Angular Momentum Transport Research Articles

Magnetic Braking during Direct Collapse Black Hole Formation

Magnetic fields are expected to be efficiently amplified during the formation of the first massive black holes via the small-scale dynamo and in the presence of strong accretion shocks occurring during gravitational collapse. Here, we analyze high-resolution cosmological magnetohydrodynamical simulations of gravitational collapse in atomic cooling halos, exploring the dynamical role of magnetic fields, particularly concerning the effect of magnetic braking and angular momentum transport. We find that after the initial amplification, magnetic fields contribute to the transport of angular momentum and reduce it compared to pure hydrodynamical simulations. However, the magnetic and Reynolds torques do not fully compensate for the inward advection of angular momentum, which still accumulates over timescales of ∼1 Myr. A Jeans analysis further shows that magnetic pressure strongly contributes to suppressing fragmentation on scales of 0.1–10 pc. Overall, the presence of magnetic fields thus aids in the transport of angular momentum and favors the formation of massive objects.

Transition to the ultimate turbulent regime in a very wide gap Taylor-Couette flow (η = 0.1) with a stationary outer cylinder

The boundary layers in turbulent Taylor-Couette flow are exposed to transitions from laminar to turbulent states if the flow is sufficiently sheared. The present study examines this particular transition from the so-called “classical” to “ultimate” regime experimentally for a very wide-gap Taylor-Couette flow with a radius ratio of and shear Reynolds numbers of up to . In order to determine the transition, the angular momentum transport is measured by using torque sensors at the inner wall. This is complemented by measuring the radial and azimuthal velocities via a time-resolved Particle-Image-Velocimetry (PIV). The transition to the ultimate regime is found at . The dimensionless angular momentum flux showed an effective scaling of for and is in agreement with the scaling laws used for the ultimate regime in narrow-gap Taylor-Couette flows. In addition, a spectral analysis was performed showing the existence of highly energetic small-scale and large-scale patterns in the classical regime whereas only highly energetic large-scale patterns were observed in the ultimate regime.

Influence of surface layer schemes on tropical cyclone Hato (2017) intensity

Three surface layer schemes (MYNN, ETA, and MM5) in the Weather Research and Forecasting (WRF 4.1) model were selected to conduct simulation experiments for tropical cyclone (TC) Hato (2017). The influence of different surface layer schemes on TC intensity was compared. Although the planetary boundary layer and land surface schemes were the same, surface layer schemes minimally affected TC tracks but significantly affected TC intensity. The highest correlation coefficient and smallest bias and root mean square error between the simulated TC intensity in the ETA and observations. The TC intensity simulated using ETA was the strongest and closest to the observations. The surface latent heat fluxes simulated using ETA at the time of the TC landing were 1200–1500 W/m2, and is 800–1200 W/m2 by MM5 and MYNN, respectively. The surface sensible heat flux simulated using ETA was 400–800 W/m2 and that simulated using MM5 and MYNN was 200–400 W/m2. The equivalent potential temperature and radial wind simulated using ETA were significantly higher than those simulated using MM5 and MYNN. The larger the energy transmitted from the surface to the tropical cyclone, the stronger the TC. The dynamic structural characteristics were consistent with the tropical cyclone intensity. The ETA indicated the strongest unstable planetary boundary layer structure, stronger convergence at the lower layer, divergence at the upper layer, vertical transport, and absolute angular momentum, and induced the formation of the strongest TC. The comparison results revealed that the surface fluxes from different surface layer schemes can affect the dynamic and thermal structures of the planetary boundary layer owing to the different stability functions. The surface fluxes were also affected by the temperature and wind in the planetary boundary layer. This interaction between the surface layer and planetary boundary layer affects the eye structure and secondary circulation of the TC and TC intensity.

Spin current driven by ultrafast magnetization of FeRh

Laser-induced ultrafast demagnetization is an important phenomenon that probes arguably the ultimate limits of the angular momentum dynamics in solid. Unfortunately, many aspects of the dynamics remain unclear except that the demagnetization transfers the angular momentum eventually to the lattice. In particular, the role and origin of electron-carried spin currents in the demagnetization process are debated. Here we experimentally probe the spin current in the opposite phenomenon, i.e., laser-induced ultrafast magnetization of FeRh, where the laser pump pulse initiates the angular momentum build-up rather than its dissipation. Using the time-resolved magneto-optical Kerr effect, we directly measure the ultrafast-magnetization-driven spin current in a FeRh/Cu heterostructure. A strong correlation between the spin current and the magnetization dynamics of FeRh is found even though the spin filter effect is negligible in this opposite process. This result implies that the angular momentum build-up is achieved by an angular momentum transfer from the electron bath (supplier) to the magnon bath (receiver) and followed by the spatial transport of angular momentum (spin current) and dissipation of angular momentum to the phonon bath (spin relaxation).

Experimental investigation of turbulent counter-rotating Taylor–Couette flows for radius ratio η = 0.1

Turbulent Taylor–Couette flow between two concentric independently rotating cylinders with a radius ratio of $\eta = 0.1$ is studied experimentally. While the scope is to study the counter-rotating cases between both cylinders, the radial and azimuthal velocity components are recorded at different horizontal planes with high-speed particle image velocimetry. The parametric study considered a set of different shear Reynolds numbers in the range of $20\,000 \leq Re_s \leq 1.31 \times 10^5$ , with different rotation ratios of $-0.06 \leq \mu \leq +0.008$ . The observed flow fields had a clear dependence on the rotation ratio, where flow patterns evolved with a more pronounced axial dependence. The angular momentum transport is computed as a result of the recorded flow fields and given by a quasi-Nusselt number. The dependence of the Nusselt number on the different rotation ratios shows a maximum for the low counter-rotating case and $\mu _{max}$ is found between $-0.011 < \mu _{max} < -0.0077$ . The Nusselt number decreases for stronger counter-rotation until a minimum is reached, where it tends to increase again for higher counter-rotation rates. The space–time behaviour of the turbulent flow showed the existence of patterns propagating from the inner region towards the outer region for all studied counter-rotating cases. In addition, patterns have been found that tend to propagate from the outer region towards the inner region with a novel character at high counter-rotation cases. These patterns enhance the angular momentum transport where a second maximum in the transport mechanism has to be expected.

Merger Conditions of Population III Protostar Binaries

Massive close binary stars with extremely small separations have been observed, and they are possible progenitors of gravitational-wave sources. The evolution of massive binaries in the protostellar accretion stage is key to understanding their formation process. We, therefore, investigate how close the protostars, consisting of a high-density core and a vast low-density envelope, can approach each other but not coalesce. To investigate the coalescence conditions, we conduct smoothed particle hydrodynamics simulations following the evolution of equal-mass binaries with different initial separations. Since Population (Pop) I and III protostars have similar interior structures, we adopt a specific Pop III model with the mass and radius of 7.75 M ⊙ and 61.1 R ⊙ obtained by the stellar evolution calculations. Our results show that the binary separation decreases due to the transport of the orbital angular momentum to spin angular momentum. If the initial separation is less than about 80% of the sum of the protostellar radius, the binary coalesces in a time shorter than the tidal lock timescale. The mass loss up to the merging is ≲3%. After coalescence, the star rotates rapidly, and its interior structure is independent of the initial separation. We conclude that there must be some orbital shrinking mechanism after the protostars contract to enter the zero-age main-sequence stage.

Post-dynamical inspiral phase of common envelope evolution

After the companion dynamically plunges through the primary’s envelope, the two cores remain surrounded by a common envelope and the decrease of the orbital period Porb stalls. The subsequent evolution has never been systematically explored with multidimensional simulations. For this study, we performed 3D hydrodynamical simulations of an envelope evolving under the influence of a central binary star using an adaptively refined spherical grid. We followed the evolution over hundreds of orbits of the central binary to characterize the transport of angular momentum by advection, gravitational torques, turbulence, and viscosity. We find that local advective torques from the mean flow and Reynolds stresses associated with the turbulent flow dominate the angular momentum transport, which occurs outward in a disk-like structure about the orbital plane and inward along the polar axis. Turbulent transport is less efficient, but can locally significantly damp or enhance the net angular momentum radial transport and may even reverse its direction. Short-term variability in the envelope is remarkably similar to circumbinary disks, including the formation and destruction of lump-like overdensities, which enhance mass accretion and contribute to the outward transport of eccentricity generated in the vicinity of the binary. If the accretion onto the binary is allowed, the orbital decay timescale settles to a nearly constant value τb ∼ 103 to 104 Porb, while preventing accretion leads to a slowly increasing τb ∼ 105 Porb at the end of our simulations. Our results suggest that the post-dynamical orbital contraction and envelope ejection will slowly continue while the binary is surrounded by gas and that τb is often much shorter than the thermal timescale of the envelope.

Distinguishing magnetized disc winds from turbulent viscosity through substructure morphology in planet-forming discs

ABSTRACT The traditional paradigm of viscosity-dominated evolution of protoplanetary discs has been recently challenged by existence of magnetized disc winds. However, distinguishing wind-driven and turbulence-driven accretion through observations has been difficult. In this study, we present a novel approach to identifying their separate contribution to angular momentum transport by studying the gap and ring morphology of planet-forming discs in the ALMA continuum. We model the gap-opening process of planets in discs with both viscous evolution and wind-driven accretion by 2D multifluid hydrodynamical simulations. Our results show that gap-opening planets in wind-driven accreting discs generate characteristic dust substructures that differ from those in purely viscous discs. Specifically, we demonstrate that discs where wind-driven accretion dominates the production of substructures exhibit significant asymmetries. Based on the diverse outputs of mock images in the ALMA continuum, we roughly divide the planet-induced features into four regimes (moderate-viscosity dominated, moderate-wind dominated, strong-wind dominated, and inviscid). The classification of these regimes sets up a potential method to constrain the strength of magnetized disc wind and viscosity based on the observed gap and ring morphology. We discuss the asymmetry feature in our mock images and its potential manifestation in ALMA observations.

Meridional circulation driven by planetary spiral wakes in radiative and magnetized protoplanetary discs

ABSTRACT We study a Jupiter-mass planet formation for the first time in radiative magnetohydrodynamics (MHD) simulations and compare it with pure hydrodynamical simulations, and also with different isothermal configurations. We found that the meridional circulation is the same in every set-up. The planetary spiral wakes drive a vertical stirring inside the protoplanetary disc and the encounter with these shock fronts also helps in delivering gas vertically on to the Hill sphere. The accretion dynamics are unchanged: the planet accretes vertically, and there is outflow in the mid-plane regions inside the Hill sphere. We determined the effective α-viscosity generated in the disc by the various angular momentum loss mechanisms, which showed that magnetic fields produce high turbulence in the ideal MHD limit, and grows from α ∼ 10−2.5 up to ∼10−1.5 after the planet spirals develop. In the HD simulations, the planetary spirals contribute to α ∼ 10−3, making this a very important angular momentum transport mechanism. Due to the various α values in the different set-ups, the gap opening is different in each case. In the radiative MHD set-ups, the high turbulent viscosity prevents gap opening, leading to a higher Hill mass, and no clear dust trapping regions. While the Hill accretion rate is $10^{-6}~ \rm {M_{Jup}\,yr^{-1}}$ in all set-ups, the accretion variability is orders of magnitude higher in radiative runs than in isothermal ones. Finally, with higher resolution runs, the magnetorotational instability started to be resolved, changing the effective viscosity and increasing the heating in the disc.

Large mass inflow rates in Saturn’s rings due to ballistic transport and mass loading

The Cassini mission provided key measurements needed to determine the absolute age of Saturn’s rings, including the extrinsic micrometeoroid flux at Saturn, the volume fraction of non-icy pollutants in the rings, and the total ring mass. These three factors constrain the ring age to be no more than a few 100 Myr (Kempf et al., 2022). Observations during the Cassini Grand Finale also showed that the rings are losing mass to the planet at a prodigious rate. Some of the mass flux falls as “ring rain” at high latitudes. However, the influx in ring rain is considerably less than the total measured mass influx of 4800 to 45000 kg s−1 at lower latitudes (Waite et al., 2018).In addition to polluting the rings, micrometeoroid impacts lead to ballistic transport, the mass and angular momentum transport due to net exchanges of meteoroid impact ejecta. Because the ejecta are predominantly prograde, they carry net angular momentum outward. As a result, ring material drifts inward toward the planet. Here, for the first time, we use a simple model to quantify this radial mass inflow rate for dense rings and find that, for plausible choices of parameters, ballistic transport and mass loading by meteoroids can produce a total inward flux of material in the inner B ring and in the C ring that is on the order of a few ⋅103 to a few ⋅104 kg s−1, in agreement with measurements during the Cassini Grand Finale. From these mass inflow rates, we estimate that the remaining ring lifetime is ∼ 15 to 400 Myr. Combining this with a revised pollution age of ∼ 120 Myr, we conclude that Saturn’s rings are not only young but ephemeral and probably started their evolution on a similar timescale to their pollution age with an initial mass of one to a few Mimas masses.In addition to showing that meteoroid impacts can produce a large sustained mass inflow through the B and C rings, this paper addresses various uncertainties and considers possible contributions by additional transport mechanisms and by external torques. We also map out a set of future research projects, including global simulations.

Testing angular momentum transport processes with asteroseismology of solar-type main-sequence stars

Context. Thanks to the so-called photometry revolution with the space-based missions CoRoT, Kepler, and TESS, asteroseismology has become a powerful tool to study the internal rotation of stars. The rotation rate depends on the efficiency of the angular momentum (AM) transport inside the star, and its study allows to constrain the internal AM transport processes, as well as improve our understanding of their physical nature. Aims. We compared the ratio of the rotation rate predicted by asteroseismology and starspot measurements of solar-type stars considering different AM transport prescriptions and investigated whether some of these prescriptions can be ruled out observationally. Methods. We conducted a two-step modelling procedure of four main-sequence stars from the Kepler LEGACY sample, which consists of an asteroseismic characterisation that serves as a guide for a modelling with rotating models, including a detailed and coherent treatment of the AM transport. The rotation profiles derived with this procedure were used to estimate the ratio of the mean asteroseismic rotation rate with the surface rotation rate from starspot measurements for each AM transport prescriptions. Comparisons between the models were then conducted. Results. In the hotter part of the Hertzsprung-Russell (HR) diagram (masses typically above ∼1.2 M⊙ at solar metallicity), models with only hydrodynamic transport processes and models with additional transport by magnetic instabilities are found to be consistent with previous measurements that observed a low degree (below 30%) of radial differential rotation between the radiative and convective zones. For these stars, which constitute a significant fraction of the Kepler LEGACY sample, a combination of asteroseismic constraints from the splitting of pressure modes and of the surface rotation rate does not allow us to conclude that an efficient AM transport is required in addition to transport by meridional circulation and shear instability alone. Even a model assuming local AM conservation cannot be ruled out. In the colder part of the HR diagram, the situation is different because of the efficient braking of the stellar surface by magnetised winds. We find a clear disagreement between the rotational properties of models that only include hydrodynamic processes and asteroseismic constraints, while models with magnetic fields correctly reproduce the observations, similarly to the solar case. Conclusions. This shows the existence of a mass regime corresponding to main-sequence F-type stars for which it is difficult to constrain the AM transport processes, unlike for hotter, Gamma Dor stars or colder, less massive solar analogues. The comparison between asteroseismic measurements and surface rotation rates enables us to easily rule out models with an inefficient transport of AM in the colder part of the HR diagram.

Asteroseismology of evolved stars to constrain the internal transport of angular momentum

Context. Asteroseismic measurements of the internal rotation rate in evolved stars pointed to a lack of angular momentum (AM) transport in stellar evolution models. Several physical processes in addition to hydrodynamical ones were proposed as candidates for the missing mechanism. Nonetheless, no current candidate can satisfy all the constraints provided by asteroseismology. Aims. We revisit the role of a candidate process whose efficiency scales with the contrast between the rotation rate of the core and the surface. This process was proposed in previous works to be related to the azimuthal magneto-rotational instability. Methods. We computed stellar evolution models of low- and intermediate-mass stars with the parametric formulation of AM transport proposed in previous works for this instability until the end of the core-helium burning for low- and intermediate-mass stars, and compare our results to the latest asteroseismic constraints available in the post-main sequence phase. Results. Both hydrogen-shell-burning stars in the red-giant branch and core-helium-burning stars of low- and intermediate-mass in the mass range 1 M⊙ ≲ M ≲ 2.5 M⊙ can be simultaneously reproduced by this kind of parametrisation. Conclusions. Given the current constraints from asteroseismology, the core rotation rate of post-main sequence stars seems to be well explained by a process whose efficiency is regulated by the internal degree of differential rotation in radiative zones.

Experimental method for investigating the formation of flow patterns in a very wide gap Taylor-Couette flow (η = 0.1).

Abstract In this study, we investigate the turbulent Taylor-Couette (TC) flow experimentally. First, in order to show the formation of the different patterns in the flow, the flow was seeded with kalliroscope particles and by applying a vertical laser sheet we were able to capture the different patterns in the flow. For a further detailed study, the flow field was measured in horizontal planes at different cylinder heights using Particle image velocimetry (PIV). The formation of patterns appears for the counter-rotation configuration where the outer cylinder rotates in the opposing direction of the inner cylinder rotation. For low shear Reynolds numbers, stable Taylor vortices fulfilling the whole gap appear for very low counter-rotation rates. While for the same rotation rates and higher shear Reynold number, large scale patterns with shorter length scale compared to the classical Taylor vortices appears, which can be described as interlaced fingers from in and outflow. The existence of these patterns leads to enhanced angular momentum transport.

Saturation of the magnetorotational instability and the origin of magnetically elevated accretion discs

ABSTRACT We propose that the strength of angular momentum transport in accretion discs threaded by net vertical magnetic field is determined by a self-regulation mechanism: the magnetorotational instability (MRI) grows until its own turbulent resistivity damps the fastest growing mode on the scale of the disc thickness. Given weak assumptions as to the structure of MRI-derived turbulence, supported by prior simulation evidence, the proposed mechanism reproduces the known scaling of the viscous α-parameter, $\alpha \propto \beta _z^{-1/2}$. Here, $\beta _z = 8\pi p_{\rm g}/B_{z0}^2$ is the initial plasma β-parameter on the disc mid-plane, Bz0 is the net field, and pg is the mid-plane gas pressure. We generalize the argument to discs with strong suprathermal toroidal magnetic fields, where the MRI growth rate is modified from the weak-field limit. Additional sources of turbulence are required if such discs are to become magnetically elevated, with the increased scale heights near the mid-plane that are seen in simulations. We speculate that tearing modes, associated with current sheets broadened by the effective resistivity, are a possible source of enhanced turbulence in elevated discs.

Magnetohydrodynamic simulations of the Tayler instability in rotating stellar interiors

ABSTRACT The Tayler instability is an important but poorly studied magnetohydrodynamic (MHD) instability that likely operates in stellar interiors. The non-linear saturation of the Tayler instability is poorly understood and has crucial consequences for dynamo action and angular momentum transport in radiative regions of stars. We perform three-dimensional MHD simulations of the Tayler instability in a cylindrical geometry, including strong buoyancy and Coriolis forces as appropriate for its operation in realistic rotating stars. The linear growth of the instability is characterized by a pre-dominantly m = 1 oscillation with growth rates roughly following analytical expectations. The non-linear saturation of the instability appears to be caused by secondary shear instabilities and is also accompanied by a morphological change in the flow. We argue, however, that non-linear saturation likely occurs via other mechanisms in real stars where the separation of scales is larger than those reached by our simulations. We also observe dynamo action via the amplification of the axisymmetric poloidal magnetic field, suggesting that Tayler instability could be important for magnetic field generation and angular momentum transport in the radiative regions of evolving stars.

Rejuvenating infall: a crucial yet overlooked source of mass and angular momentum

MHD models and the observation of accretion streamers confirmed that protostars can undergo late accretion events after the initial collapse phase. To provide better constraints, we study the evolution of stellar masses in MHD simulations of a 4 pc^{3} molecular cloud. Tracer particles allow us to accurately follow the trajectory of accreting material for all protostars and thereby constrain the accretion reservoir of the stars. The diversity of the accretion process implies that stars in the solar mass regime can have vastly different accretion histories. Some stars accrete most of their mass during the initial collapse phase, while others gain >50 % of their final mass from late infall. The angular momentum budget of stars that experience substantial late infall, so-called late accretors, is significantly higher than for stars without or with only little late accretion. As the probability of late infall increases with increasing final stellar mass, the specific angular momentum budget of higher mass stars is on average higher. The hypothetical centrifugal radius computed from the accreting particles at the time of formation is orders of magnitude higher than observed disk sizes, which emphasizes the importance of angular momentum transport during disk formation. Nevertheless, we find a correlation that the centrifugal radius is highest for stars with substantial infall, which suggests that very large disks are the result of recent infall events. There are also indications for a subtle trend of increasing centrifugal radius with increasing final stellar mass, which is in agreement with an observed marginal correlation of disk size and stellar mass. Finally, we show that late accretors become more embedded again during late infall. As a consequence, late accretors are (apparently) rejuvenated and would be classified as Class 0 objects according to their bolometric temperature despite being sim 1 Myr old.

Late-time post-merger modeling of a compact binary: effects of relativity, r-process heating, and treatment of transport

Detectable electromagnetic counterparts to gravitational waves from compact binary mergers can be produced by outflows from the black hole-accretion disk remnant during the first 10 s after the merger. Two-dimensional axisymmetric simulations with effective viscosity remain an efficient and informative way to model this late-time post-merger evolution. In addition to the inherent approximations of axisymmetry and modeling turbulent angular momentum transport by a viscosity, previous simulations often make other simplifications related to the treatment of the equation of state and turbulent transport effects. In this paper, we test the effect of these modeling choices. By evolving with the same viscosity the exact post-merger initial configuration previously evolved in Newtonian viscous hydrodynamics, we find that the Newtonian treatment provides a good estimate of the disk ejecta mass but underestimates the outflow velocity. We find that the inclusion of heavy nuclei causes a notable increase in ejecta mass. An approximate inclusion of r-process effects has a comparatively smaller effect, except for its designed effect on the composition. Diffusion of composition and entropy, modeling turbulent transport effects, has the overall effect of reducing ejecta mass and giving it a speed with lower average and more tightly-peaked distribution. Also, we find significant acceleration of outflow even at distances beyond 10 000 km, so that thermal wind velocities only asymptote beyond this radius and at higher values than often reported.

Constraining the rotation profile in a low-luminosity subgiant with a surface rotation measurement

ABSTRACT Rotationally induced mode splitting frequencies of low-luminosity subgiants suggest that angular momentum transport mechanisms are 1–2 orders of magnitude more efficient in these stars than predicted by theory. Constraints on the rotation profile of low-luminosity subgiants could be used to identify the dominant mechanism for angular momentum transport. We develop a forward model for the rotation profile given observed rotational splittings, assuming a step-like rotation profile. We identify a consistent degeneracy between the position of the profile discontinuity and the surface rotation rate. We perform mock experiments that show the discontinuity position can be better constrained with a prior on the surface rotation rate, which is informed by star spot modulations. We finally apply this approach to KIC 12508433, a well-studied low-luminosity subgiant, as an example case. With the observed surface rotation prior, we obtain a factor of 2 increase in precision of the position of strong rotation gradient. We recover the literature values of the core and surface rotation rates and find the highest support for a discontinuity in the radiative zone. Auxiliary measurements of surface rotation could substantially improve inferences on the rotation profile of low-luminosity subgiants with already available data.

Magnetism in High-Mass Stars

Magnetism is a ubiquitous property of astrophysical plasmas, yet stellar magnetism still remains far from being completely understood. In this review, we describe recent observational and modelling efforts and progress to expand our knowledge of the magnetic properties of high-mass stars. Several mechanisms (magneto-convection, mass-loss quenching, internal angular momentum transport, and magnetic braking) have significant implications for stellar evolution, populations, and end-products. Consequently, it remains an urgent issue to address and resolve open questions related to magnetism in high-mass stars.

Theoretical investigation of the occurrence of tidally excited oscillations in massive eccentric binary systems

Context. Massive and intermediate-mass stars reside in binary systems at a much higher rate than low-mass stars. At the same time, binaries containing massive main-sequence (MS) component(s) are often characterised by eccentric orbits, and can therefore be observed as eccentric ellipsoidal variables (EEVs). The orbital phase-dependent tidal potential acting on the components of EEVs can induce tidally excited oscillations (TEOs), which can affect the evolution of the binary system. Aims. We investigate how the history of resonances between the eigenmode spectra of the EEV components and the tidal forcing frequencies depends on the initial parameters of the system, limiting our study to the MS. Each resonance is a potential source of TEO. We are particularly interested in the total number of resonances, their average rate of occurrence, and their distribution in time. Methods. We synthesised 20 000 evolutionary models of the EEVs across the MS using Modules for Experiments in Stellar Astrophysics (MESA) software for stellar structure and evolution. We considered a range of masses of the primary component from 5 to 30 M⊙. Later, using the GYRE stellar non-adiabatic oscillations code, we calculated the eigenfrequencies for each model recorded by MESA. We focused only on the l = 2, m = 0, +2 modes, which are suspected of being dominant TEOs. Knowing the temporal changes in the orbital parameters of simulated EEVs and the changes in the eigenfrequency spectra for both components, we were able to determine so-called resonance curves, which describe the overall chance of a resonance occurring and therefore of a TEO occurring. We analysed the resonance curves by constructing basic statistics for them and analysing their morphology using machine learning methods, including the Uniform Manifold Approximation and Projection (UMAP) tool. Results. The EEV resonance curves from our sample are characterised by a striking diversity, including the occurrence of exceptionally long resonances or the absence of resonances for long evolutionary times. We find that the total number of resonances encountered by components in the MS phase ranges from ∼102 to ∼103, mostly depending on the initial eccentricity. We also noticed that the average rate of resonances is about an order of magnitude higher (∼102 Myr−1) for the most massive components in the assumed range than for EEVs with intermediate-mass stars (∼101 Myr−1). The distribution of resonances over time is strongly inhomogeneous, and its shape depends mainly on whether the system is able to circularise its orbit before the primary component reaches the terminal-age main sequence (TAMS). Both components may be subject to increased resonance rates as they approach the TAMS. Thanks to the low-dimensional UMAP embeddings performed for the resonance curves, we argue that their morphology changes smoothly across the resulting manifold for different initial EEV conditions. The structure of the embeddings allowed us to explore the whole space of resonance curves in terms of their morphology and to isolate some extreme cases. Conclusions. Resonances between tidal forcing frequencies and stellar eigenfrequencies cannot be considered rare events for EEVs with massive and intermediate-mass MS stars. On average, we should observe TEOs more frequently in EEVs that contain massive components than those that contain intermediate-mass ones. The TEOs will be particularly well pronounced for EEVs whose component(s) are close to the TAMS, which calls for observational verification. Given the total number of resonances and their rates, TEOs may play an important role in the transport of angular momentum within massive and intermediate-mass stars (mainly near the TAMS).