Vincent Vanlaer

Unlike other applications of observational asteroseismology, “structure inversions” constrain the physical properties of stellar interiors in a model-independent fashion. However, existing techniques—which parameterize these quantities as functions of the physical radial or mass coordinate—break down when applied to stars that differ substantially from the Sun. These difficulties may be overcome by operating in coordinate systems that have long been known to more naturally suit the physical characteristics of the measured normal modes. We derive expressions for transforming inversion kernels in the acoustic and buoyancy radial coordinates, rather than in the physical radius, and make available a numerically performant implementation. These modified inversions directly address several specific known shortcomings of existing inversion procedures. Using the buoyancy radius in gravity-mode and mixed-mode pulsators permits meaningful comparisons of stars and models with differently sized convective and radiative zones, which defeat standard inversions. Even in pressure-mode oscillators, inversions in the acoustic radial coordinate eliminate the methodological requirement for the mass and radius of the true star being needed to be known in advance.

Context. Asymmetries in the observed rotational splittings of a multiplet contain information about the star’s rotation profile and internal magnetic field. Moreover, the frequency regularities of multiplets can be used for mode identification. However, to exploit this information, highly accurate theoretical predictions are needed. Aims. We aim to quantify the difference in the predicted mode asymmetries between a 1D perturbative method and a 2D method that includes a 2D stellar structure model, which takes rotation into account. We then place these differences between 1D and 2D methods in the context of asteroseismic measurements of internal magnetic fields. We only focus on the asymmetries and not on possible additional frequency peaks that can arise when the magnetic and rotation axis are misaligned. Methods. We coupled the 1D pulsation codes GYRE and StORM to the 2D stellar structure code ESTER and compared the oscillation predictions with the results from the 2D TOP pulsation code. We focused on zero-age main-sequence models representative of rotating β Cephei pulsators spinning at up to 20 per cent of the critical Keplerian rotation rate. Specifically, we investigated low-radial-order gravity and pressure modes. Results. We find a generally good agreement between the oscillation frequencies resulting from the 1D and 2D pulsation codes. We report differences in predicted mode multiplet asymmetries of mostly below 0.06 d ⁻¹ . Since the magnetic asymmetries are small compared to the differences in the rotational asymmetries resulting from the 1D and 2D predictions, accurate measurements of the magnetic field are in most cases challenging. Conclusions. Differences in the predicted mode asymmetries of a rotating star between 1D perturbative methods and 2D non-perturbative methods can greatly hinder accurate measurements of internal magnetic fields in main-sequence pulsators with low-order modes. Nevertheless, reasonably accurate measurements could be possible with n _pg ≥ 2 modes if the internal rotation is roughly below 10 per cent of the Keplerian critical rotation frequency for (aligned) magnetic fields of the order of a few hundred kilogauss. While the differences between the 1D and 2D frequency predictions are mostly too large for internal magnetic field detections, the rotational asymmetries predicted by StORM are in general accurate enough for asteroseismic modelling of the stellar rotation in main-sequence stars with identified low-order modes.

Context. Internal magnetic fields are an elusive component of stellar structure. However, they can play an important role in stellar structure and evolution models through efficient angular momentum transport and through their impact on internal mixing. Aims. We strive to explain the nine components of one frequency multiplet identified as a low-order quadrupole gravity mode detected in the light curve of the β Cep pulsator HD 192575 assembled by the Transiting Exoplanet Survey Satellite (TESS). Methods. We updated the frequencies of the quadrupole mode under investigation using a standard pre-whitening method applied to the 1951.46 d TESS light curve. This showed that an internal magnetic field is required to simultaneously explain all nine components. We implemented theoretical pulsation computations applicable to the low-order modes of a β Cep pulsator including the Coriolis force as well as a magnetic field that is misaligned with respect to the rotation axis. We applied the theoretical description to perform asteroseismic modelling of the amplitudes and frequencies in the multiplet of the quadrupole g-mode of this evolved β Cep star. Results. Pulsation predictions based on the measured internal rotation frequency of the star cannot explain the observed nine-component frequency splittings of the quadrupole low-order gravity mode. By contrast, we show that the combined effect of the Coriolis force caused by the near-core rotation with a period of ∼5.3 d and the Lorentz force due to an internal inclined magnetic field with a maximum strength of ∼24 kG does provide a proper explanation of the nine multiplet frequencies and their relative amplitudes. Conclusions. Given HD 192575’s stellar mass of about 12 M _⊙ , this work presents the detection and magneto-gravito-asteroseismic modelling of a stable internal magnetic field buried inside an evolved rotating supernova progenitor.

Context. Rotation plays an important role in stellar evolution. However, the mechanisms behind the transport of angular momentum in stars at various stages of their evolution are not well understood. To improve our understanding of these processes, it is necessary to measure and validate the internal rotation profiles of stars across different stages of evolution and mass regimes. Aims. Our aim is to constrain the internal rotation profile of the 12-M _⊙ β Cep pulsator HD 192575 from the observed pulsational multiplets and the asymmetries of their component frequencies. Methods. We updated the forward asteroseismic modelling of HD 192575 based on new TESS observations. We inverted the rotation profile from the symmetric part of the splittings and computed the multiplet asymmetries due to the Coriolis force and stellar deformation, which we treated perturbatively. We compared the computed asymmetries with the observed asymmetries. Results. Our new forward asteroseismic modelling is in agreement with previous results but with increased uncertainties, partially due to increased frequency precision, which required us to relax certain constraints. Ambiguity in the mode identification is the main source of the uncertainty, which also affects the inferred rotation profiles. Almost all acceptable rotation profiles occur in the regime below 0.4 d ⁻¹ and favour weak radial differential rotation, with a ratio of core to envelope rotation of less than 2. We find that the quality of the match between the observed and theoretically predicted mode asymmetries is strongly dependent on the mode identification and the internal structure of the star. Conclusions. Our results offer the first detailed rotation inversion for a β Cep pulsator. They show that the rotation profile and the mode asymmetries provide a valuable tool for further constraining the evolutionary properties of HD 192575, and in particular the details of angular momentum transport in massive stars.

Data Release 3 (DR3) has published for the first time epoch photometry, BP/RP (XP) low-resolution mean spectra, and supervised classification results for millions of variable sources. This extensive dataset offers a unique opportunity to study the variability of these objects by combining multiple data products. In preparation for DR4, we propose and evaluate a machine learning methodology capable of ingesting multiple data products to achieve an unsupervised classification of stellar and quasar variability. A dataset of 4 million DR3 sources was used to train three variational autoencoders (VAEs), which are artificial neural networks (ANNs) designed for data compression and generation. One VAE was trained on XP low-resolution spectra, another on a novel approach based on the distribution of magnitude differences in the band, and the third on folded band light curves. Each source was compressed into 15 numbers, representing the coordinates in a 15-dimensional latent space generated by combining the outputs of these three models. The learned latent representation produced by the ANN effectively distinguishes between the main variability classes present in DR3, as demonstrated through both supervised and unsupervised classification analysis of the latent space. The results highlight a strong synergy between light curves and low-resolution spectral data, emphasising the benefits of combining the different data products. A 2D projection of the latent variables revealed numerous overdensities, most of which strongly correlate with astrophysical properties, showing the potential of this latent space for astrophysical discovery. We show that the properties of our novel latent representation make it highly valuable for variability analysis tasks, including classification, clustering, and outlier detection.

Context. KIC 4150611 is a high-order (seventh-order) multiple composed of a triple system with: a F1V primary (Aa), which is eclipsed on a 94.2 d period by a tight binary composed of two K/M dwarfs (Ab1 and Ab2) that also eclipse each other; an eccentric, eclipsing binary composed of two G stars (Ba and Bb); and another faint eclipsing binary composed of two stars of unknown spectral type (Ca and Cb). In addition to its many eclipses, the system is an triple-lined spectroscopic multiple (Aa, Ba, and Bb) and the primary (Aa) is a hybrid pulsator that exhibits high amplitude pressure and gravity modes (g-modes). Furthermore, its g-modes are arrayed in a period-spacing pattern, which greatly assists with mode identification and asteroseismic modelling. In aggregate, this richness in physics offers an excellent opportunity to obtain a precise physical characterisation for some of the stars in this system. Aims. In this work we estimate the stellar parameters of the primary (Aa) by performing asteroseismic analysis on its period-spacing pattern. Methods. We used the C-3PO neural network to perform asteroseismic modelling of the g-mode period-spacing pattern of Aa, examining the interplay of this information with external constraints from spectroscopy (T_eff and log(g)) and eclipse modelling (R). To estimate the level of uncertainty due to different frequency extraction and pattern identification processes, we considered four different variations of the period-spacing patterns. To better understand the correlations between and the uncertainty structure of our parameter estimates, we also employed a classical, parameter-based Markov chain Monte Carlo (MCMC) grid search on four different stellar grids. Results. The externally constrained model that best fits the period-spacing pattern arrives at estimates of the stellar properties for Aa of M = 1.51 ± 0.05 M_⊙, X_c = 0.43 ± 0.04, R = 1.66 ± 0.1 R_⊙, f_ov = 0.010, Ω_c = 1.58 ± 0.01 d⁻¹ with rigid rotation to within the measurement errors, log(T_eff) = 3.856 ± 0.008 dex, log(g) = 4.18 ± 0.04 dex, and log(L) = 0.809 ± 0.005 dex, which agree well with previous measurements from eclipse modelling, spectroscopy, and the Gaia DR3 luminosity. Conclusions. We find that the near-core properties of the best-fitting asteroseismic models are consistent with external constraints from eclipse modelling and spectroscopy. For stellar properties not related to the near-core region, external constraints on the asteroseismic best-fitting models are informative. Aa appears to be a typical example of a γ Dor star, fitting well within existing populations. We find that Aa is quasi-rigidly rotating to within the uncertainties, and note that the asteroseismic age estimate for Aa (1100 ± 100 Myr) is considerably older than the young age (35 Myr) implied by previous isochrone fits to the B binary in the literature. Our MCMC parameter-based grid search agrees well with our pattern-modelling approach. Improved future modelling could come from detailed coverage of metallicity effects and a careful treatment of envelope physics.

Context. Gravity-mode asteroseismology has significantly improved our understanding of mixing in intermediate mass stars. However, theoretical pulsation periods of stellar models remain in tension with observations, and it is often unclear how the models of these stars should be further improved. Inversions provide a path forward by directly probing the internal structure of these stars from their pulsation periods, quantifying which parts of the model are in need of improvement. This method has been used with success in the case of solar-like pulsators, but has not yet been applied to main-sequence gravity-mode pulsators. Aims. Our aim is to determine whether structure inversions for gravity-mode pulsators are feasible. We focus on the case of slowly rotating slowly pulsating B-type (SPB) stars. Methods. We computed and analyzed dipole mode kernels for three variables pairs: (ρ, c), (N², c), and (N², ρ). We assessed the potential of these kernels by predicting the oscillation frequencies of a model after perturbing its structure. We then tested two inversion methods, regularized least squares (RLS) and subtractive optimally localized averages (SOLA), using a model grid computed with the MESA stellar evolution code and the GYRE pulsation code. Results. We find that changing the stellar structure affects the oscillation frequencies in a nonlinear way. The oscillation modes for which this nonlinear dependency is the strongest are in resonance with the near-core peak in the buoyancy frequency. The near-core region of the star can be probed with SOLA, while RLS requires fine tuning to obtain accurate results. Both RLS and SOLA are strongly affected by the nonlinear dependencies on the structure differences, as these methods are based on a first-order approximation. These inversion methods need to be modified for meaningful applications of inversions to SPB stars. Conclusions. Our results show that inversions of gravity-mode pulsators are possible in principle, but that the typical inversion methods developed for solar-like oscillators are not applicable. Future work should focus on developing nonlinear inversion methods.