Gravitational microlensing as a test of stellar model atmospheres

We present calculations illustrating the potential of gravitational microlensing to discriminate between classical models of stellar surface brightness profiles and the recently computed ``Next Generation'' models of Hauschildt et al. These spherically-symmetric models include a much improved treatment of molecular lines in the outer atmospheres of cool giants -- stars which are very typical sources in Galactic bulge microlensing events. We show that the microlensing signatures of intensively monitored point and fold caustic crossing events are readily able to distinguish between NextGen and the classical models, provided a photometric accuracy of 0.01 magnitudes is reached. This accuracy is now routinely achieved by alert networks, and hence current observations can discriminate between such model atmospheres, providing a unique insight on stellar photospheres.Comment: 4 pages, 4 figures, Astronomy & Astrophysics (Letters), vol. 388, L1 (2002

Resolving Stellar Atmospheres I: The H alpha line and comparisons to microlensing observations

We present work on H alpha spectral line characteristics in PHOENIX stellar model atmospheres and their comparison to microlensing observations. We examine in detail the H alpha equivalent width (EW) and the line shape characteristics for effective temperatures of 4500K< Teff < 5600K where H alpha is a strong spectral feature. We find that H alpha EW in models calculated under the assumption of local thermodynamic equilibrium (LTE) is up to 15% smaller than in models without this assumption, non-LTE models (NLTE) and that line shapes vary significantly for the two model types. A comparison with available high quality microlensing data, capable of tracing H alpha absorption across the face of one G5III giant, shows that the LTE model that fits the EW best is about 100K hotter than and the best-fitting NLTE model has a similar Teff as predicted by the spectral type analysis of the observed star but agree within the uncertainties of the observationally derived temperature. Neither LTE nor NLTE models fit the line shape well. We suspect unmodelled chromospheric emission. Line shape diagnostics suggest lower gravities than derived for the star and are unacceptable low in the case of the LTE models. We show that EW alone is insufficient for comparison to stellar model atmospheres, but combined with a new shape parameter we define is promising. In stellar parameter ranges where the H alpha line is strong, a NLTE approach of modeling stellar atmospheres is not only beneficial but mandatory.Comment: 11 pages, 9 figures, accepted to Astronomy & Astrophysic

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&

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

New limb-darkening coefficients and synthetic photometry for model-atmosphere grids at Galactic, LMC, and SMC abundances

New grids of Atlas9 models have been calculated using revised convection parameters and updated opacity-distribution functions, for chemical compositions intended to be representative of solar, [M/H] = +0.3, +0.5, Large Magellanic Cloud (LMC), and Small Magellanic Cloud (SMC) abundances. The grids cover T(eff) = 3.5-50kK, from log(g) = 5.0 to the effective Eddington limit. Limb-darkening coefficients and synthetic photometry are presented in the UBVRIJHKLM, uvby, ugriz, WFCAM, Hipparcos/Tycho, and Kepler passbands for these models, and for Castelli's comparable `new-ODF' grids. Flux distributions are given for the new models. The sensitivity of limb-darkening coefficients to the adopted physics is illustrated

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

Limb darkening laws for two exoplanet host stars derived from 3D stellar model atmospheres

We compare limb darkening laws derived from 3D hydrodynamical model atmospheres and 1D hydrostatic MARCS models for the host stars of the two transiting exoplanet systems HD 209458 and HD 189733. The surface brightness distribution of the stellar disks is calculated using 3D LTE spectrum formation and opacity sampling. We test our predictions using least-squares fits of model light curves to primary eclipses that were observed with the Hubble Space Telescope (HST). The limb darkening law derived from the 3D model of HD 209458 between 2900 A and 5700 A produces significantly better fits to the HST data, removing systematic residuals that were previously observed for model light curves based on 1D predictions. This difference arises mainly from the shallower mean temperature structure of the 3D model, which is a consequence of the explicit simulation of surface granulation. In the case of HD 189733, the model atmospheres produce practically equivalent limb darkening curves between 2900 A and 5700 A, partly due to obstruction by spectral lines, and the data are not sufficient to distinguish between the light curves. We also analyze HST observations between 5350 A and 10500 A for this star; the 3D model leads to a better fit compared to 1D predictions. The significant improvement of fit quality for the HD 209458 system demonstrates the higher degree of realism of 3D models and the importance of surface granulation for the formation of the atmospheric radiation field of late-type stars. This result agrees well with recent investigations of limb darkening in the solar continuum and other observational tests. The case of HD 189733 is no contradiction as the model light curves are less sensitive to the temperature stratification of the atmosphere and the observed data in the 2900 A - 5700 A region are not sufficient to distinguish more clearly between 3D and 1D limb darkening.Comment: To be published in Astronomy & Astrophysics (article accepted

Discovery and Mass Measurements of a Cold, 10-Earth Mass Planet and Its Host Star

We present the discovery and mass measurement of the cold, low-mass planet MOA-2009-BLG-266Lb, made with the gravitational microlensing method. This planet has a mass of m_p = 10.4 +- 1.7 Earth masses and orbits a star of mass M_* = 0.56 +- 0.09 Solar masses at a semi-major axis of a = 3.2 (+1.9 -0.5) AU and an orbital period of P = 7.6 (+7.7 -1.5} yrs. The planet and host star mass measurements are enabled by the measurement of the microlensing parallax effect, which is seen primarily in the light curve distortion due to the orbital motion of the Earth. But, the analysis also demonstrates the capability to measure microlensing parallax with the Deep Impact (or EPOXI) spacecraft in a Heliocentric orbit. The planet mass and orbital distance are similar to predictions for the critical core mass needed to accrete a substantial gaseous envelope, and thus may indicate that this planet is a "failed" gas giant. This and future microlensing detections will test planet formation theory predictions regarding the prevalence and masses of such planets.Comment: 38 pages with 7 figure