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Register a new userHigh-precision stellar limb-darkening in exoplanetary transits
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Characterization of the atmospheres of transiting exoplanets relies on accurate measurements of the extent of the optically thick area of the planet at multiple wavelengths with a precision $lesssim$100 parts per million (ppm). Next-generation instruments onboard the James Webb Space Telescope (JWST) are expected to achieve $sim$10 ppm precision for several tens of targets. A similar precision can be obtained in modelling only if other astrophysical effects, including the stellar limb-darkening, are accounted for properly. In this paper, we explore the limits on precision due to the mathematical formulas currently adopted to approximate the stellar limb-darkening, and to the use of limb-darkening coefficients obtained either from stellar-atmosphere models or empirically. We propose a new limb-darkening law with two coefficients, `power-2, which outperforms other two-coefficient laws adopted in the literature in most cases, and particularly for cool stars. Empirical limb-darkening based on two-coefficient formulas can be significantly biased, even if the light-curve residuals are nearly photon-noise limited. We demonstrate an optimal strategy to fitting for the four-coefficients limb-darkening in the visible, using prior information on the exoplanet orbital parameters to break some of the degeneracies that otherwise would prevent the convergence of the fit. Infrared observations taken with the James Webb Space Telescope (JWST) will provide accurate measurements of the exoplanet orbital parameters with unprecedented precision, which can be used as priors to improve the stellar limb-darkening characterization, and therefore the inferred exoplanet parameters, from observations in the visible, such as those taken with Kepler/K2, JWST, other past and future instruments.
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We provide here tables of stellar limb-darkening coefficients (LDCs) for the Ariel ESA M4 space mission. These tables include LDCs corresponding to different wavelength bins and white bands for the NIRSpec, AIRS-Ch0 and AIRS-Ch1 spectrographs, and those corresponding to the VISPhot, FGS1 and FGS2 photometers. The LDCs are calculated with the open-source software ExoTETHyS for three complete grids of stellar atmosphere models obtained with the ATLAS9 and PHOENIX codes. The three model grids are complementary, as the PHOENIX code adopts more modern input physics and spherical geometry, while the models calculated with ATLAS9 cover wider ranges of stellar parameters. The LDCs obtained from corresponding models in the ATLAS9 and PHOENIX grids are compared in the main text. All together the models cover the following ranges in effective temperature ($1,500 , K le T_{mbox{eff}} le 50,000 , K$), surface gravity (0.0 dex $le log{g} le 6.0$ dex), and metallicity ($-5.0 le [M/H] le 1.0$).
We measure a tilt of 86+-6 deg between the sky projections of the rotation axis of the WASP-7 star, and the orbital axis of its close-in giant planet. This measurement is based on observations of the Rossiter-McLaughlin (RM) effect with the Planet Finder Spectrograph on the Magellan II telescope. The result conforms with the previously noted pattern among hot-Jupiter hosts, namely, that the hosts lacking thick convective envelopes have high obliquities. Because the planets trajectory crosses a wide range of stellar latitudes, observations of the RM effect can in principle reveal the stellar differential rotation profile; however, with the present data the signal of differential rotation could not be detected. The host star is found to exhibit radial-velocity noise (``stellar jitter) with an amplitude of ~30m/s over a timescale of days.
We present here the first release of the open-source python package ExoTETHyS, which aims to provide a stand-alone set of tools for modeling spectro-photometric observations of the transiting exoplanets. In particular, we describe: (1) a new calculator of stellar limb-darkening coefficients that outperforms the existing software by one order of magnitude in terms of light-curve model accuracy, i.e., down to <10 parts per million (ppm); (2) an exact transit light-curve generator based on the entire stellar intensity profile rather than limb-darkening coefficients. New tools will be added in later releases to model various effects in exoplanetary transits and eclipsing binaries. ExoTETHyS is a reference package for high-precision exoplanet atmospheric spectroscopy with the upcoming JWST and ARIEL missions.
We present a novel, iterative method using an empirical Bayesian approach for modeling the limb darkened WASP-121b transit from the TESS light curve. Our method is motivated by the need to improve $R_{p}/R_{ast}$ estimates for exoplanet atmosphere modeling, and is particularly effective with the limb darkening (LD) quadratic law requiring no prior central value from stellar atmospheric models. With the non-linear LD law, the method has all the advantages of not needing atmospheric models but does not converge. The iterative method gives a different $R_{p}/R_{ast}$ for WASP-121b at a significance level of 1$sigma$ when compared with existing non-iterative methods. To assess the origins and implications of this difference, we generate and analyze light curves with known values of the limb darkening coefficients (LDCs). We find that non-iterative modeling with LDC priors from stellar atmospheric models results in an inconsistent $R_{p}/R_{ast}$ at 1.5$sigma$ level when the known LDC values are as those previously found when modeling real data by the iterative method. In contrast, the LDC values from the iterative modeling yields the correct value of $R_{p}/R_{ast}$ to within 0.25$sigma$. For more general cases with different known inputs, Monte Carlo simulations show that the iterative method obtains unbiased LDCs and correct $R_{p}/R_{ast}$ to within a significance level of 0.3$sigma$. Biased LDC priors can cause biased LDC posteriors and lead to bias in the $R_{p}/R_{ast}$ of up to 0.82$%$, 2.5$sigma$ for the quadratic law and 0.32$%$, 1.0$sigma$ for the non-linear law. Our improvement in $R_{p}/R_{ast}$ estimation is important when analyzing exoplanet atmospheres.
We obtain high-precision limb-darkening measurements in five bands (V, V_E, I_E, I, and H) for the K3 III (Teff=4200 K, [Fe/H]=+0.3, log(g)=2.3) source of the Galactic bulge microlensing event EROS BLG-2000-5. These measurements are inconsistent with the predictions of atmospheric models at >10 sigma. While the disagreement is present in all bands, it is most apparent in I, I_E and V_E, in part because the data are better and in part because the intrinsic disagreement is stronger. We find that when limb-darkening profiles are normalized to have unit total flux, the I-band models for a broad range of temperatures all cross each other at a common point. The solar profile also passes through this point. However, the profile as measured by microlensing does not. We conjecture that the models have incorporated some aspect of solar physics that is not shared by giant atmospheres.
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