We report the discovery of 31 blue, short period, pulsators made using data taken as part of the Rapid Temporal Survey (RATS). We find they have periods between 51-83 mins and full-amplitudes between 0.05-0.65 mag. Using the period-luminosity relationship for short period pulsating stars we determine their distance. Assuming they are pulsating in either the fundamental or first over-tone radial mode the majority are located at a distance greater than 3kpc, with several being more than 20 kpc distant. Most stars are at least 1 kpc from the Galactic plane, with three being more than 10 kpc. One is located in the direction of the Galactic anti-center and has Galactocentric distance of ~30 kpc and is ~20 kpc below the plane: they are therefore potential tracers of Galactic structure. We have obtained low-resolution spectra for a small number our targets and find they have temperatures between 7200--7900K and a metal content less than Solar. The colours of the pulsators and the spectral fits to those stars for which we have spectra indicate that they are either SX Phe or delta Scuti stars. We estimate the number of SX Phe stars in our Galaxy and find significantly fewer per unit mass than reported in massive globular clusters or dwarf spheroidal galaxies.
We present results from the first two quarters of a survey to search for pulsations in compact stellar objects with the Kepler spacecraft. The survey sample and the various methods applied in its compilation are described, and spectroscopic observations are presented to separate the objects into accurate classes. From the Kepler photometry we clearly identify nine compact pulsators, and a number of interesting binary stars. Of the pulsators, one shows the strong, rapid pulsations typical for a V361 Hya type sdB variable (sdBV), seven show long-period pulsations characteristic of V1093 Her type…
We present the discovery of nonradial pulsations in five hot subdwarf B (sdB) stars based on 27 days of nearly continuous time-series photometry using the Kepler spacecraft. We find that every sdB star cooler than $\approx 27\,500\,$K that Kepler has observed (seven so far) is a long-period pulsator of the V1093~Her (PG~1716) class or a hybrid star with both short and long periods. The apparently non-binary long-period and hybrid pulsators are described here. The V1093~Her periods range from one to 4.5~h and are associated with $g-$mode pulsations. Three stars also exhibit short periods indica…
We aimed at collecting all known white dwarf pulsators with hydrogen-dominated atmospheres and list their main photometric and atmospheric parameters together with their pulsation periods and amplitudes observed at different epochs. For this purpose, we explored the pulsating white dwarf related literature with the systematic use of the SIMBAD and the NASA's Astrophysics Data System (ADS) databases. We summarized our results in four tables listing seven ZZ Ceti stars in detached white dwarf plus main-sequence binaries, seven extremely low-mass DA pulsators, three hot DAVs and 180 ZZ Ceti stars…
We present the goals, strategy and first results of the high-cadence Galactic plane survey using the Zwicky Transient Facility (ZTF). The goal of the survey is to unveil the Galactic population of short-period variable stars, including short period binaries and stellar pulsators with periods less than a few hours. Between June 2018 and January 2019, we observed 64 ZTF fields resulting in 2990 deg$^2$ of high stellar density in ZTF-$r$ band along the Galactic Plane. Each field was observed continuously for 1.5 to 6 hrs with a cadence of 40 sec. Most fields have between 200 and 400 observations …
We present the recent discovery of a new subdwarf B variable (sdBV), with an exceptionally low surface gravity. Our spectroscopy of J20136+0928 places it at Teff = 32100 +/- 500, log(g) = 5.15 +/- 0.10, and log(He/H) = -2.8 +/- 0.1. With a magnitude of B = 12.0, it is the second brightest V361 Hya star ever found. Photometry from three different observatories reveals a temporal spectrum with eleven clearly detected periods in the range 376 to 566 s, and at least five more close to our detection limit. These periods are unusually long for the V361 Hya class of short-period sdBV pulsators, but n…
Blue Large Amplitude Pulsators (BLAPs) are hot, subluminous stars undergoing rapid variability with periods of under 60 mins. They have been linked with the early stages of pre-white dwarfs and hot subdwarfs. They are a rare class of variable star due to their evolutionary history within interacting binary systems and the short timescales relative to their lifetime in which they are pulsationally unstable. All currently known BLAPs are relatively faint (15-19 mag) and are located in the Galactic plane. These stars have intrinsically blue colours but the large interstellar extinction in the Gal…
We present five new pulsating subdwarf B (sdB) stars discovered by the Kepler spacecraft during the asteroseismology survey phase. We perform time-series analysis on the nearly continuous month-long Kepler datasets of these 5 objects; these datasets provide nearly alias-free time-series photometry at unprecedented precision. Following an iterative prewhitening process we derive the pulsational frequency spectra of these stars, separating out artefacts of known instrumental origin. We find that these new pulsating sdB stars are multiperiodic long-period pulsators of the V1093 Her type, with the…
Under the Nainital-Cape Survey, eight $δ\,$Scuti type pulsators have been discovered with the pulsation periods in the range of several minutes to few hours. In order to understand these observed pulsational variabilities, we have performed non-adiabatic linear stability analyses in models of these stars having mass in the range of 1 to 3 M$_{\odot}$. Several low order p-modes are found to be unstable where the pulsation periods associated with these unstable modes are in good agreement with the observed periods. Particularly for HD$\,$118660, HD$\,$113878, HD$\,$102480, HD$\,$98851, and HD$\,…
The survey phase of the Kepler Mission includes a number of hot subdwarf B (sdB) stars to search for nonradial pulsations. We present our analysis of two sdB stars that are found to be g-mode pulsators of the V1093 Her class. These two stars also display the distinct irradiation effect typical of sdB stars with a close M-dwarf companion with orbital periods of less than half a day. Because the orbital period is so short, the stars should be in synchronous rotation, and if so, the rotation period should imprint itself on the multiplet structure of the pulsations. However, we do not find clear e…
We present the discovery of nonradial pulsations in a hot subdwarf B star based on 30.5 days of nearly continuous time-series photometry using the \emph{Kepler} spacecraft. KIC 010139564 is found to be a short-period pulsator of the V361 Hya (EC 14026) class with more than 10 independent pulsation modes whose periods range from 130 to 190 seconds. It also shows one periodicity at a period of 3165 seconds. If this periodicity is a high order g-mode, then this star may be the hottest member of the hybrid DW Lyn stars. In addition to the resolved pulsation frequencies, additional periodic variati…
We report the discovery of a new short period pulsating variable in the field of exoplanet host star XO-2. Variable has been identified while it was being used as a comparison star. In order to verify the variability of the candidate, a follow-up program was carried out. Period analysis of multi-band light curves revealed a very prominent and consistent pulsation periodicity of $P\sim0.95$ hours. Given the variability period, amplitude and the color index, the object is most likely a \emph{Delta Scuti} type variable. Absolute magnitude ($M_{v}$) and the color index $(B-V)_{0}$ of the star dete…
The short-period (P $\approx1.7$ d), Algol-type eclipsing binary KIC 7385478 consists of an F-type primary star ($M_1 \approx 1.71M_{\odot}$) and an evolved K-type secondary ($M_2 \approx 0.37M_{\odot}$) (Ozdarcan \& Ali Dal 2017). We study the variability of the {\it Kepler} light curve and attribute many frequency peaks in the Fourier spectrum to the spot modulation. These frequencies are in the form of orbital harmonics and are highly variable in amplitude. They are most likely from the mass-accreting primary star. In addition, we identify a series prograde dipole g-modes from the primary s…
In $γ$ Doradus stars, the g-mode period spacing shows an approximately linear relation with period. The slope is a new asteroseismic diagnostic, related to the rotation rate and the azimuthal order $m$. We report two automated methods, the `moving-window Fourier transform' and the `cross-correlation', to detect and measure the period spacings based on four-year light curves from the \textit{Kepler} satellite. The results show that the cross-correlation method performs better at detecting the period spacings and their slopes. In this paper, we apply our method to 22 $γ$ Dor stars with g-mode mu…
In this paper, we present TESS photometry and high-resolution spectra of the short-period Algol EW Boo. We obtained double-lined radial velocities (RVs) from the time-series spectra and measured the effective temperature of the primary star as $T_{\rm{eff,1}}$ = 8560 $\pm$ 118 K. For the orbital period study, we collected all times of minima available for over the last 30 years. It was found that the eclipse timing variation of the system could be represented by a periodic oscillation of 17.6 $\pm$ 0.3 years with a semi-amplitude of 0.0041 $\pm$ 0.0001 d. The orbital and physical parameters we…
Period-luminosity (PL) sequences of long period variables (LPVs) are commonly interpreted as different pulsation modes, but there is disagreement on the modal assignment. Here, we re-examine the observed PL sequences in the Large Magellanic Cloud, including the sequence of long secondary periods (LSPs), and their associated pulsation modes. Firstly, we theoretically model the sequences using linear, radial, non-adiabatic pulsation models and a population synthesis model of the LMC red giants. Then, we use a semi-empirical approach to assign modes to the pulsation sequences by exploiting observ…
We present an upgrade of the OGLE Collection of RR Lyrae stars in the Galactic bulge and disk. The size of our sample has been doubled and reached 78 350 RR Lyr variables, of which 56 508 are fundamental-mode pulsators (RRab stars), 21 321 pulsate solely in the first-overtone (RRc stars), 458 are classical double-mode pulsators (RRd stars), and 63 are anomalous RRd variables (including five triple-mode pulsators). For all the newly identified RR Lyr stars, we publish time-series photometry obtained during the OGLE Galaxy Variability Survey. We present the spatial distribution of RR Lyr stars o…
Blue Large-Amplitude Pulsators (BLAPs) are a new class of pulsating variable star. They are located close to the hot subdwarf branch in the Hertzsprung-Russell diagram and have spectral classes of late O or early B. Stellar evolution models indicate that these stars are likely radially pulsating, driven by iron group opacity in their interiors. A number of variable stars with a similar driving mechanism exist near the hot subdwarf branch with multi-periodic oscillations caused by either pressure (p) or gravity (g) modes. No multi-periodic signals were detected in the OGLE discovery light curve…
Based on 2-minute cadence TESS data from sectors 1-50, we report the results of the systematic extraction of $δ$ Scuti-type pulsations in the 6431 eclipsing binaries with orbital periods shorter than 13 days. A total number of 242 pulsators were found in those systems, including 143 new discoveries. We examined their pulsation properties based on the H-R diagram and the relationships between the dominant pulsation period $P_{\rm dom}$, orbital period $P_{\rm orb}$, and effective temperature $T_{\rm eff}$. As a consequence, 216 targets are likely $δ$ Scuti stars (123 new), 11 likely $γ$ Doradus…
Rossby modes are the oscillations in a rotating fluid, whose restoring force is the Coriolis force. They provide an additional diagnostic to understand the rotation of stars, which complicates asteroseismic modelling. We report 82 $γ$\,Doradus stars for which clear period spacing patterns of both gravity and Rossby modes have been detected. The period spacings of both show a quasi-linear relation with the pulsation period but the slope is negative for the gravity modes and positive for the Rossby modes. Most Rossby modes have $k=-2, m=-1$. For only one star a series of $k=-1,m=-1$ modes is see…
B-type stars are promising targets for asteroseismic modelling, since their frequency spectrum is relatively simple. We deduce and summarise observational constraints for the hybrid pulsator, HD50230, earlier reported to have deviations from a uniform period spacing of its gravity modes. The combination of spectra and a high-quality light curve measured by the CoRoT satellite allow a combined approach to fix the position of HD50230 in the HR diagram. To describe the observed pulsations, classical Fourier analysis was combined with short-time Fourier transformations and frequency spacing analys…
The Blue Large-Amplitude Pulsators (BLAPs) constitute a new class of pulsating stars. They are hot stars with effective temperatures of $T_{\rm eff}\sim 30\,000$ K and surface gravities of $\log g \sim 4.9$, that pulsate with periods in the range $\sim 20-40$ min. In Romero et al. (2018), we proposed that BLAPs are hot low-mass He-core pre-white dwarf (WD) stars that pulsate either in high-order non-radial $g$(gravity) modes or low-order radial modes, including the fundamental radial mode. The theoretical modes with periods in the observed range are unstable due to the $κ$ mechanism associated…
Following the discovery of blue large-amplitude pulsators (BLAPs), single star evolu- tion models of post red giant branch stars that have undergone a common envelope (CE) ejection in the form of a high mass loss rate have been constructed and analysed for pulsation stability. The effects of atomic diffusion, particularly radiative levitation, have been examined. Two principal models were considered, being post-CE stars of 0.31 and 0.46 M$_{\odot}$. Such stars are likely, in turn, to become either low-mass helium white dwarfs or core helium-burning extreme horizontal-branch stars. The inclusio…
Pulsating subdwarf B (sdB) stars oscillate in short-period p-modes or long-period g-modes. HS0702+6043 (DW Lyn) is one of a few objects to show characteristics of both types and is hence classified as hybrid pulsator. It is one of our targets in the EXOTIME program to search for planetary companions around extreme horizontal branch objects. In addition to the standard exercise in asteroseismology to probe the instantaneous inner structure of a star, measured changes in the pulsation frequencies as derived from an O-C diagram can be compared to theoretical evolutionary timescales. Based on the …
Characterizing bright $δ$ Scuti pulsators using TESS lightcurves
Sydney Institute for Astronomy, School of Physics, University of Sydney（悉尼大学物理学院天体物理研究所）；Centre for Astrophysics, University of Southern Queensland（南昆士兰大学天体物理学中心）；Institute for Astronomy, University of Hawaii（夏威夷大学天体物理研究所）
We present a spectroscopic and photometric analysis of the multiple system and early-type eclipsing binary SZ Cam (O9IV + B0.5V), which consists of an eclipsing SB2 pair of orbital period P=2.7 days in a long orbit (about 55 yrs) around a non-eclipsing SB1 pair of orbital period P=2.8 days. We have reconstructed the spectra of the individual components of SZ Cam from the observed composite spectra using the technique of spectral disentangling. We used them together with extensive and accurate BVI CCD photometry to obtain an orbital solution. Our photometry revealed the presence of a beta Cep v…
We present the discovery of a unique object, a chemically peculiar Ap-type star showing $δ$ Scuti pulsations which is bound in an eclipsing binary system with an orbital period shorter than 3 days. HD 99458 is, therefore, a complex astrophysical laboratory opening doors for studying various, often contradictory, physical phenomena at the same time. It is the first Ap star ever discovered in an eclipsing binary. The orbital period of 2.722 days is the second shortest among all known chemically peculiar (CP2) binary stars. Pulsations of $δ$ Scuti type are also extremely rare among CP2 stars and …
The quantity and quality of satellite photometric data strings is revealing details in Cepheid variation at very low levels. Specifically, we observed a Cepheid pulsating in the fundamental mode and one pulsating in the first overtone with the Canadian MOST satellite. The 3.7-d period fundamental mode pulsator (RT Aur) has a light curve that repeats precisely, and can be modeled by a Fourier series very accurately. The overtone pulsator (SZ Tau, 3.1 d period) on the other hand shows light curve variation from cycle to cycle which we characterize by the variations in the Fourier parameters. We …
A noticeable fraction of subdwarf B stars shows either short-period (p-mode) or long-period (g-mode) luminosity variations, with two objects so far known to exhibit hybrid behaviour, i.e. showing both types of modes at the same time. The pulsating subdwarf B star V391 Pegasi (or HS2201+2610), which is close to the two known hybrid pulsators in the log g - Teff plane, has recently been discovered to host a planetary companion. In order to learn more about the planetary companion and its possible influence on the evolution of its host star (subdwarf B star formation is still not well understood)…
The Blue Large-Amplitude Pulsators (BLAPs) constitute a new class of pulsating stars. They are hot stars with effective temperatures of ~30 000 K and surface gravities of log g ~ 4.9, that pulsate with periods in the range 20-40 min. Until now, their origin and evolutionary state, as well as the nature of their pulsations, were not been unveiled. In this paper, we propose that the BLAPs are the hot counterpart of the already known pulsating pre-Extremely Low Mass (pre-ELM) white dwarf (WD) stars, that are He-core low-mass stars resulting from interacting binary evolution. Using fully evolution…
Spectroscopic follow-up of hot subdwarf variables found in ZTF -- Atmospheric and fundamental properties of radial-mode sdB pulsators
Hamburger Sternwarte, University of Hamburg（汉堡天文台，汉堡大学）；Department of Physics and Astronomy, Texas Tech University（德克萨斯理工大学物理与天文学系）；Department of Physics and Astronomy, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校物理与天文学系）；Institut für Physik und Astronomie, Universität Potsdam（波茨坦大学物理与天文学研究所）
We present the properties of the recently discovered class of variable stars, Blue Large-Amplitude Pulsators (BLAPs). These extremely rare, short-period pulsating objects were detected thanks to regular, high-cadence observations of hundreds of millions of Milky Way stars by the OGLE variability survey. The new variables closely resemble classical pulsators, Cepheids, and RR Lyrae-type stars, but at effective temperatures at which pulsations are due to the presence of iron-group elements. Theory shows that BLAPs are evolved low-mass stars with a giant-like structure, but their origin remains a…
Pulsating stars in eclipsing binary systems are powerful tools to test stellar models. Binarity enables to constrain the pulsating component physical parameters, whose knowledge drastically improves the input physics for asteroseismic studies. The study of stellar oscillations allows us, in its turn, to improve our understanding of stellar interiors and evolution. The space mission CoRoT discovered several promising objects suitable for these studies, which have been photometrically observed with unprecedented accuracy, but needed spectroscopic follow-up. A promising target was the relatively …
We investigate the possibility of nearly-equally spaced periods in 13 hot subdwarf B (sdB) stars observed with the Kepler spacecraft and one observed with CoRoT. Asymptotic limits for gravity (g-)mode pulsations provide relationships between equal period spacings of modes with differing degrees and relationships between periods of the same radial order but differing degrees. Period transforms, Kolmogorov-Smirnov tests, and linear least-squares fits have been used to detect and determine the significance of equal period spacings. We have also used Monte Carlo simulations to estimate the likelih…
We carried out a multi-colour time-series photometric study of six stars claimed as "hybrid" p and g mode pulsators in the literature. Gamma Peg was confirmed to show short-period oscillations of the Beta Cep type and simultaneous long-period pulsations typical of Slowly Pulsating B (SPB) stars. From the measured amplitude ratios in the Stromgren uvy passbands, the stronger of the two short period pulsation modes was identified as radial; the second is l=1. Three of the four SPB-type modes are most likely l=1 or 2. Comparison with theoretical model calculations suggests that Gamma Peg is eithe…
Regular intrinsic brightness variations observed in many stars are caused by pulsations. These pulsations provide information on the global and structural parameters of the star. The pulsation periods range from seconds to years, depending on the compactness of the star and properties of the matter that forms its outer layers. Here, we report the discovery of more than a dozen of previously unknown short-period variable stars: blue large-amplitude pulsators. These objects show very regular brightness variations with periods in the range of 20-40 min and amplitudes of 0.2-0.4 mag in the optical…
We report the discovery of pulsations in the spectroscopic PG 1159 type pre-white dwarf SDSS J075415.12+085232.18. Analysis of the spectrum by Werner, Rauch and Kepler (2014) indicated Teff=120 000+/-10 000 K, log g=7.0+/-0.3, mass M=0.52+/-0.02 Msun, C/He=0.33 by number. We obtained time-series images with the SOAR 4.1 m telescope and 2.1 m Otto Struve telescope at McDonald Observatory and show the star is also a variable PG 1159 type star, with dominant period of 525 s.
Blue large-amplitude pulsators (BLAPs) are a newly discovered type of variable star. Their typical pulsation periods are on the order of a few tens of minutes, with relatively large amplitudes of 0.2-0.4 mag in optical bands, and their rates of period changes are on the order of $10^{-7} yr^{-1}$ (both positive and negative). They are extremely rare objects and attempts to explain their origins and internal structures have attracted a great deal of attention. Previous studies have proposed that BLAPs may be pre-white dwarfs, with masses around $0.3M_\odot$, or core-helium-burning stars in the …
Context. gamma Doradus (gamma Dor) are late A and F-type stars pulsating with high order gravity modes (g-modes). The existence of different evolutionary phases crossing the gamma Dor instability strip raises the question of the existence of pre-main sequence (PMS) gamma Dor stars. Aims. We intend to study the differences between the asteroseismic behaviour of PMS and main sequence (MS) gamma Dor pulsators as it is predicted by the current theory of stellar evolution and stability. Methods. We explore the adiabatic and non-adiabatic properties of high order g-modes in a grid of PMS and MS mode…
We discuss and characterise the power spectral density properties of a model aimed at describing pulsations in stars from the main-sequence to the asymptotic giant branch. We show that the predicted limit of the power spectral density for a pulsation mode in the presence of stochastic noise is always well approximated by a Lorentzian function. While in stars predominantly stochastically driven the width of the Lorentzian is defined by the mode lifetime, in stars where the driving is predominately coherent the width is defined by the amplitude of the stochastic perturbations. In stars where bot…
We study the fraction of stars in and around the δ Scuti instability strip that are pulsating, using {\em Gaia} DR2 parallaxes to derive precise luminosities. We classify a sample of over 15,000 {\em Kepler} A and F stars into δ Sct and non-δ Sct stars, paying close attention to variability that could have other origins. We find that 18 per cent of the δ Sct stars have their dominant frequency above the Kepler long-cadence Nyquist frequency (periods < 1 hr), and 30 per cent have some super-Nyquist variability. We analyse the pulsator fraction as a function of effective temperature and luminosi…
Pulsating binary stars are ideal targets for testing the theory of stellar structure and evolution. Fundamental parameters can be derived to high precision from binary modelling and provide crucial constraints for seismic modelling. High-order gravity modes are sensitive to the conditions near the convective core and therefore allow for a determination of parameters describing interior physics, especially the convective-core overshooting parameter. KIC\,10080943 is a binary system that contains two gravity- and pressure-mode hybrid pulsators. A detailed observational study has provided fundame…
Context: Several hundred candidate hybrid pulsators of type A-F have been identified from space-based observations. Their large number allows both statistical analyses and detailed investigations of individual stars. This offers the opportunity to study the full interior of the genuine hybrids, in which both low-radial-order p- and high-order g-modes are self-excited at the same time. However, a few other physical processes can also be responsible for the observed hybrid nature, related to binarity or to surface inhomogeneities. The finding that most delta Scuti stars also show long-period lig…
Blue Large Amplitude Pulsators (BLAPs) are a relatively new class of blue variable stars showing periodic variations in their light curves with periods shorter than a few tens of mins and amplitudes of more than ten percent. We report nine blue variable stars identified in the OmegaWhite survey conducted using ESO's VST, which show a periodic modulation in the range 7-37 min and an amplitude in the range 0.11-0.28 mag. We have obtained a series of followup photometric and spectroscopic observations made primarily using SALT and telescopes at SAAO. We find four stars which we identify as BLAPs,…
Following the recent discovery of a new class of pulsating star, the blue large-amplitude pulsators (BLAPs), pulsation stability analysis was carried out on evolutionary models of post-common envelope (CE) ejection stars of 0.3 and 0.46 solar masses. These models subsequently evolve to become a low-mass helium white dwarf and a core helium-burning extreme horizontal-branch star respectively. We investigate the effects of atomic diffusion, particularly radiative levitation, on the pulsation behaviour of the models. We find that when the models have effective temperatures comparable to those of …
The All Sky Automated Survey (ASAS) data, covering nearly 70% of the whole sky south of declination +28 deg, were recently used to discover about 300 Beta Cephei stars brighter than V~11.5 mag. As this means a nearly fourfold increase in the number of known stars of this type, new possibilities in studying these pulsators open up, including statistical work. The homogeneity of the ASAS survey allows us to study their distribution in the local Galaxy. We discuss this distribution in the context of the location of nearby spiral arms. In addition, we show pulsational (periods, amplitudes) propert…
We report the discovery of a post-mass transfer Gamma Doradus/Delta Scuti hybrid pulsator in the eclipsing binary KIC~9592855. This binary has a circular orbit, an orbital period of 1.2 days, and contains two stars of almost identical masses ($M_1=1.72M_{\odot}, M_2=1.71M_{\odot}$). However, the cooler secondary star is more evolved ($R_2=1.96R_{\odot}$) while the hotter primary is still on the zero-age-main-sequence ($R_1=1.53R_{\odot}$). Coeval models from single star evolution cannot explain the observed masses and radii, and binary evolution with mass-transfer needs to be invoked. After su…
Period-colour and amplitude-colour (PCAC) relations can be used to probe both the hydrodynamics of outer envelope structure and evolutionary status of Cepheids and RR Lyraes. In this work, we incorporate the PCAC relations for RR Lyraes, BL Her, W Vir and classical Cepheids in a single unifying theory that involves the interaction of the hydrogen ionization front (HIF) and stellar photosphere and the theory of stellar evolution. PC relations for RR Lyraes and classical Cepheids using OGLE-IV data are found to be consistent with this theory: RR Lyraes have shallow/sloped relations at minimum/ma…
KIC 10553698A is a hot pulsating subdwarf B (sdB) star observed by the Kepler satellite. It exhibits dipole (l = 1) and quadrupole (l = 2) gravity modes with a clear period spacing structure. The seismic properties of the KIC 10553698A provide a test of stellar evolution models, and offer a unique opportunity to determine mixing processes. We consider mixing due to convective overshooting beyond the boundary of the helium burning core. Very small overshooting ( f = 10^{-6} ) results in a progressive increase in the size of convective core. However, moderate ( f = 10^{-2} ) and small ( f = 10^{…
