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M. -A. Dupret

Publications and source records attributed to M. -A. Dupret.

At least 19 recordsLinked to original sources

On the theoretical instability strips of γ-Doradus stars including the effect of the metallicity and rotation

Recent space missions such as Kepler have provided large-scale observations of the γ-Doradus instability strips (IS), which can be used to constrain models and explore their limitations. One persistent limitation is the prediction of the blue edge of the γ- Doradus IS, where a significant number of γ-Doradus stars are observed. Despite these observational advances, no systematic study has been undertaken to explore the effects of different physical processes on the γ-Doradus. Our aim is to systematically explore the theoretical γ-Doradus IS with modern tools, accounting for the effects of rotation and metallicity, providing a large grid of models and their oscillation parameters for the scientific community. We investigated the non-adiabatic pulsation properties of stars in a grid of stellar models with masses between 1.35 M{_\odot} and 2.5 M{_\odot}, metallicities between Z= 0.01 and Z= 0.025, and solid-body rotation rates ranging from Ω = 0 to 0.5 {Ω_{crit}}, where {Ω_{crit}} denotes the critical rotation rate. We find that, across all computations, the theoretical γ-Doradus IS agrees well with the observed IS, except in the extended blue region. In terms of radial orders, our models consistently reproduce the excited modes in broad agreement with observations for l= 1, l= 2, and Rossby modes. We also show that the range of excited radial orders is strongly dependent on the effective temperature. The range of excited radial orders can be used to constrain the position of a star within the γ-Doradus IS and may provide insights into the physical mechanisms responsible for the discrepancies observed in the blue region. All computed grids are made available and include mode damping and growth rates for γ-Doradus stars, obtained with a time-dependent treatment of the convection-oscillation interaction.

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Resonance locking and tidal evolution in rotating γ-Doradus binaries

In binary systems, studying tidal interactions is key to understanding the evolution of binary populations. The primary dissipation process occurring in stars with radiative envelopes is believed to be radiative damping of high-radial-order tidally excited oscillations, which is in agreement with observations of most binary systems. However, recent studies have suggested that outside this dissipation regime, dynamical tides can act in the opposite manner (a phenomenon known as inverse tides), and resonance locking could significantly impact the orbital evolution of binary systems. We aim to study inverse tides and resonance locking by simultaneously including the effect of all the forcing frequencies and accounting for the effect of the rotation on the forced oscillations. We have developed an orbital evolution code that is coupled to a stellar oscillation code to compute on the fly the impact of dynamical tides on the rotational and orbital evolution of binary systems including multiple simultaneous forcing frequencies. We find that resonance locking can be stable over a long period of time and a source of long-term exchange of angular momentum for rapidly rotating stars. Long-term locking can increase the total angular momentum of a fast-rotating star by approximately 70% during the main sequence. For slow-rotating stars, resonance locking can slow down the rotational evolution of the system over most of the main-sequence phase, even in the presence of strong tidal interactions. This mechanism efficiently drives asynchronisation in binary systems where significant discrepancies already exist between the orbital and rotational frequencies.

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The theoretical pulsation spectra of hot B subdwarfs. Static and evolutionary STELUM models

Context. The Kepler and TESS space missions have revealed the rich gravity (g-)mode pulsation spectra of many hot subdwarf B (sdB) stars in detail. These spectra exhibit complex behaviors, with some stars exhibiting trapped modes interposing in the asymptotic period sequences of regular period spacing, while others do not. Methods. We used our STELlar modeling from the Universite de Montreal (STELUM) code to compute static (parametric) and evolutionary models of sdB stars, with different prescriptions for their chemical and thermal structures. We used our adiabatic PULSE code to compute the theoretical spectra of g-mode pulsations for degrees of l=1 to 4 and for periods between 1000 s and 15 000 s, amply covering the range of observed g-modes in these stars. Results. We show that g-mode pulsation spectra and, in particular, the appearance of trapped modes are highly dependent on the chemical and thermal structures in the models as the star evolves, particularly in the region just above the He-burning core. Depending on the prescriptions and specific evolutionary stage, we observe mainly three types of spectra for mid to high radial-order g-modes (the ones observed in sdB stars): flat spectra of nearly constant period spacing; spectra with deep minima of the period spacing interposing between modes with more regular spacing (which correspond to trapped modes); and spectra showing a wavy pattern in period spacing. For the two latter cases, we have identified the region where the modes are trapped in the star. Conclusions. Detailed comparisons with observed g-mode spectra ought to be carried out next to progress on this issue and constrain the internal structure of core-He burning stars via asteroseismology, in particular, for the region above the He-burning core.

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Detailed seismic study of Gemma (KIC11026764) using EGGMiMoSA: Unveiling the probing potential of mixed modes for subgiant stars

Context. When leaving the main sequence (MS) for the red-giant branch (RGB), subgiant stars undergo fast structural changes. Consequently, their observed oscillation spectra mirror these changes, constituting key tracers of stellar structure and evolution. However, the complexity of their spectra makes their modelling an arduous task, which few authors have undertaken. Gemma (KIC11026764) is a young subgiant with $45$ precise oscillation modes observed with Kepler, making it the ideal benchmark for seismic modelling. Aims. This study is aimed at modelling the subgiant Gemma, taking advantage of most of the precise seismic information available. This approach enables us to pave the way for the seismic modelling of evolved solar-like stars and provide the relevant insights into their structural evolution. Methods. Using our Levenberg-Marquardt stellar modelling tool, we built a family of models representative of Gemma's measured seismic indicators obtained via our seismic tool, EGGMiMoSA. We studied the structural information these indicators hold by carefully varying stellar parameters. We also complemented the characterisation with information held by \who indicators and non-seismic data. Results. From the extensive set of models we built and using most of the seismic information at hand, including two $\ell=1$ and one $\ell=2$ mixed modes, we were able to probe the chemical transition at the hydrogen-burning shell. Indeed, we have demonstrated that among our models, only the ones with the sharpest chemical gradient are able to reproduce all the seismic information considered. One possibility to account for such a gradient is the inclusion of a significant amount of overshooting, namely $α_{\textrm{ov}}=0.17$, which is unexpected for low-mass stars such as Gemma (expected mass of about $1.15~M_{\odot}$).

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Underestimation of the tidal force and apsidal motion in close binary systems by the perturbative approach: Comparisons with non-perturbative models

Stellar deformations play a significant role in the dynamical evolution of stars in binary systems, impacting the tidal dissipation and the outcomes of mass transfer processes. The prevalent method for modelling the deformations and tidal interactions of celestial bodies solely relies on the perturbative approach, which assumes that stellar deformations are minor perturbations to the spherical symmetry. An observable consequence of stellar deformations is the apsidal motion in eccentric systems. Our objective is to assert the reliability of the perturbative approach when applied to close and strongly deformed binary systems. We have developed a non-perturbative 3D modelling method designed to account for high stellar deformations to explore the limitations of the perturbative models. Our research highlights that the perturbative model becomes imprecise and underestimates the tidal force and rate of apsidal motion at a short orbital separation. This discrepancy primarily results from the first-order treatment in the perturbative approach, and cannot be rectified using straightforward mathematical corrections due to the strong non-linearity and numerous parameters of the problem. We have determined that our methodology affects the modelling of approximately 42% of observed binary systems with measured apsidal motion, introducing a discrepancy greater than 2% when the normalised orbital separation verifies q^(-1/5)a(1-e^2)/R1 < 6.5. The perturbative approach underestimates tidal interactions between bodies up to ~40% for close low-mass binaries. All the subsequent modelling is impacted by our findings, in particular, the tidal dissipation is significantly underestimated. As a result, all binary stellar models are imprecise when applied to systems with a low orbital separation, and the outcomes of these models are also affected by these inaccuracies.

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MoBiDICT: new 3D static models of close, synchronized binaries in hydrostatic equilibrium

In close binary systems, tidal interactions and rotational effects can strongly influence stellar evolution as a result of mass-transfer, common envelope phases, ... All these aspects can only be treated following improvements of theoretical models, taking into account the breaking of spherical symmetry occurring in close binaries. Current models of binary stars are relying either on the so-called "Roche model" or the perturbative approach that in each case results on several assumptions concerning the gravitational, tidal and centrifugal potentials.We developed a new non-perturbative method to compute precise structural deformation of binary system in three dimensions that is valid even in the most distorted cases. We then compared our new method to the Roche and perturbative models for different orbital separations and binary components. We found that in the most distorted cases both Roche and perturbative models are significantly underestimating the deformation of binaries. The effective gravity and the overall structural deformations are also noticeably different in the most distorted cases leading, for the interpretation of observations, to modifications of the usual gravity darkening generally obtained through the Roche model. Moreover we found that the dipolar term of the gravitational potential, usually neglected by the perturbative theory, has the same order of magnitude than the leading tidal term in the most distorted cases. We developed a new method that is capable of precisely computing the deformations of binary system composed of any type of stars, even compact objects. For all stars studied the differences in deformation with respect to the Roche or perturbative models are significant in the most distorted cases impacting both the interpretation of observations and the theoretical structural depiction of these distorted bodies.

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Apsidal motion in massive eccentric binaries in NGC 6231: The case of HD 152219

The measurement of the apsidal motion in close eccentric massive binary systems provides essential information to probe the internal structure of the stars that compose the system. Following the determination of the fundamental stellar and binary parameters, we make use of the tidally induced apsidal motion to infer constraints on the internal structure of the stars composing the binary system HD152219. The extensive set of spectroscopic, photometric, and radial velocity observations allows us to constrain the fundamental parameters of the stars together with the rate of apsidal motion of the system. Stellar structure and evolution models are further built with the Clés code testing different prescriptions for the internal mixing occurring inside the stars. The effect of stellar rotation axis misalignment with respect to the normal to the orbital plane on our interpretation of the apsidal motion in terms of internal structure constants is investigated. Made of an O9.5 III primary star (M1 = 18.64+/-0.47M${_\odot}$, R1 = 9.40+0.14-0.15R${_\odot}$, Teff,1 = 30900+/-1000 K) and a B1-2 V-III secondary star (M2 = 7.70+/-0.12M${_\odot}$, R2 = 3.69+/-0.06R${_\odot}$, Teff,2 = 21697+/-1000 K), the binary system HD152219 displays apsidal motion at a rate (1.198+/-0.300)°yr-1. The weighted-average mean of the internal structure constant of the binary system is inferred: k2 = 0.00173+/-0.00052. For the Clés models to reproduce the k2-value of the primary star, a significant enhanced mixing is required, notably through the turbulent mixing, but at the cost that other stellar parameters cannot be reproduced simultaneously. The difficulty to reproduce the k2-value simultaneously with the stellar parameters as well as the incompatibility between the age estimates of the primary and secondary stars are indications that some physics of the stellar interior are still not completely understood.

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Thorough characterisation of the 16 Cygni system Part I: Forward seismic modelling with WhoSGlAd

Context: Being part of the brightest solar-like stars, and close solar analogues, the 16 Cygni system is of great interest to the scientific community and may provide insight into the past and future evolution of our Sun. It has been observed thoroughly by the Kepler satellite, which provided us with data of an unprecedented quality. Aims: This paper is the first of a series aiming to extensively characterise the system. We test several choices of micro- and macro-physics to highlight their effects on optimal stellar parameters and provide realistic stellar parameter ranges. Methods: We used a recently developed method, WhoSGlAd, that takes the utmost advantage of the whole oscillation spectrum of solar-like stars by simultaneously adjusting the acoustic glitches and the smoothly varying trend. For each choice of input physics, we computed models which account, at best, for a set of seismic indicators that are representative of the stellar structure and are as uncorrelated as possible. The search for optimal models was carried out through a Levenberg-Marquardt minimisation. First, we found individual optimal models for both stars. We then selected the best candidates to fit both stars while imposing a common age and composition. Results: We computed realistic ranges of stellar parameters for individual stars. We also provide two models of the system regarded as a whole. We were not able to build binary models with the whole set of choices of input physics considered for individual stars as our constraints seem too stringent. We may need to include additional parameters to the optimal model search or invoke non-standard physical processes.

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Apsidal motion in the massive binary HD 152248 -- Constraining the internal structure of the stars

Apsidal motion in massive eccentric binaries offers precious information about the internal structure of the stars. This is especially true for twin binaries consisting of two nearly identical stars. We make use of the tidally induced apsidal motion in the twin binary HD152248 to infer constraints on the internal structure of the O7.5 III-II stars composing this system. We build stellar evolution models with the code Clés assuming different prescriptions for the internal mixing occurring inside the stars. We identify the models that best reproduce the observationally determined present-day properties of the components of HD152248, as well as their $k_2$, and the apsidal motion rate of the system. We analyse the impact of some poorly constrained input parameters, including overshooting, turbulent diffusion, and metallicity. We further build 'single' and 'binary' GENEC models that account for stellar rotation to investigate the impacts of binarity and rotation. We discuss some effects that could bias our interpretation of the apsidal motion in terms of the internal structure constant. Reproducing the observed $k_2$ value and rate of apsidal motion simultaneously with the other stellar parameters requires a significant amount of internal mixing or enhanced mass-loss. The results suggest that a single-star evolution model is sufficient to describe the physics inside this binary system. Qualitatively, the high turbulent diffusion required to reproduce the observations could be partly attributed to stellar rotation. Higher-order terms in the apsidal motion are negligible. Only a very severe misalignment of the rotation axes could significantly impact the rate of apsidal motion, but such a high misalignment is highly unlikely in such a binary system. We infer an age estimate of $5.15\pm0.13$ Myr for the binary and initial masses of $32.8\pm0.6$ M$_\odot$ for both stars.

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Calibration of the mixing-length parameter $α$ for the MLT and FST models by matching with CO$^5$BOLD models

The CoRoT and Kepler missions provided a wealth of high-quality data for solar-like oscillations. To make the best of such data for seismic inferences, we need theoretical models with precise near-surface structure, which has significant influence on solar-like oscillation frequencies. The mixing-length parameter, $α$, is a key factor for the near-surface structure. In the convection formulations used in evolution codes, the $α$ is a free parameter that needs to be properly specified. We calibrated $α$ values by matching entropy profiles of 1D envelope models with those of 3D CO$^5$BOLD models. For such calibration, previous works concentrated on the classical mixing-length theory (MLT). Here we also analyzed the full spectrum turbulence (FST) models. For the atmosphere part in the 1D models, we use the Eddington grey $T(τ)$ relation and the one with the solar-calibrated Hopf-like function. For both the MLT and FST models with a mixing length $l=αH_p$, calibrated $α$ values increase with increasing $g$ or decreasing $T_{\rm eff}$. For the FST models, we also calibrated values of $α^*$ defined as $l=r_{\rm top}-r+α^*H_{p,{\rm top}}$. $α^*$ is found to increase with $T_{\rm eff}$ and $g$. As for the correspondence to the 3D models, the solar Hopf-like function gives a photospheric-minimum entropy closer to a 3D model than the Eddington $T(τ)$. The structure below the photosphere depends on the convection model. However, not a single convection model gives the best correspondence since the averaged 3D quantities are not necessarily related via an EOS. Although the FST models with $l=r_{\rm top}-r+α^*H_{p,{\rm top}}$ are found to give the frequencies closest to the solar observed ones, a more appropriate treatment of the top part of the 1D convective envelope is necessary.

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PLATO as it is: a legacy mission for Galactic archaeology

Deciphering the assembly history of the Milky Way is a formidable task, which becomes possible only if one can produce high-resolution chrono-chemo-kinematical maps of the Galaxy. Data from large-scale astrometric and spectroscopic surveys will soon provide us with a well-defined view of the current chemo-kinematical structure of the Milky Way, but will only enable a blurred view on the temporal sequence that led to the present-day Galaxy. As demonstrated by the (ongoing) exploitation of data from the pioneering photometric missions CoRoT, Kepler, and K2, asteroseismology provides the way forward: solar-like oscillating giants are excellent evolutionary clocks thanks to the availability of seismic constraints on their mass and to the tight age-initial-mass relation they adhere to. In this paper we identify five key outstanding questions relating to the formation and evolution of the Milky Way that will need precise and accurate ages for large samples of stars to be addressed, and we identify the requirements in terms of number of targets and the precision on the stellar properties that are needed to tackle such questions. By quantifying the asteroseismic yields expected from PLATO for red-giant stars, we demonstrate that these requirements are within the capabilities of the current instrument design, provided that observations are sufficiently long to identify the evolutionary state and allow robust and precise determination of acoustic-mode frequencies. This will allow us to harvest data of sufficient quality to reach a 10% precision in age. This is a fundamental pre-requisite to then reach the more ambitious goal of a similar level of accuracy, which will only be possible if we have to hand a careful appraisal of systematic uncertainties on age deriving from our limited understanding of stellar physics, a goal which conveniently falls within the main aims of PLATO's core science.

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Frequency regularities of acoustic modes and multi-colour mode identification in rapidly rotating stars

Context: Mode identification has remained a major obstacle in the interpretation of pulsation spectra in rapidly rotating stars. Aims: We would like to test mode identification methods and seismic diagnostics in rapidly rotating stars, using oscillation spectra based on new theoretical predictions. Methods: We investigate the auto-correlation function and Fourier transform of theoretically calculated frequency spectra, in which modes are selected according to their visibilities. Given the difficulties in predicting intrinsic mode amplitudes, we experimented with various ad-hoc prescriptions for setting these, including using random values. Furthermore, we analyse the ratios between mode amplitudes observed in different photometric bands. Results: When non-random intrinsic mode amplitudes are used, our results show that it is possible to extract the large frequency separation or half its value, and sometimes twice the rotation rate, from the auto-correlation function. The Fourier transforms are mostly sensitive to the large frequency separation or half its value. When the intrinsic mode amplitudes include random factors, the results are far less favourable. We also find that amplitude ratios provide a good way of grouping together modes with similar characteristics. By analysing the frequencies of these groups, it is possible to constrain mode identification as well as determine the large frequency separation and the rotation rate.

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On the computation of eigenfrequencies for equilibrium models including turbulent pressure

The space-borne missions have provided a wealth of highly accurate data. However, our inability to properly model the upper-most region of solar-like stars prevents us from making the best of these observations. This problem is called "surface effect" and a key ingredient to solve it is turbulent pressure for the computation of both the equilibrium models and the oscillations. While 3D hydrodynamic simulations help to include properly the turbulent pressure in the equilibrium models, the way this surface effect is included in the computation of stellar oscillations is still subject to uncertainties. We aim at determining how to properly include the effect of turbulent pressure and its Lagrangian perturbation in the adiabatic computation of the oscillations. We also discuss the validity of the gas-gamma model (GGM) and reduced gamma model (RGM) approximations, which have been used to compute adiabatic oscillations of equilibrium models including turbulent pressure. We use a patched model of the Sun with an inner part constructed by a 1D stellar evolution code (CESTAM) and an outer part by the 3D hydrodynamical code (CO$^5$BOLD). Then, the adiabatic oscillations are computed using the ADIPLS code for the GGM and RGM and with the MAD code imposing the adiabatic condition on an existing time-dependent convection (TDC) formalism. We show that the computation of the oscillations using the TDC formalism in the adiabatic limit improves significantly the agreement with the observed frequencies compared to the GGM and RGM. Of the components of the turbulent pressure perturbation, the perturbation of the density and advection term is found to contribute most to the frequency shift. We propose a formalism to evaluate the frequency shift due to the inclusion of the term with the turbulent pressure perturbation in the variational principle in order to extrapolate our result to other stars.

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Apsidal motion in the massive binary HD152218

Massive binary systems are important laboratories in which to probe the properties of massive stars and stellar physics in general. In this context, we analysed optical spectroscopy and photometry of the eccentric short-period early-type binary HD 152218 in the young open cluster NGC 6231. We reconstructed the spectra of the individual stars using a separating code. The individual spectra were then compared with synthetic spectra obtained with the CMFGEN model atmosphere code. We furthermore analysed the light curve of the binary and used it to constrain the orbital inclination and to derive absolute masses of 19.8 +/- 1.5 and 15.0 +/- 1.1 solar masses. Combining radial velocity measurements from over 60 years, we show that the system displays apsidal motion at a rate of (2.04^{+.23}_{-.24}) degree/year. Solving the Clairaut-Radau equation, we used stellar evolution models, obtained with the CLES code, to compute the internal structure constants and to evaluate the theoretically predicted rate of apsidal motion as a function of stellar age and primary mass. In this way, we determine an age of 5.8 +/- 0.6 Myr for HD 152218, which is towards the higher end of, but compatible with, the range of ages of the massive star population of NGC 6231 as determined from isochrone fitting.

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Theoretical power spectra of mixed modes in low mass red giant stars

CoRoT and Kepler observations of red giant stars revealed very rich spectra of non-radial solar-like oscillations. Of particular interest was the detection of mixed modes that exhibit significant amplitude, both in the core and at the surface of the stars. It opens the possibility of probing the internal structure from their inner-most layers up to their surface along their evolution on the red giant branch as well as on the red-clump. Our objective is primarily to provide physical insight into the physical mechanism responsible for mixed-modes amplitudes and lifetimes. Subsequently, we aim at understanding the evolution and structure of red giants spectra along with their evolution. The study of energetic aspects of these oscillations is also of great importance to predict the mode parameters in the power spectrum. Non-adiabatic computations, including a time-dependent treatment of convection, are performed and provide the lifetimes of radial and non-radial mixed modes. We then combine these mode lifetimes and inertias with a stochastic excitation model that gives us their heights in the power spectra. For stars representative of CoRoT and Kepler observations, we show under which circumstances mixed modes have heights comparable to radial ones. We stress the importance of the radiative damping in the determination of the height of mixed modes. Finally, we derive an estimate for the height ratio between a g-type and a p-type mode. This can thus be used as a first estimate of the detectability of mixed-modes.

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Are the stars of a new class of variability detected in NGC~3766 fast rotating SPB stars?

A recent photometric survey in the NGC~3766 cluster led to the detection of stars presenting an unexpected variability. They lie in a region of the Hertzsprung-Russell (HR) diagram where no pulsation are theoretically expected, in between the $δ$ Scuti and slowly pulsating B (SPB) star instability domains. Their variability periods, between $\sim$0.1--0.7~d, are outside the expected domains of these well-known pulsators. The NCG~3766 cluster is known to host fast rotating stars. Rotation can significantly affect the pulsation properties of stars and alter their apparent luminosity through gravity darkening. Therefore we inspect if the new variable stars could correspond to fast rotating SPB stars. We carry out instability and visibility analysis of SPB pulsation modes within the frame of the traditional approximation. The effects of gravity darkening on typical SPB models are next studied. We find that at the red border of the SPB instability strip, prograde sectoral (PS) modes are preferentially excited, with periods shifted in the 0.2--0.5~d range due to the Coriolis effect. These modes are best seen when the star is seen equator-on. For such inclinations, low-mass SPB models can appear fainter due to gravity darkening and as if they were located between the $δ$~Scuti and SPB instability strips.

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The puzzling new class of variable stars in NGC 3766 : old friend pulsators?

The recent variability survey of the NGC 3766 cluster revealed a considerable number of periodic variable stars in a region of the H-R diagram where no pulsation is expected. This region lies between the instability strips of the delta Scuti and SPB stars. Moreover the periods of the new phenomenon, P~0.1-0.7 d, do not allow to associate it a priori to either of these two types of pulsations. Stars in the NGC 3766 cluster are known as fast rotators with rotational velocities typically larger than half of their critical velocity. Rotation can affect both the geometrical properties and period domain of pulsations. It also alters the apparent stellar luminosity through gravity darkening, effect seldom taken considered in theoretical studies of the rotation-pulsation interaction. We explore if both of these effects are able to deliver a consistent interpretation for the observed properties of the "new variables" in NGC 3766: explaining their presence outside the known instability strips and their variability periods. We carry out an instability analysis of SPB models within the framework of the Traditional Approximation of Rotation and study the visibility of modes according to the angle of view and rotation. We also check how gravity darkening affects the effective temperature and luminosity of stellar models for different angles of view and rotation velocities. At the red (cold) border of the instability strip, prograde sectoral modes are preferentially excited and their visibilities are maximum when seen equator-on. Furthermore low-mass SPB models seen equator-on can appear in the gap between non-rotating SPB and delta Scuti stars due to gravity darkening. In that case, periods of these most visible modes are shifted to the 0.2-0.5 d range due to the effects of the Coriolis force. We hence suggest that the new variable stars observed in NGC 3766 are actually fast rotating SPB pulsators.

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Testing convective-core overshooting using period spacings of dipole modes in red giants

Uncertainties on central mixing in main sequence (MS) and core He-burning (He-B) phases affect key predictions of stellar evolution such as late evolutionary phases, chemical enrichment, ages etc. We propose a test of the extension of extra-mixing in two relevant evolutionary phases based on period spacing Delta_P of solar-like oscillating giants. From stellar models and their corresponding adiabatic frequencies (respectively computed with ATON and LOSC codes) we provide the first predictions of the observable Delta_P for stars in the red giant branch (RGB) and in the red clump (RC). We find: i) a clear correlation between Delta_P and the mass of the helium core (M_He); the latter in intermediate-mass stars depends on the MS overshooting, hence it can be used to set constraints on extra mixing during MS when coupled with chemical composition; ii) a linear dependence of the average value of the asymptotic period spacing ( _a) during the He-B phase on the size of the convective core. A first comparison with the inferred asymptotic period spacing for Kepler RC stars suggests the need for extra mixing also during this phase, as evinced from other observational facts.

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