Asteroseismic Observations Research Articles

3D hydrodynamic simulations of massive main-sequence stars – II. Convective excitation and spectra of internal gravity waves

ABSTRACT Recent photometric observations of massive stars have identified a low-frequency power excess which appears as stochastic low-frequency variability in light-curve observations. We present the oscillation properties of high-resolution hydrodynamic simulations of a $25\,\,{\rm{M}_\odot }$ star performed with the PPMstar code. The model star has a convective core mass of $\approx 12\,\,{\rm{M}_\odot }$ and approximately half of the envelope simulated. From this simulation, we extract light curves from several directions, average them over each hemisphere, and process them as if they were real photometric observations. We show how core convection excites waves with a similar frequency as the convective time-scale in addition to significant power across a forest of low and high angular degree l modes. We find that the coherence of these modes is relatively low as a result of their stochastic excitation by core convection, with lifetimes of the order of 10s of days. Thanks to the still significant power at higher l and this relatively low coherence, we find that integrating over a hemisphere produces a power spectrum that still contains measurable power up to the Brunt–Väisälä frequency. These power spectra extracted from the stable envelope are qualitatively similar to observations, with the same order of magnitude yet lower characteristic frequency. This work further shows the potential of long-duration, high-resolution hydrodynamic simulations for connecting asteroseismic observations to the structure and dynamics of core convection and the convective boundary.

Angular momentum and chemical transport by azimuthal magnetorotational instability in radiative stellar interiors

Context. The transport of angular momentum and chemical elements within evolving stars remains poorly understood. Asteroseismic and spectroscopic observations of low-mass main sequence stars and red giants reveal that their radiative cores rotate orders of magnitude slower than classical predictions from stellar evolution models and that the abundances of their surface light elements are too small. Magnetohydrodynamic (MHD) turbulence is considered a primary mechanism to enhance the transport in radiative stellar interiors but its efficiency is still largely uncertain. Aims. We explore the transport of angular momentum and chemical elements due to azimuthal magnetorotational instability, one of the dominant instabilities expected in differentially rotating radiative stellar interiors. Methods. We employed 3D MHD direct numerical simulations in a spherical shell of unstratified and stably stratified flows under the Boussinesq approximation. The background differential rotation was maintained by a volumetric body force. We examined the transport of chemical elements using a passive scalar. Results. We provide evidence of magnetorotational instability for purely azimuthal magnetic fields in the parameter regime expected from local and global linear stability analyses. Without stratification and when the Reynolds number Re and the background azimuthal field strength are large enough, we observed dynamo action driven by the instability at values of the magnetic Prandtl number Pm in the range 0.6 − 1, which is the smallest ever reported in a global setup. When considering stable stratification at Pm = 1, the turbulence is transitional and becomes less homogeneous and isotropic upon increasing buoyancy effects. The transport of angular momentum occurs radially outward and is dominated by the Maxwell stresses when stratification is large enough. We find that the turbulent viscosity decreases when buoyancy effects strengthen and scales with the square root of the ratio of the reference rotation rate Ωa to the Brunt–Väisälä frequency N. The chemical turbulent diffusion coefficient scales with stratification similarly to the turbulent viscosity, but is lower in amplitude so that the transport of chemicals is slower than the one of angular momentum, in agreement with recent stellar evolution models of low-mass stars. Conclusions. We show that the transport induced by azimuthal magnetorotational instability scales somewhat slowly with stratification and may enforce rigid rotations of red giant cores on a timescale of a few thousand years. In agreement with recent stellar evolution models of low-mass stars, the instability transports chemical elements less efficiently than angular momentum.

Asteroseismology Applied to Constrain Structure Parameters of δ Scuti Stars

Asteroseismology is a powerful tool to probe stellar structure. Spaceborne instruments like CoRoT, Kepler, and TESS have observed the oscillations of numerous stars, among which δ Scutis are particularly interesting, owing to their fast rotation and complex pulsation mechanisms. In this work, we inferred model-dependent masses, metallicities, and ages of 60 δ Scuti stars from photometric, spectroscopic, and asteroseismic observations using least-squares minimization. These statistics have the potential to explain why only a tiny fraction of δ Scuti stars pulsate in a very clean manner. We find most of these stars with masses around 1.6 M ⊙ and metallicities below Z = 0.010. We observed a bimodality in age for these stars, with more than half the sample younger than 30 Myr, while the remaining ones were inferred to be older, i.e., hundreds of Myrs. This work emphasizes the importance of the large-frequency separation (Δν) in studies of δ Scutis. We also designed three machine-learning (ML) models that hold the potential for inferring these parameters at lower computational cost and much more rapidly. These models further revealed that constraining dipole modes can help in significantly improving age estimation and that radial modes succinctly encode information regarding luminosity and temperature. Using the ML models, we also gained qualitative insight into the importance of stellar observables in estimating mass, metallicity, and age. The effective temperature T eff strongly affects the inference of all structure parameters, and the asteroseismic offset parameter ϵ plays an essential role in the inference of age.

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.

Investigating Gaia EDR3 parallax systematics using asteroseismology of Cool Giant Stars observed by Kepler, K2, and TESS

Gaia EDR3 has provided unprecedented data that has generated a great deal of interest in the astrophysical community, even though systematics affect the reported parallaxes at the level of ∼10 μas. Independent distance measurements are available from asteroseismology of red-giant stars with measurable parallaxes, whose magnitude and colour ranges more closely reflect those of other stars of interest. In this paper we determine distances to nearly 12 500 red-giant-branch and red clump stars observed by Kepler, K2, and TESS. This was done via a grid-based modelling method, where global asteroseismic observables, and constraints on the photospheric chemical composition and on the unreddened photometry are used as observational inputs. This large catalogue of asteroseismic distances allows us to provide a first comparison with Gaia EDR3 parallaxes. Offset values estimated with asteroseismology show no clear trend with ecliptic latitude or magnitude, and the trend whereby they increase (in absolute terms) as we move towards redder colours is dominated by the brightest stars. The correction model proposed by Lindegren et al. (2021a) is not suitable for all the fields considered in this study. We find a good agreement between asteroseismic results and model predictions of the red clump magnitude. We discuss possible trends with the Gaia scan law statistics, and show that two magnitude regimes exist where either asteroseismology or Gaia provides the best precision in parallax.

Neutrinos and Asteroseismology of Stars over the Helium Flash

The helium flash, occurring in stars of 0.6–2.0 M ⊙ at the end of the red giant branch, is not observable via optical means due to the energy of the process being used to lift the core out of degeneracy. Neutrinos, which are linked to the ignition of reactions triggered during the flash and serve as the only cooling process in the inert core, can help characterize changes in internal structure. In this work, we create 18 stellar models across three mass and six metallicity values, chosen in the context of the stellar abundance problem, to compare the evolutionary path up to and probe the helium flash by conducting a detailed study of neutrino emission throughout this crucial phase of stellar evolution. We demonstrate how thermal neutrino emissions could have an imprint on global asteroseismic parameters and use them as an additional tool to infer the impact of compositional changes. We find that a precision of 0.3 μHz in the determination of Δν is enough to distinguish between between the two most prominent solar composition models and confirm that asteroseismic observation can be enough to classify a star as undergoing the process of helium subflashes. We also predict nuclear neutrino emission fluxes and their evolution for all relevant sources.

The photometric variability of massive stars due to gravity waves excited by core convection

Massive stars die in catastrophic explosions that seed the interstellar medium with heavy elements and produce neutron stars and black holes. Predictions of the explosion’s character and the remnant mass depend on models of the star’s evolutionary history. Models of massive star interiors can be empirically constrained by asteroseismic observations of gravity wave oscillations. Recent photometric observations reveal a ubiquitous red noise signal on massive main sequence stars; a hypothesized source of this noise is gravity waves driven by core convection. We present three-dimensional simulations of massive star convection extending from the star’s centre to near its surface, with realistic stellar luminosities. Using these simulations, we predict the photometric variability due to convectively driven gravity waves at the surfaces of massive stars, and find that gravity waves produce photometric variability of a lower amplitude and lower characteristic frequency than the observed red noise. We infer that the photometric signal of gravity waves excited by core convection is below the noise limit of current observations, and thus the red noise must be generated by an alternative process.

Transition of latitudinal differential rotation as a possible cause of weakened magnetic braking of solar-type stars

ABSTRACTWe investigate the role of latitudinal differential rotation (DR) in the spin evolution of solar-type stars. Recent asteroseismic observation detected the strong equator-fast DR in some solar-type stars. Numerical simulations show that the strong equator-fast DR is a typical feature of young fast-rotating stars and that this tendency is gradually reduced with stellar age. Incorporating these properties, we develop a model for the long-term evolution of stellar rotation. The magnetic braking is assumed to be regulated dominantly by the rotation rate in the low-latitude region. Therefore, in our model, stars with the equator-fast DR spin down more efficiently than those with the rigid-body rotation. We calculate the evolution of stellar rotation in ranges of stellar mass, $0.9 \, \mathrm{M}_{\odot } \le M \le 1.2\, \mathrm{M}_{\odot }$, and metallicity, $0.5\, \mathrm{Z}_{\odot } \le Z \le 2\, \mathrm{Z}_{\odot }$, where M⊙ and Z⊙ are the solar mass and metallicity, respectively. Our model, using the observed torque in the present solar wind, nicely explains both the current solar rotation and the average trend of the rotation of solar-type stars, including the dependence on metallicity. In addition, our model naturally reproduces the observed trend of the weakened magnetic braking in old slowly rotating solar-type stars because strong equator-fast DR becomes reduced. Our results indicate that latitudinal DR and its transition are essential factors that control the stellar spin down.

Improved asteroseismic inversions for red-giant surface rotation rates

Context. Asteroseismic observations of internal stellar rotation have indicated a substantial lack of angular momentum transport in theoretical models of subgiant and red-giant stars. Accurate core and surface rotation rate measurements are therefore needed to constrain the internal transport processes included in the models. Aims. We eliminate substantial systematic errors of asteroseismic surface rotation rates found in previous studies. Methods. We propose a new objective function for the optimally localised averages method of rotational inversions for red-giant stars, which results in more accurate envelope rotation rate estimates obtained from the same data. We use synthetic observations from stellar models across a range of evolutionary stages and masses to demonstrate the improvement. Results. We find that our new inversion technique allows us to obtain estimates of the surface rotation rate that are independent of the core rotation. For a star at the base of the red-giant branch, we reduce the systematic error from about 20% to a value close to 0, assuming constant envelope rotation. We also show the equivalence between this method and the method of linearised rotational splittings. Conclusions. Our new rotational inversion method substantially reduces the systematic errors of red-giant surface rotation rates. In combination with independent measures of the surface rotation rate, this will allow better constraints to be set on the internal rotation profile. This will be a very important probe for further constraining the internal angular momentum transport along the lower part of the red-giant branch.

Looking into dark matter with asteroseismology

Dark matter remains as an elusive component of modern Cosmology. According to previous research, stellar physics observables can be affected by the presence of hypothetical dark matter particles, which can be produced or accreted into the stars. Stellar pulsations are among the observables affected by dark matter, because the changes of the internal structure of the stars due to dark matter produce variations in the pulsation frequencies. We review the current research in the interplay between astroparticles, precise stellar observations, and accurate asteroseismic models, which can be extremely useful in order to constrain dark matter candidates from asteroseismic observables.

Rotation in stellar interiors: General formulation and an asteroseismic-calibrated transport by the Tayler instability

Context. Asteroseismic measurements of the internal rotation of evolved stars indicate that at least one unknown efficient angular momentum (AM) transport mechanism is needed in stellar radiative zones in addition to hydrodynamic transport processes. Aims. We investigate the impact of AM transport by the magnetic Tayler instability as a possible candidate for such a missing physical mechanism. Methods. We derived general equations for AM transport by the Tayler instability to be able to test different versions of the Tayler-Spruit (TS) dynamo by comparing rotational properties of these models with asteroseismic constraints available for sub-giant and red giant stars. Results. These general equations highlight, in a simple way, the key role played by the adopted damping timescale of the azimuthal magnetic field on the efficiency of the resulting AM transport. Using this framework, we first show that the original TS dynamo provides an insufficient coupling in low-mass red giants that have a radiative core during the main sequence (MS), as was found previously for more massive stars that develop a convective core during the MS. We find that the core rotation rates of red giant branch (RGB) stars predicted by models computed with various prescriptions for the TS dynamo are nearly insensitive to the adopted initial rotation velocity. We then derived a new calibrated version of the original TS dynamo and find that the damping timescale adopted for the azimuthal field in the original TS dynamo has to be increased by a factor of about 200 to correctly reproduce the core rotation rates of stars on the RGB. This calibrated version predicts no correlation of the core rotation rates with the stellar mass for RGB stars in good agreement with asteroseismic observations. Moreover, it correctly reproduces the core rotation rates of clump stars similarly to a revised prescription proposed recently. Interestingly, this new calibrated version of the TS dynamo is found to be in slightly better agreement with the core rotation rates of sub-giant stars, while simultaneously better accounting for the evolution of the core rotation rates along the RGB compared to the revised dynamo version. These results were obtained with both the Geneva and the MESA stellar evolution codes.

Deciphering stellar chorus: apollinaire, a Python 3 module for Bayesian peakbagging in helioseismology and asteroseismology

Since the asteroseismic revolution, the availability of efficient and reliable methods to extract stellar-oscillation mode parameters has been an important part of modern stellar physics. In the fields of helio- and asteroseismology, these methods are usually referred to as peakbagging. Here, we introduce the apollinaire module, a new Python 3 open-source Markov chain Monte Carlo (MCMC) framework dedicated to peakbagging. We extensively describe the theoretical framework necessary to understand MCMC peakbagging methods for disk-integrated helio- and asteroseismic observations. In particular, we present the models that are used to estimate the posterior probability function in a peakbagging framework. A description of the apollinaire module is then provided. We explain how the module enables stellar background, p-mode global pattern, and individual-mode parameter extraction. By taking into account instrumental specificities, stellar inclination angle, rotational splittings, and asymmetries, the module allows a large variety of p-mode models to be fitted that are suited for solar and stellar data analysis with different instruments. After presenting a validation of the module with a Monte Carlo fitting trial on synthetic data, it is benchmarked by comparing its outputs with results obtained with other peakbagging codes. We present our analysis of the power spectral density (PSD) of 89 one-year subseries of GOLF observations. We also selected six stars from the Kepler LEGACY sample in order to demonstrate the code abilities on asteroseismic data. The parameters we extract with apollinaire are in good agreement with those presented in the literature and demonstrate the precision and reliability of the module.

Asteroseismology of the dip structure in period-spacings of rapidly rotating γ Doradus stars caused by the coupling between core and envelope oscillations

ABSTRACT Recent asteroseismic observations by the Kepler space mission have revealed the dip fine structure in the period-spacing versus period diagram of rapidly rotating γ Doradus stars. Following the successful reproduction of the dip structure by numerical calculations in previous studies, we present in this paper the physical mechanism of how the dip is formed as a result of the interaction between the gravito-inertial waves in the radiative envelope and the pure inertial waves in the convective core. We analytically describe the wave solutions in both of the radiative envelope and the convective core, and match them at the interface to construct an eigenmode. We have found from the analysis the following points: the dip structure is mainly controlled by a parameter that has an inverse correlation with Brunt–Väisälä frequency at the interface; the depth and the width of the dip is shallower and larger, respectively, as the parameter gets large; the shape of the dip can be approximated by the Lorentzian function; the period at the central position of the dip is equal to or slightly smaller than that of the involved pure inertial mode in the convective core. We have also understood based on the evolutionary models of main-sequence stars that the parameter is inversely correlated with the chemical composition gradient at the convective-core boundary. The dip structure thus would provide information about the poorly-understood physical processes, such as diffusion, convective overshooting and rotational mixing, around the boundary between the convective core and the radiative envelope.

Determining the Age for the Red Giants KIC 9145955 and KIC 9970396 by Gravity-dominated Mixed Modes

Determining the ages and helium core sizes of red giants is a challenging problem. To estimate the age and helium core size precisely requires a good understanding of the internal structure of the red giant. The properties of the g-dominated mixed modes of red giants are closely related to their inner radiative cores, especially the central helium core. Thus, the g-dominated mixed modes are useful indicators for probing the properties of the helium core and constraining the age of red giants. In our previous work, we have estimated the helium core sizes of the red giants KIC 9145955 and KIC 9970396 by asteroseismic models. In this work, we take a further step to calibrate the ages and core overshooting parameters for these two red giants. We find that the ages of these two stars are 4.61 ± 0.23 and 6.13 ± 0.19 Gyr, respectively. From a comparative study, we find that, for a single red giant, the age estimated by the asteroseismology of g-dominated mixed modes is likely to be more precise than that estimated by the combination of the asteroseismic (Δν and ΔP obs) and spectroscopic (T eff and [Fe/H]) observations. In addition, we estimate the core overshooting parameters of these two stars. We find that the overshooting parameter f ov of KIC 9145955 and KIC 9970396 was probably overestimated in previous works.

Coupling between turbulence and solar-like oscillations: A combined Lagrangian PDF/SPH approach

Context. The development of space-borne missions such as CoRoT and Kepler now provides us with numerous and precise asteroseismic measurements that allow us to put better constraints on our theoretical knowledge of the physics of stellar interiors. In order to utilise the full potential of these measurements, however, we need a better theoretical understanding of the coupling between stellar oscillations and turbulent convection. Aims. The aim of this series of papers is to build a new formalism specifically tailored to study the impact of turbulence on the global modes of oscillation in solar-like stars. In building this formalism, we circumvent some fundamental limitations inherent to the more traditional approaches, in particular the need for separate equations for turbulence and oscillations, and the reduction of the turbulent cascade to a unique length and timescale. In this first paper we derive a linear wave equation that directly and consistently contains the turbulence as an input to the model, and therefore naturally contains the information on the coupling between the turbulence and the modes through the stochasticity of the equations. Methods. We use a Lagrangian stochastic model of turbulence based on probability density function methods to describe the evolution of the properties of individual fluid particles through stochastic differential equations. We then transcribe these stochastic differential equations from a Lagrangian frame to a Eulerian frame more adapted to the analysis of stellar oscillations. We combine this method with smoothed particle hydrodynamics, where all the mean fields appearing in the Lagrangian stochastic model are estimated directly from the set of fluid particles themselves, through the use of a weighting kernel function allowing to filter the particles present in any given vicinity. The resulting stochastic differential equations on Eulerian variables are then linearised. As a first step the gas is considered to follow a polytropic relation, and the turbulence is assumed anelastic. Results. We obtain a stochastic linear wave equation governing the time evolution of the relevant wave variables, while at the same time containing the effect of turbulence. The wave equation generalises the classical, unperturbed propagation of acoustic waves in a stratified medium (which reduces to the exact deterministic wave equation in the absence of turbulence) to a form that, by construction, accounts for the impact of turbulence on the mode in a consistent way. The effect of turbulence consists of a non-homogeneous forcing term, responsible for the stochastic driving of the mode, and a stochastic perturbation to the homogeneous part of the wave equation, responsible for both the damping of the mode and the modal surface effects. Conclusions. The stochastic wave equation obtained here represents our baseline framework to properly infer properties of turbulence-oscillation coupling, and can therefore be used to constrain the properties of the turbulence itself with the help of asteroseismic observations. This will be the subject of the rest of the papers in this series.

BESTP — An automated Bayesian modeling tool for asteroseismology

Asteroseismic observations are crucial to constrain stellar models with precision. Bayesian Estimation of STellar Parameters (BESTP) is a tool that utilizes Bayesian statistics and nested sampling Monte Carlo algorithm to search for the stellar models that best match a given set of classical and asteroseismic constraints from observations. The computation and evaluation of models are efficiently performed in an automated and multi-threaded way. To illustrate the capabilities of BESTP, we estimate fundamental stellar properties for the Sun and the red-giant star HD 222076. In both cases, we find models that are consistent with observations. We also evaluate the improvement in the precision of stellar parameters when the oscillation frequencies of individual modes are included as constraints, compared to the case when only the large frequency separation is included. For the solar case, the uncertainties of estimated masses, radii and ages are reduced by 0.7%, 0.3% and 8% respectively. For HD 222076, they are reduced even more noticeably by 2%, 0.5% and 4.7% respectively. We also note an improvement of 10% for the age of HD 222076 when the Gaia parallax is included as a constraint compared to the case when only the large separation is included as a constraint.

The BAyesian STellar algorithm (BASTA): a fitting tool for stellar studies, asteroseismology, exoplanets, and Galactic archaeology

ABSTRACT We introduce the public version of the BAyesian STellar Algorithm (BASTA), an open-source code written in Python to determine stellar properties based on a set of astrophysical observables. BASTA has been specifically designed to robustly combine large data sets that include asteroseismology, spectroscopy, photometry, and astrometry. We describe the large number of asteroseismic observations that can be fit by the code and how these can be combined with atmospheric properties (as well as parallaxes and apparent magnitudes), making it the most complete analysis pipeline available for oscillating main-sequence, subgiant, and red giant stars. BASTA relies on a set of pre-built stellar isochrones or a custom-designed library of stellar tracks, which can be further refined using our interpolation method (both along and across stellar tracks or isochrones). We perform recovery tests with simulated data that reveal levels of accuracy at the few percent level for radii, masses, and ages when individual oscillation frequencies are considered, and show that asteroseismic ages with statistical uncertainties below 10 per cent are within reach if our stellar models are reliable representations of stars. BASTAis extensively documented and includes a suite of examples to support easy adoption and further development by new users.

A calibration of the Rossby number from asteroseismology

Stellar activity and rotation are tightly related in a dynamo process. Our understanding of this mechanism is mainly limited by our capability of inferring the properties of stellar turbulent convection. In particular, the convective turnover time is a key ingredient through the estimation of the stellar Rossby number, which is the ratio of the rotation period and the convective turnover time. In this work, we propose a new calibration of the (B − V) color index dependence of the convective turnover time, hence, of the stellar Rossby number. Our new calibration is based on the stellar structure properties inferred through the detailed modeling of solar-like pulsators using asteroseismic observables. We show the impact of this calibration via a stellar activity-Rossby number diagram by applying it to a sample of about 40 000 stars observed with Kepler and for which the values for the photometric activity proxy S​ph and surface rotation periods are available. Additionally, we provide a new calibration for the convective turnover time as function of the (GBP − GRP) color index for allowing applicability in the ESA Gaia photometric passbands.

Probing the temperature gradient in the core boundary layer of stars with gravito-inertial modes

Aims. We investigated the thermal and chemical structure in the near-core region of stars with a convective core by means of gravito-inertial modes. We determined the probing power of different asteroseismic observables and fitting methodologies. We focus on the case of the B-type star KIC 7760680, rotating at a quarter of its critical rotation velocity. Methods. We computed grids of 1D stellar structure and evolution models for two different prescriptions of the temperature gradient and mixing profile in the near-core region. We determined which of these prescriptions is preferred according to the prograde dipole modes detected in 4 yr Kepler photometry of KIC 7760680. We considered different sets of asteroseismic observables and compared the outcomes of the regression problem for a χ2 and a Mahalanobis distance merit function, where the latter takes into account realistic uncertainties for the theoretical predictions and the former does not. Results. Period spacings of modes with consecutive radial order offer a better diagnostic than mode periods or mode frequencies for asteroseismic modelling of stars revealing only high-order gravito-inertial modes. We find KIC 7760680 to reveal a radiative temperature gradient in models with convective boundary mixing, but less complex models without such mixing are statistically preferred for this rotating star, revealing extremely low vertical envelope mixing. Conclusions. Our results strongly suggest the use of measured individual period spacing values for modes of consecutive radial order as an asteroseismic diagnostic for stellar modelling of B-type pulsators with gravito-inertial modes.

Anisotropic turbulent transport with horizontal shear in stellar radiative zones

Context.Turbulent transport in stellar radiative zones is a key ingredient of stellar evolution theory, but the anisotropy of the transport due to the stable stratification and the rotation of these regions is poorly understood. The assumption of shellular rotation, which is a cornerstone of the so-called rotational mixing, relies on an efficient horizontal transport. However, this transport is included in many stellar evolution codes through phenomenological models that have never been tested.Aims.We investigate the impact of horizontal shear on the anisotropy of turbulent transport.Methods.We used a relaxation approximation (also known asτapproximation) to describe the anisotropising effect of stratification, rotation, and shear on a background turbulent flow by computing velocity correlations.Results.We obtain new theoretical scalings for velocity correlations that include the effect of horizontal shear. These scalings show an enhancement of turbulent motions, which would lead to a more efficient transport of chemicals and angular momentum, in better agreement with helio- and asteroseismic observations of rotation in the whole Hertzsprung-Russell diagram. Moreover, we propose a new choice for the non-linear time used in the relaxation approximation, which characterises the source of the turbulence.Conclusions.For the first time, we describe the effect of stratification, rotation, and vertical and horizontal shear on the anisotropy of turbulent transport in stellar radiative zones. The new prescriptions need to be implemented in stellar evolution calculations. To do so, it may be necessary to implement non-diffusive transport.