arXiv subjects

K. Belkacem

Publications and source records attributed to K. Belkacem.

At least 19 recordsLinked to original sources

arXiv2026

The PLATO field selection process III. Selection of the Prime Sample for the LOPS2 field

The PLanetary Transits and Oscillations of stars (PLATO) mission will begin its four-year nominal mission in early 2027 by monitoring its Long-duration Observation Phase field at South (LOPS2) for at least two years continuously. The primary aim of PLATO is a very ambitious and challenging one: the discovery of Earth-like planets in the habitable zone of nearby and bright solar analogues. To this purpose, the PLATO Mission Consortium, through its Ground-based Observing Program, will perform the follow-up needed to confirm part of the candidate planets photometrically detected by PLATO and measure their masses through radial velocity curves. For the LOPS2, the Ground-based Observing Program is committed (as part of the PLATO mission) to follow-up the candidate exoplanets discovered orbiting the 15,000 high-quality target subset of the PLATO Input Catalog (PIC) known as the Prime Sample. The Prime Sample will be made public nine months before launch in the context of the first Guest Observer call for proposals to be issued by the European Space Agency. Here, we present the quantitative metrics and thresholds defined to select and prioritize the Prime Sample. Our method is perfectly general and suitable to rank any list of stars surveyed for transiting planets. We also describe the astrophysical properties of the LOPS2 Prime Sample, both in a statistical sense and for some specific targets of interest.

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arXiv2026

The PLATO Input Catalogue of targets (tPIC) for the first Long Pointing Field

The ESA PLAnetary Transits and Oscillations of stars (PLATO) mission is designed to detect terrestrial planets in the habitable zones of solar-type stars. Owing to telemetry constraints, the selection of PLATO targets must be performed in advance. In this paper, we present the first public release of the PLATO Input Catalogue of targets (tPIC2.2), which provides the list of stars that will be observed during the PLATO first Long-duration Observation Phase field at South (LOPS2) as part of its core science program. We exploit astrometric and photometric data from Gaia Data Release 3 (DR3), together with three-dimensional maps of the local interstellar medium, to identify stars belonging to the PLATO stellar samples as from mission requirements. The tPIC comprises 217,741 stars, including 202,315 FGK dwarfs and subgiants, 15,037 M dwarfs and 789 known planet host stars. The median distances of the samples are 512 pc for FGK stars and 133 pc for M dwarfs. We estimate interstellar reddening for almost all targets and develop an algorithm to infer fundamental stellar parameters (effective temperature, radius, and mass) in an homogeneous way from astrometric and photometric observables. The tPIC fulfills all the science requirements of the PLATO mission. The tPIC also includes a list of stars that host known exoplanets (confirmed or still candidate), located within the LOPS2 field.

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arXiv2026

Magnetohydrodynamic instabilities in stellar radiative regions. I. Linear study of shear-driven instabilities

This paper is the first in a series investigating magnetohydrodynamic instabilities that may contribute to angular-momentum transport and magnetic-field evolution in stellar radiative zones. We focus on shear-driven instabilities, specifically the Goldreich-Schubert-Fricke (GSF) instability and the magnetorotational instability (MRI), which are expected to play key roles in the internal dynamics of radiative regions. We carried out a local linear stability analysis using a numerical approach that extends beyond classical limiting cases and includes stabilizing effects such as stratification and magnetic tension, allowing the exploration of realistic flow regimes. These results were validated through a global mode analysis in a Taylor-Couette configuration. We recovered the standard MRI and azimuthal MRI stability criteria and quantified the effects of stratification, magnetic tension, and diffusion on their growth. In strongly sheared regimes, we derived a new criterion for the magnetised GSF (MGSF) instability and clarified the transition from SMRI to MGSF as stratification and magnetic effects narrow the unstable domain. We also provided approximate growth-time formulae that identify the dominant instability under given stellar conditions and can be implemented in 1D stellar evolution codes. Global Taylor-Couette calculations validate the local WKB analysis. Applied to subgiants and young red giants, our results show that shear-driven instabilities can grow rapidly for magnetic fields below 100 kG. Strong axial fields (100 kG) confined to the hydrogen-burning shell suppress instabilities unless the shear is sufficiently distant. These results support incorporating our criteria and growth estimates into stellar evolution models to assess the efficiency of shear-driven transport.

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arXiv2026

Extra modes in helium-core-burning stars probing an infra core cavity

Dipole mixed modes observed in the oscillation pattern of red giant stars probe the radiative regions in the stellar core. Oscillation spectra of helium-core-burning stars sometimes show extra peaks that remain unexplained by the dipole mixed-mode pattern expected from the coupling of a radiative cavity in the stellar core and a pressure cavity in the stellar envelope. We use the asymptotic expansion developed for a multi-cavity star in order to characterize these extra peaks. The analytical resonance condition of the multi-cavity gravito-acoustic modes, with two inner gravity cavities and an outer pressure cavity, helps us explain that the apparent extra peaks are dipole mixed modes that follow the 3-cavity oscillation pattern. The derivation of the two asymptotic period spacings associated with the two distinct regions in the radiative core provides an estimate of the full radiative cavity. Our results provide new constraints for analysing the overshoot or mixing in the core of helium-core-burning stars. An important structure discontinuity inside the radiative core may explain the larger than expected observed period spacings.

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arXiv2025

Selection and characterisation of the M-dwarf targets in the PLATO Input Catalogue

The ESA's PLAnetary Transits and Oscillations of Stars (PLATO) mission aims to detect planets orbiting around dwarfs and subgiant stars with spectral type F5 or later, including M-dwarfs. The PLATO Input Catalogue (PIC) contains all targets available for observation by the nominal science. The latest version, PIC2.1.0.1, focuses on the Southern PLATO field, named LOPS2, selected as the first long observation field, and includes the P4 sample, one of the four target samples outlined in the Science Requirement Document. P4 includes the M-dwarfs with magnitudes V < 16 located within LOPS2. A characterisation of the M-dwarfs in the PIC is essential for assessing their potentiality to host exoplanets, and eventually estimate the hosted planet(s) properties. The purpose of this paper is to describe how we selected the P4 M-dwarf targets, and obtained their fundamental parameters and properties. In this work, we introduce the P4 sample and detail the methodologies adopted for the measurement of their stellar parameters. Based on a statistical analysis of the P4 sample, we assess both the photometric and volume completeness, and classify the stellar populations according to their Galactic spatial-velocity components. The adopted stellar parameters are validated by comparison with independent methods from the literature used to estimate stellar radii. The P4 sample is compliant with the PLATO science requirements. Being magnitude limited, its volume completeness decreases going towards distances larger than 30 pc, where late-type targets are progressively less covered. The observed large spread in the colour-magnitude diagram is likely due to the combination of several effects such as metallicity, age, binarity and activity. The strategy we adopted for deriving stellar parameters provides results consistent with those obtained in the literature with different and independent methods.

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arXiv2025

A new particle-based code for Lagrangian stochastic models applied to stellar turbulent convection

The inclusion of convection in stellar evolution models lacks realism, especially near convective-radiative interfaces. Furthermore, the interaction of convection with oscillations prevent us from accurately predicting seismic frequencies, and therefore from fully exploiting the asteroseismic data of low-mass stars. We aim to develop a new formalism to model the one-point statistics of stellar convection, to implement it in a new numerical code, and to validate this implementation against benchmark cases. This new formalism is based on Lagrangian Probability Density Function (PDF) methods, where a Fokker-Planck equation for the PDF of particle-based turbulent properties is integrated in time. We then develop a Monte-Carlo implementation of this method, where the flow is represented by a large number of notional particles acting as realisations of the PDF. Notional particles interact with each other through the time- and space-dependent mean flow, which is estimated from the particle realisations through a scheme similar to Smoothed Particle Hydrodynamics. We establish a model for the evolution of turbulent properties along Lagrangian trajectories applicable to stellar turbulent convection, with only a minimal number of physical assumptions necessary to close the system. In particular, no closure is needed for the non-linear advection terms, which are included exactly through the Lagrangian nature of formalism. The numerical implementation of this new formalism allows us to extract time-dependent maps of the statistical properties of turbulent convection in a way which is not possible in grid-based large-eddy simulations, in particular the turbulent pressure, Reynolds stress tensor, internal energy variance and convective flux.

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arXiv2024

Measuring stellar surface rotation and activity with the PLATO mission -- I. Strategy and application to simulated light curves

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

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arXiv2024

Predicted asteroseismic detection yield for solar-like oscillating stars with PLATO

We determine the expected yield of detections of solar-like oscillations for the PLATO ESA mission. We used a formulation from the literature to calculate the probability of detection and validated it with Kepler data. We then applied this approach to the PLATO P1 and P2 samples with the lowest noise level and the much larger P5 sample, which has a higher noise level. We used the information available in in the PIC 1.1.0, including the current best estimate of the signal-to-noise ratio. We also derived relations to estimate the uncertainties of seismically inferred stellar mass, radius and age and applied those relations to the main sequence stars of the PLATO P1 and P2 samples with masses equal to or below 1.2 $\rm{M}_\odot$ for which we had obtained a positive seismic detection. We found that one can expect positive detections of solar-like oscillations for more than 15 000 FGK stars in one single field after a two-years run of observation. For main sequence stars with masses $\leq 1.2 \rm{M}_\odot$, we found that about 1131 stars satisfy the PLATO requirements for the uncertainties of the seismically inferred stellar masses, radii and ages in one single field after a two-year run of observation. The baseline observation programme of PLATO consists in observing two fields of similar size (in the Southern and Northern hemispheres) for two years each. The expected seismic yields of the mission are more 30000 FGK dwarfs and subgiants with positive detections of solar-like oscillations, enabling to achieve the mission stellar objectives. The PLATO mission should produce a sample of seismically extremely well characterized stars of quality equivalent to the Kepler Legacy sample but containing a number of stars $\sim$ 80 times larger if observing two PLATO fields for two years each. They will represent a goldmine which will make possible significant advances in stellar modelling.

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arXiv2024

Locked differential rotation in core-helium burning red giants

Oscillation modes of a mixed character are able to probe the inner region of evolved low-mass stars and offer access to a range of information, in particular, the mean core rotation. Ensemble asteroseismology observations are then able to provide clear views on the transfer of angular momentum when stars evolve as red giants. Previous catalogs of core rotation rates in evolved low-mass stars have focussed on hydrogen-shell burning stars. Our aim is to complete the compilation of rotation measurements toward more evolved stages, with a detailed analysis of the mean core rotation in core-helium burning giants. The asymptotic expansion for dipole mixed modes allows us to fit oscillation spectra of red clump stars and derive their core rotation rates. We used a range of prior seismic analyses, complete with new data, to get statistically significant results. We measured the mean core rotation rates for more than 1500 red clump stars. We find that the evolution of the core rotation rate in core-helium-burning stars scales with the inverse square of the stellar radius, with a small dependence on mass. Assuming the conservation of the global angular momentum, a simple model allows us to infer that the mean core rotation and envelope rotation are necessarily coupled. The coupling mechanism ensures that the differential rotation in core-helium-burning red giants is locked.

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arXiv2022

Coupling between turbulence and solar-like oscillations: A combined Lagrangian PDF/SPH approach. II - Mode driving, damping and modal surface effect

The first paper of this series established a linear stochastic wave equation for solar-like p-modes, correctly taking the effect of turbulence thereon into account. In this second paper, we aim at deriving simultaneous expressions for the excitation rate, damping rate, and modal surface effect associated with any given p-mode, as an explicit function of the statistical properties of the turbulent velocity field. We reduce the stochastic wave equation to complex amplitude equations for the normal oscillating modes of the system. We then derive the equivalent Fokker-Planck equation for the real amplitudes and phases of all the oscillating modes of the system simultaneously. The effect of the finite-memory time of the turbulent fluctuations (comparable to the period of the modes) on the modes themselves is consistently and rigorously accounted for, by means of the simplified amplitude equation formalism. This formalism accounts for mutual linear mode coupling in full, and we then turn to the special single-mode case. This allows us to derive evolution equations for the mean energy and mean phase of each mode, from which the excitation rate, the damping rate, and the modal surface effect naturally arise. We show that the expression for the excitation rate of the modes is identical to previous results obtained through a different modelling approach, thus supporting the validity of the formalism presented here. We also recover the fact that the damping rate and modal surface effect correspond to the real and imaginary part of the same single complex quantity. We explicitly separate the different physical contributions to these observables, in particular the turbulent pressure contribution and the joint effect of the pressure-rate-of-strain correlation and the turbulent dissipation. We show that the former dominates for high-frequency modes and the latter for low-frequency modes.

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arXiv2021

Coupling between turbulence and solar-like oscillations: a combined Lagrangian PDF/SPH approach. I -- The stochastic wave equation

Aims. This series of papers aims at building a new formalism specifically tailored to study the impact of turbulence on the global modes of oscillation in solar-like stars. This first paper aims at deriving 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 an 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. 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 to a form that, by construction, accounts for the impact of turbulence on the mode in a consistent way. The effect of turbulence consists in 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.

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arXiv2021

PLATO Hare-and-Hounds exercise: Asteroseismic model fitting of main-sequence solar-like pulsators

Asteroseismology is a powerful tool to infer fundamental stellar properties. The use of these asteroseismic-inferred properties in a growing number of astrophysical contexts makes it vital to understand their accuracy. Consequently, we performed a hare-and-hounds exercise where the hares simulated data for 6 artificial main-sequence stars and the hounds inferred their properties based on different inference procedures. To mimic a pipeline such as that planned for the PLATO mission, all hounds used the same model grid. Some stars were simulated using the physics adopted in the grid, others a different one. The maximum relative differences found (in absolute value) between the inferred and true values of the mass, radius, and age were 4.32 per cent, 1.33 per cent, and 11.25 per cent, respectively. The largest systematic differences in radius and age were found for a star simulated assuming gravitational settling, not accounted for in the model grid, with biases of -0.88 per cent (radius) and 8.66 per cent (age). For the mass, the most significant bias (-3.16 per cent) was found for a star with a helium enrichment ratio outside the grid range. Moreover, a ~7 per cent dispersion in age was found when adopting different prescriptions for the surface corrections or shifting the classical observations by $\pm 1σ$. The choice of the relative weight given to the classical and seismic constraints also impacted significantly the accuracy and precision of the results. Interestingly, only a few frequencies were required to achieve accurate results on the mass and radius. For the age the same was true when at least one $l=2$ mode was considered.

astro-ph.SR↗

arXiv2021

Surface effects and turbulent pressure. Assessing the Gas-$Γ_1$ and Reduced-$Γ_1$ empirical models

The use of the full potential of stellar seismology is made difficult by the improper modeling of the upper-most layers of solar-like stars and their influence on the modeled frequencies. Our knowledge on these \emph{surface effects} has improved thanks to the use of 3D hydrodynamical simulations but the calculation of eigenfrequencies relies on empirical models for the description of the Lagrangian perturbation of turbulent pressure: the reduced-$Γ_1$ model (RGM) and the gas-$Γ_1$ model (GGM). Starting from the fully compressible turbulence equations, we derive both the GGM and RGM models using a closure to model the flux of turbulent kinetic energy. It is found that both models originate from two terms: the source of turbulent pressure due to compression produced by the oscillations and the divergence of the flux of turbulent pressure. It is also demonstrated that they are both compatible with the adiabatic approximation but also imply a number of questionable assumptions mainly regarding mode physics. Among others hypothesis, one has to neglect the Lagrangian perturbation of the dissipation of turbulent kinetic energy into heat and the Lagrangian perturbation of buoyancy work.

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arXiv2020

Velocity-intensity asymmetry reversal of solar radial p-modes

The development of space-borne missions has significantly improved the quality of the measured spectra of solar-like oscillators. Their $p$-mode line profiles can now be resolved, and the asymmetries inferred for a variety of stars other than the Sun. However, it has been known for a long time that the asymmetries of solar $p$-modes are reversed between the velocity and the intensity spectra. Understanding the origin of this reversal is necessary in order to use asymmetries as a tool for seismic diagnosis. For stars other than the Sun, only the intensity power spectrum is sufficiently resolved to allow for an estimation of mode asymmetries. We recently developed an approach designed to model and predict these asymmetries in the velocity power spectrum of the Sun and to successfully compare them to their observationally derived counterparts. In this paper we expand our model and predict the asymmetries featured in the intensity power spectrum. We find that the shape of the mode line profiles in intensity is largely dependent on how the oscillation-induced variations of the radiative flux are treated, and that modelling it realistically is crucial to understanding asymmetry reversal. Perturbing a solar-calibrated grey atmosphere model, and adopting the quasi-adiabatic framework as a first step, we reproduce the asymmetries observed in the solar intensity spectrum for low-frequency modes. We conclude that, unlike previously thought, it is not necessary to invoke an additional mechanism (e.g. non-adiabatic effects, coherent non-resonant background signal) to explain asymmetry reversal. This additional mechanism is necessary, however, to explain asymmetry reversal for higher-order modes.

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arXiv2020

Modelling the asymmetries of the Sun's radial $p$-mode line profiles

In this paper, we aim to develop a predictive model for solar radial $p$-mode line profiles in the velocity spectrum. Unlike the approach favoured by prior studies, this model is not described by free parameters and we do not use fitting procedures to match the observations. Instead, we use an analytical turbulence model coupled with constraints extracted from a 3D hydrodynamic simulation of the solar atmosphere. We then compare the resulting asymmetries with their observationally derived counterpart. We find that stochastic excitation localised beneath the mode upper turning point generates negative asymmetry for $ν< ν_\text{max}$ and positive asymmetry for $ν> ν_\text{max}$. On the other hand, stochastic excitation localised above this limit generates negative asymmetry throughout the $p$-mode spectrum. As a result of the spatial extent of the source of excitation, both cases play a role in the total observed asymmetries. By taking this spatial extent into account and using a realistic description of the spectrum of turbulent kinetic energy, both a qualitative and quantitative agreement can be found with solar observations perfoemed by the GONG network. We also find that the impact of the correlation between acoustic noise and oscillation is negligible for mode asymmetry in the velocity spectrum.

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arXiv2019

Probing the mid-layer structure of red giants I. Mixed-mode coupling factor as a seismic diagnosis

The space-borne missions CoRoT and Kepler have already brought stringent constraints on the internal structure of low-mass evolved stars, a large part of which results from the detection of mixed modes. However, all the potential of these oscillation modes as a diagnosis of the stellar interior has not been fully exploited yet. In particular, the coupling factor or the gravity-offset of mixed modes, $q$ and $\varepsilon_{\rm g}$, are expected to provide additional constraints on the mid-layers of red giants, which are located between the hydrogen-burning shell and the neighborhood of the base of the convective zone. In the present paper, we investigate the potential of the coupling factor in probing the mid-layer structure of evolved stars. Guided by typical stellar models and general physical considerations, we modeled the coupling region along with evolution. We subsequently obtained an analytical expression of $q$ based on the asymptotic theory of mixed modes and compared it to observations. We show that the value of $q$ is degenerate with respect to the thickness of the coupling evanescent region and the local density scale height. A structural interpretation of the global variations in $q$ observed on the subgiant and the red giant branches, as well as on the red clump, was obtained in the light of this model. We demonstrate that $q$ has the promising potential to probe the migration of the base of the convective region as well as convective extra-mixing in evolved red giant stars with typically $ν_{\rm max} \lesssim 100~μ$Hz. We also show that the frequency-dependence of $q$ cannot be neglected in the oscillation spectra of such stars, which is in contrast with what is assumed in the current measurement methods. This analytical study paves the way for a more quantitative exploration of the link of $q$ with the internal properties of evolved stars using stellar models.

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arXiv2019

The PLATO Solar-like Light-curve Simulator: A tool to generate realistic stellar light-curves with instrumental effects representative of the PLATO mission

The preparation of science objectives of the ESA's PLATO space mission will require the implementation of hare-and-hound exercises relying on the massive generation of representative simulated light-curves. We developed a light-curve simulator named the PLATO Solar-like Light-curve Simulator (PSLS) in order to generate light-curves representative of typical PLATO targets, i.e. showing simultaneously solar-like oscillations, stellar granulation, and magnetic activity. At the same time, PSLS also aims at mimicking in a realistic way the random noise and the systematic errors representative of the PLATO multi-telescope concept. To quantify the instrumental systematic errors, we performed a series of simulations at pixel level that include various relevant sources of perturbations expected for PLATO. From the simulated pixels, we extract the photometry as planned on-board. The simulated light-curves are then corrected for instrumental effects using the instrument Point Spread Functions reconstructed on the basis of a microscanning technique that will be operated during the in-flight calibration phases. These corrected light-curves are then fitted by a parametric model, which we incorporated in PSLS. We show that the instrumental systematic errors dominate the signal only at frequencies below 20muHz and are found to mainly depend on stellar magnitude and on the detector charge transfer inefficiency. To illustrate how realistic our simulator is, we compared its predictions with observations made by Kepler on three typical targets and found a good qualitative agreement with the observations. PSLS reproduces the main properties of expected PLATO light-curves. Its speed of execution and its inclusion of relevant stellar signals as well as sources of noises representative of the PLATO cameras make it an indispensable tool for the scientific preparation of the PLATO mission.

astro-ph.IM↗

arXiv2019

Solar $p$-mode damping rates: insight from a 3D hydrodynamical simulation

Space-borne missions CoRoT and Kepler have provided a rich harvest of high-quality photometric data for solar-like pulsators. It is now possible to measure damping rates for hundreds of main-sequence and thousands of red-giant. However, among the seismic parameters, mode damping rates remain poorly understood and thus barely used for inferring the physical properties of stars. Previous approaches to model mode damping rates were based on mixing-length theory or a Reynolds-stress approach to model turbulent convection. While able to grasp the main physics of the problem, those approaches are of little help to provide quantitative estimates as well as a definitive answer on the relative contribution of each physical mechanism. Our aim is thus to assess the ability of 3D hydrodynamical simulations to infer the physical mechanisms responsible for damping of solar-like oscillations. To this end, a solar high-spatial resolution and long-duration hydrodynamical 3D simulation computed with the ANTARES code allows probing the coupling between turbulent convection and the normal modes of the simulated box. Indeed, normal modes of the simulation experience realistic driving and damping in the super-adiabatic layers of the simulation. Therefore, investigating the properties of the normal modes in the simulation provides a unique insight into the mode physics. We demonstrate that such an approach provides constraints on the solar damping rates and is able to disentangle the relative contribution related to the perturbation of the turbulent pressure, the gas pressure, the radiative flux, and the convective flux contributions. Finally, we conclude that using the normal modes of a 3D numerical simulation is possible and is potentially able to unveil the respective role of the different physical mechanisms responsible for mode damping provided the time-duration of the simulation is long enough.

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