Period Spacing Patterns Research Articles

The asteroseismic imprints of mass transfer

We present new simulations investigating the impact of mass transfer on the asteroseismic signals of slowly pulsating B stars. We used MESA to simulate the evolution of a binary star system and GYRE to compute the asteroseismic properties of the accretor star. We show that, compared to a single star of the same final mass, a star that has undergone accretion (of non-enriched material) has a significantly different internal structure, which is evident in both the hydrogen abundance profile and the Brunt-Väisälä frequency profile. These differences result in significant changes in the observed period spacing patterns, implying that one may use this as a diagnostic to test whether a star’s core has been rejuvenated as a result of accretion. We show that it is essential to consider the full multimodal posterior distributions when fitting stellar properties of mass-gainers to avoid drawing misleading conclusions. Even with these considerations, stellar ages will be significantly underestimated when assuming single star evolution for a mass-gainer. We find that future detectors with improved uncertainties would rule out single star models with the correct mass and central hydrogen fraction. Our proof of principle analysis demonstrates the need to further investigate the impact of binary interactions on stellar asteroseismic signals for a wide range of parameters, such as the initial mass, the amount of mass transferred, and the age of the accretor star at the onset of mass transfer.

Asteroseismology of the young open cluster NGC 2516

Context. Asteroseismic modelling of isolated stars presents significant challenges due to the difficulty in accurately determining stellar parameters, particularly the stellar age. These challenges can be overcome by observing stars in open clusters whose coeval members share an initial chemical composition. The light curves from the all-sky survey by the Transiting Exoplanet Survey Satellite (TESS) allow us to investigate and analyse stellar variations in clusters with an unprecedented level of detail for the first time. Aims. We aim to detect gravity-mode oscillations in the early-type main-sequence members of the young open cluster NGC 2516 to deduce their internal rotation rates. Methods. We selected the 301 member stars with no more than mild contamination as our sample. We analysed the full-frame image light curves, which provide nearly continuous observations in the first and third years of TESS monitoring. We also collected high-resolution spectra using the Fiber-fed Extended Range Optical Spectrograph for the g-mode pulsators, with the aim of assessing the Gaia effective temperatures and gravities and preparing for future seismic modelling. Results. By fitting the theoretical isochrones to the colour-magnitude diagram of a cluster, we determined an age of 102 ± 15 Myr and inferred that the extinction at 550 nm (A0) is 0.53 ± 0.04 mag. We identified 147 stars with surface-brightness modulations: 24 with gravity (g-)mode pulsations (γ Doradus or slowly pulsating B-type stars) and 35 with pressure (p-)mode pulsations (δ Sct stars). When sorted by colour index, the amplitude spectra of the δ Sct stars show a distinct ordering and reveal a discernible frequency-temperature relationship. The near-core rotation rates, measured from period spacing patterns in two slowly pulsating B-type (SPB) stars and nine γ Dor stars, reach up to 3 d−1. This is at the high end of the values found from Kepler data of field stars of similar variability type. The γ Dor stars of NGC 2516 have internal rotation rates as high as 50% of their critical value, whereas the SPB stars exhibit rotation rates close to their critical rate. Although the B-type stars are rotating rapidly, we did not find long-term brightness and colour variations in the mid-infrared, which suggests that there are no disc or shell formation events in our sample. We also discussed the results of our spectroscopic observations for the g-mode pulsators.

Asteroseismic modelling of the chemically peculiar B-type pulsator with an asymptotic period spacing – a Cen

ABSTRACT A Cen is recognized as a magnetic variable star with peculiar helium abundance. The presence of large surface spots induces flux modulation, allowing for the derivation of the surface rotational period (∼8.8 d). TESS photometry has unveiled additional signals that we interpreted as SPB-type pulsation. Furthermore, we managed to find a regular period spacing pattern and hence identified pulsational modes. We performed an asteroseismic analysis that resulted in constraints for internal structure of the star. Taking into account the surface rotation period derived from spots and the internal rotation obtained from asteroseismology, we concluded that the gradient of the rotational velocity in the radial direction is very small, indicating nearly solid body rotation. We also constrained overshooting from the convective core, as well as the mass and metallicity of the star.

Two High-amplitude δ Scuti–γ Doradus Hybrids Constrained by the Radial Fundamental p and Equally Spaced g Modes

Based on 2 minutes cadence TESS data, we investigate pulsations of TIC 65138566 and TIC 139729335 and discover them to be two new high-amplitude δ Scuti stars with equally spaced g modes. We recognize the radial fundamental mode f 1 = 18.3334 c d−1 and the first overtone f 3 = 23.6429 c d−1 for TIC 65138566, and identify the highest peak f 1 = 19.0955 c d−1 as the radial fundamental mode for TIC 139729335. For g modes, both stars display a regular period spacing of 2413 s. Through detailed seismological analysis, we deduce that these period-spacing patterns correspond to modes with ℓ = 1. Moreover, our analysis reveals that with increases in masses and metallicities, the star should display a higher degree of evolution to match a specific period spacing Π0. Conversely, the star should have a lower extent of evolution to match the radial fundamental mode. These two contradictory behaviors allow us to precisely obtain stellar physical parameters. TIC 65138566 and TIC 139729335 are determined to be two main-sequence stars that have almost the same range of masses and metallicities, with M = 1.36 ± 0.06 M ⊙ and Z = 0.005 ± 0.002. The hydrogen abundance in the core of TIC 65138566 is estimated to be about 0.28, while TIC 139729335 has a slightly higher value of around 0.31. Finally, we suggest that the high-amplitude δ Scuti–γ Doradus star TIC 308396022 is a main-sequence star with M = 1.54 ± 0.08 M ⊙, Z = 0.007 ± 0.001, and X c = 0.18 ± 0.02.

Mode coupling coefficients between the convective core and radiative envelope of γ Doradus and slowly pulsating B stars

Context. Signatures of coupling between an inertial mode in the convective core and a gravito-inertial mode in the envelope have been found in four-year Kepler light curves of 16 rapidly rotating γ Doradus (γ Dor) stars. This makes it possible to obtain a measurement of the rotation frequency in their convective core. Despite their similar internal structure and available data, inertial modes have not yet been reported for slowly pulsating B (SPB) stars. Aims. We aim to provide a numerical counterpart of the recently published theoretical expressions for the mode-coupling coefficients, ε and ε̃. These coefficients represent the two cases of a continuous and a discontinuous Brunt-Väisälä frequency profile at the core-envelope interface, respectively. We consider γ Dor and SPB stars to shed light on the difference between these two classes of intermediate-mass gravito-inertial mode pulsators in terms of core and envelope mode coupling. Methods. We used asteroseismic forward models of two samples consisting of 26 SPB stars and 37 γ Dor stars to infer their numerical values of ε and ε̃. For both samples, we also computed: the linear correlation coefficients between ε or ε̃ and the near-core rotation frequency, the chemical gradient, the evolutionary stage, the convective core masses and radii, and the Schönberg-Chandrasekhar limiting mass representing the maximum mass of an inert helium core at central hydrogen exhaustion that can still withstand the pressure of the overlaying envelope. Results. The asteroseismically inferred values of ε and ε̃ for the two samples are between 0.0 and 0.34. While ε is most strongly correlated with the near-core rotation frequency for γ Dor stars, the fractional radius of the convective core instead provides the tightest correlation for SPB stars. We find ε to decrease mildly as the stars evolve. For the SPB stars, ε and ε̃ have similar moderate correlations with respect to the core properties. For the γ Dor stars, ε̃ reveals systematically lower and often no correlation to the core properties; their ε is mainly determined by the near-core rotation frequency. The Schönberg-Chandrasekar limit is already surpassed by the more massive SPB stars, while none of the γ Dor stars have reached it yet. Conclusions. Our asteroseismic results for the mode coupling support the theoretical interpretation and reveal that young, fast-rotating γ Dor stars are most suitable for undergoing couplings between inertial modes in the rotating convective core and gravito-inertial modes in the radiative envelope. The phenomenon has been found in 2.4% of such pulsators with detected period spacing patterns, whereas it has not been seen in any of the SPB stars so far.

Semi-analytical Expression of G-mode Period Spacing: The Case of Brunt–Väisälä Frequency with Not a Jump but a Ramp

To decipher complex patterns of gravity-mode period spacings observed for intermediate-mass main-sequence stars is an important step toward a better understanding of the structure and dynamics in the deep radiative region of the stars. In this study, we apply the JWKB approximation to derive a semi-analytical expression of the g-mode period spacing pattern, for which the gradient in the Brunt–Väisälä frequency is taken into account. The formulation includes the term P −1 B ⋆, where P and B ⋆ represent the g-mode period and degree of the structural variation, the latter of which especially is related to the steepness of the gradient of the Brunt–Väisälä frequency. Tests with one-dimensional stellar models show that the semi-analytical expression derived in this study is useful for inferring the degree of the structural variation B ⋆ with an accuracy of ∼10 % in the case of relatively massive intermediate-mass models with the mass M larger than 3 M ⊙. The newly formulated expression will possibly allow us to put further constraints on, e.g., mixing processes inside intermediate-mass main-sequence g-mode pulsators such as β Cep, SPB, and γ Dor stars that have been principal targets in asteroseismology.

Detection and Seismic Study of Gravity and Rossby Mode Pulsations in Four Contact Binaries

We report the detection of gravity (g) and Rossby (r) mode pulsations of four short-period eclipsing binaries, KIC 5439790, KIC 7501230, KIC 9350889, and KIC 9453192 based on the 4 yr Kepler high-precision photometry. Light-curve modeling reveals that the four binaries are all contact systems with small mass ratios. We study the short-term variability of the light-curve residuals after the removal of the binary model and attribute them to the g- and r-mode pulsations that stem from the primary stars. By introducing a new criterion, we attempt to identify period-spacing patterns in the Fourier spectra, which refers to the determination of the rotation rates of stellar interior and envelope as well as the asymptotic period spacings of the pulsating stars. It is interesting to find that the rotation rates of the stellar envelopes are all nearly equal to the orbits. The near-core rotations, however, are significantly slower by about 10%. Based on the derived asymptotic period spacings, stellar parameters were constrained from asteroseismology models. The pulsators are revealed to be evolved main-sequence stars with high metallicities.

Tidally perturbed gravity-mode pulsations in a sample of close eclipsing binaries

Context. Thanks to the high-precision photometry from space missions such as Kepler and TESS, tidal perturbations and tilting of pulsations have been detected in more than a dozen binary systems. However, only two of these were gravity-mode (g-mode) pulsators. Aims. We aim to detect tidally perturbed g modes in additional binary systems and characterise them observationally. Methods. We performed a custom data reduction of the available Kepler and TESS photometry of a well-studied, published sample of 35 binary systems with γ Doradus (γ Dor) pulsators. For each target, we modelled the binary signal using a sum of 100 sine waves with frequencies at orbital harmonics and measured significant pulsation frequencies in an iterative pre-whitening analysis of the residual light curve. Pulsations are labelled as tidally perturbed g modes if they are part of both period-spacing patterns and multiplets spaced by integer multiples of the orbital frequency. After visual inspection and confirmation, the properties of these targets and g modes were characterised. Results. We detect tidally perturbed g-mode pulsations for five short-period binaries that are circularised and (almost) synchronously rotating: KIC 3228863, KIC 3341457, KIC 4947528, KIC 9108579, and KIC 12785282. Tidally perturbed g modes that occur within the same star and have the same mode identification (k, m), are found to have near-identical relative amplitude and phase modulations, which are within their respective 1 − σ uncertainties and also identical for the Kepler and TESS photometric passbands. By contrast, pulsations with different mode identifications (k, m) are found to exhibit different modulations. Moreover, the observed amplitude and phase modulations are correlated, indicating that the binary tides primarily distort the g-mode amplitudes on the stellar surface. The phase modulations are then primarily a geometric effect of the integration of the stellar flux over the visible stellar surface. All selected binaries also exhibit signal that resembles rotational modulation in the Fourier domain. In the case of KIC 3228863, this is caused by the presence of the known tertiary component, and for the other systems we hypothesise that it is caused by temperature variations on the stellar surface. Alternatively, the signal can be made up of overstable convective modes in the stellar core or may belong to the non-pulsating companion. Conclusions. While g-mode pulsation periods are known to be a direct probe of the deep interior stellar structure, the binary tides that cause the pulsation modulations are dominant in the outer stellar layers. Hence, in the future, tidally perturbed g modes may allow us to carry out core-to-surface asteroseismic modelling of tidally distorted stars.

Internal rotation and buoyancy travel time of 60 γ Doradus stars from uninterrupted TESS light curves spanning 352 days

Context. Gamma Doradus (hereafter γ Dor) stars are gravity-mode pulsators whose periods carry information about their internal structure. These periods are especially sensitive to the internal rotation and chemical mixing, two processes that are currently not well constrained in the theory of stellar evolution. Aims. We aim to identify the pulsation modes and deduce the internal rotation and buoyancy travel time for 106 γ Dor stars observed by the Transiting Exoplanet Survey Satellite (TESS) mission in its southern continuous viewing zone (hereafter S-CVZ). We rely on 140 previously detected period-spacing patterns, that is, series of (near-)consecutive pulsation mode periods. Methods. We used the asymptotic expression to compute gravity-mode frequencies for ranges of the rotation rate and buoyancy travel time that cover the physical range in γ Dor stars. Those frequencies were fitted to the observed period-spacing patterns by minimising a custom cost function. The effects of rotation were evaluated using the traditional approximation of rotation, using the stellar pulsation code GYRE. Results. We obtained the pulsation mode identification, internal rotation, and buoyancy travel time for 60 TESS γ Dor stars. For the remaining 46 targets, the detected patterns were either too short or contained too many missing modes for unambiguous mode identification, and longer light curves are required. For the successfully analysed stars, we found that period-spacing patterns from 1-yr-long TESS light curves can constrain the internal rotation and buoyancy travel time to a precision of 0.03 d-1 and 400 s, respectively, which is about half as precise as literature results based on 4-yr-long Kepler light curves of γ Dor stars.

A new window to tidal asteroseismology: non-linearly excited stellar eigenmodes and the period spacing pattern in KOI-54

ABSTRACT We revisit the tidally excited oscillations (TEOs) in the A-type main-sequence eccentric binary KOI-54, the prototype of heartbeat stars. Although the linear tidal response of the star is a series of orbital-harmonic frequencies which are not stellar eigenfrequencies, we show that the non-linearly excited non-orbital-harmonic TEOs are eigenmodes. By carefully choosing the modes which satisfy the mode-coupling selection rules, a period spacing (ΔP) pattern of quadrupole gravity modes (ΔP ≈ 2520–2535 s) can be discerned in the Fourier spectrum, with a detection significance level of $99.9{{\ \rm per\ cent}}$. The inferred period spacing value agrees remarkably well with the theoretical l = 2, m = 0 g modes from a stellar model with the measured mass, radius, and effective temperature. We also find that the two largest-amplitude TEOs at N = 90, 91 harmonics are very close to resonance with l = 2, m = 0 eigenmodes, and likely come from different stars. Previous works on tidal oscillations primarily focus on the modelling of TEO amplitudes and phases, the high sensitivity of TEO amplitude to the frequency detuning (tidal forcing frequency minus the closest stellar eigenfrequency) requires extremely dense grids of stellar models and prevents us from constraining the stellar physical parameters easily. This work, however, opens the window of real tidal asteroseismology by using the eigenfrequencies of the star inferred from the non-linear TEOs and possibly very-close-to-resonance linear TEOs. Our seismic modelling of these identified eigen g-modes shows that the best-matching stellar models have (M ≈ 2.20, 2.35 M⊙) and super-solar metallicity, in good agreement with previous measurements.

Detection of period-spacing patterns due to the gravity modes of rotating dwarfs in the TESS southern continuous viewing zone

Context.The theory of stellar evolution presents shortcomings when confronted with asteroseismic probes of interior physical properties. The differences between observations and theory are often great because stellar models have mainly been calibrated from observables connected to the surface of stars. Period-spacing patterns caused by gravity modes are a particularly powerful asteroseismic tool that are useful for probing the near-core rotation and mixing of chemical elements in main-sequence stars with convective cores.Aims.We aim to compose a catalog of intermediate-mass stars in the Transiting Exoplanet Survey Satellite (TESS) southern continuous viewing zone (CVZ) to reveal period-spacing patterns caused by gravity modes for use in future asteroseismic modeling.Methods.TESS full frame images (FFI) were inspected to select stars of intermediate- and high-mass using color-magnitude criteria. Light curves were extracted from custom masks per star, adopting stringent constraints on the aperture masks and contamination. The extracted light curves were subject to iterative prewhitening to detect gravity modes. We developed a method relying on the assumption that period spacings are an approximately linear function of the mode periods to build a template pattern. This template was used to extract the patterns and their uncertainties, relying on a bootstrap approach.Results.Our TESS catalog of high-quality period-spacing patterns is the first of its kind and contains 140 gravity-mode patterns in 106 γ Dor stars and two slowly pulsating B-type (SPB) stars. Half of these patterns contain seven or more measured mode periods and the longest pattern contains 20 modes. We provide the community with a convenient software tool to search for period-spacing patterns and to process the extracted light curves.Conclusions.Our catalog offers a fruitful starting point for future gravity-mode asteroseismology of rotating dwarfs with convective cores in the southern hemisphere.

Seismic modelling of a very young SPB star – KIC 8264293

ABSTRACT KIC 8264293 is a fast-rotating B-type pulsator observed by Kepler satellite. Its photometric variability is mainly due to pulsations in high-order g modes. Besides, we detected a weak Hα emission. Thus, the second source of variability is the fluctuation in a disc around the star. The pulsational spectrum of KIC 8264293 reveals a frequency grouping and period spacing pattern. Here, we present the thorough seismic analysis of the star based on these features. Taking into account the position of the star in the HR diagram and fitting the 14 frequencies that form the period spacing, we constrain the internal structure of the star. We conclude that the star barely left the zero-age main sequence and the best seismic model has $M = 3.54\, \mathrm{M}_{\odot }$, $V_\mathrm{rot}=248\, \mathrm{km\, s}^{-1}$, and Z = 0.0112. We found the upper limit on the mixing at the edge of the convective core, with the overshooting parameter up to fov = 0.03. On the other hand, we were not able to constrain the envelope mixing for the star. To excite the modes in the observed frequency range, we had to modify the opacity data. Our best seismic model with an opacity increase by 100 per cent at the ‘nickel’ bump log T = 5.46 explains the whole instability. KIC 8264293 is the unique, very young star pulsating in high-order g modes with the Be feature. However, it is not obvious whether the source of this circumstellar matter is the ejection of mass from the underlying star or whether the star has retained its protostellar disc.

Towards a systematic treatment of observational uncertainties in forward asteroseismic modelling of gravity-mode pulsators

Context.In asteroseismology, the pulsation mode frequencies of a star are the fundamental data that are compared to theoretical predictions to determine a star’s interior physics. Recent significant advances in the numerical, theoretical, and statistical asteroseismic methods applied to main-sequence stars with convective cores have renewed interest in investigating the propagation of observational uncertainties within a forward asteroseismic modelling framework.Aims.We aim to quantify the impact of various choices made throughout the observational aspects of extracting pulsation mode frequencies in main-sequence stars with gravity modes.Methods.We use a well-studied benchmark slowly pulsating B star, KIC 7760680, to investigate the sensitivity of forward asteroseismic modelling to various sources of observational uncertainty that affect the precision of the input pulsation mode frequencies.Results.We quantify the impact of the propagation of the observational uncertainties involved in forward asteroseismic modelling. We find that one of the largest sources of uncertainty in our benchmark star is in the manual building of period spacing patterns, such that the inclusion of a potentially ambiguous pulsation mode frequency may yield differences in model parameters of up to 10% for mass and age depending on the radial order of the mode.Conclusions.We conclude that future asteroseismic studies of main-sequence stars with a convective core should quantify and include observational uncertainties introduced by the light curve extraction, iterative pre-whitening, and the building of period spacing patterns, as these propagate into the final modelling results.

TIC 308396022: δ Scuti–γ Doradus hybrid with large-amplitude radial fundamental mode and regular g-mode period spacing

We analyse the pulsating behaviour of TIC 308396022, based on observations by the TESS mission. The star is a high-amplitude δ Sct star that shows a very rich amplitude spectrum using the 3-yr light curve. Among these frequencies, the strongest peak of f1 = 13.20362567(12) d−1 is identified as the radial fundamental mode, and we also find the first and second overtones (f2 and f3). In the low-frequency range (< 2.5 d−1), 22 peaks are identified as gravity modes, which show a regular period spacing of about 2460 s and have an angular degree of l = 1. The period spacing pattern does not show a significant downward trend, suggesting the star is rotating slowly. We note that this is a δ Sct–γ Dor hybrid star containing a high-amplitude radial fundamental mode and a regular g-mode period spacing pattern. With the O − C analysis, we find the star shows a significant time delay, implying that the star has a companion and it is likely to be a white dwarf. The history of possible mass transfer provides a great opportunity for testing the current theories of binary evolution, mass transfer, and pulsation.

Detection of non-linear resonances among gravity modes of slowly pulsating B stars: Results from five iterative pre-whitening strategies

Context. Slowly pulsating B (SPB) stars are main-sequence multi-periodic oscillators that display non-radial gravity modes. For a fraction of these pulsators, 4-year photometric light curves obtained with the Kepler space telescope reveal period spacing patterns from which their internal rotation and mixing can be inferred. In this inference, any direct resonant mode coupling is usually ignored. Aims. We re-analyse the light curves of a sample of 38 known Kepler SPB stars. For 26 of them, the internal structure, including rotation and mixing, was recently inferred from their dipole prograde oscillation modes. Our aim is to detect direct non-linear resonant mode coupling among the largest-amplitude gravity modes. Methods. We extract up to 200 periodic signals per star with five different iterative pre-whitening strategies based on linear and non-linear regression applied to the light curves. We then identify candidate coupled gravity modes by verifying whether they fulfil resonant phase relations. Results. For 32 of the 38 SPB stars we find at least one candidate resonance that is detected in both the linear and the best non-linear regression model fit to the light curve and involves at least one of the two largest-amplitude modes. Conclusions. The majority of the Kepler SPB stars reveal direct non-linear resonances based on the largest-amplitude modes. These stars are thus prime targets for the non-linear asteroseismic modelling of intermediate-mass dwarfs to assess the importance of mode couplings in probing their internal physics.

The traditional approximation of rotation for rapidly rotating stars and planets

Context. The traditional approximation of rotation (TAR) is a treatment of the hydrodynamic equations of rotating and stably stratified fluids in which the action of the Coriolis acceleration along the direction of the entropy and chemical stratifications is neglected because it is weak in comparison with the buoyancy Archimedean force. This leads to the neglect of the horizontal projection of the rotation vector in the equations for the dynamics of gravito-inertial waves (GIWs). The dependent variables in those equations then become separable into radial and horizontal parts as in the non-rotating case. The TAR is built on the assumptions that the star is spherical (i.e., its centrifugal deformation is neglected) and uniformly rotating. However, it has recently been generalised to include the effects of a moderate centrifugal deformation using a perturbative approach. Aims. We study the feasibility of carrying out a new generalisation to account for the centrifugal acceleration in the case of strongly deformed uniformly and rapidly rotating stars (and planets), and to identify the validity domain of this approximation. Methods. We built a complete formalism analytically that allows the study of the dynamics of GIWs in spheroidal coordinates which take the flattening of uniformly and rapidly rotating stars into account by assuming the hierarchies of frequencies adopted within the TAR in the spherical case. Results. Using 2D stellar models, we determine the validity domain of the generalised TAR as a function of the rotation rate of the star normalised by its critical angular velocity and its pseudo-radius. Assuming the anelastic and the two-dimensional Jeffreys-Wentzel-Kramers-Brillouin approximations, we derive a generalised Laplace tidal equation for the horizontal eigenfunctions of the GIWs and their asymptotic wave periods, which can be used to probe the structure and dynamics of rotating deformed stars with asteroseismology. The generalised TAR where the centrifugal deformation of a star (or planet) is taken into account non-perturbatively allows us to identify, within the framework of 2D Evolution STEllaire en Rotation models, the validity domain of this approximation which is reduced by increasing the rate of rotation. We can affirm with a level of confidence of 90% that the TAR remains applicable in all the space domain of deformed stars rotating at a rotation rate lower than 20% of the critical rotation rate. Conclusions. A new generalisation of the TAR, which takes the centrifugal acceleration into account in a non-perturbative way, is derived. This generalisation allows us to study the detectability and the signature of the centrifugal effects on GIWs in rapidly rotating deformed stars (and planets). We found that the effects of the centrifugal acceleration in rapidly rotating early-type stars on GIWs are theoretically detectable in modern space photometry using observations from Kepler. We found also, by comparing the period spacing pattern computed with the standard and the generalised TAR, that the centrifugal acceleration affects the period spacing by increasing its values for low radial orders and by decreasing them slightly for high radial orders.

Constraining stellar evolution theory with asteroseismology of γ Doradus stars using deep learning

Context. The efficiency of the transport of angular momentum and chemical elements inside intermediate-mass stars lacks proper calibration, thereby introducing uncertainties on a star’s evolutionary pathway. Improvements require better estimation of stellar masses, evolutionary stages, and internal mixing properties. Aims. Our aim was to develop a neural network approach for asteroseismic modelling, and test its capacity to provide stellar masses, ages, and overshooting parameter for a sample of 37 γ Doradus stars; these parameters were previously determined from their effective temperature, surface gravity, near-core rotation frequency, and buoyancy travel time Π0. Here our goal is to perform the parameter estimation from modelling of individual periods measured for dipole modes with consecutive radial order rather than from Π0. We assess whether fitting these individual mode periods increases the capacity of the parameter estimation. Methods. We trained neural networks to predict theoretical pulsation periods of high-order gravity modes (n ∈ [15, 91]), and to predict the luminosity, effective temperature, and surface gravity for a given mass, age, overshooting parameter, diffusive envelope mixing, metallicity, and near-core rotation frequency. We applied our neural networks for Computing Pulsation Periods and Photospheric Observables (C-3PO) to our sample and compute grids of stellar pulsation models for the estimated parameters. Results. We present the near-core rotation rates (from the literature) as a function of the inferred stellar age and critical rotation rate. We assessed the rotation rates of the sample near the start of the main sequence assuming rigid rotation. Furthermore, we measured the extent of the core overshoot region and find no correlation with mass, age, or rotation. Finally, for one star in our sample, KIC 12066947, we find indications of mode coupling in the period spacing pattern which we cannot reproduce with mode trapping. Conclusions. The neural network approach developed in this study allows the derivation of stellar properties dominant for stellar evolution, such as mass, age, and extent of core-boundary mixing. It also opens a path for future estimation of mixing profiles throughout the radiative envelope, with the aim of inferring these profiles for large samples of γ Doradus stars.

A comparison of the dynamical and model-derived parameters of the pulsating eclipsing binary KIC 9850387

Context. One-dimensional stellar evolutionary models incorporate interior mixing profiles as a simplification of multi-dimensional physical processes that have a significant impact on the evolution and lifetime of stars. As such, the proper calibration of interior mixing profiles is required for the reconciliation of observational parameters and theoretical predictions. The modelling and analysis of pulsating stars in eclipsing binary systems that display gravity-mode (g-mode) oscillations allows for the precise constraints on the interior mixing profiles through the combination of spectroscopic, binary and asteroseismic obervables. Aims. We aim to unravel the interior mixing profile of the pulsating eclipsing binary KIC 9850387 by comparing its dynamical parameters and the parameters derived through a combination of evolutionary and asteroseismic modelling. Methods. We created a grid of stellar evolutionary models using the stellar evolutionary code MESA and performed an isochrone-cloud (isocloud) based evolutionary modelling of the system. We then generated a grid of pulsational models using the stellar pulsation code GYRE based on the age constraints from the evolutionary modelling. Finally, we performed asteroseismic modelling of the observed ℓ = 1 and ℓ = 2 period-spacing patterns, utilising different combinations of observational constraints, merit functions, and asteroseismic observables to obtain strong constraints on the interior properties of the primary star. Results. Through a combination of asteroseismic modelling and dynamical constraints, we found that the system comprises two main-sequence components at an age of 1.2 ± 0.1 Gyr. We also observed that asteroseismic modelling provided stronger constraints on the interior properties than evolutionary modelling. Overall, we found high levels of interior mixing, when compared to similar studies, for the primary star. We posited that this is a result of intrinsic non-tidal mixing mechanisms due to a similar observed behaviour in single stars. We investigated the high-frequency regime of KIC 9850387 and found evidence of the surface effect due to the systematic frequency offset of the theoretical modes from the nearest observed modes. We also found evidence of rotational splitting in the form of a prograde-retrograde dipole g1 mode doublet with a missing zonal mode, implying an envelope rotational frequency that is three times higher than the core rotational frequency and about 20 times slower than the orbital frequency, but we note that this result is based completely on the rotational splitting of a single dipole mode. Conclusions. We find that the dynamical parameters and the parameters extracted from the asteroseismic modelling of period-spacing patterns are only barely compliant, reinforcing the need for homogeneous analyses of samples of pulsating eclipsing binaries that aim to calibrating interior mixing profiles.

Tango of celestial dancers: A sample of detached eclipsing binary systems containingg-mode pulsating components

Context.Eclipsing binary systems with components that pulsate in gravity modes (gmodes) allow for simultaneous and independent constraints of the chemical mixing profiles of stars. The high precision of the dynamical masses and radii as well as the imposition of identical initial chemical compositions and equivalent ages provide strong constraints during the modelling ofg-mode period-spacing patterns.Aims.We aim to assemble a sample ofg-mode pulsators in detached eclipsing binaries with the purpose of finding good candidates for future evolutionary and asteroseismic modelling. In addition, we present a case study of the eclipsing binary KIC9850387, identified as our most promising candidate, and detail the results of the observational spectroscopic, photometric, and asteroseismic analysis of the system.Methods.We selected all of the detached eclipsing binaries in theKeplereclipsing binary catalogue withKeplerInput Catalogue (KIC) temperatures between 6000 K and 10 000 K, and performed a visual inspection to determine the presence and density ofgmodes, and the presence ofg-mode period-spacing patterns in their frequency spectra. We then characterised our sample based on theirg-mode pulsational parameters and binary and atmospheric parameters. A spectroscopic follow-up of our most promising candidate was then performed, and the orbital elements of the system were extracted. We then performed spectral disentangling followed by atmospheric modelling and abundance analysis for the primary star. We utilised an iterative approach to simultaneously optimise the pulsational and eclipse models, and subsequently performed an analysis of the pressure- (p-) andg-mode pulsational frequencies.Results.We compiled a sample of 93Keplereclipsing binary stars withg-mode pulsating components and identified clearg-mode period-spacing patterns in the frequency spectra of seven of these systems. We also identified 11 systems that contained hybridp- andg-mode pulsators. We found that theg-mode pulsational parameters and the binary and atmospheric parameters of our sample are weakly correlated at best, as expected for detached main-sequence binaries. We find that the eclipsing binary KIC9850387 is a double-lined spectroscopic binary in a near-circular orbit with a hybridp- andg-mode pulsating primary withMp= 1.66−0.01+0.01M⊙andRp= 2.154−0.004+0.002R⊙, and a solar-like secondary withMs= 1.062−0.005+0.003M⊙andRs= 1.081−0.002+0.003R⊙. We findℓ = 1 andℓ = 2 period-spacing patterns in the frequency spectrum of KIC9850387 spanning more than ten radial orders each, which will allow for stringent constraints of stellar structure during future asteroseismic modelling.

The effect of tides on near-core rotation: analysis of 35 Kepler γ Doradus stars in eclipsing and spectroscopic binaries

ABSTRACT We systematically searched for gravity- and Rossby-mode period spacing patterns in Kepler eclipsing binaries with γ Doradus pulsators. These stars provide an excellent opportunity to test the theory of tidal synchronization and angular momentum transport in F- and A-type stars. We discovered 35 systems that show clear patterns, including the spectroscopic binary KIC 10080943. Combined with 45 non-eclipsing binaries with γ Dor components that have been found using pulsation timing, we measured their near-core rotation rates and asymptotic period spacings. We find that many stars are tidally locked if the orbital periods are shorter than 10 d, in which the near-core rotation periods given by the traditional approximation of rotation are consistent with the orbital period. Compared to the single stars, γ Dor stars in binaries tend to have slower near-core rotation rates, likely a consequence of tidal spin-down. We also find three stars that have extremely slow near-core rotation rates. To explain these, we hypothesize that unstable tidally excited oscillations can transfer angular momentum from the star to the orbit, and slow the star below synchronism, a process we refer to as ‘inverse tides’.