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 (Strömgren, 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 g′s ranging from 0.0 to 5.0, –5.0 ≤ log M/H ≤ +1, 2000 K ≤ Teff ≤ 50 000 K and for five values of the microturbulent velocity. ATLAS and PHOENIX plane-parallel atmosphere models were used for all computations.
Kepler allows the measurement of starspot variability in a large sample of field red giants for the first time. With a new method that combines autocorrelation and wavelet decomposition, we measure ...361 rotation periods from the full set of 17 377 oscillating red giants in our sample. This represents 2.08% of the stars, consistent with the fraction of spectroscopically detected rapidly rotating giants in the field. The remaining stars do not show enough variability to allow us to measure a reliable surface rotation period. Because the stars with detected rotation periods have measured oscillations, we can infer their global properties, e.g. mass and radius, and quantitatively evaluate the predictions of standard stellar evolution models as a function of mass. Consistent with results for cluster giants when we consider only the 4881 intermediate-mass stars, M > 2.0 M⊙ from our full red giant sample, we do not find the enhanced rates of rapid rotation expected from angular momentum conservation. We therefore suggest that either enhanced angular momentum loss or radial differential rotation must be occurring in these stars. Finally, when we examine the 575 low-mass (M< 1.1 M⊙) red clump stars in our sample, which were expected to exhibit slow (non-detectable) rotation, 15% of them actually have detectable rotation. This suggests a high rate of interactions and stellar mergers on the red giant branch.
ABSTRACT The precision of photometric and spectroscopic observations has been systematically improved in the last decade, mostly thanks to space-borne photometric missions and ground-based ...spectrographs dedicated to finding exoplanets. The field of eclipsing binary stars strongly benefited from this development. Eclipsing binaries serve as critical tools for determining fundamental stellar properties (masses, radii, temperatures, and luminosities), yet the models are not capable of reproducing observed data well, either because of the missing physics or because of insufficient precision. This led to a predicament where radiative and dynamical effects, insofar buried in noise, started showing up routinely in the data, but were not accounted for in the models. PHOEBE (PHysics Of Eclipsing BinariEs; http://phoebe-project.org) is an open source modeling code for computing theoretical light and radial velocity curves that addresses both problems by incorporating missing physics and by increasing the computational fidelity. In particular, we discuss triangulation as a superior surface discretization algorithm, meshing of rotating single stars, light travel time effects, advanced phase computation, volume conservation in eccentric orbits, and improved computation of local intensity across the stellar surfaces that includes the photon-weighted mode, the enhanced limb darkening treatment, the better reflection treatment, and Doppler boosting. Here we present the concepts on which PHOEBE is built and proofs of concept that demonstrate the increased model fidelity.
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.
Abstract
We present the first short time-scale (∼hours to days) optical variability study of a large sample of active galactic nuclei (AGNs) observed with the Kepler/K2 mission. The sample contains ...252 AGN observed over four campaigns with ∼30 min cadence selected from the Million Quasar Catalogue with R magnitude <19. We performed time series analysis to determine their variability properties by means of the power spectral densities (PSDs) and applied Monte Carlo techniques to find the best model parameters that fit the observed power spectra. A power-law model is sufficient to describe all the PSDs of our sample. A variety of power-law slopes were found indicating that there is not a universal slope for all AGNs. We find that the rest-frame amplitude variability in the frequency range of 6 × 10−6–10−4 Hz varies from 1to10 per cent with an average of 1.7 per cent. We explore correlations between the variability amplitude and key parameters of the AGN, finding a significant correlation of rest-frame short-term variability amplitude with redshift. We attribute this effect to the known ‘bluer when brighter’ variability of quasars combined with the fixed bandpass of Kepler data. This study also enables us to distinguish between Seyferts and blazars and confirm AGN candidates. For our study, we have compared results obtained from light curves extracted using different aperture sizes and with and without detrending. We find that limited detrending of the optimal photometric precision light curve is the best approach, although some systematic effects still remain present.
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. 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 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.
The Kepler space mission provided near-continuous and high-precision photometry of about 207 000 stars, which can be used for asteroseismology. However, for successful seismic modeling it is equally ...important to have accurate stellar physical parameters. Therefore, supplementary ground-based data are needed. We report the results of the analysis of high-resolution spectroscopic data of A- and F-type stars from the Kepler field, which were obtained with the HERMES spectrograph on the Mercator telescope. We determined spectral types, atmospheric parameters and chemical abundances for a sample of 117 stars. Hydrogen Balmer, Fe i, and Fe ii lines were used to derive effective temperatures, surface gravities, and microturbulent velocities. We determined chemical abundances and projected rotational velocities using a spectrum synthesis technique. The atmospheric parameters obtained were compared with those from the Kepler Input Catalogue (KIC), confirming that the KIC effective temperatures are underestimated for A stars. Effective temperatures calculated by spectral energy distribution fitting are in good agreement with those determined from the spectral line analysis. The analysed sample comprises stars with approximately solar chemical abundances, as well as chemically peculiar stars of the Am, Ap, and λ Boo types. The distribution of the projected rotational velocity, vsin i, is typical for A and F stars and ranges from 8 to about 280 km s−1, with a mean of 134 km s−1.
Context. The study of stellar activity is important because it can provide new constraints for dynamo models when combined with surface rotation rates and the depth of the convection zone. We know ...that the dynamo mechanism, which is believed to be the main process that rules the magnetic cycle of solar-like stars, results from the interaction between (differential) rotation, convection, and magnetic field. The Kepler mission has already been collecting data for a large number of stars during four years allowing us to investigate magnetic stellar cycles. Aims. We investigated the Kepler light curves to look for magnetic activity or even hints of magnetic activity cycles. Based on the photometric data we also looked for new magnetic indexes to characterise the magnetic activity of the stars. Methods. We selected a sample of 22 solar-like F stars that have a rotation period shorter than 12 days. We performed a time-frequency analysis using the Morlet wavelet yielding a magnetic proxy for our sample of stars. We computed the magnetic index Sph as the standard deviation of the whole time series and the index ⟨ Sph ⟩, which is the mean of standard deviations measured in subseries of length five times the rotation period of the star. We defined new indicators, such as the contrast between high and low activity, to take into account the fact that complete magnetic cycles are not observed for all the stars. We also inferred the Rossby number of the stars and studied their stellar background. Results. This analysis shows different types of behaviour in the 22 F stars. Two stars show behaviour very similar to magnetic activity cycles. Five stars show long-lived spots or active regions suggesting the existence of active longitudes. Two stars in our sample seem to have a decreasing or increasing trend in the temporal variation of the magnetic proxies. Finally, the last group of stars shows magnetic activity (with the presence of spots) but no sign of cycle.
Context. γ Doradus and δ Scuti pulsators cover the transition region between low mass and massive main-sequence stars, and as such, are critical for testing stellar models. When they reside in binary ...systems, we can combine two independent methods to derive critical information, such as precise fundamental parameters to aid asteroseismic modelling. In the Kepler light curve of KIC 10080943, clear signatures of gravity- and pressure-mode pulsations have been found. Ground-based spectroscopy revealed this target to be a double-lined binary system. Aims. We present the analysis of four years of Kepler photometry and high-resolution spectroscopy to derive observational constraints with which to evaluate theoretical predictions of the stellar structure and evolution for intermediate-mass stars. Methods. We used the method of spectral disentangling to determine atmospheric parameters for both components and derive the orbital elements. With phoebe, we modelled the ellipsoidal variation and reflection signal of the binary in the light curve and used classical Fourier techniques to analyse the pulsation modes. Results. We show that the eccentric binary system KIC 10080943 contains two hybrid pulsators with masses M1 = 2.0 ± 0.1 M⊙ and M2 = 1.9 ± 0.1 M⊙, with radii R1 = 2.9 ± 0.1 R⊙ and R2 = 2.1 ± 0.2 R⊙. We detect rotational splitting in the g and p modes for both stars and use them to determine a first rough estimate of the core-to-surface rotation rates for the two components, which will be improved by future detailed seismic modelling.
ABSTRACT We report the discovery of four short-period eclipsing systems in the Kepler light curves, consisting of an A-star primary and a low-mass white dwarf (WD) secondary (dA+WD)-KIC 4169521, ...KOI-3818, KIC 2851474, and KIC 9285587. The systems show BEaming, Ellipsoidal and Reflection (BEER) phase modulations together with primary and secondary eclipses. These add to the 6 Kepler and 18 WASP short-period eclipsing dA+WD binaries that were previously known. The light curves, together with follow-up spectroscopic observations, allow us to derive the masses, radii, and effective temperatures of the two components of the four systems. The orbital periods, of 1.17-3.82 days, and WD masses, of 0.19-0.22 M , are similar to those of the previously known systems. The WD radii of KOI-3818, KIC 2851474, and KIC 9285587 are 0.026, 0.035, and 0.026 R , respectively, the smallest WD radii derived so far for short-period eclipsing dA+WD binaries. These three binaries extend the previously known population to older systems with cooler and smaller WD secondaries. KOI-3818 displays evidence for a fast-rotating primary and a minute but significant eccentricity, ∼1.5 × 10−3. These features are probably the outcome of the mass-transfer process.
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