S. Bloemen

Gravity and limb-darkening coefficients for the Kepler, CoRoT, Spitzer, uvby, UBVRIJHK, and Sloan photometric systems

Aims. The complex physics of close binary stars is made even more challenging by the proximity effects that affect it. Understanding the influence of these proximity effects is one of the most important tasks in theoretical stellar astrophysics. It is crucial to know how the specific intensity is distributed over the stellar disk for a correct modelling of the light curves of eclipsing binaries and planetary transits. To provide theoretical input for light curve modelling codes, we present new calculations of gravity- and limb-darkening coefficients for a wide range of effective temperatures, gravities, metallicities, and microturbulent velocities. Methods. We computed limb-darkening coefficients for several atmosphere models, which cover the transmission curves of the Kepler, CoRoT, and Spitzer space missions as well as more widely used passbands (Stromgren, Johnson-Cousins, Sloan). In addition to these computations, which were made adopting the least-square method, we also performed calculations for the bi-parametric approximations by adopting the flux conservation method to provide users with an additional tool to estimate the theoretical error bars. To facilitate the modelling of the effects of tidal and rotational distortions, we computed the gravity-darkening coefficients y(λ) using the same models of stellar atmospheres as for the limb-darkening. Compared to previous work, a more general differential equation was used, which now takes into account local gravity variations and the effects of convection. Results. The limb-darkening coefficients were computed with a higher numerical resolution (100 μ points instead of 15 or 17, as is often used in the ATLAS models), and five equations were used to describe the specific intensities (linear, quadratic, root-square, logarithmic, and a 4-coefficient law). Concerning the gravity-darkening coefficients, the influence of the local gravity on y(λ) is shown as well as the effects of convection, which turn out to be very significant for cool stars. The results are tabulated for log gs ranging from 0.0 to 5.0, -5.0 ≤ log [M/H] < +1, 2000 K ≤ T eff ≤ 50 000 K and for five values of the microturbulent velocity. ATLAS and PHOENIX plane-parallel atmosphere models were used for all computations.

Transiting circumbinary planets Kepler-34 b and Kepler-35 b

Most Sun-like stars in the Galaxy reside in gravitationally bound pairs of stars (binaries). Although long anticipated, the existence of a ‘circumbinary planet’ orbiting such a pair of normal stars was not definitively established until the discovery of the planet transiting (that is, passing in front of) Kepler-16. Questions remained, however, about the prevalence of circumbinary planets and their range of orbital and physical properties. Here we report two additional transiting circumbinary planets: Kepler-34 (AB)b and Kepler-35 (AB)b, referred to here as Kepler-34 b and Kepler-35 b, respectively. Each is a low-density gas-giant planet on an orbit closely aligned with that of its parent stars. Kepler-34 b orbits two Sun-like stars every 289 days, whereas Kepler-35 b orbits a pair of smaller stars (89% and 81% of the Sun’s mass) every 131 days. The planets experience large multi-periodic variations in incident stellar radiation arising from the orbital motion of the stars. The observed rate of circumbinary planets in our sample implies that more than ∼1% of close binary stars have giant planets in nearly coplanar orbits, yielding a Galactic population of at least several million.

Spin down of the core rotation in red giants

Context. The space mission Kepler provides us with long and uninterrupted photometric time series of red giants. We are now able to probe the rotational behaviour in their deep interiors using the observations of mixed modes. Aims. We aim to measure the rotational splittings in red giants and to derive scaling relations for rotation related to seismic and fundamental stellar parameters. Methods. We have developed a dedicated method for automated measurements of the rotational splittings in a large number of red giants. Ensemble asteroseismology, namely the examination of a large number of red giants at different stages of their evolution, allows us to derive global information on stellar evolution. Results. We have measured rotational splittings in a sample of about 300 red giants. We have also shown that these splittings are dominated by the core rotation. Under the assumption that a linear analysis can provide the rotational splitting, we observe a small increase of the core rotation of stars ascending the red giant branch. Alternatively, an important slow down is observed for red-clump stars compared to the red giant branch. We also show that, at fixed stellar radius, the specific angular momentum increases with increasing stellar mass. Conclusions. Ensemble asteroseismology indicates what has been indirectly suspected for a while: our interpretation of the observed rotational splittings leads to the conclusion that the mean core rotation significantly slows down during the red giant phase. The slow-down occurs in the last stages of the red giant branch. This spinning down explains, for instance, the long rotation periods measured in white dwarfs.

Rotation and magnetism of Kepler pulsating solar-like stars - Towards asteroseismically calibrated age-rotation relations

Kepler ultra-high precision photometry of long and continuous observations provides a unique dataset in which surface rotation and variability can be studied for thousands of stars. Because many of these old field stars also have independently measured asteroseismic ages, measurements of rotation and activity are particularly interesting in the context of age-rotation-activity relations. In particular, age-rotation relations generally lack good calibrators at old ages, a problem that this Kepler sample of old-field stars is uniquely suited to address. We study the surface rotation and photometric magnetic activity of a subset of 540 solar-like stars on the main-sequence and the subgiant branch for which stellar pulsations have been measured. The rotation period was determined by comparing the results from two different analysis methods: i) the projection onto the frequency domain of the time-period analysis, and ii) the autocorrelation function of the light curves. Reliable surface rotation rates were then extracted by comparing the results from two different sets of calibrated data and from the two complementary analyses. General photometric levels of magnetic activity in this sample of stars were also extracted by using a photometric activity index, which takes into account the rotation period of the stars. We report rotation periods for 310 out of 540 targets (excluding known binaries and candidate planet-host stars); our measurements span a range of 1 to 100 days. The photometric magnetic activity levels of these stars were computed, and for 61.5% of the dwarfs, this level is similar to the range, from minimum to maximum, of the solar magnetic activity. We demonstrate that hot dwarfs, cool dwarfs, and subgiants have very different rotation-age relationships, highlighting the importance of separating out distinct populations when interpreting stellar rotation periods. Our sample of cool dwarf stars with age and metallicity data of the highest quality is consistent with gyrochronology relations reported in the literature.

First Kepler results on compact pulsators – I. Survey target selection and the first pulsators

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 of a V361 Hya-type sdB variable (sdBV); seven show long-period pulsation characteristics of V1093 Her-type sdBVs; and one shows low-amplitude pulsations with both short and long periods. We derive effective temperatures and surface gravities for all the subdwarf B stars in the sample and demonstrate that below the boundary region where hybrid sdB pulsators are found, all our targets are pulsating. For the stars hotter than this boundary temperature a low fraction of strong pulsators (<10 per cent) is confirmed. Interestingly, the short-period pulsator also shows a low-amplitude mode in the long-period region, and several of the V1093 Her pulsators show low-amplitude modes in the short-period region, indicating that hybrid behaviour may be common in these stars, also outside the boundary temperature region where hybrid pulsators have hitherto been found.

Kepler observations of the beaming binary KPD 1946+4340

The Kepler Mission has acquired 33.5 d of continuous 1-min photometry of KPD 1946+4340, a short-period binary system that consists of a subdwarf B star (sdB) and a white dwarf. In the light curve, eclipses are clearly seen, with the deepest occurring when the compact white dwarf crosses the disc of the sdB (0.4 per cent) and the more shallow ones (0.1 per cent) when the sdB eclipses the white dwarf. As expected, the sdB is deformed by the gravitational field of the white dwarf, which produces an ellipsoidal modulation of the light curve. Spectacularly, a very strong Doppler beaming (also known as Doppler boosting) effect is also clearly evident at the 0.1 per cent level. This originates from the sdB’s orbital velocity, which we measure to be 164.0 ± 1. 9k m s −1 from supporting spectroscopy. We present light-curve models that account for all these effects, as well as gravitational lensing, which decreases the apparent radius of the white dwarf by about 6 per cent, when it eclipses the sdB. We derive system parameters and uncertainties from the light curve using Markov chain Monte Carlo simulations. Adopting a theoretical white dwarf mass–radius relation, the mass of the subdwarf is found ,

KIC 4544587: an eccentric, short-period binary system with δ Sct pulsations and tidally excited modes

We present Kepler photometry and ground-based spectroscopy of KIC 4544587, a short-period eccentric eclipsing binary system with self-excited pressure and gravity modes, tidally excited modes, tidally influenced p modes and rapid apsidal motion of 182 yr per cycle. The primary and secondary components of KIC 4544587 reside within the d Scuti and γ Dor instability region of the Hertzsprung-Russell diagram, respectively. By applying the binary modelling software PHOEBE to prewhitenedKepler photometric data and radial velocity data obtained using the William Herschel Telescope and 4-m Mayall telescope at Kitt Peak Northern Observatory (KPNO), the fundamental parameters of this important system have been determined, including the stellarmasses, 1.98±0.07 and 1.60±0.06 M⊙, and radii, 1.76±0.03 and 1.42±0.02R⊙, for the primary and secondary components, respectively. Frequency analysis of the residual data revealed 31 modes, 14 in the gravity mode region and 17 in the pressure mode region. Of the 14 gravity modes, 8 are orbital harmonics: a signature of tidal resonance. While the measured amplitude of these modes may be partially attributed to residual signal from binary model subtraction, we demonstrate through consideration of the folded light curve that these frequencies do in fact correspond to tidally excited pulsations. Furthermore, we present an echelle diagram of the pressure mode frequency region (modulo the orbital frequency) and demonstrate that the tides are also influencing the p modes. A first look at asteroseismology hints that the secondary component is responsible for the p modes, which is contrary to our expectation that the hotter star should pulsate in higher radial overtone, higher frequency p modes. ©2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

Deviations from a uniform period spacing of gravity modes in a massive star

The life of a star is dominantly determined by the physical processes in the stellar interior. Unfortunately, we still have a poor understanding of how the stellar gas mixes near the stellar core, preventing precise predictions of stellar evolution. The unknown nature of the mixing processes as well as the extent of the central mixed region is particularly problematic for massive stars. Oscillations in stars with masses a few times that of the Sun offer a unique opportunity to disentangle the nature of various mixing processes, through the distinct signature they leave on period spacings in the gravity mode spectrum. Here we report the detection of numerous gravity modes in a young star with a mass of about seven solar masses. The mean period spacing allows us to estimate the extent of the convective core, and the clear periodic deviation from the mean constrains the location of the chemical transition zone to be at about 10 per cent of the radius and rules out a clear-cut profile.

Kepler Eclipsing Binary Stars. III. Classification of Kepler Eclipsing Binary Light Curves with Locally Linear Embedding

We present an automated classification of 2165 Kepler eclipsing binary (EB) light curves that accompanied the second Kepler data release. The light curves are classified using locally linear embedding, a general nonlinear dimensionality reduction tool, into morphology types (detached, semi-detached, overcontact, ellipsoidal). The method, related to a more widely used principal component analysis, produces a lower-dimensional representation of the input data while preserving local geometry and, consequently, the similarity between neighboring data points. We use this property to reduce the dimensionality in a series of steps to a one-dimensional manifold and classify light curves with a single parameter that is a measure of detachedness of the system. This fully automated classification correlates well with the manual determination of morphology from the data release, and also efficiently highlights any misclassified objects. Once a lower-dimensional projection space is defined, the classification of additional light curves runs in a negligible time and the method can therefore be used as a fully automated classifier in pipeline structures. The classifier forms a tier of the Kepler EB pipeline that pre-processes light curves for the artificial intelligence based parameter estimator.

Pulsating red giant stars in eccentric binary systems discovered from Kepler space-based photometry : A sample study and the analysis of KIC 5006817

Context. The unparalleled photometric data obtained by NASA’s Kepler Space Telescope has led to improved understanding of red giant stars and binary stars. Seismology allows us to constrain the properties of red giants. In addition to eclipsing binaries, eccentric non-eclipsing binaries that exhibit ellipsoidal modulations have been detected with Kepler. Aims. We aim to study the properties of eccentric binary systems containing a red giant star and to derive the parameters of the primary giant component. Methods. We applied asteroseismic techniques to determine the masses and radii of the primary component of each system. For a selected target, light and radial velocity curve modelling techniques were applied to extract the parameters of the system and its primary component. Stellar evolution and its effects on the evolution of the binary system were studied from theoretical models. Results. The paper presents the asteroseismic analysis of 18 pulsating red giants in eccentric binary systems, for which masses and radii were constrained. The orbital periods of these systems range from 20 to 440 days. The results of our ongoing radial velocity monitoring programme with the Hermes spectrograph reveal an eccentricity range of e= 0.2 to 0.76. As a case study we present a detailed analysis of KIC 5006817, whose rich oscillation spectrum allows for detailed seismic analysis. From seismology we constrain the rotational period of the envelope to be at least 165 d, which is roughly twice the orbital period. The stellar core rotates 13 times faster than the surface. From the spectrum and radial velocities we expect that the Doppler beaming signal should have a maximum amplitude of 300 ppm in the light curve. Fixing the mass and radius to the asteroseismically determined values, we find from our binary modelling a value of the gravity darkening exponent that is significantly larger than expected. Through binary modelling, we determine the mass of the secondary component to be 0.29± 0.03 M . Conclusions. For KIC 5006817 we exclude pseudo-synchronous rotation of the red giant with the orbit. The comparison of the results from seismology and modelling of the light curve shows a possible alignment of the rotational and orbital axis at the 2σ level. Red giant eccentric systems could be progenitors of cataclysmic variables and hot subdwarf B stars.Context. The unparalleled photometric data obtained by NASA’s Kepler Space Telescope has led to improved understanding of red giant stars and binary stars. Seismology allows us to constrain the properties of red giants. In addition to eclipsing binaries, eccentric non-eclipsing binaries that exhibit ellipsoidal modulations have been detected with Kepler. Aims. We aim to study the properties of eccentric binary systems containing a red giant star and to derive the parameters of the primary giant component. Methods. We applied asteroseismic techniques to determine the masses and radii of the primary component of each system. For a selected target, light and radial velocity curve modelling techniques were applied to extract the parameters of the system and its primary component. Stellar evolution and its effects on the evolution of the binary system were studied from theoretical models. Results. The paper presents the asteroseismic analysis of 18 pulsating red giants in eccentric binary systems, for which masses and radii were constrained. The orbital periods of these systems range from 20 to 440 days. The results of our ongoing radial velocity monitoring programme with the Hermes spectrograph reveal an eccentricity range of e = 0.2 to 0.76. As a case study we present a detailed analysis of KIC 5006817, whose rich oscillation spectrum allows for detailed seismic analysis. From seismology we constrain the rotational period of the envelope to be at least 165 d, which is roughly twice the orbital period. The stellar core rotates 13 times faster than the surface. From the spectrum and radial velocities we expect that the Doppler beaming signal should have a maximum amplitude of 300 ppm in the light curve. Fixing the mass and radius to the asteroseismically determined values, we find from our binary modelling a value of the gravity darkening exponent that is significantly larger than expected. Through binary modelling, we determine the mass of the secondary component to be 0.29 ± 0.03 M� . Conclusions. For KIC 5006817 we exclude pseudo-synchronous rotation of the red giant with the orbit. The comparison of the results from seismology and modelling of the light curve shows a possible alignment of the rotational and orbital axis at the 2σ level. Red giant eccentric systems could be progenitors of cataclysmic variables and hot subdwarf B stars.