of V1298 Tau is about 1.5 times stronger than that of the Sun. When coupling our data with previous photometric results from K2 and TESS and assuming circular orbits for all four planets, we report a 3.9σ detection of the radial velocity signature of the outermost planet (e), associated with a most probable mass, density, and orbital period of $M_\mathrm{e}=0.95^{+0.33}_{-0.24}$ MꝜ, $\rho _\mathrm{e}=1.66^{+0.61}_{-0.48}$$\rm g\, cm^{-3}$, and Pe = 53.0039 ± 0.0001 d, respectively. For the three inner planets, we only derive 99 per cent confidence upper limits on their mass of 0.44, 0.22, and 0.25 MꝜ, for b, c, and d, respectively.

Dependence of Stellar Differential Rotation on Effective Temperature and Rotation: An Analysis from Starspot Transit Mapping

Stellar rotation is crucial for studying stellar evolution, since it provides information about age, angular momentum transfer, and magnetic fields of stars. In the case of the Sun, due to its proximity, detailed observation of sunspots at various latitudes and longitudes allows a precise estimation of the solar rotation period and its differential rotation. Here, we present for the first time an analysis of stellar differential rotation using starspot transit mapping as a means of detecting differential shear in solar-type and M stars. The aim of this study is to investigate the relationship between rotational shear, ΔΩ, and both the star's effective temperature (T eff) and its average rotation period (). We present differential rotation profiles derived from previously collected spot transit mapping data for 13 slowly rotating stars (P rot ≥ 4.5 days), with spectral types ranging from M to F, which were observed by the Kepler and CoRoT satellites. Our findings reveal a significant negative correlation between rotational shear and the mean period of stellar rotation (correlation coefficient of −0.77), which may be an indicator of stellar age. On the other hand, a weak correlation was observed between differential rotation and the effective temperature of the stars. Overall, the study provides valuable insights into the complex relationship between stellar parameters and differential rotation, which may enhance our understanding of stellar evolution and magnetic dynamos.

Composite Preambles Based on Differential Phase Rotations for Grant-Free Random Access Systems

With the advantages of low signaling overhead and latency, grant-free random access (GFRA) becomes a promising technology for supporting massive machine-type communications (mMTC), but poses new challenges for active user detection (AUD) and channel estimation (CE), whose performance mainly depends on the preamble detection. In this paper, we design the composite preamble based on differential phase rotations by aggregating orthogonal Zadoff-Chu (ZC) sequences and multiple root ZC sequences with differential phase rotations to reduce the probability of preamble collisions, thereby improving the performance of AUD and CE. In particular, differential phase rotations extend the preamble set size so that users colliding in orthogonal sequences can be distinguished by phase rotations. In addition, it also reduces non-orthogonal interference and thus reduces CE errors. The preamble detection algorithm and CE scheme are proposed, along with the theoretical analysis of AUD and CE performance to verify the effectiveness of the designed preamble. In addition, the proposed preamble is extended to combine phase rotations with cyclic shifts to further enlarge the preamble set size with low non-orthogonality. Simulation results show that the proposed composite preamble outperforms existing preambles in terms of the probability of detection and CE accuracy.

Differential Rotation for Different-sized Sunspot Groups Early Observed by the OGAUC

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 <100 millionths of the solar hemisphere (msh)) rotate faster than larger ones (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.

Coronal bright point statistics

Context. The corona of the Sun is the part of the solar atmosphere with temperatures of over one million Kelvin, which needs to be heated internally in order to exist. This heating mechanism remains a mystery; we see large magnetically active regions in the photosphere lead to strong extreme UV (EUV) emission in the corona. On much smaller scales (on the order of tens of Mm), there are bipolar and multipolar regions that can be associated with evenly sized coronal bright points (CBPs). Aims. Our aim was to study the properties of CBPs in a statistical sense and to use continuous data from the SDO spacecraft, which makes it possible to track CBPs over their whole lifetime. Furthermore, we tested various rotation-speed profiles for CBPs in order to find out if the lower corona is co-rotating with the photosphere. Then we compiled a database with about 346 CBPs together with information of their sizes, shapes, appearance and disappearance, and their visibility in the EUV channels of the AIA instrument. We want to verify our methods with similar previous studies. Methods. We used the high-cadence data of the largest continuous SDO observation interval in 2015 to employ an automated tracking algorithm for CBPs. Some of the information (e.g., the total lifetime, the characteristic shape, and the magnetic polarities below the CBPs) still requires human interaction. Results. In this work we present statistics on fundamental properties of CBPs along with some comparison tables that relate, for example, the CBP lifetime with their shape. CBPs that are visible in all AIA channels simultaneously seem to be brighter in total and also have a stronger heating, and hence a higher total radiation flux. We compared the EUV emission visibility in different AIA channels with the CBP’s shape and lifetime. From the tracking algorithm we confirm a strict co-rotation of the CBPs with the photospheric differential rotation. Conclusions. The tracked CBPs have a typical lifetime of about 1–6 h, while the hottest and brightest ones seem to exist for significantly longer time, up to 24 h. Furthermore, the merging of two CBPs seems not to have an influence on the overall size of the persisting CBP. Finally, fainter and cooler CBPs tend to have only weaker magnetic polarities, which clearly supports a coronal bright point heating mechanism based on magnetic energy dissipation.

SOLAR-TYPE ECLIPSING BINARY KIC 4832197: PHYSICAL PROPERTIES AND INTRINSIC VARIABILITY OF THE COMPONENTS

Comprehensive analysis of optical spectroscopy and space photometry of the solar type eclipsing binary system KIC 4832197 is presented. The system is composed of F7V + F9V components with masses of M1 = 1.16 ± 0.12 M☉, M2 = 1.07 ± 0.10 M☉ and radii of R1 = 1.26 ± 0.04 R☉, R2 = 1.03 ± 0.03 R☉. The position of the components on the Log Teff – Log L/L☉ plane suggests an age of 2.8 ± 0.8 Gyr for the system. Inspection of out-of-eclipse brightness in time reveals a wave-like variability pattern, whose amplitude and shape quickly change on order of days. Frequency analysis of this variability results in two significant peaks in the amplitude spectrum, which are interpreted as rotational modulation of spots on the components. Assuming both spots are on the same component, a lower limit for the differential rotation coeffcient is computed as k = 0.12, which is weaker compared to the solar value of k☉ = 0.189.

Magnetic fields of low-mass main sequences stars: non-linear dynamo theory and mean-field numerical simulations

ABSTRACT Our theoretical and numerical analysis have suggested that for low-mass main sequences stars (of the spectral classes from M5 to G0) rotating much faster than the Sun, the generated large-scale magnetic field is caused by the mean-field α2Ω dynamo, whereby the α2 dynamo is modified by a weak differential rotation. Even for a weak differential rotation, the behaviour of the magnetic activity is changed drastically from aperiodic regime to non-linear oscillations and appearance of a chaotic behaviour with increase of the differential rotation. Periods of the magnetic cycles decrease with increase of the differential rotation, and they vary from tens to thousand years. This long-term behaviour of the magnetic cycles may be related to the characteristic time of the evolution of the magnetic helicity density of the small-scale field. The performed analysis is based on the mean-field simulations (MFS) of the α2Ω and α2 dynamos and a developed non-linear theory of α2 dynamo. The applied MFS model was calibrated using turbulent parameters typical for the solar convective zone.

Effects of the centrifugal force in stellar dynamo simulations

Context. The centrifugal force is often omitted from simulations of stellar convection either for numerical reasons or because it is assumed to be weak compared to the gravitational force. However, the centrifugal force might be an important factor in rapidly rotating stars, such as solar analogs, due to its Ω2 scaling, where Ω is the rotation rate of the star. Aims. We study the effects of the centrifugal force in a set of 21 semi-global stellar dynamo simulations with varying rotation rates. Included in the set are three control runs aimed at distinguishing the effects of the centrifugal force from the nonlinear evolution of the solutions. Methods. We solved the 3D magnetohydrodynamic equations with the PENCIL CODE in a solar-like convective zone in a spherical wedge setup with a 2π azimuthal extent. The rotation rate and the amplitude of the centrifugal force were varied. We decomposed the magnetic field into spherical harmonics and studied the migration of azimuthal dynamo waves (ADWs), the energy of different large-scale magnetic modes, and differential rotation. Results. In the regime with the lowest rotation rates, Ω = 5 − 10 Ω⊙, where Ω⊙ is the rotation rate of the Sun, we see no marked changes in either the differential rotation or the magnetic field properties. For intermediate rotation, Ω = 20 − 25 Ω⊙, we identify an increase in the differential rotation as a function of centrifugal force. The axisymmetric magnetic energy tends to decrease with centrifugal force, while the non-axisymmetric one increases. The ADWs are also affected, especially in the propagation direction. In the most rapidly rotating set with Ω = 30 Ω⊙, these changes are more pronounced, and in one case the propagation direction of the ADW changes from prograde to retrograde. The control runs suggest that the results are a consequence of the centrifugal force and not due to the details of the initial conditions or the history of the run. Conclusions. We find that the differential rotation and properties of the ADWs only change as a function of the centrifugal force when rotation is rapid enough.

Eruptivity Criteria for Solar Coronal Flux Ropes in Magnetohydrodynamic and Magnetofrictional Models

We investigate which scalar quantity or quantities can best predict the loss of equilibrium and subsequent eruption of magnetic flux ropes in the solar corona. Our models are initialized with a potential magnetic arcade, which is then evolved by means of two effects on the lower boundary: first, a gradual shearing of the arcade, modeling differential rotation on the solar surface; and second, supergranular diffusion. These result in flux cancellation at the polarity inversion line and the formation of a twisted flux rope. We use three model setups: full magnetohydrodynamics (MHD) in cartesian coordinates, and the magnetofrictional (MF) model in both cartesian and polar coordinates. The flux ropes are translationally invariant, allowing for very fast computational times and thus a comprehensive parameter study, comprising hundreds of simulations and thousands of eruptions. Similar flux rope behavior is observed using either magnetofriction or MHD, and there are several scalar criteria that could be used as proxies for eruptivity. The most consistent predictor of eruptions in either model is the squared current in the axial direction of the rope, normalized by the relative helicity, although a variation on the previously proposed eruptivity index is also found to perform well in both the MF and MHD simulations.

Asteroseismology and Spectropolarimetry of the Exoplanet Host Star λ Serpentis

The bright star λ Ser hosts a hot Neptune with a minimum mass of 13.6 M ⊕ and a 15.5 day orbit. It also appears to be a solar analog, with a mean rotation period of 25.8 days and surface differential rotation very similar to the Sun. We aim to characterize the fundamental properties of this system and constrain the evolutionary pathway that led to its present configuration. We detect solar-like oscillations in time series photometry from the Transiting Exoplanet Survey Satellite, and we derive precise asteroseismic properties from detailed modeling. We obtain new spectropolarimetric data, and we use them to reconstruct the large-scale magnetic field morphology. We reanalyze the complete time series of chromospheric activity measurements from the Mount Wilson Observatory, and we present new X-ray and ultraviolet observations from the Chandra and Hubble space telescopes. Finally, we use the updated observational constraints to assess the rotational history of the star and estimate the wind braking torque. We conclude that the remaining uncertainty on the stellar age currently prevents an unambiguous interpretation of the properties of λ Ser, and that the rate of angular momentum loss appears to be higher than for other stars with a similar Rossby number. Future asteroseismic observations may help to improve the precision of the stellar age.

Angular momentum and lithium transport from main sequence to sub-giant and red giant low-mass stars

Context. Asteroseismology provides a unique opportunity to probe the interiors of evolved stars and constrain their internal rotation. The correct reproduction of the core rotation evolution has not yet been achieved, although it is key to understanding the internal processes involved in low-mass stars. Aims. We explore the efficiency required to reproduce the general behaviour of the transport of angular momentum along the evolution in view of asteroseismic constraints from giant low-mass stars. We analyse the consequences and predictions for lithium and beryllium surface abundances from the main sequence to red giant phase. Methods. We computed a series of models, which included atomic diffusion, rotation-induced mixing, magnetic braking, and additional processes tailored for main sequence low-mass stars. We extended these models to more evolved phases and investigated an updated angular momentum transport by including a time-dependent extra viscosity related to the azimuthal magneto-rotational instability. We compared our predictions to the asteroseismic measurements of the core and surface rotation of a sample of sub-giant and red giant stars. We compared the model predictions for the lithium and beryllium surface evolution with the available observations. Results. We confirm that a time-dependent additional viscosity νadd(t) is required to reproduce the general behaviour of the core rotation rate along successive stellar evolutionary phases given the dependence on the differential rotation and the mass. We show that it results in stronger lithium and beryllium depletions for low-mass stars over evolution. We confirm that predicted lithium abundances at the red giant bump by classical models, commonly used as references, cannot reproduce the lithium depletion along the main sequence and evolved phases of stellar evolution. We show that the observed amount of lithium of stars less massive than 1 M⊙ leads to a discrepancy between model predictions and observations at the red giant bump. Conclusions. We show that a semi-parametric model can reproduce the rotational behaviour along the first phases of evolution well, with the exception of the sharp transition observed during the sub-giant phase. This suggests that two distinct transport processes may be involved. The processes required to transport chemicals during the main sequence phase and angular momentum until the red giant phase impact the lithium depletion all along the evolutionary duration. A good prediction of the lithium abundance at young phases places strong constraints on the predicted one at more evolved phases. It also highlights discrepancies between models and observations for the lowest mass stars and impacts the threshold that defines lithium-rich giant stars, showing that classical models tend to overestimate this threshold.

Kinematics and stability of high-mass protostellar disk candidates at sub-arcsecond resolution

Context. The fragmentation mode of high-mass molecular clumps and the accretion processes that form the most massive stars (M ≳ 8 M⊙) are still not well understood. A growing number of case studies have found massive young stellar objects (MYSOs) to harbour disk-like structures, painting a picture that the formation of high-mass stars may proceed through disk accretion, similar to that of lower-mass stars. However, the properties of such structures have yet to be uniformly and systematically characterised. Aims. The aim of this work is to uniformly study the kinematic properties of a large sample of MYSOs and characterise the stability of possible circumstellar disks against gravitational fragmentation. Methods. We have undertaken a large observational programme (CORE) making use of interferometric observations from the Northern Extended Millimetre Array (NOEMA) for a sample of 20 luminous (L &gt; 104 L⊙) protostellar objects in the 1.37 mm wavelength regime in both continuum and spectral line emission, reaching 0.4″ resolution (800 au at 2 kpc). Results. We present the gas kinematics of the full sample and detect dense gas emission surrounding 15 regions within the CORE sample. Using the dense gas tracer CH3CN, we find velocity gradients across 13 cores perpendicular to the directions of bipolar molecular outflows, making them excellent disk candidates. The extent of the CH3CN emission tracing the disk candidates varies from 1800 to 8500 au. Analysing the free-fall to rotational timescales, we find that the sources are rotationally supported. The rotation profiles of some disk candidates are well described by differential rotation while for others the profiles are poorly resolved. Fitting the velocity profiles with a Keplerian model, we find protostellar masses in the range of ~ 10–25 M⊙. Modelling the level population of CH3CN (12K–11K) K = 0–6 lines, we present temperature maps and find median temperature in the range 70–210 K with a diversity in distributions. Radial profiles of the specific angular momentum (j) for the best disk candidates span a range of 1–2 orders of magnitude, on average ~10−3 km s−1 pc, and they follow j ∝ r1.7, which is consistent with a poorly resolved rotating and infalling envelope-disk model. Studying the Toomre stability of the disk candidates, we find almost all (11 out of 13) disk candidates to be prone to fragmentation due to gravitational instabilities at the scales probed by our observations, as a result of their high disk to stellar mass ratio. In particular, disks with masses greater than ~ 10–20% of the mass of their host (proto)stars are Toomre unstable, and more luminous YSOs tend to have disks that are more massive compared to their host star and hence more prone to fragmentation. Conclusions. In this work, we show that most disk structures around high-mass YSOs are prone to disk fragmentation early in their formation due to their high disk to stellar mass ratio. This impacts the accretion evolution of high-mass protostars which will have significant implications for the formation of the most massive stars.