Massive and intermediate mass stars play a crucial role in astrophysics. Indeed, massive stars are the main producers of heavy elements, explode in supernovae at the end of their short lifetimes, and may be the progenitors of gamma ray bursts. Intermediate mass stars, although not destined to explode in supernovae, display similar phenomena, are much more numerous, and have some of the richest pulsation spectra. A key to understanding these stars is understanding the effects of rapid rotation on their structure and evolution. These effects include centrifugal deformation and gravity darkening which can be observed immediately, and long terms effects such as rotational mixing due to shear turbulence, which prolong stellar lifetime, modify chemical yields, and impact the stellar remnant at the end of their lifetime. In order to understand these effects, a number of models have been and are being developed over the past few years. These models lead to increasingly sophisticated predictions which need to be tested through observations. A particularly promising source of constraints is seismic observations as these may potentially lead to detailed information on their internal structure. However, before extracting such information, a number of theoretical and observational hurdles need to be overcome, not least of which is mode identification. The present proceedings describe recent progress in modelling these stars and show how an improved understanding of their pulsations, namely frequency patterns, mode visibilities, line profile variations, and mode excitation, may help with deciphering seismic observations.
We present a new analysis of the rapidly oscillating Ap (roAp) star, 2MASS J$19400781-4420093$ (J1940; $V=13.1$). The star was discovered using SuperWASP broadband photometry to have a frequency of 176.39 d$^{-1}$ (2041.55 $μ$Hz; $P = 8.2$ min; Holdsworth et al. 2014a) and is shown here to have a peak-to-peak amplitude of 34 mmag. J1940 has been observed during three seasons at the South African Astronomical Observatory, and has been the target of a Whole Earth Telescope campaign. The observations reveal that J1940 pulsates in a distorted quadrupole mode with unusual pulsational phase variatio…
One of the greatest challenges in interpreting the pulsations of rapidly rotating stars is mode identification, i.e. correctly matching theoretical modes to observed pulsation frequencies. Indeed, the latest observations as well as current theoretical results show the complexity of pulsation spectra in such stars, and the lack of easily recognisable patterns. In the present contribution, the latest results on non-adiabatic effects in such pulsations are described, and we show how these come into play when identifying modes. These calculations fully take into account the effects of rapid rotati…
Very high precision seismic space missions such as CoRoT and Kepler provide the means for testing the modelling of transport processes in stellar interiors. For some stars, such as $δ$ Scuti $γ$ Doradus and Be stars, for instance, the observed pulsation spectra are modified by rotation to such an extent that it prevents any fruitful interpretation. Our aim is to characterise acoustic pulsation spectra of realistic stellar models in order to be able to interpret asteroseismic data from such stars. The 2-dimensional oscillation code ACOR, which treats rotation in a non-perturbative manner, is us…
We present the first short time scale observations of the roAp star gamma Equ in linear polarized light obtained with the PEPSI polarimeter installed at the LBT. These observations are used to search for pulsation variability in Stokes Q and U line profiles belonging to different elements. The atmospheres of roAp stars are significantly stratified with spectral lines of different elements probing different atmospheric depths. roAp stars with strong magnetic fields, such as gamma Equ with a magnetic field modulus of 4kG and a pulsation period of 12.21min, are of special interest because the eff…
Large-scale variability in macroturbulence driven by pulsations in the rapidly rotating massive star Zeta Oph from high-cadence ESPRESSO spectroscopy and TESS photometry
This work explores a Pulsationally Driven Orbital Mass Ejection (PDOME) model for the launching of Classical Be star disks. Under this model, a combination of rapid rotation and non-radial pulsation modes contribute to placing material into the circumstellar environment. Several varieties of non-radial pulsation modes, characterized by their propagation direction and the relative phase of their velocity and density perturbations, are considered. As well, the orbital stability of material launched by such a mechanism is investigated.
Context. Gamma Doradus (hereafter $γ$~Dor) stars are gravity-mode pulsators whose periods carry information about the internal structure of the star. 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 previou…
We present the results of a multisite photometric observing campaign on the rapidly oscillating Ap (roAp) star 2MASS 16400299-0737293 (J1640; $V=12.7$). We analyse photometric $B$ data to show the star pulsates at a frequency of $151.93$ d$^{-1}$ ($1758.45 μ$Hz; $P=9.5$ min) with a peak-to-peak amplitude of 20.68 mmag, making it one of the highest amplitude roAp stars. No further pulsation modes are detected. The stellar rotation period is measured at $3.6747\pm0.0005$ d, and we show that rotational modulation due to spots is in anti-phase between broadband and $B$ observations. Analysis and m…
HD49330 is a Be star that underwent an outburst during its five-month observation with the CoRoT satellite. An analysis of its light curve revealed several independent p and g pulsation modes, in addition to showing that the amplitude of the modes is directly correlated with the outburst. We modelled the results obtained with CoRoT. We modelled the flattening of the structure of the star due to rapid rotation in two ways: Chandrasekhar-Milne's expansion and 2D structure computed with ROTORC. We then modelled kappa-driven pulsations. We also adapted the formalism of the excitation and amplitude…
Heartbeat stars are eccentric (e > 0.2) ellipsoidal variables whose light curves resemble a cardiogram. We present the observations and corresponding model of KIC 3749404, a highly eccentric (e = 0.66), short period (P = 20.3 d) heartbeat star with tidally induced pulsations. A binary star model was created using PHOEBE, which we modified to include tidally induced pulsations and Doppler boosting. The morphology of the photometric periastron variation (heartbeat) depends strongly on the eccentricity, inclination and argument of periastron. We show that the inclusion of tidally induced pulsatio…
We present an analysis of the first Kepler K2 mission observations of a rapidly oscillating Ap (roAp) star, HD 24355 ($V=9.65$). The star was discovered in SuperWASP broadband photometry with a frequency of 224.31 d$^{-1}$, (2596.18 $μ$Hz; $P = 6.4$ min) and an amplitude of 1.51 mmag, with later spectroscopic analysis of low-resolution spectra showing HD 24355 to be an A5 Vp SrEu star. The high precision K2 data allow us to identify 13 rotationally split sidelobes to the main pulsation frequency of HD 24355. This number of sidelobes combined with an unusual rotational phase variation show this…
Pulsations of rapidly rotating stars: I. The ACOR numerical code
非常高精度的地震空间任务，如CoRoT和开普勒提供了测试恒星内部传输过程建模的手段。对于某些恒星，例如类太阳恒星和红巨星，测量到旋转分裂。然而，为了充分利用这些分裂并约束旋转轮廓，需要能够准确地计算它们。对于其他一些恒星，例如$δ$ Scuti和Be星，观测到的脉动光谱被旋转改变到这样的程度，以至于对旋转效应的微扰处理不再有效。我们在这里提出了一个新的二维非微扰代码，称为ACOR（\textit{Adiabatic Code of Oscillation including Rotation}），它使我们能够计算绝热非径向脉动的旋转恒星，而不作任何假设的球形的恒星，流体性质（即斜压）或旋转配置文件。二维非微扰计算充分考虑了恒星的离心畸变，并包括科里奥利加速度的全部影响。数值方法的基础上的频谱方法的角度部分的模式，和四阶有限差分法的径向部分。我们测试和评估的准确性的计算进行比较，与那些来自TOP（\textit{Two-dimensional Oscillation Program}）相同的多方模型。我们通过避免交叉现象说明了快速旋转对恒星脉动的影响。与简单模型的TOP比较表明，该代码是稳定的，并且在近临界旋转速率下给出了准确的结果。
In this work, we report the discovery of the rapidly evolving high-amplitude $δ$ Scuti star KIC 6382916 (J19480292+4146558) which is crossing the Hertzsprung gap. According to the analysis of the archival data, we find three independent pulsation modes, whose amplitudes and frequencies vary distinctly in 4 years. The linear period variation rates of the first two modes are about 3-4 times larger than the best seismic model constructed by the standard evolution theory, while that of the third one is about 8 times larger than the first two modes. What is more interesting is that, almost all the …
We present an analysis of high time resolution spectra of the chemically peculiar Ap star HD 213637. The star shows rapid radial velocity variations with a period close to the photometric pulsation period. Radial velocity pulsation amplitudes vary significantly for different rare earth elements. The highest pulsation amplitudes belong to lines of TbIII ~360 m/s, PrII ~250 m/s and PrIII ~230 m/s . We did not detect any pulsations from spectral lines of EuII and in Halpha, in contrast to many other roAp stars. We also did not find radial velocity pulsations using spectral lines of other chemical…
The detection of pulsations in white dwarfs with low mass offers the possibility of probing their internal structure through asteroseismology and place constraints on the binary evolutionary processes involved in their formation. In this paper we assess the impact of stable H burning on the pulsational stability properties of low-mass He-core white dwarf models resulting from binary star evolutionary calculations. We found that, apart from a dense spectrum of unstable radial modes and nonradial $g$- and $p$-modes driven by the $κ$-mechanism due to the partial ionization of H in the stellar env…
Apart from recent progress in Gamma Dor stars, identifying modes in rapidly rotating stars is a formidable challenge due to the lack of simple, easily identifiable frequency patterns. As a result, it is necessary to look to observational methods for identifying modes. Two popular techniques are spectroscopic mode identification based on line profile variations (LPVs) and photometric mode identification based on amplitude ratios and phase differences between multiple photometric bands. In this respect, the BRITE constellation is particularly interesting as it provides space-based multi-colour p…
We present the analysis of K2 short cadence data of the rapidly oscillating Ap (roAp) star, 33 Librae (HD 137949). The precision afforded to the K2 data allow us to identify at least 11 pulsation modes in this star, compared to the three previously reported. Reoccurring separations between these modes leads us to suggest a large frequency separation, $Δν$, of 78.9 $μ$Hz, twice that reported in the literature. Other frequency separations we detect may represent the small frequency separation, $δν$, but this is inconclusive at this stage due to magnetic perturbation of the frequencies. Due to th…
KIC 10685175 (TIC 264509538) was discovered to be a rapidly oscillating Ap star from {\it Kepler} long cadence data using super-Nyquist frequency analysis. It was re-observed by TESS with 2-min cadence data in Sectors 14 and 15. We analyzed the TESS light curves, finding that the previously determined frequency is a Nyquist alias. The revised pulsation frequency is $191.5151 \pm 0.0005$d$^{-1}$ ($P = 7.52$min) and the rotation frequency is $0.32229 \pm 0.00005$d$^{-1}$ ($P_{\rm rot} = 3.1028$d). The star is an oblique pulsator with pulsation amplitude modulated by the rotation, reaching pulsat…
Is a 1D perturbative method sufficient for asteroseismic modelling of $β$ Cephei pulsators? Implications for measurements of rotation and internal magnetic fields
We perform a search for rapidly oscillating Ap stars in the Kepler long-cadence data, where true oscillations above the Nyquist limit of 283.21 μHz can be reliably distinguished from aliases as a consequence of the barycentric time corrections applied to the Kepler data. We find evidence for rapid oscillations in six stars: KIC 6631188, KIC 7018170, KIC 10685175, KIC 11031749, KIC 11296437 and KIC 11409673, and identify each star as chemically peculiar through either pre-existing classifications or spectroscopic measurements. For each star, we identify the principal pulsation mode, and are abl…
计算了二维旋转10 Mo ZAMS恒星模型的均匀旋转和一种特殊形式的微分旋转产生的模式分裂。的模式分裂的字符的变化被跟踪作为一个函数的均匀的旋转速率，它被发现，只有相对较慢的旋转速率之前，模式分裂变得不对称的方位角对称（m=0）模式。增加的旋转产生各个模式相对于彼此的逐渐改变的模式。在相对低的旋转速率下，大的模式分裂开始与由不同的径向和纬向模式产生的模式分裂重叠。模式分裂模式的差分旋转的恒星，我们的模型是不同的均匀旋转的恒星，使模式分裂的内部角动量分布的一个可能的判别式，如果一个假设的模式识别的艰巨挑战可以克服。
We collected a sample of ten hitherto unidentified SPB stars with the aim of describing their pulsational properties and identifying pulsational modes. Photometric time series data from various surveys were collected and analyzed using diverse frequency search algorithms. We calculated astrophysical parameters and investigated the location of our sample stars in the \logTeff\ versus \logl\ diagram. Current pulsational models were calculated and used for the identification of pulsational modes in our sample stars. An extensive grid of stellar models along with their g-mode eigenfrequencies was …
Low- and intermediate-mass stars eject much of their mass during the late, red giant branch (RGB) phase of evolution. The physics of their strong stellar winds is still poorly understood. In the standard model, stellar pulsations extend the atmosphere, allowing a wind to be driven through radiation pressure on condensing dust particles. Here we investigate the onset of the wind, using nearby RGB stars drawn from the Hipparcos catalogue. We find a sharp onset of dust production when the star first reaches a pulsation period of 60 days. This approximately co-incides with the point where the star…
Asteroseismology is a powerful tool for probing the internal structures of stars by using their natural pulsation frequencies. It relies on identifying sequences of pulsation modes that can be compared with theoretical models, which has been done successfully for many classes of pulsators, including low-mass solar-type stars, red giants, high-mass stars and white dwarfs. However, a large group of pulsating stars of intermediate mass--the so-called delta Scuti stars--have rich pulsation spectra for which systematic mode identification has not hitherto been possible. This arises because only a s…
After an optical peak, a classical or recurrent nova settles into a brief (days to years) period of quasi-stable thermonuclear burning in a compact configuration nearly at the white dwarf (WD) radius. During this time, the underlying WD becomes visible as a strong emitter of supersoft X-rays. Observations during this phase have revealed oscillations in the X-ray emission with periods on the order of tens of seconds. A proposed explanation for the source of these oscillations are internal gravity waves excited by nuclear reactions at the base of the hydrogen-burning layer. In this work, we pres…
Recent numerical and theoretical considerations have shown that low-degree acoustic modes in rapidly rotating stars follow an asymptotic formula and recent observations of pulsations in rapidly rotating delta Scuti stars seem to match these expectations. However, a key question is whether strong gradients or discontinuities can adversely affect this 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 t…
The stellar parameters of RR Lyrae stars vary considerably over a pulsation cycle, and their determination is crucial for stellar modelling. We present a detailed spectroscopic analysis of the pulsating star RR Lyr, the prototype of its class, over a complete pulsation cycle, based on high-resolution spectra collected at the 2.7-m telescope of McDonald Observatory. We used simultaneous photometry to determine the accurate pulsation phase of each spectrum and determined the effective temperature, the shape of the depth-dependent microturbulent velocity, and the abundance of several elements, fo…
Non-radial pulsations have been identified in a number of accreting white dwarfs in cataclysmic variables. These stars offer insight into the excitation of pulsation modes in atmospheres with mixed compositions of hydrogen, helium, and metals, and the response of these modes to changes in the white dwarf temperature. Among all pulsating cataclysmic variable white dwarfs, GW Librae stands out by having a well-established observational record of three independent pulsation modes that disappeared when the white dwarf temperature rose dramatically following its 2007 accretion outburst. Our analysi…
