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 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…
We consider the issue of excessive TTV noise observed for the exoplanet HD 189733 b. Trying to explain it through the host star photospheric activity, we model the stellar surface brightness as a random field, then characterize statistical properties of the resulting transit signal perturbation and compute individual corrections to transit timings uncertainties. We find that possible effect of the photospheric brightness field can explain only a minor portion ($\sim 10$ s) of the observed ($\sim 70$ s) TTV excess of HD 189733, suggesting that the rest should be attributed to other sources. Reg…
We present results of numerical simulations of flux and linear polarization variations in transiting exoplanetary systems, caused by the host star disk symmetry breaking. We consider different configurations of planetary transits depending on orbital parameters. Starspot contribution to the polarized signal is also estimated. Applying the method to known systems and simulating observational conditions, a number of targets is selected where transit polarization effects could be detected. We investigate several principal benefits of the transit polarimetry, particularly, for determining orbital …
We describe how the accurate characterization of exoplanetary atmospheres in the ELT and JWST era will inevitably require taking into consideration the stellar inhomogeneities caused by convection and magnetic fields. The existing evidence that demonstrates the mixture of stellar and planetary signatures in observed transiting spectra is presented. Finally, we discuss how to disentangle these two components through a multipronged approach that includes new solar reference spectra, improved MHD modeling, and synergistic collaborations between the communities involved, from solar to stellar and …
We developed a dedicated statistical test for a massive detection of spot- and facula-crossing anomalies in multiple exoplanetary transit lightcurves, based on the frequentist $p$-value thresholding. This test was used to augment our algorithmic pipeline for transit lightcurves analysis. It was applied to $1598$ amateur and professional transit observations of $26$ targets being monitored in the EXPANSION project. We detected $109$ statistically significant candidate events revealing a roughly $2:1$ asymmetry in favor of spots-crossings over faculae-crossings. Although some candidate anomalies…
The discovery of transiting extrasolar planets has enabled us a number of interesting stduies. Transit photometry reveals the radius and the orbital inclination of transiting planets, and thereby we can learn the true mass and the density of respective planets by the combined information of radial velocity measurements. In addition, follow-up observations of transiting planets such as secondary eclipse, transit timing variations, transmission spectroscopy, and the Rossiter-McLaughlin effect provide us information of their dayside temperature, unseen bodies in systems, planetary atmospheres, an…
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…
Independent Component Analysis (ICA) has recently been shown to be a promising new path in data analysis and de-trending of exoplanetary time series signals. Such approaches do not require or assume any prior or auxiliary knowledge on the data or instrument in order to de-convolve the astrophysical light curve signal from instrument or stellar systematic noise. These methods are often known as 'blind source separation' (BSS) algorithms. Unfortunately all BSS methods suffer from a amplitude and sign ambiguity of their de-convolved components which severely limits these methods in low signal-to-…
Transiting extrasolar planets provide an opportunity to study the mass-radius relation of planets as well as their internal structure. The existence of a secondary eclipse enables further study of the thermal properties of the the planet by observing at infrared wavelengths. The probability of an observable secondary eclipse depends upon the orbital parameters of the planet, particularly eccentricity and argument of periastron. Here we provide analytical expressions for these probabilities, investigate their properties, and calculate their values for the known extrasolar planets. We furthermor…
The Near Earth Object Surveillance Satellite (NEOSSat) is a Canadian-led 15 cm Earth-orbiting telescope originally designed to detect asteroids near the Sun. Its design is however also suitable for the observation of exoplanetary transits of bright stars. We used the NEOSSat platform to perform followup observations of several Transiting Exoplanets Survey Satellite (TESS) targets, both as a demonstration of NEOSSat capabilities for exoplanetary science and improve the orbital ephemerides and properties of these exoplanet systems. We are able to recover / confirm the orbital properties of such …
We determine the starspot detection rate in exoplanetary transit light curves for M and K dwarf stars observed by the Transiting Exoplanet Survey Satellite (TESS) using various starspot filling factors and starspot distributions. We used $3.6\times10^9$ simulations of planetary transits around spotted stars using the transit-starspot model \prism. The simulations cover a range of starspot filling factors using one of three distributions: uniform, polar-biased, and mid-latitude. After construction of the stellar disc and starspots, we checked the transit cord for starspots and examined the chan…
The precise derivation of transit depths from transit light curves is a key component for measuring exoplanet transit spectra, and henceforth for the study of exoplanet atmospheres. However, it is still deeply affected by various kinds of systematic errors and noise. In this paper we propose a new detrending method by reconstructing the stellar flux baseline during transit time. We train a probabilistic Long Short-Term Memory (LSTM) network to predict the next data point of the light curve during the out-of-transit, and use this model to reconstruct a transit-free light curve - i.e. including …
Most future surveys designed to discover transiting exoplanets, including TESS and PLATO, will target bright (V<13) and nearby solar-type stars having a spectral type later than F5. In order to enhance the probability of identifying transits, these surveys must cover a very large area on the sky, because of the intrinsically low areal density of bright targets. Unfortunately, no existing catalog of stellar parameters is both deep and wide enough to provide a homogeneous input list. As the first Gaia data release exploitable for this purpose is expected to be released not earlier than late 2017…
Precise exoplanet characterization requires precise classification of exoplanet host stars. The masses of host stars are commonly estimated by comparing their spectra to those predicted by stellar evolution models. However, spectroscopically determined properties are difficult to measure accurately for stars that are substantially different from the Sun, such as M-dwarfs and evolved stars. Here, we propose a new method to dynamically measure the masses of transiting planets near mean-motion resonances and their host stars by combining observations of transit timing variations with radial veloc…
We perform a series of time dependent Magnetohydrodynamic simulations of the HD 189733 star-planet system in order to predict radio transit modulations due to the interaction between the stellar wind and planetary magnetic field. The simulation combines a model for the stellar corona and wind with an exoplanet that is orbiting the star in a fully dynamic, time-dependent manner. Our simulations generate synthetic radio images that enable us to obtain synthetic radio lightcurves in different frequencies. We find a clear evidence for the planetary motion in the radio light curves. Moreover, we fi…
We study the long-term time-scale (i.e. period comaprable to the orbital period of the outer perturber object) transit timing variations in transiting exoplanetary systems which contain a further, more distant (a_2>>a_1) either planetary, or stellar companion. We give an analytical form of the O-C diagram (which describes such TTV-s) in trigonometric series, valid for arbitrary mutual inclinations, up to the sixth order in the inner eccentricity. We show that the dependence of the O-C on the orbital and physical parameters can be separated into three parts. Two of these are independent of the …
Observations of exoplanetary systems provide clues about the intrinsic distribution of planetary systems, their architectures, and how they formed. We develop a forward modelling framework for generating populations of planetary systems and "observed" catalogues by simulating the Kepler detection pipeline (SysSim). We compare our simulated catalogues to the Kepler DR25 catalogue of planet candidates, updated to include revised stellar radii from Gaia DR2. We constrain our model based on the observed 1D marginal distributions of orbital periods, period ratios, transit depths, transit depth rati…
A search for extrasolar planetary transits using the extended Kepler mission (K2) campaigns 9 and 11 revealed five new candidates towards the Galactic bulge. The stars EPIC 224439122, 224560837, 227560005, 230778501 and 231635524 are found to have low amplitude transits consistent with extrasolar planets, with periods P = 35.1695, 3.6390, 12.4224, 17.9856, and 5.8824 days, respectively. The K2 data and existing optical photometry are combined with the multi-band near-IR photometry of the VVV survey and 2MASS in order to measure accurate physical parameters for the host stars. We then measure t…
We present EXOFAST, a fast, robust suite of routines written in IDL which is designed to fit exoplanetary transits and radial velocity variations simultaneously or separately, and characterize the parameter uncertainties and covariances with a Differential Evolution Markov Chain Monte Carlo method. We describe how our code incorporates both data sets to simultaneously derive stellar parameters along with the transit and RV parameters, resulting in more self-consistent results on an example fit of the discovery data of HAT-P-3b that is well-mixed in under five minutes on a standard desktop comp…
One of the persistent complications in searches for transiting exoplanets is the low percentage of the detected candidates that ultimately prove to be planets, which significantly increases the load on the telescopes used for the follow-up observations to confirm or reject candidates. Several attempts have been made at creating techniques that can pare down candidate lists without the need of additional observations. Some of these techniques involve a detailed analysis of light curve characteristics; others estimate the stellar density or some proxy thereof. In this paper, we extend upon this …
It has been posited that lunar eclipse observations may help predict the in-transit signature of Earth-like extrasolar planets. However, a comparative analysis of the two phenomena addressing in detail the transport of stellar light through the planet's atmosphere has not yet been presented. Here, we proceed with the investigation of both phenomena by making use of a common formulation. Our starting point is a set of previously unpublished near-infrared spectra collected at various phases during the August 2008 lunar eclipse. We then take the formulation to the limit of an infinitely distant o…
Here we present juliet, a versatile tool for the analysis of transits, radial-velocities, or both. juliet is built over many available tools for the modelling of transits, radial-velocities and stochastic processes (here modelled as Gaussian Processes; GPs) in order to deliver a tool/wrapper which can be used for the analysis of transit photometry and radial-velocity measurements from multiple instruments at the same time, using nested sampling algorithms which allows it to not only perform a thorough sampling of the parameter space, but also to perform model comparison via bayesian evidences.…
Stellar high-energy radiation (X-ray and extreme ultraviolet, XUV) drives atmospheric escape in close-in exoplanets. Given that stellar irradiation depends on the stellar magnetism and that stars have magnetic cycles, we investigate how cycles affect the evolution of exoplanetary atmospheric escape. Firstly, we consider a hypothetical HD209458b-like planet orbiting the Sun. For that, we implement the observed solar XUV radiation available over one and a half solar cycles in a 1D hydrodynamic escape model of HD209458b. We find that atmospheric escape rates show a cyclic variation (from 7.6 to 1…
The measurement of an exoplanet's oblateness and obliquity provides insights into the planet's internal structure and formation history. Previous work using small differences in the shape of the transit light curve has been moderately successful, but was hampered by the small signal and extreme photometric precision required. The measurement of changes in transit depth, caused by the spin precession of an oblate planet, was proposed as an alternative method. Here, we present the first attempt to measure these changes. Using Kepler photometry, we examined the brown dwarf Kepler-39b and the warm…
(Shortened) We have used the measured properties of the stars in the 79 exoplanetary systems with one or more planets that have been observed in transit, to estimate each system's present habitability. The measured stellar properties have been used to determine the present location of the classical habitable zone (HZ). To establish habitability we use the estimated distances from the giant planet(s) within which an Earth-like planet would be inside the gravitational reach of the giant. Of the 79 transiting systems known in April 2010, only 2 do not offer safe havens to Earth-like planets in th…
It has been shown that spectroscopy of transiting extrasolar planets can potentially provide a wealth of information about their atmospheres. Herein, we set up the inverse problem in spectroscopic retrieval. We use non-linear optimal estimation to retrieve the atmospheric state (pioneered for Earth sounding by Rodgers 1976, 2000). The formulation quantifies the the degrees-of-freedom and information content of the spectrum with respect to geophysical parameters; herein, we focus specifically on temperature and composition. First, we apply the technique to synthetic near infrared spectra, and e…
We present the analysis of 4 months of Kepler photometry of the K4V star HAT-P-11, including 26 transits of its "super-Neptune" planet. The transit data exhibit numerous anomalies that we interpret as passages of the planet over dark starspots. These spot-crossing anomalies preferentially occur at two specific phases of the transit. These phases can be understood as the intersection points between the transit chord and the active latitudes of the host star, where starspots are most abundant. Based on the measured characteristics of spot-crossing anomalies, and previous observations of the Ross…
Catholic University of America（美国天主教大学）；Tel Aviv University（特拉维夫大学）；ThetaRay（ThetaRay公司）
A novel artificial intelligence (AI) technique that uses machine learning (ML) methodologies combines several algorithms, which were developed by ThetaRay, Inc., is applied to NASA's Transiting Exoplanets Survey Satellite (TESS) dataset to identify exoplanetary candidates. The AI/ML ThetaRay system is trained initially with Kepler exoplanetary data and validated with confirmed exoplanets before its application to TESS data. Existing and new features of the data, based on various observational parameters, are constructed and used in the AI/ML analysis by employing semi-supervised and unsupervis…
The WASP-148 planetary system has a rare architecture with a transiting Saturn-mass planet on a tight orbit which is accompanied by a slightly more massive planet on a nearby outer orbit. Using new space-born photometry and ground-based follow-up transit observations and data available in literature, we performed modeling that accounts for gravitational interactions between both planets. Thanks to the new transit timing data for planet b, uncertainties of orbital periods and eccentricities for both planets were reduced relative to previously published values by a factor of 3-4. Variation in tr…
Transmission spectroscopy can be used to constrain the properties of exoplanetary atmospheres. During a transit, the light blocked from the atmosphere of the planet leaves an imprint in the light coming from the star. This has been shown for many exoplanets with different techniques, with both photometry and spectroscopy. We aim at testing chromatic line-profile tomography as a new tool to investigate exoplanetary atmospheres. The signal imprinted on the cross-correlation function (CCF) by a planet transiting its star is dependent on the planet-to-star radius ratio. We want to verify if the pr…
Useful information can be retrieved by analysing the transit light curve of a planet-hosting star or induced radial velocity oscillations. However, inferring the physical parameters of the planet, such as mass, size, and semi-major axis, requires preliminary knowledge of some parameters of the host star, especially its mass or radius, which are generally inferred through theoretical evolutionary models. We seek to present and test a whole algorithm devoted to the complete characterisation of an exoplanetary system thanks to the global analysis of photometric or radial velocity time series comb…
We present time series photometry and constraints on additional planets in five of the exoplanetary systems studied by the EPOCh (Extrasolar Planet Observation and Characterization) component of the NASA EPOXI mission: HAT-P-4, TrES-3, TrES-2, WASP-3, and HAT-P-7. We conduct a search of the high-precision time series for photometric transits of additional planets. We find no candidate transits with significance higher than our detection limit. From Monte Carlo tests of the time series using putative periods from 0.5 days to 7 days, we demonstrate the sensitivity to detect Neptune-sized compani…
Context. Collecting a large variety of exoplanetary atmosphere measurements is crucial to improve our understanding of exoplanets. In this context, it is likely that the field would benefit from broad species surveys, particularly using transit spectroscopy, which is the most successful technique of exoplanetary atmosphere characterization so far. Aims: Our goal is to develop a model-unbiased technique using transit spectroscopy to analyze every qualified atomic spectral line in exoplanetary transit data, and search for relative absorption, that is, a decrease in the flux of the line when the …
Detection of a planetary ring of exoplanets remains as one of the most attractive but challenging goals in the field. We present a methodology of a systematic search for exoplanetary rings via transit photometry of long-period planets. The methodology relies on a precise integration scheme we develop to compute a transit light curve of a ringed planet. We apply the methodology to 89 long-period planet candidates from the Kepler data so as to estimate, and/or set upper limits on, the parameters of possible rings. While a majority of our samples do not have a sufficiently good signal-to-noise ra…
Transmission spectra of exoplanetary atmospheres have been used to infer the presence of clouds/hazes. Such inferences are typically based on spectral slopes in the optical deviant from gaseous Rayleigh scattering or low-amplitude spectral features in the infrared. We investigate three observable metrics that could allow constraints on cloud properties from transmission spectra, namely, the optical slope, the uniformity of this slope, and condensate features in the infrared. We derive these metrics using model transmission spectra considering Mie extinction from a wide range of condensate spec…
In this paper a homomorphic filtering scheme is proposed to improve the estimation of the planet/star radius ratio in astronomical transit signals. The idea is to reduce the effect of the short-term earth atmosphere variations. A two-step method is presented to compute the parameters of the transit curve from both the unfiltered and filtered data. A Monte Carlo analysis is performed by using correlated and uncorrelated noise to determine the parameters of the proposed FFT filter. The method is tested with observations of WASP-19b and WASP-17b obtained with the FORS2 instrument at the Very Larg…
20573 simulations of planetary transits around spotted stars were conducted using the transit-starspot model, \texttt{PRISM}. In total 3888 different scenarios were considered using three different host star spectral types, M4V, M1V and K5V. The mean amplitude of the starspot anomaly was measured and compared to the photometric precision of the light curve, to determine if the starspot anomaly's characteristic "blip" was noticeable in the light curve. The simulations show that, starspot anomalies will be observable in TESS 2\,min cadence data. The smallest starspot detectable in TESS transit l…
Knowledge of an exoplanet's oblateness and obliquity would give clues about its formation and internal structure. In principle, a light curve of a transiting planet bears information about the planet's shape, but previous work has shown that the oblateness-induced signal will be extremely difficult to detect. Here we investigate the potentially larger signals due to planetary spin precession. The most readily detectable effects are transit depth variations (T$δ$V) in a sequence of light curves. For a planet as oblate as Jupiter or Saturn, the transit depth will undergo fractional variations of…
CONTEXT. It is theoretically possible for rings to have formed around extrasolar planets in a similar way to that in which they formed around the giant planets in our solar system. However, no such rings have been detected to date. AIMS: We aim to test the possibility of detecting rings around exoplanets by investigating the photometric and spectroscopic ring signatures in high-precision transit signals. METHODS: The photometric and spectroscopic transit signals of a ringed planet is expected to show deviations from that of a spherical planet. We used these deviations to quantify the detectabi…
The fields of astronomy and astrophysics are currently engaged in an unprecedented era of discovery as recent missions have revealed thousands of exoplanets orbiting other stars. While the Kepler Space Telescope mission has enabled most of these exoplanets to be detected by identifying transiting events, exoplanets often exhibit additional photometric effects that can be used to improve the characterization of exoplanets. The EXONEST Exoplanetary Explorer is a Bayesian exoplanet inference engine based on nested sampling and originally designed to analyze archived Kepler Space Telescope and CoR…
We are witness to a great and increasing interest in internal structure, composition and evolution of exoplanets. However, direct measurements of exoplanetary mass and radius cannot be uniquely interpreted in terms of interior structure, justifying the need for an additional observable. The second degree fluid Love number, $k_2$, is proportional to the concentration of mass towards the body's center, hence providing valuable additional information about the internal structure. When hydrostatic equilibrium is assumed for the planetary interior, $k_2$ is a direct function of the planetary shape.…
NASA's Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called CORBITS which, given a collection of conjectured exoplanets orbiting a star…
The discovery of rings around extrasolar planets ("exorings") is one of the next breakthroughs in exoplanetary research. Previous studies have explored the feasibility of detecting exorings with present and future photometric sensitivities by seeking anomalous deviations in the residuals of a standard transit light curve fit, at the level of ~100 ppm for Kronian rings. In this work, we explore two much larger observational consequences of exorings: (1) the significant increase in transit depth that may lead to the misclassification of ringed planetary candidates as false-positives and/or the u…
Transiting exoplanets provide detailed access to their atmospheres, as the planet's signal can be effectively separated from that of its host star. For transiting exoplanets three fundamental atmospheric measurements are possible: transmission spectra - where atmospheric absorption features are detected across an exoplanets limb during transit, emission spectra - where the day-side average emission of the planet is detected during secondary eclipse events, and phase curves - where the spectral emission of the planet is mapped globally following the planet around its orbit. All of these techniq…
Exoplanets, or planets outside our own solar system, have long been of interest to astronomers; however, only in the past two decades have scientists had the technology to characterize and study planets so far away from us. With advanced telescopes and spectrometers, astronomers are discovering more exoplanets every year. The two most prolific methods for detecting exoplanets, radial velocity, which measures the wobble of an exoplanet's parent star, and transit, which detects the passage of a planet in front of its star, are responsible for the discovery of the vast majority of exoplanets we k…
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 polarization state of starlight reflected by a planetary atmosphere uniquely reveals coverage, particle size, and composition of aerosols as well as changing cloud patterns. It is not possible to obtain a comparable level of detailed from flux-only observations. Furthermore, polarization observations can probe the atmosphere of planets independently of the orbital geometry (i.e., transiting and non-transiting planets). We show that a high-resolution spectropolarimeter with a broad wavelength coverage, particularly if attached to a large space telescope, would enable simultaneous study of t…
We perform numerical calculations of the expected transit timing variations (TTVs) induced on a Hot-Jupiter by an Earth-mass perturber. Motivated by the recent discoveries of retrograde transiting planets, we concentrate on an investigation of the effect of varying relative planetary inclinations, up to and including completely retrograde systems. We find that planets in low order (E.g. 2:1) mean-motion resonances (MMRs) retain approximately constant TTV amplitudes for $0<\,^{\circ}i<170\,^{\circ}$, only reducing in amplitude for $i > 170\,^{\circ}$. Systems in higher order MMRs (E.g. 5:1) inc…
We propose a novel approach to utilize low-cadence photometric surveys for exoplanetary transit search. Even if transits are undetectable in the survey database alone, it can still be useful for finding preferred times for directed follow-up observations that will maximize the chances to detect transits. We demonstrate the approach through a few simulated cases. These simulations are based on the Hipparcos Epoch Photometry data base, and the transiting planets whose transits were already detected there. In principle, the approach we propose will be suitable for the directed follow-up of the ph…
We present photometry of 4 transits of the exoplanet WASP-4b, each with a precision of approximately 500 ppm and a time sampling of 40-60s. We have used the data to refine the estimates of the system parameters and ephemerides. During two of the transits we observed a short-lived, low-amplitude anomaly that we interpret as the occultation of a starspot by the planet. We also find evidence for a pair of similar anomalies in previously published photometry. The recurrence of these anomalies suggests that the stellar rotation axis is nearly aligned with the orbital axis, or else the star spot wou…
It has been widely thought that measuring the misalignment angle between the orbital plane of a transiting exoplanet and the spin of its host star was a good discriminator between different migration processes for hot-Jupiters. Specifically, well-aligned hot-Jupiter systems (as measured by the Rossiter-McLaughlin effect) were thought to have formed via migration through interaction with a viscous disk, while misaligned systems were thought to have undergone a more violent dynamical history. These conclusions were based on the assumption that the planet-forming disk was well-aligned with the ho…
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…
