Limb darkening in spherical stellar atmospheres

(Abridged) Context. Stellar limb darkening, I({\mu} = cos{\theta}), is an important constraint for microlensing, eclipsing binary, planetary transit, and interferometric observations, but is generally treated as a parameterized curve, such as a linear-plus-square-root law. Many analyses assume limb-darkening coefficients computed from model stellar atmospheres. However, previous studies, using I({\mu}) from plane- parallel models, have found that fits to the flux-normalized curves pass through a fixed point, a common {\mu} location on the stellar disk, for all values of T eff, log g and wavelength. Aims. We study this fixed {\mu}-point to determine if it is a property of the model stellar atmospheres or a property of the limb-darkening laws. Furthermore, we use this limb-darkening law as a tool to probe properties of stellar atmospheres for comparison to limb- darkening observations. Methods. Intensities computed with plane-parallel and spherically-symmetric Atlas models (characterized by the three fundamental parameters L\star, M\star and R\star) are used to reexamine the existence of the fixed {\mu}-point for the parametrized curves. Results. We find that the intensities from our spherical models do not have a fixed point, although the curves do have a minimum spread at a {\mu}-value similar to the parametrized curves. We also find that the parametrized curves have two fixed points, {\mu}1 and {\mu}2, although {\mu}2 is so close to the edge of the disk that it is missed using plane-parallel atmospheres. We also find that the spherically- symmetric models appear to agree better with published microlensing observations relative to plane-parallel models.Comment: 8 pages, 8 figures, figures 4 and 6 have lower resolution. A&A in pres

Using limb darkening to measure fundamental parameters of stars

Context. Limb darkening is an important tool for understanding stellar atmospheres, but most observations measuring limb darkening assume various parameterizations that yield no significant information about the structure of stellar atmospheres. Aims. We use a specific limb-darkening relation to study how the best-fit coefficients relate to fundamental stellar parameters from spherically symmetric model stellar atmospheres. Methods. Using a grid of spherically symmetric Atlas model atmospheres, we compute limb-darkening coefficients, and develop a novel method to predict fundamental stellar parameters. Results. We find our proposed method predicts the mass of stellar atmosphere models given only the radius and limb-darkening coefficients, suggesting that microlensing, interferometric, transit and eclipse observations can constrain stellar masses. Conclusions. This novel method demonstrates that limb-darkening parameterizations contain important information about the structure of stellar atmospheres, with the potential to be a valuable tool for measuring stellar masses.Comment: 8 pages, 6 figures, 2 tables, A&A accepte

Effect of NLTE model atmospheres on photometric amplitudes and phases of early B-type pulsating stars

We study all possible sources of inaccuracy in theoretical values of the photometric observables, i.e. amplitude ratios and phase differences, of early B-type main sequence pulsators. Here, we discuss effects of parameters coming from both models of stellar atmospheres and linear nonadiabatic theory of stellar pulsation. In particular, we evaluate for the first time the effect of the departure from the LTE approximation. The atmospheric input comes from line-blanketed, LTE and NLTE plane-parallel, hydrostatic models. To compute the limb-darkening coefficients for NLTE models, we use the Least-Square Method taking into account the accuracy of the flux conservation. We present effects of NLTE atmospheres, chemical composition and opacities on theoretical values of the photometric observables of early B-type pulsators. To this end, we compute tables with the passband fluxes, flux derivatives over effective temperature and gravity as well as the non-linear limb-darkening coefficients in 12 most often used passbands, i.e. in the Str\"omgern system, $uvby$, and in the Johnson-Cousins-Glass system, $UBVRIJHK$. We make these tables public available at the Wroc{\l}aw HELAS Web page, http://helas.astro.uni.wroc.pl.Comment: 13 pages, 2 tables, 17 figues submitted to A&

Limb-darkening measurements for a cool red giant in microlensing event OGLE 2004-BLG-482

Aims: We present a detailed analysis of OGLE 2004-BLG-482, a relatively high-magnification single-lens microlensing event which exhibits clear extended-source effects. These events are relatively rare, but they potentially contain unique information on the stellar atmosphere properties of their source star, as shown in this study. Methods: Our dense photometric coverage of the overall light curve and a proper microlensing modelling allow us to derive measurements of the OGLE 2004-BLG-482 source star's linear limb-darkening coefficients in three bands, including standard Johnson-Cousins I and R, as well as in a broad clear filter. In particular, we discuss in detail the problems of multi-band and multi-site modelling on the expected precision of our results. We also obtained high-resolution UVES spectra as part of a ToO programme at ESO VLT from which we derive the source star's precise fundamental parameters. Results: From the high-resolution UVES spectra, we find that OGLE 2004-BLG-482's source star is a red giant of MK type a bit later than M3, with Teff = 3667 +/- 150 K, log g = 2.1 +/- 1.0 and an assumed solar metallicity. This is confirmed by an OGLE calibrated colour-magnitude diagram. We then obtain from a detailed microlensing modelling of the light curve linear limb-darkening coefficients that we compare to model-atmosphere predictions available in the literature, and find a very good agreement for the I and R bands. In addition, we perform a similar analysis using an alternative description of limb darkening based on a principal component analysis of ATLAS limb-darkening profiles, and also find a very good agreement between measurements and model predictions.Comment: Accepted in A&

Planetary Microlensing at High Magnification

Simulations of planetary microlensing at high magnification that were carried out on a cluster computer are presented. It was found that the perturbations due to two-thirds of all planets occur in the time interval [-0.5t_FWHM, 0.5t_ FWHM] with respect to the peak of the microlensing light curve, where t_FWHM is typically about 14 hours. This implies that only this restricted portion of the light curve need be intensively monitored for planets, a very significant practical advantage. Nearly all planetary detections in high magnification events will not involve caustic crossings. We discuss the issues involved in determining the planetary parameters in high magnification microlensing events. Earth mass planets may be detected with 1-m class telescopes if their projected orbital radii lie within about 1.5 - 2.5 AU. Giant planets are detectable over a much larger region. For multi-planet systems the perturbations due to individual planets can be separated under certain conditions. The size of the source star needs to be determined independently, but the presence of spots on the source star is likely to be negligible, as is the effect of planetary motion during an event.Comment: 12 pages, 13 embedded figures, accepted for publication by MNRA

Probing the atmosphere of the bulge G5III star OGLE-2002-BUL-069 by analysis of microlense H alpha line

We discuss high-resolution, time-resolved spectra of the caustic exit of the binary microlensing event OGLE 2002-BUL-69 obtained with UVES on the VLT. The source star is a G5III giant in the Galactic Bulge. During such events, the source star is highly magnified, and a strong differential magnification around the caustic resolves its surface. Using an appropriate model stellar atmosphere generated by the NextGEN code we obtained a model light curve for the caustic exit and compared it with a dense set of photometric observations obtained by the PLANET microlensing follow up network. We further compared predicted variations in the H alpha equivalent width with those measured from our spectra. While the model and observations agree in the gross features, there are discrepancies suggesting shortcomings in the model, particularly for the H alpha line core, where we have detected amplified emission from the stellar chromosphere as the source star's trailing limb exited the caustic. This achievement became possible by the provision of the OGLE-III Early Warning System, a network of small telescopes capable of nearly-continuous round-the-clock photometric monitoring, on-line data reduction, daily near-real-time modelling in order to predict caustic crossing parameters, and a fast and efficient response of a 8m-class telescope to a ``Target-Of-Opportunity'' observation request.Comment: 4 pages Latex, 3 figures, accepted for publication to astronomy and astrophysics letter

A comparative study of the electrochemical properties of vitamin B-6 related compounds at physiological pH

A comparative study of vitamin B6 group and related compounds in buffered solutions using electrochemical techniques has been performed at neutral pH. Irreversible bi- or tetra-electronic processes are observed for these substances, and the electron transfer coefficient (αn) calculated. It was concluded that either the first or second electron transfer were the rate determining step of the electrode process. The diffusion coefficient of these substances was calculated and the values given follow an inverse tendency to the molecular size. For aldehydes the values obtained were corrected of the hydration reaction. It is important to remark that catalytic waves were reported for the first time for these compounds. Using a model involving the nitrogen of the basic structure the kinetic constants were calculated for most of them

MOA-2010-BLG-477Lb: constraining the mass of a microlensing planet from microlensing parallax, orbital motion and detection of blended light

Microlensing detections of cool planets are important for the construction of an unbiased sample to estimate the frequency of planets beyond the snow line, which is where giant planets are thought to form according to the core accretion theory of planet formation. In this paper, we report the discovery of a giant planet detected from the analysis of the light curve of a high-magnification microlensing event MOA-2010-BLG-477. The measured planet-star mass ratio is $q=(2.181\pm0.004)\times 10^{-3}$ and the projected separation is $s=1.1228\pm0.0006$ in units of the Einstein radius. The angular Einstein radius is unusually large $\theta_{\rm E}=1.38\pm 0.11$ mas. Combining this measurement with constraints on the "microlens parallax" and the lens flux, we can only limit the host mass to the range $0.13<M/M_\odot<1.0$. In this particular case, the strong degeneracy between microlensing parallax and planet orbital motion prevents us from measuring more accurate host and planet masses. However, we find that adding Bayesian priors from two effects (Galactic model and Keplerian orbit) each independently favors the upper end of this mass range, yielding star and planet masses of $M_*=0.67^{+0.33}_{-0.13}\ M_\odot$ and $m_p=1.5^{+0.8}_{-0.3}\ M_{\rm JUP}$ at a distance of $D=2.3\pm0.6$ kpc, and with a semi-major axis of $a=2^{+3}_{-1}$ AU. Finally, we show that the lens mass can be determined from future high-resolution near-IR adaptive optics observations independently from two effects, photometric and astrometric.Comment: 3 Tables, 12 Figures, accepted in Ap

Gravitational Lensing

Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so far. It has two parts. In the first, starting from the equation of geodesic deviation, the equations of thin and extended gravitational lensing are derived. In the second, gravitational lensing by stars and planets, galaxies, galaxy clusters and large-scale structures is discussed and summarised.Comment: Invited review article to appear in Classical and Quantum Gravity, 85 pages, 15 figure