Kepler observations of δ Scuti stars

All stars in the Kepler field brighter than 12.5 magnitude have been classified according to variability type. A catalogue of {\delta} Scuti and {\gamma} Doradus stars is presented. The problem of low frequencies in {\delta} Sct stars, which occurs in over 98 percent of these stars, is discussed. Gaia DR2 parallaxes were used to obtain precise luminosities, enabling the instability strips of the two classes of variable to be precisely defined. Surprisingly, it turns out that the instability region of the {\gamma} Dor stars is entirely within the {\delta} Sct instability strip. Thus {\gamma}Dor stars should not be considered a separate class of variable. The observed red and blue edges of the instability strip do not agree with recent model calculations. Stellar pulsation occurs in less than half of the stars in the instability region and arguments are presented to show that this cannot be explained by assuming pulsation at a level too low to be detected. Precise Gaia DR2 luminosities of high-amplitude {\delta} Sct stars (HADS) show that most of these are normal {\delta} Sct stars and not transition objects. It is argued that current ideas on A star envelopes need to be revised.

Numerous candidate hybrid stars of type δ Scuti–γ Doradus have been identified with the Kepler satellite. However, many of them lie outside the theoretically expected instability strip for hybrid pulsation, where δ Sct and γ Dor pulsations can be simultaneously excited. We postulate that some of these pulsating stars may not be genuine hybrid pulsators but rather magnetic δ Sct stars, for which the rotational modulation from spots on the surface associated with the magnetic field produces frequencies in the same domain as γ Dor pulsations. We search for the presence of a magnetic field in a small sample of selected hybrid δ Sct–γ Dor stars using spectropolarimetry. At the time of observations, the only δ Sct star known to have a magnetic field was HD 188774 with a field strength of a few hundred Gauss. Our observations were thus tailored to detect fields of this typical strength. We find no magnetic field in the hybrid candidate stars we observed. However, two of the three other magnetic δ Sct stars discovered since these observations have much weaker fields than HD 188774, and are of dynamo origin rather than fossil fields. It is likely that our observations are not sensitive enough to detect such dynamo magnetic fields in the cooler stars of our sample if they are present. This work nevertheless provides reliable upper limits on possible fossil fields in the hotter stars, pointing towards typically weaker fields in δ Sct stars than in OBA stars in general.

Observations of the pulsations of stars can be used to infer their interior structure and test theoretical models. The main sequence $\gamma$ Doradus (Dor) and $\delta$ Scuti (Sct) stars with masses 1.2-2.5 $M_{\sun}$ are particularly useful for these studies. The $\gamma$ Dor stars pulsate in high-order $g$ modes with periods of order 1 day, driven by convective blocking at the base of their envelope convection zone. The $\delta$ Sct stars pulsate in low-order $g$ and $p$ modes with periods of order 2 hours, driven by the $\kappa$ mechanism operating in the Heii ionization zone. Theory predicts an overlap region in the Hertzsprung-Russell diagram between instability regions, where 'hybrid' stars pulsating in both types of modes should exist. The two types of modes with properties governed by different portions of the stellar interior provide complementary model constraints. Among the known $\gamma$ Dor and $\delta$ Sct stars, only four have been confirmed as hybrids. Now, analysis of combined Quarter 0 and Quarter 1 Kepler data for hundreds of variable stars shows that the frequency spectra are so rich that there are practically no pure $\delta$ Sct or $\gamma$ Dor pulsators, i.e. essentially all of the stars show frequencies in both the $\delta$ Sct and $\gamma$ Dor frequency range. A new observational classification scheme is proposed that takes into account the amplitude as well as the frequency, and is applied to categorize 234 stars as $\delta$ Sct, $\gamma$ Dor, $\delta$ Sct/$\gamma$ Dor or $\gamma$ Dor/$\delta$ Sct hybrids.

A new perspective of pulsation in stars within the δ Scuti instability strip has recently emerged as a result of Kepler observations. The majority of stars within the instability strip do not pulsate and practically all δ Scuti stars contain low frequencies. Because γ Doradus stars co-exist with δ Sct stars in the same region of the instability strip, it follows that γ Dor stars are driven by the same mechanism as δ Sct stars. The difference must be due to different mode selection processes. The search for an unknown damping factor which is missing from the models will be essential for further progress. Maia variables and hot γ Dor stars are briefly discussed. Luminosities of roAp stars obtained from Gaia DR2 parallaxes and spectroscopic effective temperatures show that the roAp stars are slightly evolved with temperatures in the range 6300–8300 K, considerably cooler than predicted by the models. The roAp stars and stars with solar-like oscillations share the same mass - temperature - luminosity relation, but with frequencies which are about 50 percent higher. This suggests that roAp frequencies are determined by the critical acoustic frequency, but this frequency is larger than in standard models, perhaps as a result of a temperature inversion in the atmosphere.

We identify stars in the $\delta$ Sct instability strip that do not pulsate in p modes at the 50-$\mu$mag limit, using Kepler data. Spectral classification and abundance analyses from high-resolution spectroscopy allow us to identify chemically peculiar stars, in which the absence of pulsations is not surprising. The remaining stars are chemically normal, yet they are not $\delta$ Sct stars. Their lack of observed p modes cannot be explained through any known mechanism. However, they are mostly distributed around the edges of the $\delta$ Sct instability strip, which allows for the possibility that they actually lie outside the strip once the uncertainties are taken into account. We investigated the possibility that the non-pulsators inside the instability strip could be unresolved binary systems, having components that both lie outside the instability strip. If misinterpreted as single stars, we found that such binaries could generate temperature discrepancies of $\sim$300 K -- larger than the spectroscopic uncertainties, and fully consistent with the observations. After these considerations, there remains one chemically normal non-pulsator that lies in the middle of the instability strip. This star is a challenge to pulsation theory. However, its existence as the only known star of its kind indicates that such stars are rare. We conclude that the $\delta$ Sct instability strip is pure, unless pulsation is shut down by diffusion or another mechanism, which could be interaction with a binary companion.

The hot $\gamma$~Doradus stars have multiple low frequencies characteristic of $\gamma$~Dor or SPB variables, but are located between the red edge of the SPB and the blue edge of the $\gamma$~Dor instability strips where all low-frequency modes are stable in current models of these stars. Though $\delta$~Sct stars also have low frequencies, there is no sign of high frequencies in hot $\gamma$~Dor stars. We obtained spectra to refine the locations of some of these stars in the H-R diagram and conclude that these are, indeed, anomalous pulsating stars. The Maia variables have multiple high frequencies characteristic of $\beta$~Cep and $\delta$~Sct stars, but lie between the red edge of the $\beta$~Cep and the blue edge of the $\delta$~Sct instability strips. We compile a list of all Maia candidates and obtain spectra of two of these stars. Again, it seems likely that these are anomalous pulsating stars which are currently not understood.

We present LAMOST data on 168 γ Doradus (γ Dor) pulsating stars including stellar atmospheric parameters of 137 variables and spectral types for all of the samples. The distributions of period (P), temperature (T), gravitational acceleration (log(g)) and metallicity [Fe/H] are shown. It is found that most γ Dor variables are main-sequence stars with early F spectral types and temperatures from 6880 K to 7280 K. They are slightly more metal poor than the Sun with a metallicity range from −0.4 to 0. On the H-R and log g–T diagrams, both the γ Dor and δ Scuti (δ Sct) stars occupy in the same region and some are beyond the borders predicted by current stellar pulsation theories. It is discovered that the physical properties of γ Dor stars are similar to those of long-period δ Sct (P > 0.3 d) stars. The stellar atmospheric parameters are all correlated with the pulsation period for short-period δ Sct variables (P < 0.3 d), but there are no such relations for γ Dor or long-period δ Sct stars. These results reveal that γ Dor and long-period δ Sct are the same group of pulsating stars and they are different from short-period δ Sct variables. Meanwhile, 33 γ Dor stars are identified as candidates of binary or multiple systems.

Context. Pulsating extremely low-mass pre-white dwarf stars (pre-ELMV), with masses between ~0.15 M⊙ and ~0.30 M⊙, constitute a new class of variable stars showing g- and possibly p-mode pulsations with periods between 320 and 6000 s (frequencies between 14.4 and 270 c/d), driven by the κ mechanism operating in the second He ionization zone. On the other hand, main sequence δ Scuti stars, with masses between 1.2 and 2.5 M⊙, pulsate in low-order g and p modes with periods in the range [700–28 800] s (frequencies in the range [3–123] c/d), driven by the κ mechanism operating in the He II ionization zone and the turbulent pressure acting in the HI ionization layer. Interestingly enough, the instability strips of pre-ELM white dwarf and δ Scuti stars nearly overlap in the Teff vs. log g diagram, leading to a degeneracy when spectroscopy is the only tool to classify the stars and pulsation periods only are considered. Aims. Pre-ELM white dwarf and δ Scuti stars are in very different stages of evolution and therefore their internal structure is very distinct. This is mirrored in their pulsational behavior, thus employing asteroseismology should allow us to distinguish between these groups of stars despite their similar atmospheric parameters. Methods. We have employed adiabatic and non-adiabatic pulsation spectra for models of pre-ELM white dwarfs and δ Scuti stars, and compare their pulsation periods, period spacings, and rates of period change. Results. Unsurprisingly, we found substantial differences in the period spacing of δ Scuti and pre-ELM white dwarf models. Even when the same period range is observed in both classes of pulsating stars, the modes have distinctive signature in the period spacing and period difference values. For instance, the mean period difference of p-modes of consecutive radial orders for δ Scuti model are at least four times longer than the mean period spacing for the pre-ELM white dwarf model in the period range [2000–4600] s (frequency range [18.78–43.6] c/d). In addition, the rate of period change is two orders of magnitudes larger for the pre-ELM white dwarfs compared to δ Scuti stars. In addition, we also report the discovery of a new variable star, SDSSJ075738.94+144827.50, located in the region of the Teff versus log g diagram where these two kind of stars coexist. Conclusions.The characteristic spacing between modes of consecutive radial orders (p as well as g modes) and the large differences found in the rates of period change for δ Scuti and pre-ELM white dwarf stars suggest that asteroseismology can be employed to discriminate between these two groups of variable stars. Furthermore, we found that SDSSJ075738.94+144827.50 exhibits a period difference between p modes characteristic of a δ Sct star, assuming consecutive radial order for the observed periods.

The present observational status of the δ Sct stars, γ Dor stars and roAp stars is discussed. The δ Sct stars are the most intensively observed of the three groups, but it has become clear that there are severe problems in extracting asteroseismic information from them. Dozens of frequencies are observed, but hundreds of frequencies are predicted from the models; unique matches of observation and theory still elude us. The δ Sct stars are observationally complex — some recent ‘best case’ campaigns are discussed. It is possible that substantial observational advances for δ Sct stars may need to await upcoming satellite missions. New γ Dor stars are being discovered frequently, and new behaviour is being found for them. They constitute an observationally young field. Their pulsational frequency range is being expanded, their position in the HR diagram is becoming better known (but is yet to be fully constrained), and the possibility exists of hybrid γ Dor — δ Sct stars that have great asteroseismic promise, although it is clear such stars are rare, if they do exist. It has been observationally challenging to extract more than a few frequencies for any γ Dor star so far. Exciting spectroscopic discoveries of new behaviour in roAp stars promise unprecedented information about the structure of the peculiar atmospheres of those stars — pulsation amplitude and phase in 3D, magnetic field structure in 3D, abundance stratification in 3D, realistic T-τ for the most peculiar stars — as well as entirely new information about the interaction of pulsation, rotation and magnetic fields. Recent theoretical work has led to new understanding of the previously inexplicable frequency spacing of HR 1217 with new Whole Earth Telescope observations supporting this theory. An ‘improved oblique pulsator model’ has been developed in which the pulsation axis is not the magnetic axis; this model has passed several observational tests and new ones are being devised to examine it further.

The \(\delta \) Sct stars are by far the most common type of pulsating stars at spectral type A. In this, the most extensive review of \(\delta \) Sct stars in the Kepler era, the following topics are discussed: the \(\delta \) Sct instability strip; pulsation amplitudes and frequency ranges of the class; mode selection and identification; and the influence of rotation, evolution, and metallicity on pulsation. The \(\gamma \) Dor variables and the overlap of their instability strip with the \(\delta \) Sct instability strip are outlined, before a short description of especially interesting case-studies is presented, pointing to further reading.

The different research teams involved in the study of δ Sct stars have slightly changed their strategy in the past years. The observational effort to secure worldwide coverage of case studies has been continued, but the requirements have become more severe, especially about target characterization and frequency resolution.After the successful launch of the Canadian satellite MOST, which will be the pioneer of asteroseismology from space, the future missions are programmed to properly take into account the need for adequate frequency resolution: COROT will spent 30 and 150 d (additional and core programs, respectively) on the target, while EDDINGTON will spend up to 3yr. Such a requirement is a direct consequence of the observational results on δ Sct, γ Dor, SPB, and other stars obtained from ground. It should be noted that without these results (see Poretti 2000 for a review about δ Sct stars) the scientific background of the space missions would be much less defined and the risks of incomplete results (owing to inaccurate selection of targets, insufficient resolution, underestimate of the influence of the rotation) much higher.

The literature on Am stars is extensively reviewed, paying particular attention to abundance anomalies and the state of Am-star models in light of pulsations found in many of these objects. A new study into the non-\(\delta \) Sct A stars using Kepler data, and the spectroscopic classification of two thirds of them as chemically peculiar stars is also performed with complementary abundance analyses. Although there are chemically normal \(\gamma \) Dor stars in the \(\delta \) Sct instability strip without \(\delta \) Sct pulsation, the least variable stars (without \(\gamma \) Dor pulsation either) are chemically peculiar, and some strongly so. The \(\rho \) Pup stars of spectral type A/F are reviewed. For this group there is a consensus that they are the evolved Am stars. This chapter also reviews a class of B stars—it offers one of the few reviews of the ‘sn’ stars, whose spectra display both sharp and nebulous lines, and proposes a link between these and the Ap stars. Additionally, the two main theories for the origin of abundance anomalies in \(\lambda \) Boo stars are discussed and it is suggested that both of them imply the \(\lambda \) Boo stars contain a high fraction of pulsators—a suggestion that is backed up by observations in the literature.

The work reported here demonstrates that it is possible to accurately determine surface gravities of δ Scuti (δ Sct) stars using the frequency content from high-precision photometry and a measurement of the parallax. Using a sample of 10 eclipsing binary systems with a δ Sct component and the unique δ Sct star discovered with a transiting planet, WASP-33, we were able to refine the Δν–$\bar{\rho }$ relation. Using this relation and parallaxes, we obtained independent values for the masses and radii, allowing us to calculate the surface gravities without any constraints from spectroscopic or binary analysis. A remarkably good agreement was found between our results and those published, extracted from the analysis of the radial velocities and light curves of the systems. This reinforces the potential of Δν as a valuable observable for δ Sct stars and settles the degeneracy problem for the log g determination through spectroscopy.

Context.The multiscale entropy assesses the complexity of a signal across different timescales. It originates from the biomedical domain and was recently successfully used to characterize light curves as part of a supervised machine learning framework to classify stellar variability.Aims.We aim to explore the behavior of the multiscale entropy in detail by studying its algorithmic properties in a stellar variability context and by linking it with traditional astronomical time series analysis methods and metrics such as the Lomb-Scargle periodogram. We subsequently use the multiscale entropy as the basis for an interpretable clustering framework that can distinguish hybrid pulsators with bothp- and g-modes from stars with onlyp-mode pulsations, such asδScuti (δSct) stars, or from stars with onlyg-mode pulsations, such asγDoradus (γDor) stars.Methods.We calculate the multiscale entropy for a set ofKeplerlight curves and simulated sine waves. We link the multiscale entropy to the type of stellar variability and to the frequency content of a signal through a correlation analysis and a set of simulations. The dimensionality of the multiscale entropy is reduced to two dimensions and is subsequently used as input to the HDBSCAN density-based clustering algorithm in order to find the hybrid pulsators within sets ofδSct andγDor stars that were observed byKepler.Results.We find that the multiscale entropy is a powerful tool for capturing variability patterns in stellar light curves. The multiscale entropy provides insights into the pulsation structure of a star and reveals how short- and long-term variability interact with each other based on time-domain information only. We also show that the multiscale entropy is correlated to the frequency content of a stellar signal and in particular to the near-core rotation rates ofg-mode pulsators. We find that our new clustering framework can successfully identify the hybrid pulsators with bothp- andg-modes in sets ofδSct andγDor stars, respectively. The benefit of our clustering framework is that it is unsupervised. It therefore does not require previously labeled data and hence is not biased by previous knowledge.

The Kepler spacecraft is providing time series of photometric data with micromagnitude precision for hundreds of A-F type stars. We present a first general characterization of the pulsational behaviour of A-F type stars as observed in the Kepler light curves of a sample of 750 candidate A-F type stars. We propose three main groups to describe the observed variety in pulsating A-F type stars: gamma Dor, delta Sct, and hybrid stars. We assign 63% of our sample to one of the three groups, and identify the remaining part as rotationally modulated/active stars, binaries, stars of different spectral type, or stars that show no clear periodic variability. 23% of the stars (171 stars) are hybrid stars, which is a much larger fraction than what has been observed before. We characterize for the first time a large number of A-F type stars (475 stars) in terms of number of detected frequencies, frequency range, and typical pulsation amplitudes. The majority of hybrid stars show frequencies with all kinds of periodicities within the gamma Dor and delta Sct range, also between 5 and 10 c/d, which is a challenge for the current models. We find indications for the existence of delta Sct and gamma Dor stars beyond the edges of the current observational instability strips. The hybrid stars occupy the entire region within the delta Sct and gamma Dor instability strips, and beyond. Non-variable stars seem to exist within the instability strips. The location of gamma Dor and delta Sct classes in the (Teff,logg)-diagram has been extended. We investigate two newly constructed variables 'efficiency' and 'energy' as a means to explore the relation between gamma Dor and delta Sct stars. Our results suggest a revision of the current observational instability strips, and imply an investigation of other pulsation mechanisms to supplement the kappa mechanism and convective blocking effect to drive hybrid pulsations.