arXiv subjects

S. Mathis

Publications and source records attributed to S. Mathis.

At least 37 records · Page 2Linked to original sources

arXiv2021

Dynamical tide in stellar radiative zones. General formalism and evolution for low-mass stars

[Abridged] Most exoplanets detected so far are close-in planets, which are likely to be affected by tidal dissipation in their host star. To get a complete picture of the evolution of star-planet systems one needs to consider the impact of tides within both stellar radiative and convective zones. We aim to provide a general formalism to assess tidal dissipation in stellar radiative zones for all spectral types, allowing for the study of the dynamics of a given system throughout stellar evolution. We investigate the influence of stellar structure and evolution on tidal dissipation in the radiative core of low-mass stars. From the study of adiabatic oscillations throughout the star, we compute the energy flux transported by progressive internal gravity waves and the induced tidal torque. We then study the influence of stellar structure and evolution on tidal dissipation of solar-type stars from the pre-main sequence (PMS) to the red giant branch (RGB). For a given star-planet system, tidal dissipation reaches a maximum value on the pre-main sequence for all stellar masses. On the main sequence (MS), it decreases to become almost constant. The dissipation is then several orders of magnitude smaller for F-type stars than for G and K-type stars. During the Sub-Giant phase and the RGB, tidal dissipation increases by several orders of magnitude, along with the expansion of the stellar envelope. We show that the dissipation of the dynamical tide in the convective zone dominates the evolution of the system during most of the PMS and the beginning of the main sequence. Tidal dissipation in the radiative zone then becomes the strongest contribution during the Sub-Giant phase and the RGB. We also find that the dissipation of a metal-poor star is stronger than the dissipation of a metal-rich star during the PMS, the Sub-Giant phase and the RGB.

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arXiv2021

Magnetic signatures on mixed-mode frequencies. I. An axisymmetric fossil field inside the core of red giants

The discovery of the moderate differential rotation between the core and the envelope of evolved solar-like stars could be the signature of a strong magnetic field trapped inside the radiative interior. The population of intermediate-mass red giants presenting a surprisingly low-amplitude of their mixed modes could also arise from the effect of an internal magnetic field. Indeed, stars more massive than about 1.1Ms are known to develop a convective core during their main sequence, which could relax into a strong fossil magnetic field trapped inside the core of the star for the rest of its evolution. The observations of mixed modes can constitute an excellent probe of the deepest layers of evolved solar-like stars. The magnetic perturbation on mixed modes may thus be visible in asteroseismic data. To unravel which constraints can be obtained from observations, we theoretically investigate the effects of a plausible mixed axisymmetric magnetic field with various amplitudes on the mixed-mode frequencies of evolved solar-like stars. The first-order frequency perturbations are computed for dipolar and quadrupolar mixed modes. These computations are carried out for a range of stellar ages, masses, and metallicities. We show that typical fossil-field strengths of 0.1-1 MG, consistent with the presence of a dynamo in the convective core during the main sequence, provoke significant asymmetries on mixed-mode frequency multiplets during the red-giant branch. We show that these signatures may be detectable in asteroseismic data for field amplitudes small enough for the amplitude of the modes not to be affected by the conversion of gravity into Alfven waves inside the magnetised interior. Finally, we infer an upper limit for the strength of the field, and the associated lower limit for the timescale of its action, to redistribute angular momentum in stellar interiors.

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arXiv2021

Spectroscopic and seismic analysis of red giants in eclipsing binaries discovered by Kepler

Eclipsing binaries (EBs) are unique benchmarks for stellar evolution. On the one hand, detached EBs hosting at least one star with detectable solar-like oscillations constitute ideal test objects to calibrate asteroseismic measurements. On the other hand, the oscillations and surface activity of stars that belong to EBs offer unique information about the evolution of binary systems. This paper builds upon previous works dedicated to red giant stars (RG) in EBs -- 20 known systems so far -- discovered by the NASA Kepler mission. Here we report the discovery of 16 RGs in EBs also from the Kepler data. This new sample includes three SB2-EBs with oscillations and six close systems where the RG display a clear surface activity and complete oscillation suppression. Based on dedicated high-resolution spectroscopic observations (Apache Point Observatory, Observatoire de Haute Provence), we focus on three main aspects. From the extended sample of 14 SB2-EBs, we first confirm that the simple application of the asteroseismic scaling relations to RGs overestimates masses and radii of RGs, by about 15% and 5%. This bias can be reduced by employing either new asteroseismic reference values for RGs, or model-based corrections of the asteroseismic parameters. Secondly, we confirm that close binarity leads to a high level of photometric modulation (up to 10%), and a suppression of solar-like oscillations. In particular, we show that it reduces the lifetime of radial modes by a factor of up to 10. Thirdly, we use our 16 new systems to complement previous observational studies that aimed at constraining tidal dissipation in interacting binaries. In particular, we identify systems with circular orbits despite relatively young ages, which suggests exploring complementary tidal dissipation mechanisms in the future. Finally, we report the measurements of mass, radius, and age of three M-dwarf companion stars.

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arXiv2021

The complex interplay between tidal inertial waves and zonal flows in differentially rotating stellar and planetary convective regions I. Free waves

Quantifying tidal interactions in close-in two-body systems is of prime interest since they have a crucial impact on the architecture and on the rotational history of the bodies. Various studies have shown that the dissipation of tides in either body is very sensitive to its structure and to its dynamics, like differential rotation which exists in the outer convective enveloppe of solar-like stars and giant gaseous planets. In particular, tidal waves may strongly interact with zonal flows at the so-called corotation resonances, where the wave's Doppler-shifted frequency cancels out. We aim to provide a deep physical understanding of the dynamics of tidal inertial waves at corotation resonances, in the presence of differential rotation profiles typical of low-mass stars and giant planets. By developping an inclined shearing box, we investigate the propagation and the transmission of free inertial waves at corotation, and more generally at critical levels, which are singularities in the governing wave differential equation. Through the construction of an invariant called the wave action flux, we identify different regimes of wave transmission at critical levels, which are confirmed with a one-dimensional three-layer numerical model. We find that inertial waves can be either fully transmitted, strongly damped, or even amplified after crossing a critical level. The occurrence of these regimes depends on the assumed profile of differential rotation, on the nature as well as the latitude of the critical level, and on wave parameters such as the inertial frequency and the longitudinal and vertical wavenumbers. Waves can thus either deposit their action flux to the fluid when damped at critical levels, or they can extract action flux to the fluid when amplified at critical levels. Both situations could lead to significant angular momentum exchange between the tidally interacting bodies.

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arXiv2020

The impact of a fossil magnetic field on dipolar mixed-mode frequencies in sub- and red-giant stars

Stars more massive than $\sim 1.3$ M$_\odot$ are known to develop a convective core during the main-sequence: the dynamo process triggered by this convection could be the origin of a strong magnetic field inside the core of the star, trapped when it becomes stably stratified and for the rest of its evolution. The presence of highly magnetized white dwarfs strengthens the hypothesis of buried fossil magnetic fields inside the core of evolved low-mass stars. If such a fossil field exists, it should affect the mixed modes of red giants as they are sensitive to processes affecting the deepest layers of these stars. The impact of a magnetic field on dipolar oscillations modes was one of Pr. Michael J. Thompson's research topics during the 90s when preparing the helioseismic SoHO space mission. As the detection of gravity modes in the Sun is still controversial, the investigation of the solar oscillation modes did not provide any hint of the existence of a magnetic field in the solar radiative core. Today we have access to the core of evolved stars thanks to the asteroseismic observation of mixed modes from CoRoT, Kepler, K2 and TESS missions. The idea of applying and generalizing the work done for the Sun came from discussions with Pr. Michael Thompson in early 2018 before we loss him. Following the path we drew together, we theoretically investigate the effect of a stable axisymmetric mixed poloidal and toroidal magnetic field, aligned with the rotation axis of the star, on the mixed modes frequencies of a typical evolved low-mass star. This enables us to estimate the magnetic perturbations to the eigenfrequencies of mixed dipolar modes, depending on the magnetic field strength and the evolutionary state of the star. We conclude that strong magnetic fields of $\sim$ 1MG should perturbe the mixed-mode frequency pattern enough for its effects to be detectable inside current asteroseismic data.

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arXiv2020

Lithium depletion and angular momentum transport in solar-type stars

Transport processes occurring in the radiative interior of solar-type stars are evidenced by the surface variation of light elements, in particular Li, and the evolution of their rotation rates. For the Sun, inversions of helioseismic data indicate that the radial profile of angular velocity in its radiative zone is nearly uniform, which implies the existence of angular momentum transport mechanisms. While there are many independent transport models for angular momentum and chemical species, there is a lack of self-consistent theories that permit stellar evolution models to simultaneously match the present-day observations of solar lithium abundances and radial rotation profiles. We explore how additional transport processes can improve the agreement between evolutionary models of rotating stars and observations. We constrain the resulting models by simultaneously using the evolution of the surface rotation rate and Li abundance in the solar-type stars of open clusters, and the solar surface and internal rotation profile as inverted from helioseismology. We show the relevance of penetrative convection for the depletion of Li. The rotational dependence of the depth of penetrative convection yields an anti-correlation between the initial rotation rate and Li depletion in our models of solar-type stars that is in agreement with the observed trend. Simultaneously, the addition of an ad hoc vertical viscosity leads to efficient transport of angular momentum between the core and the envelope. We also self-consistently compute for the first time the thickness of the tachocline and find that it is compatible with helioseismic estimations. However, the main sequence depletion of Li in solar-type stars is only reproduced when adding a parametric turbulent mixing below the convective envelope. The need for additional transport processes in stellar evolution models is confirmed.

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arXiv2020

A model of rotating convection in stellar and planetary interiors: II -- gravito-inertial wave generation

Gravito-inertial waves are excited at the interface of convective and radiative regions and by the Reynolds stresses in the bulk of the convection zones of rotating stars and planets. Such waves have notable asteroseismic signatures in the frequency spectra of rotating stars, particularly among rapidly rotating early-type stars, which provides a means of probing their internal structure and dynamics. They can also transport angular momentum, chemical species, and energy from the excitation region to where they dissipate in radiative regions. To estimate the excitation and convective parameter dependence of the amplitude of those waves, a monomodal model for stellar and planetary convection as described in Paper I is employed, which provides the magnitude of the rms convective velocity as a function of rotation rate. With this convection model, two channels for wave driving are considered: excitation at a boundary between convectively stable and unstable regions and excitation due to Reynolds-stresses. Parameter regimes are found where the sub-inertial waves may carry a significant energy flux, depending upon the convective Rossby number, the interface stiffness, and the wave frequency. The super-inertial waves can also be enhanced, but only for convective Rossby numbers near unity. Interfacially excited waves have a peak energy flux near the lower cutoff frequency when the convective Rossby number of the flows that excite them are below a critical Rossby number that depends upon the stiffness of the interface, whereas that flux decreases when the convective Rossby number is larger than this critical Rossby number.

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arXiv2020

Transport of angular momentum by stochastically excited waves as an explanation for the outburst of the rapidly rotating Be star HD49330

HD49330 is a Be star that underwent an outburst during its five-month observation with the CoRoT satellite. An analysis of its light curve revealed several independent p and g pulsation modes, in addition to showing that the amplitude of the modes is directly correlated with the outburst. We modelled the results obtained with CoRoT. We modelled the flattening of the structure of the star due to rapid rotation in two ways: Chandrasekhar-Milne's expansion and 2D structure computed with ROTORC. We then modelled kappa-driven pulsations. We also adapted the formalism of the excitation and amplitude of stochastically excited gravito-inertial modes to rapidly rotating stars, and we modelled those pulsations as well. We find that while pulsation p modes are excited by the kappa mechanism, the observed g modes are a result of stochastic excitation. In contrast, g and r waves are stochastically excited in the convective core and transport angular momentum to the surface, increasing its rotation rate. This destabilises the external layers of the star, which then emits transient stochastically excited g waves. These transient waves produce most of the low-frequency signal detected in the CoRoT data and ignite the outburst. During this unstable phase, p modes disappear at the surface because their cavity is broken. Following the outburst and ejection of the surface layer, relaxation occurs, making the transient g waves disappear and p modes reappear. This work includes the first coherent model of stochastically excited gravito-inertial pulsation modes in a rapidly rotating Be star. It provides an explanation for the correlation between the variation in the amplitude of frequencies detected in the CoRoT data and the occurrence of an outburst. This scenario could apply to other pulsating Be stars, providing an explanation to the long-standing questions surrounding Be outbursts and disks.

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arXiv2019

Does magnetic field impact tidal dynamics inside the convective zone of low-mass stars along their evolution?

The dissipation of the kinetic energy of wave-like tidal flows within the convective envelope of low-mass stars is one of the key physical mechanisms that shapes the orbital and rotational dynamics of short-period exoplanetary systems. Although low-mass stars are magnetically active objects, the question of how the star's magnetic field impacts large-scale tidal flows and the excitation, propagation and dissipation of tidal waves still remains open. Our goal is to investigate the impact of stellar magnetism on the forcing of tidal waves, and their propagation and dissipation in the convective envelope of low-mass stars as they evolve. We have estimated the amplitude of the magnetic contribution to the forcing and dissipation of tidally induced magneto-inertial waves throughout the structural and rotational evolution of low-mass stars (from M to F-type). For this purpose, we have used detailed grids of rotating stellar models computed with the stellar evolution code STAREVOL. The amplitude of dynamo-generated magnetic fields is estimated via physical scaling laws at the base and the top of the convective envelope. We find that the large-scale magnetic field of the star has little influence on the excitation of tidal waves in the case of nearly-circular orbits and coplanar hot-Jupiter planetary systems, but that it has a major impact on the way waves are dissipated. Our results therefore indicate that a full magneto-hydrodynamical treatment of the propagation and dissipation of tidal waves is needed to properly assess the impact of star-planet tidal interactions throughout the evolutionary history of low-mass stars hosting short-period massive planets.

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arXiv2019

$\varepsilon$ Lupi: measuring the heartbeat of a doubly-magnetic massive binary with BRITE-Constellation

$\varepsilon$ Lupi A is a binary system consisting of two main sequence early B-type stars Aa and Ab in a short period, moderately eccentric orbit. The close binary pair is the only doubly-magnetic massive binary currently known. Using photometric data from the BRITE-Constellation we identify a modest heartbeat variation. Combining the photometry with radial velocities of both components we determine a full orbital solution including empirical masses and radii. These results are compared with stellar evolution models as well as interferometry and the differences discussed. We also find additional photometric variability at several frequencies, finding it unlikely these frequencies can be caused by tidally excited oscillations. We do, however, determine that these signals are consistent with gravity mode pulsations typical for slowly pulsating B stars. Finally we discuss how the evolution of this system will be affected by magnetism, determining that tidal interactions will still be dominant.

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arXiv2019

Period spacings of gravity modes in rapidly rotating magnetic stars I. Axisymmetric fossil field with poloidal and toroidal components

Context. Stellar magnetic fields are one of the candidates often invoked to explain the missing transport of angular momentum observed in the models of stellar interiors. However, the properties of an internal magnetic field and the consequences of its presence on stellar evolution are largely unknown. Aims. We study the effect of an axisymmetric internal magnetic field on the frequency of gravity modes in rapidly rotating stars to check whether gravity modes can be used to detect and probe such a field. Methods. Rotation is taken into account using the traditional approximation of rotation and the effect of the magnetic field is computed using a perturbative approach. As a proof of concept, we compute frequency shifts due to a mixed (i.e. with both poloidal and toroidal components) fossil magnetic field for a representative model of a known magnetic, rapidly rotating, slowly pulsating B-type star, namely HD 43317. Results. We find that frequency shifts induced by the magnetic field scale with the square of its amplitude. A magnetic field with a near-core strength of order 150 kG (which is consistent with the observed surface field strength of order 1 kG) leads to signatures that are detectable in period spacings for high-radial-order gravity modes. Conclusions. The predicted frequency shifts can be used to constrain internal magnetic fields and offers the potential for a significant step forward in our interpretation of the observed structure of gravity-mode period spacing patterns in rapidly rotating stars.

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arXiv2019

Observations of tides and circularization in red-giant binaries from Kepler photometry

Binary stars are places of complex stellar interactions. While all binaries are in principle converging towards a state of circularization, many eccentric systems are found even in advanced stellar phases. In this work we discuss the sample of binaries with a red-giant component, discovered from observations of the NASA Kepler space mission. We first discuss which effects and features of tidal interactions are detectable in photometry, spectroscopy and the seismic analysis. In a second step, the sample of binary systems observed with Kepler, is compared to the well studied sample of Verbunt & Phinney (1995, hereafter VP95). We find that this study of circularization of systems hosting evolving red-giant stars with deep convective envelopes is also well applicable to the red-giant binaries in the sample of Kepler stars.

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arXiv2019

The effects of rotation on wave-induced transport in stars: the case of an intermediate-mass star

Internal gravity waves propagate in stellar radiative zones and transport angular momentum throughout the evolution of stars, shaping the internal rotation pro le of these regions. We use the analytical study of Andreé et al. (2018) to assess the impact of rotation and differential rotation on the thermal dissipation of internal gravity waves near the equatorial plane, without making any assumption on the relative strength of rotation relative to that of the background stable stratification. This dissipation is one of the mechanisms allowing a wave-induced deposition/extraction of angular momentum. Here, we apply the analysis to a 3 solar mass star of which we have computed the one-dimensional evolution, from the pre-main sequence to the end of the main sequence. We show that rotation and differential rotation do not significantly modify the efficiency of the damping of internal gravity waves by thermal diffusion, except very close to their excitation region.

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arXiv2018

Evolution of star-planet systems under magnetic braking and tidal interaction

With the discovery over the last two decades of a large diversity of exoplanetary systems, it is now of prime importance to characterize star-planet interactions and how such systems evolve. We address this question by studying systems formed by a solar-like star and a close-in planet. We focus on the stellar wind spinning down the star along its main sequence phase and tidal interaction causing orbital evolution of the systems. Despite recent significant advances in these fields, all current models use parametric descriptions to study at least one of these effects. Our objective is to introduce simultaneously ab-initio prescriptions of the tidal and braking torques, so as to improve our understanding of the underlying physics. We develop a 1D numerical model of coplanar circular star-planet systems taking into account stellar structural changes, wind braking and tidal interaction and implement it in a code called ESPEM. We follow the secular evolution of the stellar rotation assuming a bi-layer internal structure, and of the semi-major axis of the orbit. After comparing our predictions to recent observations and models, we perform tests to emphasize the contribution of ab-initio prescriptions. Our secular model of stellar wind braking reproduces well the recent observations of stellar rotation in open clusters. Our results show that a planet can affect the rotation of its host star and that the resulting spin-up or spin-down depends on the orbital semi-major axis and on the joint influence of magnetic and tidal effects. The ab-initio prescription for tidal dissipation that we used predicts fast outward migration of massive planet orbiting fast-rotating young stars. Finally, we provide the reader with a criterion based on the system's characteristics that allows us to assess whether or not the planet will undergo orbital decay due to tidal interaction.

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arXiv2018

The effects of rotation on wave-induced transport in stars: from weakly to strongly stratified radiative zones

Internal waves propagating in stellar radiative zones can lead to efficient angular momentum transport, that should occur throughout the whole lifetime of stars. They thus play a key role in shaping the internal rotation profile of these regions, that can be probed by asteroseismology. We present a new analytical study of their propagation and dissipation near the equatorial plane. We include the effects of rotation and differential rotation without making any assumption on their relative strength relative to that of the background stable stratification. This analytical framework allows in principle to scan the efficiency of the wave-induced transport of angular momentum. The computations goes from the pre-main sequence, during which the restoring forces associated with rotation and stratification can be of the same order, to the later stages of evolution, for which stratification tends to dominate over rotation. A first application to the case of a sun-like star is finally discussed.

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arXiv2018

On the sensitivity of gravito-inertial modes to differential rotation in intermediate-mass main-sequence stars

Context. While rotation has a major impact on stellar structure and evolution, its effects are not well understood. Thanks to high- quality and long timebase photometric observations obtained with recent space missions, we are now able to study stellar rotation more precisely. Aims. We aim to constrain radial differential rotation profiles in gamma Doradus (gamma Dor) stars, and to develop new theoretical seismic diagnosis for such stars with rapid and potentially non-uniform rotation. Methods. We derive a new asymptotic description which accounts for the impact of weak differential near-core rotation on gravity- mode period spacings. The theoretical predictions are illustrated from pulsation computations with the code GYRE and compared with observations of gamma Dor stars. When possible, we also derive the surface rotation rates in these stars by detecting and analysing signatures of rotational modulation, and compute the core-to-surface rotation ratios. Results. Stellar rotation has to be strongly differential before its effects on period spacing patterns can be detected, unless multiple period spacing patterns can be compared. Six stars in our sample exhibit a single unexplained period spacing pattern of retrograde modes. We hypothesise that these are Yanai modes. Finally, we find signatures of rotational spot modulation in the photometric data of eight targets. Conclusions. If only one period spacing pattern is detected and analysed for a star, it is difficult to detect differential rotation. A rigidly rotating model will often provide the best solution. Differential rotation can only be detected when multiple period spacing patterns have been found for a single star or its surface rotation rate is known as well. This is the case for eight stars in our sample, revealing surface-to-core rotation ratios between 0.95 and 1.05.

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arXiv2018

Testing tidal theory for evolved stars by using red-giant binaries observed by Kepler

Tidal interaction governs the redistribution of angular momentum in close binary stars and planetary systems and determines the systems evolution towards the possible equilibrium state. Turbulent friction acting on the equilibrium tide in the convective envelope of low-mass stars is known to have a strong impact on this exchange of angular momentum in binaries. Moreover, theoretical modelling in recent literature as well as presented in this paper suggests that the dissipation of the dynamical tide, constituted of tidal inertial waves propagating in the convective envelope, is weak compared to the dissipation of the equilibrium tide during the red-giant phase. This prediction is confirmed when we apply the equilibrium-tide formalism developed by Zahn (1977), Verbunt & Phinney (1995), and Remus, Mathis & Zahn (2012) onto the sample of all known red-giant binaries observed by the NASA Kepler mission. Moreover, the observations are adequately explained by only invoking the equilibrium tide dissipation. Such ensemble analysis also benefits from the seismic characterisation of the oscillating components and surface rotation rates. Through asteroseismology, previous claims of the eccentricity as an evolutionary state diagnostic are discarded. This result is important for our understanding of the evolution of multiple star and planetary systems during advanced stages of stellar evolution.

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arXiv2018

Forward seismic modelling of the pulsating magnetic B-type star HD 43317

The large-scale magnetic fields detected at the surface of about 10% of hot stars extend into the stellar interior, where they may alter the structure. Deep inner regions of stars are only observable using asteroseismology. Here, we investigated the pulsating magnetic B3.5V star HD43317, inferred its interior properties and assessed whether the dipolar magnetic field with a surface strength of $B_p = 1312 \pm 332$G caused different properties compared to those of non-magnetic stars. We analysed the latest version of the star's 150d CoRoT light curve and extracted 35 significant frequencies, 28 of which were determined to be independent and not related to the known surface rotation period of $P_{\rm rot} = 0.897673$d. We performed forward seismic modelling based on non-magnetic, non-rotating 1D MESA models and the adiabatic module of the pulsation code GYRE, utilizing a grid-based approach. Our aim was to estimate the stellar mass, age, and convective core overshooting. The GYRE calculations were done for uniform rotation with $P_{\rm rot}$. This modelling was able to explain 16 of the 28 frequencies as gravity modes belonging to retrograde modes with $(\ell, m) = (1, -1)$ and $(2, -1)$ period spacing patterns and one distinct prograde $(2,2)$ mode. The modelling resulted in a stellar mass $M_{\star} = 5.8^{+0.1}_{-0.2}$$\mathrm{M_{\odot}}$, a central hydrogen mass fraction $X_c = 0.54^{+0.01}_{-0.02}$, and exponential convective core overshooting parameter $f_{\rm ov} = 0.004^{+0.014}_{-0.002}$. The low value for $f_{\rm ov}$ is compatible with the suppression of near-core mixing due to a magnetic field but the uncertainties are too large to pinpoint such suppression as the sole physical interpretation. $[...]$

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