We present the discovery of non-radial pulsations in five hot subdwarf B (sdB) stars based on 27 d of nearly continuous time series photometry using the Kepler spacecraft. We find that every sdB star ...cooler than ≈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 1 to 4.5 h and are associated with g-mode pulsations. Three stars also exhibit short periods indicative of p-modes with periods of 2–5 min and in addition, these stars exhibit periodicities between both classes from 15 to 45 min. We detect the coolest and longest-period V1093 Her-type pulsator to date, KIC010670103 (Teff≈ 20 900 K, Pmax≈ 4.5 h) as well as a suspected hybrid pulsator, KIC002697388, which is extremely cool (Teff≈ 23 900 K) and for the first time hybrid pulsators which have larger g-mode amplitudes than p-mode ones. All of these pulsators are quite rich with many frequencies and we are able to apply asymptotic relationships to associate periodicities with modes for KIC010670103. Kepler data are particularly well suited for these studies as they are long duration, extremely high duty cycle observations with well-behaved noise properties.
2M1938+4603 (KIC 9472174) displays a spectacular light curve dominated by a strong reflection effect and rather shallow, grazing eclipses. The orbital period is 0.126 d, the second longest period yet ...found for an eclipsing sdB+dM, but still close to the minimum 0.1-d period among such systems. The phase-folded Kepler light curve was used to detrend the orbital effects from the data set. The amplitude spectrum of the residual light curve reveals a rich collection of pulsation peaks spanning frequencies from ∼50 to 4500 μHz. The presence of a complex pulsation spectrum in both the p- and g-mode regions has never before been reported in a compact pulsator. Eclipsing sdB+dM stars are very rare, with only seven systems known and only one with a pulsating primary. Pulsating stars in eclipsing binaries are especially important since they permit masses derived from seismological model fits to be cross-checked with orbital mass constraints. We present a first analysis of this star based on the Kepler 9.7-d commissioning light curve and extensive ground-based photometry and spectroscopy that allow us to set useful bounds on the system parameters. We derive a radial-velocity amplitude K1 = 65.7 ± 0.6 km s −1, inclination angle , and find that the masses of the components are M1 = 0.48 ± 0.03 M⊙ and M2 = 0.12 ± 0.01 M⊙.
We present Kepler satellite photometry of KIC 10661783, a short-period binary star system which shows total eclipses and multiperiodic δ Scuti pulsations. A frequency analysis of the ...eclipse-subtracted light curve reveals at least 68 frequencies, of which 55 or more can be attributed to pulsation modes. The main limitation on this analysis is the frequency resolution within the 27-d short-cadence light curve. Most of the variability signal lies in the frequency range 18-31 d−1, with amplitudes between 0.1 and 4 mmag. One harmonic term (2f) and a few combination frequencies (fi
+fj
) have been detected. From a plot of the residuals versus orbital phase, we assign the pulsations to the primary star in the system. The pulsations were removed from the short-cadence data and the light curve was modelled using the Wilson-Devinney code. We are unable to get a perfect fit due to the residual effects of pulsations and also to the treatment of reflection and reprocessing in the light-curve model. A model where the secondary star fills its Roche lobe is favoured, which means that KIC 10661783 can be classified as an oEA system. Further photometric and spectroscopic observations will allow the masses and radii of the two stars to be measured to high precision and hundreds of δ Scuti pulsation frequencies to be resolved. This could lead to unique constraints on theoretical models of δ Scuti stars, if the evolutionary history of KIC 10661783 can be accounted for.
Observations of the rotation rates of horizontal branch (HB) stars show puzzling systematics. In particular, cooler HB stars often show rapid rotation (with velocities in excess of 10 km s ...super(-1)), while hotter HB stars (those with T sub(eff) in excess of 11,000 K) typically show much smaller rotation velocities of 8 km s super(-1) or less. Simple models of angular momentum evolution of stars from the main sequence through the red giant branch fail to explain these effects. Assuming solid body rotation throughout produces models that rotate much too slowly. On the other hand, assuming local conservation of angular momentum, but with solid body rotation in the convective regions, produces HB models that also rotate too slowly at all T sub(eff) but preserve a rapidly rotating core. In these cases, the observed angular velocities of HB stars require that some of the angular momentum stored in the core reaches the surface. Models that assume constant specific angular momentum in the surface convection zone have faster rotation in the envelope; while the predictions of these models match the observed rotation rates of the cooler HB stars, hot HB stars rotate more slowly than the models. Thus, while there is not yet a coherent explanation of the trends of rotation on the HB, evolutionary models in all cases preserve a rapidly rotating core. To test the idea that HB stars contain such a core, one can appeal to detailed computations of trace element abundances and rotational mixing. However, a more direct probe is available to test these limiting cases of angular momentum evolution. Some of the hottest horizontal branch stars are members of the pulsating sdB class. They frequently show rich pulsation spectra characteristic of nonradially pulsating stars. Thus, their pulsations probe the internal rotation of these stars and should show the effects of rapid rotation in their cores. Using models of sdB stars that include angular momentum evolution, we explore this possibility and show that some of the sdB pulsators may indeed have rapidly rotating cores.
Context. There are many unknowns in the formation of subdwarf B stars. Different formation channels are considered to be possible and to lead to a variety of helium-burning subdwarfs. All seismic ...models to date, however, assume that a subdwarf B star is a post-helium-flash-core surrounded by a thin inert layer of hydrogen. Aims. We examine an alternative formation channel, in which the subdwarf B star originates from a massive (>~2 $M_{\odot}$) red giant with a non-degenerate helium-core. Although these subdwarfs may evolve through the same region of the $\log g-T_{\rm eff}$ diagram as the canonical post-flash subdwarfs, their interior structure is rather different. We examine how this difference affects their pulsation modes and whether it can be observed. Methods. Using detailed stellar evolution calculations we construct subdwarf B models from both formation channels. The iron accumulation in the driving region due to diffusion, which causes the excitation of the modes, is approximated by a Gaussian function. The pulsation modes and frequencies are calculated with a non-adiabatic pulsation code. Results. A detailed comparison of two subdwarf B models from different channels, but with the same $\log g$ and Teff, shows that their mode excitation is different. The excited frequencies are lower for the post-flash than for the post-non-degenerate subdwarf B star. This is mainly due to the differing chemical composition of the stellar envelope. A more general comparison between two grids of models shows that the excited frequencies of most post-non-degenerate subdwarfs cannot be well-matched with the frequencies of post-flash subdwarfs. In the rare event that an acceptable seismic match is found, additional information, such as mode identification and $\log g$ and Teff determinations, allows us to distinguish between the two formation channels.
We put asteroseismological constraints on the internal rotation profile of the GW Vir (PG1159-type) star PG 0122+200. To this end we employ a state-of-the-art asteroseismological model for this star ...and assess the expected frequency splittings induced by rotation adopting a forward approach in which we compare the theoretical frequency separations with the observed ones assuming different types of plausible internal rotation profiles. We also employ two asteroseismological inversion methods for the inversion of the rotation profile of PG 0122+200. We find evidence for differential rotation in this star. We demonstrate that the frequency splittings of the rotational multiplets exhibited by PG 0122+200 are compatible with a rotation profile in which the central regions are spinning about 2.4 times faster than the stellar surface.
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 data sets of these five objects; these data sets provide nearly alias-free time series photometry at unprecedented precision. Following an iterative pre-whitening 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 number of periodicities ranging from eight (KIC 8302197) to 53 (KIC 11558725). The frequencies and amplitudes are typical of g-mode pulsators of this type. We do not find any evidence for binarity in the five stars from their observed pulsation frequencies. As these are g-mode pulsators, we briefly looked for period spacings for mode identification and found average spacings of about 260 and 145 s. This may indicate l= 1 and 2 patterns. Some modes may show evidence of rotational splitting. These discoveries complete the list of compact pulsators found in the survey phase. Of the 13 compact pulsators, only one star was identified as a short-period (p-mode) V361 Hya pulsator, while all other new pulsators turned out to be V1093 Her class objects. Among the latter objects, two of them seemed to be pure V1093 Her while the others show additional low-amplitude peaks in the p-mode frequency range, suggesting their hybrid nature. Authenticity of these peaks will be tested with longer runs currently under analysis.
Context. The TESS satellite was launched in 2018 to perform high-precision photometry from space over almost the whole sky in a search for exoplanets orbiting bright stars. This instrument has opened ...new opportunities to study variable hot subdwarfs, white dwarfs, and related compact objects. Targets of interest include white dwarf and hot subdwarf pulsators, both carrying high potential for asteroseismology. Aims. We present the discovery and detailed asteroseismic analysis of a new g-mode hot B subdwarf (sdB) pulsator, EC 21494−7018 (TIC 278659026), monitored in TESS first sector using 120-s cadence. Methods. The TESS light curve was analyzed with standard prewhitening techniques, followed by forward modeling using our latest generation of sdB models developed for asteroseismic investigations. By simultaneously best-matching all the observed frequencies with those computed from models, we identified the pulsation modes detected and, more importantly, we determined the global parameters and structural configuration of the star. Results. The light curve analysis reveals that EC 21494−7018 is a sdB pulsator counting up to 20 frequencies associated with independent g-modes. The seismic analysis singles out an optimal model solution in full agreement with independent measurements provided by spectroscopy (atmospheric parameters derived from model atmospheres) and astrometry (distance evaluated from Gaia DR2 trigonometric parallax). Several key parameters of the star are derived. Its mass (0.391 ± 0.009 M⊙) is significantly lower than the typical mass of sdB stars and suggests that its progenitor has not undergone the He-core flash; therefore this progenitor could originate from a massive (≳2 M⊙) red giant, which is an alternative channel for the formation of sdBs. Other derived parameters include the H-rich envelope mass (0.0037 ± 0.0010 M⊙), radius (0.1694 ± 0.0081 R⊙), and luminosity (8.2 ± 1.1 L⊙). The optimal model fit has a double-layered He+H composition profile, which we interpret as an incomplete but ongoing process of gravitational settling of helium at the bottom of a thick H-rich envelope. Moreover, the derived properties of the core indicate that EC 21494−7018 has burnt ∼43% (in mass) of its central helium and possesses a relatively large mixed core (Mcore = 0.198 ± 0.010 M⊙), in line with trends already uncovered from other g-mode sdB pulsators analyzed with asteroseismology. Finally, we obtain for the first time an estimate of the amount of oxygen (in mass; X(O)core = 0.16+0.13−0.05 X ( O ) core = 0 . 16 − 0.05 + 0.13 $ X(\mathrm{O})_{\mathrm{core}}=0.16_{-0.05}^{+0.13} $ ) produced at this stage of evolution by an helium-burning core. This result, along with the core-size estimate, is an interesting constraint that may help to narrow down the still uncertain 12C(α, γ)16O nuclear reaction rate.
Abstract
Kawaler et al. present a variational expression for the eigenfrequencies associated with stellar oscillations. We highlight and correct a typographical error in the weight functions ...appearing in these expressions, and validate the correction numerically.
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