High-resolution transmission spectroscopy is a powerful method for probing the extended atmospheres of short-period exoplanets. With the advancement of ultra-stable echelle spectrographs and the advent of 30-meter class telescopes on the horizon, even minor observational and physical effects will become important when modeling atmospheric absorption of atomic species. In this work we demonstrate how the non-uniform temperature across the surface of a fast rotating star, i.e., gravity darkening, can affect the observed transmission spectrum in a handful of atomic transitions commonly observed in short-period exoplanet atmospheres. We simulate transits of the ultra-hot Jupiters KELT-9 b and HAT-P-70 b but our results are applicable to all short-period gas giants transiting rapidly rotating stars. In general, we find that gravity darkening has a small effect on the average transmission spectrum but can change the shape of the absorption light curve, similar to the effect observed in broadband photometric transits. While the magnitude of gravity darkening effects are on the same order as the noise in transmission spectra observed with 10-meter class telescopes, future high-quality spectroscopic light curves for individual atomic absorption lines collected with 30-meter class telescopes will need to account for this effect.
This paper is part of an effort to correct the transmission spectra of a transiting planet orbiting an active star. In Paper I (Cracchiolo et al. 2020) we have demonstrated a methodology to minimize the potential bias induced by unocculted star spots on the transmission spectrum, assuming a spot model parameterized by filling factor and temperature. In this work we introduce the limb darkening effect, therefore the position of the spot in the stellar disk and the impact parameter of the transiting planet now play a key role. The method is tested on simulations of planetary transits of three re…
The transit method, employed by MOST, \emph{Kepler}, and various ground-based surveys has enabled the characterization of extrasolar planets to unprecedented precision. These results are precise enough to begin to measure planet atmosphere composition, planetary oblateness, star spots, and other phenomena at the level of a few hundred parts-per-million. However, these results depend on our understanding of stellar limb darkening, that is, the intensity distribution across the stellar disk that is sequentially blocked as the planet transits. Typically, stellar limb darkening is assumed to be a …
The detection of the first exoplanet paved the way into the era of transit photometry space missions with a revolutionary photometric precision that aim at discovering new exoplanetary systems around different types of stars. With this high precision, it is possible to derive very accurately the radii of exoplanets which is crucial for constraining their type and composition. However, it requires an accurate description of host stars, especially their center-to-limb variation of intensities (so called limb darkening) as it affects the planet-to-star radius ratio determination. We aim at improv…
We release the first grid of stellar limb-darkening coefficients (LDCs) and intensity profiles (IPs) computed by the consortium of the PLAnetary Transits and Oscillations of stars (PLATO), the next medium-class (M3) mission under development by the European Space Agency (ESA) to be launched in 2026. We have performed spectral synthesis with \texttt{TurboSpectrum} on a grid of \texttt{MARCS} model atmospheres. Finally, we adopted \texttt{ExoTETHyS} to convolve the high-resolution spectra ($R=2\times10^5$) with the state-of-the-art response functions for all the PLATO cameras, and computed the L…
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…
We compute the emergent stellar spectra from the UV to far infrared for different viewing angles using realistic 3D model atmospheres for a large range in stellar parameters to predict the stellar limb darkening. We have computed full 3D LTE synthetic spectra based on 3D radiative hydrodynamic atmosphere models from the Stagger-grid. From the resulting intensities at different wavelength, we derived coefficients for the standard limb darkening laws considering a number of often-used photometric filters. Furthermore, we calculated theoretical transit light curves, in order to quantify the diffe…
Limb-darkening is fundamental in determining transit lightcurve shapes, and is typically modeled by a variety of laws that parametrize the intensity profile of the star that is being transited. Confronted with a transit lightcurve, some authors fix the parameters of these laws, the so-called limb-darkening coefficients (LDCs), while others prefer to let them float in the lightcurve fitting procedure. Which of these is the best strategy, however, is still unclear, as well as how and by how much each of these can bias the retrieved transit parameters. In this work we attempt to clarify those poi…
The ability to observe extrasolar planets transiting their stars has profoundly changed our understanding of these planetary systems. However, these measurements depend on how well we understand the properties of the host star, such as radius, luminosity and limb darkening. Traditionally, limb darkening is treated as a parameterization in the analysis, but these simple parameterizations are not accurate representations of actual center-to-limb intensity variations (CLIV) to the precision needed for interpreting these transit observations. This effect leads to systematic errors for the measured…
The depth of an exoplanetary transit in the light curve of a distant star is commonly approximated as the squared planet-to-star radius ratio, (R_p/R_s)^2. Stellar limb darkening, however, results in significantly deeper transits. Here we derive analytical solutions to the overshoot of the mid-transit depth caused by stellar limb darkening compared to the (R_p/R_s)^2 estimate for arbitrary transit impact parameters. In turn, this allows us to compute the true planet-to-star radius ratio from the transit depth for a given parameterization of a limb darkening law and for a known transit impact p…
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 mathemat…
Limb darkening is an important stellar phenomenon and must be accounted for in the study of stellar spectra, eclipsing binaries, transiting planetary systems, and microlensing events. The power-2 limb-darkening law provides a good match to the specific intensities predicted by stellar atmosphere models: it is better than other two-parameter laws and is only surpassed by the four-parameter law. Predictions of the limb-darkening coefficients for the power-2 law are not widely available. We therefore compute them, using stellar atmosphere models generated by the ATLAS (plane-parallel) code. Limb-…
WASP-33 is one of the few $δ$ Sct stars with a known planetary companion. By analyzing the stellar oscillations, we search for possible star-planet interactions in the pattern of the pulsation. We made use of the Transit and Light Curve Modeller (TLCM) to solve the light curve from the Transiting Exoplanet Survey Satellite (TESS). We include gravity darkening into our analysis. The stellar oscillation pattern of WASP-33 clearly shows signs of several tidally perturbed modes. We find that there are peaks in the frequency spectrum that are at or near the $3$rd, $12$th and $25$th orbital harmonic…
Limb darkening laws are convenient parameterizations of the stellar intensity center-to-limb variation, and their use is ubiquitous in eclipse and transit modeling. But they are not "laws" in any sense -- they are simple approximations of the real intensity variations, and their limitations are becoming more and more apparent as stellar atmosphere models improve and higher precision data become available. When fitting eclipses and transit light curves, one would ideally like to use model intensities that are based on fundamental stellar parameters such as the mass, radius, and effective temper…
Where does the simplified Stellar Contamination Model fail in Exoplanet Transmission Spectroscopy?
Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；Center for Radio Astronomy and Astrophysics Mackenzie (CRAAM), Mackenzie Presbyterian University（麦肯锡长老会大学射电天体物理学中心）
We release a new grid of stellar limb-darkening coefficients (LDCs, using the quadratic, power-2 and claret-4 laws) and intensity profiles for the Kepler, U, B, V and R passbands, based on STAGGER model atmospheres. The data can be downloaded from Zenodo (doi:10.5281/zenodo.5593162). We compare the newly-released LDCs, computed by ExoTETHyS, with previously published values, based on the same atmospheric models using a so-called "SPAM" procedure. The SPAM method relies on synthetic light curves in order to compute the LDCs that best represent the photometry of exoplanetary transits. We confirm…
Power-2 limb-darkening coefficients for the $uvby$, $UBVRIJHK$, SDSS $ugriz$, Gaia, Kepler, TESS, and CHEOPS photometric systems II. PHOENIX spherically symmetric stellar atmosphere models
Inaccurate limb-darkening models can be a significant source of error in the analysis of the light curves for transiting exoplanet and eclipsing binary star systems. To test the accuracy of published limb-darkening models, I have compared limb-darkening profiles predicted by stellar atmosphere models to the limb-darkening profiles measured from high-quality light curves of 43 FGK-type stars in transiting exoplanet systems observed by the Kepler and TESS missions. The comparison is done using the parameters $h^{\prime}_1 = I_λ(\frac{2}{3})$ and $h^{\prime}_2 = h^{\prime}_1 - I_λ(\frac{1}{3})$, …
Although the main goal of the Transiting Exoplanet Survey Satellite (\textit{TESS}) is to search for new transiting exoplanets, its data can also be used to study in further detail already known systems. The \textit{TESS} bandpass is particularly interesting to study the limb-darkening effect of the stellar host which is imprinted in transit lightcurves, as the widely used \textsc{phoenix} and \textsc{atlas} stellar models predict different limb-darkening profiles. Here we study this effect by fitting the transit lightcurves of 176 known exoplanetary systems observed by \textit{TESS}, which al…
Published photometry of fading events in the PTFO 8-8695 system is modelled using improved treatments of stellar geometry, surface intensities, and, particularly, gravity darkening, with a view to testing the planetary-transit hypothesis. Variability in the morphology of fading events can be reproduced by adopting convective-envelope gravity darkening, but near-critical stellar rotation is required. This leads to inconsistencies with spectroscopic observations; the model also predicts substantial photometric variability associated with stellar precession, contrary to observations. Furthermore,…
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 lat…
We present here the first application of Stellar and Exoplanetary Atmospheres Bayesian Analysis Simultaneous Spectroscopy (SEA BASS) on real datasets. SEA BASS is a scheme that enables the simultaneous derivation of four-coefficient stellar limb-darkening profiles, transit depths, and orbital parameters from exoplanetary transits at multiple wavelengths. It relies on the wavelength-independence of the system geometry and on the reduced limb-darkening effect in the infrared. This approach has been introduced by Morello et al. (2017) (without the SEA BASS acronym), who discuss several tests on s…
MASCARA-4 b is a hot Jupiter in a highly-misaligned orbit around a rapidly-rotating A3V star that was observed for 54 days by the Transiting Exoplanet Survey Satellite (\tess). We perform two analyses of MASCARA-4 b using a stellar gravity-darkened model. First, we measure MASCARA-4 b's misaligned orbital configuration by modeling its \tess~photometric light curve. We take advantage of the asymmetry in MASCARA-4 b's transit due to its host star's gravity-darkened surface to measure MASCARA-4 b's true spin-orbit angle to be $104^{\circ+7^\circ}_{-13^\circ}$. We also detect a $\sim4σ$ secondary …
Analysis of the transit light curve deformed by the stellar gravity darkening allows us to photometrically measure both components of the spin-orbit angle $ψ$, its sky projection $λ$ and inclination of the stellar spin axis $i_\star$. In this paper, we apply the method to two transiting hot Jupiter systems monitored with the Kepler spacecraft, Kepler-13A and HAT-P-7. For Kepler-13A, we find $i_\star=81^\circ\pm5^\circ$ and $ψ=60^\circ\pm2^\circ$ adopting the spectroscopic constraint $λ=58.6^\circ\pm2.0^\circ$ by Johnson et al. (2014). In our solution, the discrepancy between the above $λ$ and …
The CARMENES search for exoplanets around M dwarfs. A homogeneous catalogue of projected rotational velocities accounting for limb-darkening
Instituto de Astrofísica de Andalucía, CSIC（安达卢西亚天体物理研究所，西班牙高等科学研究委员会）；INAF- Palermo Astronomical Observatory（意大利国家天体物理研究所巴勒莫天文台）；Institut für Astrophysik und Geophysik, Georg-August-Universität Göttingen（哥廷根大学天体物理学与地球物理学研究所）；Centro de Astrobiología, CSIC-INTA（天体生物学中心，西班牙高等科学研究委员会-国家航空航天技术研究所）；Universidad de Granada（格拉纳达大学）；Landessternwarte, Zentrum für Astronomie der Universität Heidelberg（海德堡大学天文学中心州立天文台）
提出一种结合真实临边昏暗模型的过采样卷积方法，从 CARMENES 光谱精确测量 M 矮星的投影自转速度，构建了目前最大的均匀星表，测量精度显著优于文献。
Stellar spectra contain a large amount of information about the conditions in stellar atmospheres. However, extracting this information is challenging and demands comprehensive numerical modelling. Here, we present stellar spectra synthesized using the recently developed state-of-the-art MPS-ATLAS code on a fine grid of stellar fundamental parameters. These calculations have been extensively validated against solar and stellar observations and can be used for various astrophysical applications. The spectra are available at the Max Planck Digital Library (MPDL, https://edmond.mpdl.mpg.de/datase…
We present Subaru/SCExAO+CHARIS broadband ($JHK$-band) integral field spectroscopy of HD 34700 A. CHARIS data recover HD 34700 A's disk ring and confirm multiple spirals discovered in Monnier et al. (2019). We set limits on substellar companions of $\sim12\ M_{\rm Jup}$ at $0\farcs3$ (in the ring gap) and $\sim5\ M_{\rm Jup}$ at $0\farcs75$ (outside the ring). The data reveal darkening effects on the ring and spiral, although we do not identify the origin of each feature such as shadows or physical features related to the outer spirals. Geometric albedoes converted from the surface brightness …
We present ten high-precision light curves of four transits in the XO-1 planetary system, obtained using $u$, $g$, $r$, redshifted H$α$, $I$ and $z$ filters. We use these to measure the physical properties, orbital ephemeris, and a transmission spectrum of the planet covering the full optical wavelength range. We augment this with published HST/WFC3 observations to construct a transmission spectrum of the planet covering 0.37 to 1.65 $μ$m. Our best-fitting model to this spectrum is for a H$_2$/He-rich atmosphere containing water (3.05$σ$ confidence), nitrogen-bearing molecules NH$_3$ and HCN (…
I model the effect of rapid stellar rotation on a planet's insolation. Fast-rotating stars have induced pole-to-equator temperature gradients (known as gravity-darkening) of up to several thousand Kelvin that affect the star's luminosity and peak emission wavelength as a function of latitude. When orbiting such a star, a planet's annual insolation can strongly vary depending on its orbit inclination. Specifically, inclined orbits result in temporary exposure to the star's hotter poles. I find that gravity-darkening can drive changes in a planet's equilibrium temperature of up to $\sim15\%$ due…
To a first approximation, the microlensing phenomenon is achromatic, and great advancement has been achieved in the interpretation of the achromatic signals, which among other achievements has led to the discovery and characterization of well above $100$ new exoplanets. At higher order accuracy in the observations, microlensing has a chromatic component (a color term) which has so far been much less explored. Here, we analyze the chromatic microlensing effect of $4$ different physical phenomena, which have the potential to add important new knowledge about the stellar properties not easily rea…
During primary transits, the spectral signatures of an exoplanet atmosphere can be measured using transmission spectroscopy. The goal of this work is to accurately measure the atomspheric sodium absorption light curve in HD189733b, correcting for the effects of stellar differential limb-darkening, stellar activity and a "bump" caused by the changing radial velocity of the exoplanet. In fact, due to the high cadence and quality of our data, it is the first time that the last feature can be detected even by visual inspection. We use 244 high-resolution optical spectra taken by the UVES instrumen…
The orbital sampling effect (OSE) appears in phase-folded transit light curves of extrasolar planets with moons. Analytical OSE models have hitherto neglected stellar limb darkening and non-zero transit impact parameters and assumed that the moon is on a circular, co-planar orbit around the planet. Here, we present an analytical OSE model for eccentric moon orbits, which we implement in a numerical simulator with stellar limb darkening that allows for arbitrary transit impact parameters. We also describe and publicly release a fully numerical OSE simulator (PyOSE) that can model arbitrary incl…
Transmission spectra of exoplanets orbiting active stars suffer from wavelength-dependent effects due to stellar photospheric heterogeneity. WASP-19b, an ultra-hot Jupiter (T$_{eq}$ $\sim$ 2100 K), is one such strongly irradiated gas-giant orbiting an active solar-type star. We present optical (520-900 nm) transmission spectra of WASP-19b obtained across eight epochs using the Gemini Multi-Object Spectrograph (GMOS) on the Gemini-South telescope. We apply our recently developed Gaussian Processes regression based method to model the transit light curve systematics and extract the transmission …
Due to stellar rotation, the observed radial velocity of a star varies during the transit of a planet across its surface, a phenomenon known as the Rossiter-McLaughlin (RM) effect. The amplitude of the RM effect is related to the radius of the planet which, because of differential absorption in the planetary atmosphere, depends on wavelength. Therefore, the wavelength-dependent RM effect can be used to probe the planetary atmosphere. We measure for the first time the RM effect of the Earth transiting the Sun using a lunar eclipse observed with the ESO HARPS spectrograph. We analyze the observe…
Aims. We aim to investigate the origin of the discrepant results reported in the literature about the presence of Na I in the atmosphere of HD209458 b, based on low- and high-resolution transmission spectroscopy. Methods. We generated synthetic planetary atmosphere models and we compared them with the transmission light curves and spectra observed in previous studies. Our models account for the stellar limb-darkening and Rossiter-McLaughlin (RM) effects, and contemplate various possible scenarios for the planetary atmosphere. Results. We reconciled the discrepant results by identifying a range…
Mostly multiband photometric transit observations have been used so far to retrieve broadband transmission spectra of transiting exoplanets in order to study their atmosphere. An alternative method has been proposed and has only been used once to recover transmission spectra using chromatic Rossiter-McLaughlin observations. Stellar activity has been shown to potentially imitate narrow and broadband features in the transmission spectra retrieved from multiband photometric observations; however, there has been no study regarding the influence of stellar activity on the retrieved transmission spe…
The impact of unocculted stellar surface heterogeneities in the form of cool spots and hot faculae on the spectrum of a transiting planet has been a daunting problem for the characterization of exoplanet atmospheres. The wavelength-dependent nature of stellar surface heterogeneities imprinting their signatures on planetary transmission spectra are of concern particularly for systems of sub-Neptunes orbiting M-dwarfs. Here we present a systematic exploration of the impact of this spot-contamination on simulated near infrared transmission spectra of sub-Neptune planets. From our analysis, we fin…
In-depth studies of exoplanetary atmospheres are starting to become reality. In order to unveil their properties in detail, we need spectra with a higher S/N and also more sophisticated analysis methods. With high-resolution spectrographs, we can not only detect the sodium feature in the atmosphere of exoplanets, but also characterize it by studying its line profile. After finding a clearly w-shaped sodium line profile in the transmission spectrum of HD189733b, we investigated possible sources of contamination given by the star and tried to correct for these spurious deformations. By analyzing…
Transmission spectroscopy during planetary transits is expected to be a major source of information on the atmospheres of small (approximately Earth-sized) exoplanets in the next two decades. This technique, however, is intrinsically affected by stellar spectral contamination caused by the fact that stellar photo- and chromospheres are not perfectly homogeneous. Such stellar contamination will often reach or exceed the signal introduced by the planetary spectral features. Finding effective methods to correct stellar contamination -- or at least to quantify its possible range -- for the most im…
We present an attempt to improve models of the Rossiter-McLaughlin effect by relaxing several restrictive assumptions. We consider the entire multiline stellar spectrum rather than just a single line, use no assumptions about the shape of the lines profiles, and allow arbitrary size ratio for the star and its eclipser. However, we neglect the effect of macro-turbulence and differential rotation. We construct our model as a power series in the stellar rotation velocity, $V\sin i$, giving a closed set of analytic formulae for up to three terms, and assuming quadratic limb-darkening law. We consi…
The goal of this study is to assess the impact of the stellar spots on the extraction of the planetary transmission spectra observed by ARIEL. We develop a method to model the stellar spectrum of a star in the presence of spots by using the out-of-transit observations. It is based on a chi squared minimization procedure of the out-of-transit spectrum on a grid of stellar spectra with different sizes and temperatures of the spots. The approach allows us also to study the temporal evolution of the spots when comparing stellar spectra observed at different epochs. We also present a method to corr…
Transmission spectra probe the atmospheres of transiting exoplanets, but these observations are also subject to signals introduced by magnetic active regions on host stars. Here we outline scientific opportunities in the next decade for providing useful constraints on stellar photospheres and inform interpretations of transmission spectra of the smallest ($R<4\,R_{\odot}$) exoplanets. We identify and discuss four primary opportunities: (1) refining stellar magnetic active region properties through exoplanet crossing events; (2) spectral decomposition of active exoplanet host stars; (3) joint r…
Transmission spectroscopy characterizes the wavelength dependence of transit depth, revealing atmospheric absorption features in planetary terminator regions. In this context, different optical transmission spectra of HAT-P-12b reported in previous studies exhibited discrepant atmospheric features (e.g., Rayleigh scattering, alkali absorption). We aim to understand the atmosphere of HAT-P-12b using two transit spectroscopic observations by the Gran Telescopio CANARIAS (GTC), and to search for evidence of stellar activity contaminating the transmission spectra, which might be the reason behind …
