Rotational Evolution Research Articles

Toroidal plasma acceleration due to NBI fast ion losses in LTX-β

The recent Lithium Tokamak Experiment-Beta (LTX-β) upgrade includes the addition of neutral beam injection (NBI) in the same direction as the plasma current (co-I P ) and a new toroidal Mirnov array for MHD characterization. In initial NBI experiments, a spontaneously rotating n = 1 MHD mode is seen to accelerate during NBI in the counter-beam direction, accompanied by a rise in electron density consistent with the beam-injected inventory but without a clear increase in plasma pressure. Together with analytic and numerical modeling of beam optics and fast ion confinement, these observations indicate the prompt loss of all or nearly all beam ions. However, the same modeling also suggests that planned upgrades to the Ohmic heating system should provide the fast ion confinement necessary for beam heating and core fueling. A simple analytic model relates the momentum confinement time to the observed evolution of mode rotation due to the combination of NBI momentum coupling, fast ion loss , and anomalous viscous torques, yielding values consistent with past measurements of electron energy confinement time τ E,e .

Creep tide model for the three-body problem

We present a tidal model for treating the rotational evolution in the general three-body problem with arbitrary viscosities, in which all the masses are considered to be extended and all the tidal interactions between pairs are taken into account. Based on the creep tide theory, we present a set of differential equations that describes the rotational evolution of each body, in a formalism that is easily extensible to the N tidally interacting body problem. We apply our model to the case of a circumbinary planet and use a Kepler-38 like binary system as a working example. We find that, in this low planetary eccentricity case, the most likely final stationary rotation state is the 1:1 spin–orbit resonance, considering an arbitrary planetary viscosity inside the estimated range for the Solar System planets. The timescales for reaching the equilibrium state are expected to be approximately millions of years for stiff bodies but can be longer than the age of the system for planets with a large gaseous component. We derive analytical expressions for the mean rotational stationary state, based on high-order power series of the ratio of the semimajor axes a1∕a2 and low-order expansions of the eccentricities. These are found to very accurately reproduce the mean behaviour of the low-eccentric numerical integrations for arbitrary planetary relaxation factors, and up to a1∕a2 ~ 0.4. Our analytical model is used to predict the stationary rotation of the Kepler circumbinary planets and we find that most of them are probably rotating in a subsynchronous state, although the synchrony shift is much less important than our previous estimations. We present a comparison of our results with those obtained with the Constant Time Lag and find that, as opposed to the assumptions in our previous works, the cross torques have a non-negligible net secular contribution, and must be taken into account when computing the tides over each body in an N-extended-body system from an arbitrary reference frame. These torques are naturally taken into account in the creep theory. In addition to this, the latter formalism considers more realistic rheology that proved to reduce to the Constant Time Lag model in the gaseous limit and also allows several additional relevant physical phenomena to be studied.

Multiscale behaviour of stellar activity and rotation of the planet host Kepler-30

Context. The Kepler-30 system consists of a G dwarf star with a rotation period of ~16 days and three planets orbiting almost coplanar with periods ranging from 29 to 143 days. Kepler-30 is a unique target with which to study stellar activity and rotation in a young solar-like star accompanied by a compact planetary system. Aims. We use about 4 yr of high-precision photometry collected by the Kepler mission to investigate the fluctuations caused by photospheric convection, stellar rotation, and starspot evolution as a function of timescale. Our main goal is to apply methods for the analysis of time-series to find the timescales of the phenomena that affect the light variations. We correlate those timescales with periodicities in the star and the planetary system. Methods. We model the flux rotational modulation induced by active regions using spot modelling and apply the Multifractal Detrending Moving Average algorithm in standard and multiscale versions to analyse the behaviour of variability and light fluctuations that can be associated with stellar convection and the evolution of magnetic fields on timescales ranging from less than 1 day up to about 35 days. The light fluctuations produced by stellar activity can be described by the multifractal Hurst index that provides a measure of their persistence. Results. The spot modelling indicates a lower limit to the relative surface differential rotation of ΔΩ∕Ω ~ 0.02 ± 0.01 and suggests a short-term cyclic variation in the starspot area with a period of ~34 days, which is close to the synodic period of 35.2 days of the planet Kepler-30b. By subtracting the two time-series of the simple aperture photometry and pre-search data conditioning Kepler pipelines, we reduce the rotational modulation and find a 23.1-day period close to the synodic period of Kepler-30c. This period also appears in the multifractal analysis as a crossover of the fluctuation functions associated with the characteristic evolutionary timescales of the active regions in Kepler-30 as confirmed by spot modelling. These procedures and methods may be greatly useful for analysing current TESS and future PLATO data.

The contribution of alpha particles to the solar wind angular momentum flux in the inner heliosphere

Context. An accurate assessment of the Sun’s angular momentum (AM) loss rate is an independent constraint for models that describe the rotation evolution of Sun-like stars. Aims. In situ measurements of the solar wind taken by Parker Solar Probe (PSP), at radial distances of ~28−55 R⊙, are used to constrain the solar wind AM-loss rate. For the first time with PSP, this includes a measurement of the alpha particle contribution. Methods. The mechanical AM flux in the solar wind protons (core and beam), and alpha particles, was determined as well as the transport of AM through stresses in the interplanetary magnetic field. The solar wind AM flux was averaged over three hour increments, so that our findings more accurately represent the bulk flow. Results. During the third and fourth perihelion passes of PSP, the alpha particles contain around a fifth of the mechanical AM flux in the solar wind (the rest is carried by the protons). The proton beam is found to contain ~10−50% of the proton AM flux. The sign of the alpha particle AM flux is observed to correlate with the proton core. The slow wind has a positive AM flux (removing AM from the Sun as expected), and the fast wind has a negative AM flux. As with previous works, the differential velocity between the alpha particles and the proton core tends to be aligned with the interplanetary magnetic field. Conclusions. In future, by utilising the trends in the alpha-proton differential velocity, it may be possible to estimate the alpha particle contribution when only measurements of the proton core are available. Based on the observations from this work, the alpha particles contribute an additional 10−20% to estimates of the solar wind AM-loss rate which consider only the proton and magnetic field contributions. Additionally, the AM flux of the proton beam can be just as significant as the alpha particles, and so neither should be neglected in future studies.

Magnetic and tidal migration of close-in planets

Context.Over the last two decades, a large population of close-in planets has been detected around a wide variety of host stars. Such exoplanets are likely to undergo planetary migration through magnetic and tidal interactions.Aims.We aim to follow the orbital evolution of a planet along the structural and rotational evolution of its host star, simultaneously taking into account tidal and magnetic torques, in order to explain some properties of the distribution of observed close-in planets.Methods.We rely on a numerical model of a coplanar circular star–planet system called ESPEM, which takes into account stellar structural changes, wind braking, and star–planet interactions. We browse the parameter space of the star–planet system configurations and assess the relative influence of magnetic and tidal torques on its secular evolution. We then synthesize star–planet populations and compare their distribution in orbital and stellar rotation periods toKeplersatellite data.Results.Magnetic and tidal interactions act together on planetary migration and stellar rotation. Furthermore, both interactions can dominate secular evolution depending on the initial configuration of the system and the evolutionary phase considered. Indeed, tidal effects tend to dominate for high stellar and planetary masses as well as low semi-major axis; they also govern the evolution of planets orbiting fast rotators while slower rotators evolve essentially through magnetic interactions. Moreover, three populations of star–planet systems emerge from the combined action of both kinds of interactions. First, systems undergoing negligible migration define an area of influence of star–planet interactions. For sufficiently large planetary magnetic fields, the magnetic torque determines the extension of this region. Next, planets close to fast rotators migrate efficiently during the pre-main sequence, which engenders a depleted region at low rotation and orbital periods. Then, the migration of planets close to slower rotators, which happens during the main sequence, may lead to a break in gyrochronology for high stellar and planetary masses. This also creates a region at high rotation periods and low orbital periods not populated by star–planet systems. We also find that star–planet interactions significantly impact the global distribution in orbital periods by depleting more planets for higher planetary masses and planetary magnetic fields. However, the global distribution in stellar rotation periods is marginally affected, as around 0.5% of G-type stars and 0.1% of K-type stars may spin up because of planetary engulfment. More precisely, star–planet magnetic interactions significantly affect the distribution of super-Earths around stars with a rotation period higher than around 5 days, which improves the agreement between synthetic populations and observations at orbital periods of less than 1 day. Tidal effects for their part shape the distribution of giant planets.

The active lives of stars: A complete description of the rotation and XUV evolution of F, G, K, and M dwarfs

Aims. We study the evolution of the rotation and the high energy X-ray, extreme ultraviolet (EUV), and Ly-α emission for F, G, K, and M dwarfs, with masses between 0.1 and 1.2 M⊙, and provide a freely available set of evolutionary tracks for use in planetary atmosphere studies. Methods. We develop a physical rotational evolution model constrained by observed rotation distributions in young stellar clusters. Using rotation, X-ray, EUV, and Ly-α measurements, we derive empirical relations for the dependences of high energy emission on stellar parameters. Our description of X-ray evolution is validated using measurements of X-ray distributions in young clusters. Results. A star’s X-ray, EUV, and Ly-α evolution is determined by its mass and initial rotation rate, with initial rotation being less important for lower mass stars. At all ages, solar mass stars are significantly more X-ray luminous than lower mass stars and stars that are born as rapid rotators remain highly active longer than those born as slow rotators. At all evolutionary stages, habitable zone planets receive higher X-ray and EUV fluxes when orbiting lower mass stars due to their longer evolutionary timescales. The rates of flares follow similar evolutionary trends with higher mass stars flaring more often than lower mass stars at all ages, though habitable zone planets are likely influenced by flares more when orbiting lower mass stars. Conclusions. Our results show that single decay laws are insufficient to describe stellar activity evolution and highlight the need for a more comprehensive description based on the evolution of rotation that also includes the effects of short-term variability. Planets at similar orbital distances from their host stars receive significantly more X-ray and EUV energy over their lifetimes when orbiting higher mass stars. The common belief that M dwarfs are more X-ray and EUV active than G dwarfs is justified only when considering the fluxes received by planets with similar effective temperatures, such as those in the habitable zone.

The Onset of Chaos in Permanently Deformed Binaries from Spin–Orbit and Spin–Spin Coupling

Abstract Permanently deformed objects in binary systems can experience complex rotation evolution, arising from the extensively studied effect of spin–orbit coupling as well as more nuanced dynamics arising from spin–spin interactions. The ability of an object to sustain an aspheroidal shape largely determines whether or not it will exhibit nontrivial rotational behavior. In this work, we adopt a simplified model of a gravitationally interacting primary and satellite pair, where each body’s quadrupole moment is approximated by two diametrically opposed point masses. After calculating the net gravitational torque on the satellite from the primary, as well as the associated equations of motion, we employ a Hamiltonian formalism that allows for a perturbative treatment of the spin–orbit and retrograde and prograde spin–spin coupling states. By analyzing the resonances individually and collectively, we determine the criteria for resonance overlap and the onset of chaos, as a function of orbital and geometric properties of the binary. We extend the 2D planar geometry to calculate the obliquity evolution. This calculation indicates that satellites in spin–spin resonances undergo precession when inclined out of the plane, but they do not tumble. We apply our resonance overlap criteria to the contact binary system (216) Kleopatra, and find that its satellites, Cleoselene and Alexhelios, may plausibly be exhibiting chaotic rotational dynamics from the overlap of the spin–orbit and retrograde spin–spin resonances. While this model is, by construction, generalizable to any binary system, it will be particularly useful for studies of small bodies in the Solar System, whose irregular shapes make them ideal candidates for exotic rotational states.

Weakened magnetic braking supported by asteroseismic rotation rates of Kepler dwarfs

Studies using asteroseismic ages and rotation rates from star-spot rotation have indicated that standard age-rotation relations may break down roughly half-way through the main sequence lifetime, a phenomenon referred to as weakened magnetic braking. While rotation rates from spots can be difficult to determine for older, less active stars, rotational splitting of asteroseismic oscillation frequencies can provide rotation rates for both active and quiescent stars, and so can confirm whether this effect really takes place on the main sequence. We obtained asteroseismic rotation rates of 91 main sequence stars showing high signal-to-noise modes of oscillation. Using these new rotation rates, along with effective temperatures, metallicities and seismic masses and ages, we built a hierarchical Bayesian mixture model to determine whether the ensemble more closely agreed with a standard rotational evolution scenario, or one where weakened magnetic braking takes place. The weakened magnetic braking scenario was found to be 98.4% more likely for our stellar ensemble, adding to the growing body of evidence for this stage of stellar rotational evolution. This work represents the largest catalogue of seismic rotation on the main sequence to date, opening up possibilities for more detailed ensemble analysis of rotational evolution with Kepler.

Cooperative evolution of polar distortion and nonpolar rotation of oxygen octahedra in oxide heterostructures.

Polarity discontinuity across LaAlO3/SrTiO3 (LAO/STO) heterostructures induces electronic reconstruction involving the formation of two-dimensional electron gas (2DEG) and structural distortions characterized by antiferrodistortive (AFD) rotation and ferroelectric (FE) distortion. We show that AFD and FE modes are cooperatively coupled in LAO/STO (111) heterostructures; they coexist below the critical thickness (t c) and disappear simultaneously above t c with the formation of 2DEG. Electron energy-loss spectroscopy and density functional theory (DFT) calculations provide direct evidence of oxygen vacancy (V O) formation at the LAO (111) surface, which acts as the source of 2DEG. Tracing the AFD rotation and FE distortion of LAO reveals that their evolution is strongly correlated with V O distribution. The present study demonstrates that AFD and FE modes in oxide heterostructures emerge as a consequence of interplay between misfit strain and polar field, and further that their combination can be tuned to competitive or cooperative coupling by changing the interface orientation.

Searching for new solar twins: The Inti survey for the Northern Sky

ABSTRACT Solar twins are key in different areas of astrophysics, however only just over a hundred were identified and well-studied in the last two decades. In this work, we take advantage of the very precise Gaia (DR2/EDR3), Tycho, and 2MASS photometric systems to create the ${{Inti}}$ survey of new solar twins in the Northern Hemisphere. The spectra of our targets were initially obtained with spectrographs of moderate resolution (ARCES and Goodman spectrographs with R = 31 500 and 11 930, respectively) to find the best solar twin candidates and then observed at McDonald Observatory with higher resolving power (TS23, R = 60 000) and signal-to-noise ratio (SNR ∼ 300–500). The stellar parameters were estimated through the differential spectroscopic equilibrium relative to the Sun, which allow us to achieve a high internal precision (σ(Teff) = 15 K, σ(log g) = 0.03 dex, σ($\rm {[Fe/H]}$) = 0.01 dex, and σ(vt) = 0.03 km s−1). We propose a new class of stars with evolution similar to the Sun: solar proxy, which is useful to perform studies related to the evolution of the Sun, such as its rotational and magnetic evolution. Its definition is based on metallicity (−0.15 dex ≤ $\rm {[Fe/H]}$ ≤ + 0.15 dex) and mass (0.95 M⊙ ≤ M ≤ 1.05 M⊙) constraints, thus assuring that the star follows a similar evolutionary path as the Sun along the main sequence. Based on this new definition, we report 70 newly identified solar proxies, 46 solar analogues, and 13 solar-type stars. In addition, we identified nine close solar twins whose stellar parameters are the most similar to those of the Sun.

Unexpected coexistence of radiation and absorption in rotationally excited nitrogen molecular ions

ABSTRACT We studied the dynamic evolution of the rotational states by measuring the laserlike narrow-bandwidth coherent radiation of from to . The coexistence of radiation and absorption was observed when the ratio of population in the and states is around unity. The absorption turns up on the blue side of the radiation with a time delay of 250 fs. Based on a semiclassical radiation and absorption model, it was found that the fast rotational temperature evolution, determining the population distribution on the rotational states, holds the key to understand this behaviour.

Mapping the core of the Tarantula Nebula with VLT-MUSE

We present the spectroscopic analysis of 333 OB-type stars extracted from VLT-MUSE observations of the central 30 × 30 pc of NGC 2070 in the Tarantula Nebula on the Large Magellanic Cloud, the majority of which are analysed for the first time. The distribution of stars in the spectroscopic Hertzsprung-Russell diagram (sHRD) shows 281 stars in the main sequence. We find two groups in the main sequence, with estimated ages of 2.1 ± 0.8 and 6.2 ± 2 Myr. A subgroup of 52 stars is apparently beyond the main sequence phase, which we consider to be due to emission-type objects and/or significant nebular contamination affecting the analysis. As in previous studies, stellar masses derived from the sHRD are systematically larger than those obtained from the conventional HRD, with the differences being largest for the most massive stars. Additionally, we do not find any trend between the estimated projected rotational velocity and evolution in the sHRD. The projected rotational velocity distribution presents a tail of fast rotators that resembles findings in the wider population of 30 Doradus. We use published spectral types to calibrate the He Iλ4921/He IIλ5411 equivalent-width ratio as a classification diagnostic for early-type main sequence stars when the classical blue-visible region is not observed. Our model-atmosphere analyses demonstrate that the resulting calibration is well correlated with effective temperature.

Metallicity-dependent wind parameter predictions for OB stars

ABSTRACTMass-loss rates and terminal wind velocities are key parameters that determine the kinetic wind energy and momenta of massive stars. Furthermore, accurate mass-loss rates determine the mass and rotational velocity evolution of mass stars, and their fates as neutron stars and black holes in function of metallicity (Z). Here, we update our Monte Carlo mass-loss Recipe with new dynamically consistent computations of the terminal wind velocity – as a function of Z. These predictions are particularly timely as the Hubble Space Telescope Ultraviolet Legacy Library of Young Stars as Essential Standards (ULLYSES) project will observe ultraviolet spectra with blue-shifted P Cygni lines of hundreds of massive stars in the low-Z Large and Small Magellanic Clouds (SMC), as well as sub-SMC metallicity hosts. Around 35 000 K, we uncover a weak-wind ‘dip’ and we present diagnostics to investigate its physics with ULLYSES and X-Shooter data. We discuss how the dip may provide important information on wind-driving physics, and how this is of key relevance towards finding a new gold-standard for OB star mass-loss rates. For B supergiants below the Fe iv to iii bi-stability jump, the terminal velocity is found to be independent of Z and M, while the mass-loss rate still varies as $\dot{M} \propto Z^{0.85}$. For O-type stars above the bi-stability jump we, find a terminal-velocity dependence of $\mbox{$v _{\infty }$}\propto Z^{0.19}$ and the Z-dependence of the mass-loss rate is found to be as shallow as $\dot{M} \propto Z^{0.42}$, implying that to reproduce the ‘heavy’ black holes from LIGO/Virgo, the ‘low Z’ requirement becomes even more stringent than was previously anticipated.

Effect of release conditions on casualty risk factor in uncontrolled re-entry of large space debris

Abstract In this research, two existing re-entry models, the Debris Risk Assessment and Mitigation Analysis (DRAMA) model and the Debris Assessment Software (DAS) are used to study the influences of varying the parameters of the debris disposal orbit and its release conditions on the resultant casualty risk factor. With this perspective, the de-orbiting stage of an active debris removal (ADR) mission can be designed such that the parameters of the disposal orbit minimize the casualty risk of large debris re-entry, while maintaining feasible fuel and time constraints on the de-orbit manoeuvre. With respect to release conditions, the effect of introducing a small-magnitude impulse onto the debris at the release is studied, consequently showing that the casualty risk factor can be lowered even further. The change in the risk factor that results from an impulse is highly dependent on both the magnitude and the direction of the impulse with respect to the debris flight path. Furthermore, it has previously been demonstrated that the orientation and surface area of a piece of debris at the onset of re-entry have a significant impact on the characteristics of the re-entry. To this end, the coupled orbit-attitude propagator developed in our prior work, Debris SPin/Orbit Simulation Environment (D-SPOSE), is used to analyze the rotational state evolution of the debris between its release at ~ 200 km and the onset of re-entry assumed at ~ 125 km altitude. The debris is released with various attitude orientations, and the implications of the attitude state during descent on the DRAMA re-entry analysis are discussed.

Exploring the consequences of external photoevaporation of circumstellar disks on the rotational evolution of low mass stars

Exploring the consequences of external photoevaporation of circumstellar disks on the rotational evolution of low mass stars

Magnetic Braking of Accreting T Tauri Stars: Effects of Mass Accretion Rate, Rotation, and Dipolar Field Strength

The rotational evolution of accreting pre-main-sequence stars is influenced by its magnetic interaction with its surrounding circumstellar disk. Using the PLUTO code, we perform 2.5D magnetohydrodynamic, axisymmetric, time-dependent simulations of star-disk interaction---with an initial dipolar magnetic field structure, and a viscous and resistive accretion disk---in order to model the three mechanisms that contribute to the net stellar torque: accretion flow, stellar wind, and magnetospheric ejections (periodic inflation and reconnection events). We investigate how changes in the stellar magnetic field strength, rotation rate, and mass accretion rate (changing the initial disk density) affect the net stellar torque. All simulations are in a net spin-up regime. We fit semi-analytic functions for the three stellar torque contributions, allowing for the prediction of the net stellar torque for our parameter regime, and the possibility of investigating spin-evolution using 1D stellar evolution codes. The presence of an accretion disk appears to increase the efficiency of stellar torques compared to isolated stars, for cases with outflow rates much smaller than accretion rates, because the star-disk interaction opens more of the stellar magnetic flux compared to that from isolated stars. In our parameter regime, a stellar wind with a mass loss rate of $\approx 1 \%$ of the mass accretion rate is capable of extracting $\lesssim 50 \%$ of the accreting angular momentum. These simulations suggest that achieving spin-equilibrium in a representative T Tauri case within our parameter regime, e.g., BP Tau, would require a wind mass loss rate of $\approx 25\%$ of the mass accretion rate.

Binary-driven stellar rotation evolution at the main-sequence turn-off in star clusters

ABSTRACT The impact of stellar rotation on the morphology of star cluster colour–magnitude diagrams is widely acknowledged. However, the physics driving the distribution of the equatorial rotation velocities of main-sequence turn-off stars is as yet poorly understood. Using Gaia Data Release 2 photometry and new Southern African Large Telescope medium-resolution spectroscopy, we analyse the intermediate-age ($\sim 1\text{-}{\rm Gyr}$-old) Galactic open clusters NGC 3960, NGC 6134, and IC 4756 and develop a novel method to derive their stellar rotation distributions based on SYCLIST stellar rotation models. Combined with literature data for the open clusters NGC 5822 and NGC 2818, we find a tight correlation between the number ratio of slow rotators and the clusters’ binary fractions. The blue-main-sequence stars in at least two of our clusters are more centrally concentrated than their red-main-sequence counterparts. The origin of the equatorial stellar rotation distribution and its evolution remains as yet unidentified. However, the observed correlation in our open cluster sample suggests a binary-driven formation mechanism.

Ultrafast carrier and spin dynamics in GaMnAs across the Curie temperature

The carrier and spin dynamics of the diluted ferromagnetic semiconductor GaMnAs are crucial to understanding its ferromagnetic nature, especially near the Curie temperature (TC). Herein, transient differential reflectivity measurements and the temporal evolution of Kerr rotation are shown using ultrafast optical spectroscopy at various temperatures. The energy and angular momentum transfer routes after femtosecond laser pumping are revealed. The hole dynamics consist of two processes: a fast process that arises from carrier recombination and a slow process caused by carrier–lattice interactions. The spin dynamics are determined from the spin–orbital coupling and spin–lattice interactions in the ferromagnetic and paramagnetic phases, respectively. Critical phenomena are observed from the competition between the hole-mediated ferromagnetic orders and thermal perturbations near TC. These experimental results provide deep insights into the ultrafast decay behavior in GaMnAs, which is regarded as one of the most promising spintronic materials.

Lithium depletion and angular momentum transport in solar-type stars

Context. Transport processes occurring in the radiative interior of solar-type stars are evidenced by the surface variation of light elements, in particular 7Li, and the evolution of their rotation rates. For the Sun, inversions of helioseismic data indicate that the radial profile of angular velocity in its radiative zone is nearly uniform, which implies the existence of angular momentum transport mechanisms that are efficient over evolutionary timescales. While there are many independent transport models for angular momentum and chemical species, there is a lack of self-consistent theories that permit stellar evolution models to simultaneously match the present-day observations of solar lithium abundances and radial rotation profiles. Aims. We explore how additional transport processes can improve the agreement between evolutionary models of rotating stars and observations for 7Li depletion, the rotation evolution of solar-type stars, and the solar rotation profile. Methods. Models of solar-type stars are computed including atomic diffusion and rotation-induced mixing with the code STAREVOL. We explore different additional transport processes for chemicals and for angular momentum such as penetrative convection, tachocline mixing, and additional turbulence. We constrain the resulting models by simultaneously using the evolution of the surface rotation rate and 7Li abundance in the solar-type stars of open clusters with different ages, and the solar surface and internal rotation profile as inverted from helioseismology when our models reach the age of the Sun. Results. We show the relevance of penetrative convection for the depletion of 7Li in pre-main sequence and early main sequence stars. The rotational dependence of the depth of penetrative convection yields an anti-correlation between the initial rotation rate and 7Li depletion in our models of solar-type stars that is in agreement with the observed trend. Simultaneously, the addition of an ad hoc vertical viscosity νadd leads to efficient transport of angular momentum between the core and the envelope during the main sequence evolution and to solar-type models that match the observed profile of the Sun. We also self-consistently compute for the first time the thickness of the tachocline and find that it is compatible with helioseismic estimations at the age of the Sun, but we highlight that the associated turbulence does not allow the observed 7Li depletion to be reproduced. The main sequence depletion of 7Li in solar-type stars is only reproduced when adding a parametric turbulent mixing below the convective envelope. Conclusions. The need for additional transport processes in stellar evolution models for both chemicals and angular momentum in addition to atomic diffusion, meridional circulation, and turbulent shear is confirmed. We identify the rotational dependence of the penetrative convection as a key process. Two additional and distinct parametric turbulent mixing processes (one for angular momentum and one for chemicals) are required to simultaneously explain the observed surface 7Li depletion and the solar internal rotation profile. We highlight the need of additional constraints for the internal rotation of young solar-type stars and also for the beryllium abundances of open clusters in order to test our predictions.

Sliding Impact Mechanism of Square Roadway Based on Complex Function Theory

To clarify the process of stress change and plastic zone evolution of square roadways under high-stress conditions, the rotational square expansion plastic zone evolution model of square roadway was established by theoretical analysis, numerical simulation, and engineering verification. The shear slip impact stress criterion of square roadway based on complex variable function theory was studied, and the law of surrounding rock stress distribution, plastic zone expansion, elastic energy density, local energy release rate (LERR), and total energy release of square roadway were analyzed. The results show that the compressive stress is concentrated in the four corners of the roadway after the roadway excavated and transfers with the change of plastic zone. Main shear failures start from the four corners and develop in a rotating square shape, forming square failure zones I and II. The square failure zone I is connected with the roadway contour and rotated 45°. The square failure zone II is connected with the square failure zone I and rotated 45°. When the original rock stress is low, the surrounding rock tends to be stable after the square shear slip line field formed. When the original rock stress is high, the shear failure of the surrounding rock continues to occur after the square failure zone II formed, showing a spiral slip line. Corners of the square roadway and square failure zones I and II are the main energy accumulation and release areas. The maximum elastic energy density and LERR increase exponentially with the ratio of vertical stress to uniaxial compressive strength (Ic). When square corners of the roof are changed to round corners, the plastic zone of the roof expands to form an arch structure. The maximum elastic energy density decreases by 22%, which reduces the energy level and possibility of rock burst. This study enriches the failure mechanism of roadway sliding impact. It can provide a basic theoretical reference for the design of the new roadway section and support form based on the prevention of rock burst.