Frequency analysis of δ Scuti stars towards the Galactic bulge

We have performed a frequency analysis of 10,092 δ Scuti-type stars detected in the fourth phase of the Optical Gravitational Lensing Experiment (OGLE) towards the Galactic bulge, which is the most numerous homogeneous sample of δ Scuti stars observed so far. The main goal was to search for stars pulsating in at least two radial modes simultaneously. We have found 3083 candidates for such stars, which is the largest set obtained to date. Among them, 2655 stars pulsate in two radial modes, 414 stars pulsate in three radial modes, and 14 stars pulsate in four radial modes at the same time. We report the identification of 221 δ Scuti stars pulsating in the fundamental mode, first overtone, and third overtone simultaneously. We show the most populated Petersen and Bailey diagrams and discuss statistical properties of the identified frequencies based on this numerous sample. Additionally, we present theoretical predictions of period ratios for δ Scuti stars pulsating in overtones from the fourth to the seventh.

Oscillations of 2D ESTER models

Context. Recent numerical and theoretical considerations have shown that low-degree acoustic modes in rapidly rotating stars follow an asymptotic formula. In parallel, recent studies have revealed the presence of regular pulsation frequency patterns in rapidly rotating δ Scuti stars that seem to match theoretical expectations. Aims. In this context, a key question is whether strong gradients or discontinuities can adversely affect the asymptotic frequency pattern to the point of hindering its identification. Other important questions are how rotational splittings are affected by the 2D rotation profiles expected from baroclinic effects and whether it is possible to probe the rotation profile using these splittings. Methods. In order to address these questions, we numerically calculate stellar pulsation modes in continuous and discontinuous rapidly rotating models produced by the 2D Evolution STEllaire en Rotation (ESTER) code. This code self-consistently calculates the rotation profile based on baroclinic effects and uses a spectral multi-domain approach, thus making it possible to introduce discontinuities at the domain interfaces without loss of numerical accuracy. The pulsation calculations are carried out using an adiabatic version of the Two-dimensional Oscillation Program (TOP) code. The variational principle is then used to confirm the high numerical accuracy of the pulsation frequencies and to derive an integral formula for the generalised rotational splittings. Acoustic glitch theory, combined with ray dynamics, is applied to the discontinuous models in order to interpret their pulsation spectra. Results. Our results show that the generalised rotational splittings are very well approximated by the integral formula, except for modes involved in avoided crossings. This potentially allows the application of inverse theory for probing the rotation profile. We also show that glitch theory applied along the island mode orbit can correctly predict the periodicity of the glitch frequency pattern produced by the discontinuity or Γ1 dip related to the He II ionisation zone in some of the models. Furthermore, the asymptotic frequency pattern remains sufficiently well preserved to potentially allow its detection in observed stars.

The complex fossil magnetic field of the δ Scuti star HD 41641

ABSTRACT Only three magnetic δ Scuti stars are known as of today. HD 41641 is a δ Scuti star showing chemical peculiarities and rotational modulation of its light curve, making it a good magnetic candidate. We acquired spectropolarimetric observations of this star with NARVAL at Télescope Bernard Lyot (TBL) to search for the presence of a magnetic field and characterize it. We indeed clearly detect a magnetic field in HD 41641, making it the fourth known magnetic δ Scuti star. Our analysis shows that the field is of fossil origin, like magnetic OBA stars, but with a complex field structure rather than the much more usual dipolar structure.

β Cas: The first δ Scuti star with a dynamo magnetic field

Context. F-type stars are characterised by several physical processes such as different pulsation mechanisms, rotation, convection, diffusion, and magnetic fields. The rapidly rotating δ Scuti star β Cas can be considered as a benchmark star to study the interaction of several of these effects. Aims. We investigate the pulsational and magnetic field properties of β Cas. We also determine the star’s apparent fundamental parameters and chemical abundances. Methods. Based on photometric time series obtained from three different space missions (BRITE-Constellation, SMEI, and TESS), we conduct a frequency analysis and investigate the stability of the pulsation amplitudes over four years of observations. We investigate the presence of a magnetic field and its properties using spectropolarimetric observations taken with the Narval instrument by applying the least-squares deconvolution and Zeeman-Doppler imaging techniques. Results. The star β Cas shows only three independent p-mode frequencies down to the few ppm-level; its highest amplitude frequency is suggested to be an n = 3, ℓ = 2, m = 0 mode. Its magnetic field structure is quite complex and almost certainly of a dynamo origin. The atmosphere of β Cas is slightly deficient in iron peak elements and slightly overabundant in C, O, and heavier elements. Conclusions. Atypically for δ Scuti stars, we can only detect three pulsation modes down to exceptionally low noise levels for β Cas. The star is also one of very few δ Scuti pulsators known to date to show a measurable magnetic field and the first δ Scuti star with a dynamo magnetic field. These characteristics make β Cas an interesting target for future studies of dynamo processes in the thin convective envelopes of F-type stars, the transition region between fossil and dynamo fields, and the interaction between pulsations and magnetic field.

Asteroseismic Analysis of δ Scuti Components of Binary Systems: The Case of KIC 8504570

The present work concerns the Asteroseismology of the Kepler-detached eclipsing binary KIC 8504570. Particularly, it focuses on the pulsational behaviour of the oscillating component of this system and the estimation of its physical parameters in order to enrich the so far poor sample of systems of this kind. Using spectroscopic observations, the spectral type of the primary component was determined and used to create accurate light curve models and estimate its absolute parameters. The light curve residuals were subsequently analysed using Fourier transformation techniques to obtain the pulsation models. Theoretical models of δ Scuti stars were employed to identify the oscillation modes of the six detected independent frequencies of the pulsator. In addition, more than 385 combination frequencies were also detected. The absolute and the pulsational properties of the δ Scuti star of this system are discussed and compared with all the currently known similar cases. Moreover, using a recent(empirical) luminosity–pulsation period relationship for δ Scuti stars, the distance of the system was estimated.

Asteroseismology of two Kepler detached eclipsing binaries

The present work contains light curve, spectroscopic, and asteroseismic analyses for KIC 04851217 and KIC 10686876. These systems are detached eclipsing binaries hosting a pulsating component of δ Scuti type and have been observed with the unprecedented accuracy of the Kepler space telescope. Using ground-based spectroscopic observations, the spectral types of the primary components of the systems were estimated as A6V and A5V for KIC 04851217 and KIC 10686876, respectively, with an uncertainty of one subclass. The present spectral classification, together with literature radial velocity curves, were used to model the light curves of the systems and, therefore, to calculate the absolute parameters of their components with a higher degree of certainty. The photometric data were analysed using standard eclipsing binary modeling techniques, while their residuals were further analysed using Fourier transformation techniques to extract the pulsation frequencies of their host δ Scuti stars. The oscillation modes of the independent frequencies were identified using theoretical models of δ Scuti stars. The distances of the systems were calculated using the relation between the luminosity and the pulsation period for δ Scuti stars. Here, the physical and the oscillation properties of the pulsating components of these systems are discussed and compared with others of the same type. Moreover, using all the currently known cases of δ Scuti stars in detached binaries, updated correlations between orbital and dominant pulsation periods and between log g and pulsation periods are derived. It can concluded that the proximity of the companion plays significant role in the evolution of the pulsational frequencies.

Study of the low-order Δν–ρ¯ relation for moderately rotating δ Scuti stars and its impact on their characterization

ABSTRACT The large separation in the low-radial order regime is considered as a highly valuable observable to derive mean densities of δ Scuti stars, due to its independence with rotation. Up to now, theoretical studies of this Δν–${\bar{\rho}}$ relation have been limited to 1D non-rotating models and 2D pseudo-evolutionary models. The present work aims at completing this scenario by investigating quantitatively the impact of rotation in this relation on a large grid of 1D asteroseismic models representative of δ Scuti stars. These include rotation effects on both the stellar evolution and the interaction with pulsation. This allowed us to compute the stellar deformation, get the polar and equatorial radii, and correct the stellar mean densities. We found that the new Δν–${\bar{\rho}}$ relation for rotating models is compatible with previous works. We explained the dispersion of the points around the linear fits as caused mainly by the distribution of the stellar mass, and partially by the evolutionary stage. The new fit is found to be close to the previous theoretical studies for lower masses ($1.3\!-\!1.81\, \mathrm{M}_{\odot }$). However, the opposite holds for the observations: For the higher masses ($1.81\!-\!3\, \mathrm{M}_{\odot }$), the fit is more compatible with the empirical relation. To avoid such discrepancies, we provided new limits to the fit that encompass any possible dependence on mass. We applied these results to characterize the two well-known δ Scuti stars observed by CoRoT, HD 174936 and HD 174966, and compared the physical parameters with those of previous works. The inclusion of rotation in the modelling causes a tendency towards greater masses, radii, and luminosities, and lower density values. Comparison between Δν and Gaia’s luminosities also allowed us to constrain the inclination angles and rotational velocities of both stars. The present results pave the way to systematically constrain the angle of inclination (and thereby the actual surface rotation velocity) of δ Scuti stars.

Unveiling the power spectra of δ Scuti stars with TESS

Thanks to high-precision photometric data legacy from space telescopes like CoRoT and Kepler, the scientific community could detect and characterize the power spectra of hundreds of thousands of stars. Using the scaling relations, it is possible to estimate masses and radii for solar-type pulsators. However, these stars are not the only kind of stellar objects that follow these rules: δ Scuti stars seem to be characterized with seismic indexes such as the large separation (Δν). Thanks to long-duration high-cadence TESS light curves, we analysed more than two thousand of this kind of classical pulsators. In that way, we propose the frequency at maximum power (νmax) as a proper seismic index since it is directly related with the intrinsic temperature, mass and radius of the star. This parameter seems not to be affected by rotation, inclination, extinction or resonances, with the exception of the evolution of the stellar parameters. Furthermore, we can constrain rotation and inclination using the departure of temperature produced by the gravity-darkening effect. This is especially feasible for fast rotators as most of δ Scuti stars seem to be.

The pulsation properties of λ bootis stars I. the southern TESS sample

ABSTRACT We analyse TESS light curves for 70 southern λ Boo stars to identify binaries and to determine which of them pulsate as δ Scuti stars. We find two heartbeat stars and two eclipsing binaries among the sample. We calculate that 81 per cent of λ Boo stars pulsate as δ Sct variables, which is about twice that of normal stars over the same parameter space. We determine the temperatures and luminosities of the λ Boo stars from photometry and Gaia DR2 parallaxes. A subset of 40 λ Boo stars have 2-min TESS data, reliable temperatures and luminosities, and δ Sct pulsation. We use Petersen diagrams (period ratios), échelle diagrams, and the period–luminosity relation to identify the fundamental mode in 20 of those 40 stars and conclude that a further 8 stars are not pulsating in this mode. For the remaining 12, the fundamental mode cannot be unambiguously identified. Further mode identification is possible for 12 of the fundamental mode pulsators that have regular sequences of pulsation overtones in their échelle diagrams. We use stellar evolution models to determine statistically that the λ Boo stars are only superficially metal weak. Simple pulsation models also better fit the observations at a metallicity of Z = 0.01 than at Z = 0.001. The TESS observations reveal the great potential of asteroseismology on λ Boo stars, for determining precise stellar ages and shedding light on the origin(s) of the λ Boo phenomenon.