Eclipsing binaries observed with the WIRE satellite. II, β Aurigae and non-linear limb darkening in light curves

Aims. We present the most precise light curve ever obtained of a detached eclipsing binary star and use it investigate the inclusion of non-linear limb darkening laws in light curve models of eclipsing binaries. This light curve, of the bright eclipsing system β Aurigae, was obtained using the star tracker aboard the wire satellite and contains 30 000 datapoints with a point-to-point scatter of 0.3mmag. Methods. We analyse the wire light curve using a version of the ebop code modified to include non-linear limb darkening laws and to directly incorporate observed times of minimum light and spectroscopic light ratios into the photometric solution as individual observations. We also analyse the dataset with the Wilson-Devinney code to ensure that the two models give consistent results. Results. ebop is able to provide an excellent fit to the high-precision wire data.Whilst the fractional radii of the stars are only defined to a precision of 5% by this light curve, including an accurate published spectroscopic light ratio improves this dramatically to 0.5%. Using non-linear limb darkening improves the quality of the fit significantly compared to the linear law and causes the measured radii to increase by 0.4%. It is possible to derive all of the limb darkening coefficients from the light curve, although they are strongly correlated with each other. The fitted coefficients agree with theoretical predictions to within their fairly large error estimates. We were able to obtain a reasonably good fit to the data using the Wilson-Devinney code, but only using the highest available integration accuracy and by iterating for a long time. Bolometric albedos of 0.6 were found, which are appropriate to convective rather than radiative envelopes. Conclusions. The radii and masses of the components of β Aur are RA = 2.762 ± 0.017 R, RB = 2.568 ± 0.017 R, MA = 2.376 ±0.027 M and MB = 2.291 ± 0.027 M, where A and B denote the primary and secondary star, respectively. Theoretical stellar evolutionary models can match these parameters for a solarmetal abundance and an age of 450−500 Myr. The Hipparcos trigonometric parallax and an interferometrically-derived orbital parallax give distances to β Aur which are in excellent agreement with each other and with distances derived using surface brightness relations and several sets of empirical and theoretical bolometric corrections

High-precision photometry by telescope defocussing. III. The transiting planetary system WASP-2

We present high-precision photometry of three transits of the extrasolar planetary system WASP-2, obtained by defocussing the telescope, and achieving point-to-point scatters of between 0.42 and 0.73 mmag. These data are modelled using the JKTEBOP code, and taking into account the light from the recently-discovered faint star close to the system. The physical properties of the WASP-2 system are derived using tabulated predictions from five different sets of stellar evolutionary models, allowing both statistical and systematic errorbars to be specified. We find the mass and radius of the planet to be M_b = 0.847 +/- 0.038 +/- 0.024 Mjup and R_b = 1.044 +/- 0.029 +/- 0.015 Rjup. It has a low equilibrium temperature of 1280 +/- 21 K, in agreement with a recent finding that it does not have an atmospheric temperature inversion. The first of our transit datasets has a scatter of only 0.42 mmag with respect to the best-fitting light curve model, which to our knowledge is a record for ground-based observations of a transiting extrasolar planet.Comment: Accepted for publication in MNRAS. 9 pages, 3 figures, 10 table

On stellar limb darkening and exoplanetary transits

This paper examines how to compare stellar limb-darkening coefficients evaluated from model atmospheres with those derived from photometry. Different characterizations of a given model atmosphere can give quite different numerical results (even for a given limb-darkening `law'), while light-curve analyses yield limb-darkening coefficients that are dependent on system geometry, and that are not directly comparable to any model-atmosphere representation. These issues are examined in the context of exoplanetary transits, which offer significant advantages over traditional binary-star eclipsing systems in the study of stellar limb darkening. `Like for like' comparisons between light-curve analyses and new model-atmosphere results, mediated by synthetic photometry, are conducted for a small sample of stars. Agreement between the resulting synthetic-photometry/atmosphere-model (SPAM) limb-darkening coefficients and empirical values ranges from very good to quite poor, even though the targets investigated show only a small dispersion in fundamental stellar parameters.Comment: Accepted, MNRAS, 4/8/201

Post common envelope binaries from SDSS. II : identification of 9 close binaries with VLT/FORS2

Context. Post common envelope binaries (PCEBs) consisting of a white dwarf and a main sequence star are ideal systems to use to calibrate current theories of angular momentum loss in close compact binary stars. The potential held by PCEBs for further development of close binary evolution could so far not be exploited due to the small number of known systems and the inhomogeneity of the sample. The Sloan Digital Sky Survey is changing this scene dramatically, as it is very efficient in identifying white dwarf/main sequence (WDMS) binaries, including both wide systems whose stellar components evolve like single stars and − more interesting in the context of close binary evolution − PCEBs. Aims. We pursue a large-scale follow-up survey to identify and characterise the PCEBs among the WDMS binaries that have been found with SDSS. We use a two-step strategy with the identification of PCEBs among WDMS binaries in the first phase and orbital period determinations in the second phase. Here we present first results of our ESO-VLT/FORS2 pilot study that targets the identification of the PCEBs among the fainter (g >∼18.5) SDSSWDMS binaries. Methods. From published SDSS catalogues we selected 26 WDMS binaries to be observed with ESO-VLT/FORS2 in service mode. The design of the observations was to get two spectra per object separated by at least one night.We used the Na I λλ 8183.27, 8194.81 doublet to measure radial velocity variations of our targets and a spectral decomposition/fitting technique to determine the white dwarf effective temperatures and surface gravities, masses, and secondary star spectral types for all WDMS binaries in our sample. Results. Among the 26 observed WDMS binaries, we find 9 strong PCEB candidates showing clear (≥3σ) radial velocity variations, and we estimate the fraction of PCEBs among SDSS WDMS binaries to be ∼35 ± 12%. We find indications of a dependence of the relative number of PCEBs among SDSSWDMS binaries on the spectral type of the secondary star. These results are subject to small number statistics and need to be confirmed by additional observations. Using Magellan-Clay/LDSS3, we measured the orbital periods of two PCEB candidates, SDSS J1047+0523 and SDSS J1414–0132, to be 9.17 h and 17.48 h, respectively. Conclusions. This pilot study demonstrates that our survey is highly efficient in identifying PCEBs among the SDSSWDMS binaries, and it will indeed provide the observational parameters that are needed to constrain the theoretical models of close binary evolution

Multilevel convergence analysis of multigrid-reduction-in-time

This paper presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles, with different relaxation schemes, by deriving the respective residual and error propagation operators. The residual and error operators are functions of the time stepping operator, analyzed directly and bounded in norm, both numerically and analytically. We present various upper bounds of different computational cost and varying sharpness. These upper bounds are complemented by proposing analytic formulae for the approximate convergence factor of V-cycle algorithms that take the number of fine grid time points, the temporal coarsening factors, and the eigenvalues of the time stepping operator as parameters. The paper concludes with supporting numerical investigations of parabolic (anisotropic diffusion) and hyperbolic (wave equation) model problems. We assess the sharpness of the bounds and the quality of the approximate convergence factors. Observations from these numerical investigations demonstrate the value of the proposed multilevel convergence framework for estimating MGRIT convergence a priori and for the design of a convergent algorithm. We further highlight that observations in the literature are captured by the theory, including that two-level Parareal and multilevel MGRIT with F-relaxation do not yield scalable algorithms and the benefit of a stronger relaxation scheme. An important observation is that with increasing numbers of levels MGRIT convergence deteriorates for the hyperbolic model problem, while constant convergence factors can be achieved for the diffusion equation. The theory also indicates that L-stable Runge-Kutta schemes are more amendable to multilevel parallel-in-time integration with MGRIT than A-stable Runge-Kutta schemes.Comment: 26 pages; 17 pages Supplementary Material

Kepler-539: a young extrasolar system with two giant planets on wide orbits and in gravitational interaction

We confirm the planetary nature of Kepler-539b (aka Kepler object of interest K00372.01), a giant transiting exoplanet orbiting a solar-analogue G2 V star. The mass of Kepler-539b was accurately derived thanks to a series of precise radial velocity measurements obtained with the CAFE spectrograph mounted on the CAHA 2.2m telescope. A simultaneous fit of the radial-velocity data and Kepler photometry revealed that Kepler-539b is a dense Jupiter-like planet with a mass of Mp = 0.97 Mjup and a radius of Rp = 0.747 Rjup, making a complete circular revolution around its parent star in 125.6 days. The semi-major axis of the orbit is roughly 0.5 au, implying that the planet is at roughly 0.45 au from the habitable zone. By analysing the mid-transit times of the 12 transit events of Kepler-539b recorded by the Kepler spacecraft, we found a clear modulated transit time variation (TTV), which is attributable to the presence of a planet c in a wider orbit. The few timings available do not allow us to precisely estimate the properties of Kepler-539c and our analysis suggests that it has a mass between 1.2 and 3.6 Mjup, revolving on a very eccentric orbit (0.4<e<0.6) with a period larger than 1000 days. The high eccentricity of planet c is the probable cause of the TTV modulation of planet b. The analysis of the CAFE spectra revealed a relatively high photospheric lithium content, A(Li)=2.48 dex, which, together with both a gyrochronological and isochronal analysis, suggests that the parent star is relatively young.Comment: 11 pages, 14 figures, accepted for publication in Astronomy & Astrophysic

Stellar Limb-Darkening Coefficients for CoRot and Kepler

Transiting exoplanets provide unparalleled access to the fundamental parameters of both extrasolar planets and their host stars. We present limb-darkening coefficients (LDCs) for the exoplanet hunting CoRot and Kepler missions. The LDCs are calculated with ATLAS stellar atmospheric model grids and span a wide range of Teff, log g, and metallically [M/H]. Both CoRot and Kepler contain wide, nonstandard response functions, and are producing a large inventory of high-quality transiting lightcurves, sensitive to stellar limb darkening. Comparing the stellar model limb darkening to results from the first seven CoRot planets, we find better fits are found when two model intensities at the limb are excluded in the coefficient calculations. This calculation method can help to avoid a major deficiency present at the limbs of the 1D stellar models.Comment: Accepted for publication in A&A. 4 pages, 2 figures, 2 tables. Full versions of tables 1 and 2 containing limb-darkening coefficients available at http://vega.lpl.arizona.edu/~sing