Exoplanet Radius Research Articles

Characteristics of Multiplanetary Systems with One Host Star

The characteristics of 100 multiplanetary systems with single central stars of different spectral classes were examined. The data for these systems were taken from the NASA Exoplanet Archive. Among the systems, those were selected for which the exoplanet mass and radius were simultaneously known. For 293 planets from these systems masses, radii, orbital radii, orbital periods, and types of exoplanets were analyzed. It occurred that the rarest type in such systems were terrestrial planets and after them the gas giants. Most of the exoplanets belonged to the type of super-earths. The distribution of the number of planets in a system showed that systems with many exoplanets are less common than those with a smaller number. The system with the largest number of exoplanets in this sample is TRAPPIST-1 (7 planets systems). The properties of exoplanets in multiplanetary systems with one host star in terms of characteristics, orbital sizes, and number of planets, are investigated and compared with the Solar system. It turned out that the Solar system is rather an exception to the considered extrasolar multiplanetary systems.

Revisiting mass–radius relationships for exoplanet populations: a machine learning insight

ABSTRACT The growing number of exoplanet discoveries and advances in machine learning techniques have opened new avenues for exploring and understanding the characteristics of worlds beyond our Solar system. In this study, we employ efficient machine learning approaches to analyse a data set comprising 762 confirmed exoplanets and eight Solar system planets, aiming to characterize their fundamental quantities. By applying different unsupervised clustering algorithms, we classify the data into two main classes: ‘small’ and ‘giant’ planets, with cut-off values at Rp = 8.13R⊕ and Mp = 52.48M⊕. This classification reveals an intriguing distinction: giant planets have lower densities, suggesting higher H–He mass fractions, while small planets are denser, composed mainly of heavier elements. We apply various regression models to uncover correlations between physical parameters and their predictive power for exoplanet radius. Our analysis highlights that planetary mass, orbital period, and stellar mass play crucial roles in predicting exoplanet radius. Among the models evaluated, the Support Vector Regression consistently outperforms others, demonstrating its promise for obtaining accurate planetary radius estimates. Furthermore, we derive parametric equations using the M5P and Markov Chain Monte Carlo methods. Notably, our study reveals a noteworthy result: small planets exhibit a positive linear mass–radius relation, aligning with previous findings. Conversely, for giant planets, we observe a strong correlation between planetary radius and the mass of their host stars, which might provide intriguing insights into the relationship between giant planet formation and stellar characteristics.

The Exoplanet Radius Valley from Gas-driven Planet Migration and Breaking of Resonant Chains

The size frequency distribution of exoplanet radii between 1 and 4R ⊕ is bimodal with peaks at ∼1.4 R ⊕ and ∼2.4 R ⊕, and a valley at ∼1.8 R ⊕. This radius valley separates two classes of planets—usually referred to as “super-Earths” and “mini-Neptunes”—and its origin remains debated. One model proposes that super-Earths are the outcome of photoevaporation or core-powered mass loss stripping the primordial atmospheres of the mini-Neptunes. A contrasting model interprets the radius valley as a dichotomy in the bulk compositions, where super-Earths are rocky planets and mini-Neptunes are water-ice-rich worlds. In this work, we test whether the migration model is consistent with the radius valley and how it distinguishes these views. In the migration model, planets migrate toward the disk’s inner edge, forming a chain of planets locked in resonant configurations. After the gas disk dispersal, orbital instabilities “break the chains” and promote late collisions. This model broadly matches the period-ratio and planet-multiplicity distributions of Kepler planets and accounts for resonant chains such as TRAPPIST-1, Kepler-223, and TOI-178. Here, by combining the outcome of planet formation simulations with compositional mass–radius relationships and assuming the complete loss of primordial H-rich atmospheres in late giant impacts, we show that the migration model accounts for the exoplanet radius valley and the intrasystem uniformity (“peas in a pod”) of Kepler planets. Our results suggest that planets with sizes of ∼1.4 R ⊕ are mostly rocky, whereas those with sizes of ∼2.4 R ⊕ are mostly water-ice-rich worlds. Our results do not support an exclusively rocky composition for the cores of mini-Neptunes.

Large Interferometer For Exoplanets (LIFE)

Context.The Large Interferometer For Exoplanets (LIFE) initiative is developing the science and a technology road map for an ambitious space mission featuring a space-based mid-infrared (MIR) nulling interferometer in order to detect the thermal emission of hundreds of exoplanets and characterize their atmospheres.Aims.In order to quantify the science potential of such a mission, in particular in the context of technical trade-offs, an instrument simulator is required. In addition, signal extraction algorithms are needed to verify that exoplanet properties (e.g., angular separation and spectral flux) contained in simulated exoplanet data sets can be accurately retrieved.Methods.We present LIFEsim, a software tool developed for simulating observations of exoplanetary systems with an MIR space-based nulling interferometer. It includes astrophysical noise sources (i.e., stellar leakage and thermal emission from local zodiacal and exozodiacal dust) and offers the flexibility to include instrumental noise terms in the future. Here, we provide some first quantitative limits on instrumental effects that would allow the measurements to remain in the fundamental noise limited regime. We demonstrate updated signal extraction approaches to validating signal-to-noise ratio (S/N) estimates from the simulator. Monte Carlo simulations are used to generate a mock survey of nearby terrestrial exoplanets and determine to which accuracy fundamental planet properties can be retrieved.Results.LIFEsimprovides an accessible way to predict the expected S/N of future observations as a function of various key instrument and target parameters. The S/Ns of the extracted spectra are photon noise dominated, as expected from our current simulations. Signals from multi-planet systems can be reliably extracted. From single-epoch observations in our mock survey of small (R <1.5REarth) planets orbiting within the habitable zones of their stars, we find that typical uncertainties in the estimated effective temperature of the exoplanets are ≲10%, for the exoplanet radius ≲20%, and for the separation from the host star ≲2%. Signal-to-noise-ratio values obtained in the signal extraction process deviate by less than 10% from purely photon-counting statistics-based S/Ns.Conclusions.LIFEsimhas been sufficiently well validated so that it can be shared with a broader community interested in quantifying various exoplanet science cases that a future space-based MIR nulling interferometer could address. Reliable signal extraction algorithms exist, and our results underline the power of the MIR wavelength range for deriving fundamental exoplanet properties from single-epoch observations.

New Perspectives on the Exoplanet Radius Gap from a Mathematica Tool and Visualized Water Equation of State

Abstract Recent astronomical observations obtained with the Kepler and TESS missions and their related ground-based follow-ups revealed an abundance of exoplanets with a size intermediate between Earth and Neptune (1 R ⊕ ≤ R ≤ 4 R ⊕). A low occurrence rate of planets has been identified at around twice the size of Earth (2 × R ⊕), known as the exoplanet radius gap or radius valley. We explore the geometry of this gap in the mass–radius diagram, with the help of a Mathematica plotting tool developed with the capability of manipulating exoplanet data in multidimensional parameter space, and with the help of visualized water equations of state in the temperature–density (T–ρ) graph and the entropy–pressure (s–P) graph. We show that the radius valley can be explained by a compositional difference between smaller, predominantly rocky planets (<2 × R ⊕) and larger planets (>2 × R ⊕) that exhibit greater compositional diversity including cosmic ices (water, ammonia, methane, etc.) and gaseous envelopes. In particular, among the larger planets (>2 × R ⊕), when viewed from the perspective of planet equilibrium temperature (T eq), the hot ones (T eq ≳ 900 K) are consistent with ice-dominated composition without significant gaseous envelopes, while the cold ones (T eq ≲ 900 K) have more diverse compositions, including various amounts of gaseous envelopes.

Hidden Water in Magma Ocean Exoplanets

Abstract We demonstrate that the deep volatile storage capacity of magma oceans has significant implications for the bulk composition, interior, and climate state inferred from exoplanet mass and radius data. Experimental petrology provides the fundamental properties of the ability of water and melt to mix. So far, these data have been largely neglected for exoplanet mass–radius modeling. Here we present an advanced interior model for water-rich rocky exoplanets. The new model allows us to test the effects of rock melting and the redistribution of water between magma ocean and atmosphere on calculated planet radii. Models with and without rock melting and water partitioning lead to deviations in planet radius of up to 16% for a fixed bulk composition and planet mass. This is within the current accuracy limits for individual systems and statistically testable on a population level. Unrecognized mantle melting and volatile redistribution in retrievals may thus underestimate the inferred planetary bulk water content by up to 1 order of magnitude.

Characterization of 92 southern TESS candidate planet hosts and a new photometric [Fe/H] relation for cool dwarfs

ABSTRACT We present the results of a medium-resolution optical spectroscopic survey of 92 cool ($3000 \,\mathrm{ K}\lesssim T_{\rm eff} \lesssim 4500\,$K) southern TESS candidate planet hosts, and describe our spectral fitting methodology used to recover stellar parameters. We quantify model deficiencies at predicting optical fluxes, and while our technique works well for Teff, further improvements are needed for [Fe/H]. To this end, we developed an updated photometric [Fe/H] calibration for isolated main-sequence stars built upon a calibration sample of 69 cool dwarfs in binary systems, precise to $\pm 0.19\,$dex, from supersolar to metal poor, over 1.51 < Gaia (BP − RP) < 3.3. Our fitted Teff and R⋆ have median precisions of 0.8 per cent and 1.7 per cent, respectively, and are consistent with our sample of standard stars. We use these to model the transit light curves and determine exoplanet radii for 100 candidate planets to 3.5 per cent precision and see evidence that the planet radius gap is also present for cool dwarfs. Our results are consistent with the sample of confirmed TESS planets, with this survey representing one of the largest uniform analyses of cool TESS candidate planet hosts to date.

A Mini-Neptune and a Radius Valley Planet Orbiting the Nearby M2 Dwarf TOI-1266 in Its Venus Zone: Validation with the Habitable-zone Planet Finder

Abstract We report on the validation of two planets orbiting the nearby (36 pc) M2 dwarf TOI-1266 observed by the TESS mission. This system is one of a few M dwarf multiplanet systems with close-in planets where the inner planet is substantially larger than the outer planet. The inner planet is sub-Neptune-sized (R = 2.46 ± 0.08 R ⊕) with an orbital period of 10.9 days, while the outer planet has a radius of R ⊕ and resides in the exoplanet radius valley—the transition region between rocky and gaseous planets. With an orbital period of 18.8 days, the outer planet receives an insolation flux of 2.4 times that of Earth, similar to the insolation of Venus. Using precision near-infrared radial velocities with the Habitable-zone Planet Finder Spectrograph, we place upper mass limits of 15.9 and 6.4 M ⊕ at 95% confidence for the inner and outer planet, respectively. A more precise mass constraint of both planets, achievable with current radial velocity instruments given the host star brightness (V = 12.9, J = 9.7), will yield further insights into the dominant processes sculpting the exoplanet radius valley.

A Relationship between Stellar Age and Spot Coverage

Abstract We investigate starspot distributions consistent with space-based photometry of F, G, and K stars in six stellar associations ranging in age from 10 Myr to 4 Gyr. We show that a simple light-curve statistic called the “smoothed amplitude” is proportional to stellar age as t −1/2, following a Skumanich-like spin-down relation. We marginalize over the unknown stellar inclinations by forward modeling the ensemble of light curves for direct comparison with the Kepler, K2, and TESS photometry. We sample the posterior distributions for spot coverage with approximate Bayesian computation. We find typical spot coverages in the range 1%–10%, which decrease with increasing stellar age. The spot coverage is proportional to t n where n = −0.37 ± 0.16, also statistically consistent with a Skumanich-like t −1/2 decay of starspot coverage with age. We apply two techniques to estimate the spot coverage of young exoplanet-hosting stars likely to be targeted for transmission spectroscopy with the James Webb Space Telescope, and estimate the bias in exoplanet radius measurements due to varying starspot coverage.

The stellar variability noise floor for transiting exoplanet photometry with PLATO

ABSTRACT One of the main science motivations for the ESA PLAnetary Transit and Oscillations (PLATO) mission is to measure exoplanet transit radii with 3 per cent precision. In addition to flares and starspots, stellar oscillations and granulation will enforce fundamental noise floors for transiting exoplanet radius measurements. We simulate light curves of Earth-sized exoplanets transiting continuum intensity images of the Sun taken by the Helioseismic and Magnetic Imager (HMI) instrument aboard the Solar Dynamics Observatory (SDO) to investigate the uncertainties introduced on the exoplanet radius measurements by stellar granulation and oscillations. After modelling the solar variability with a Gaussian process, we find that the amplitude of solar oscillations and granulation is of order 100 ppm – similar to the depth of an Earth transit – and introduces a fractional uncertainty on the depth of transit of 0.73 per cent assuming four transits are observed over the mission duration. However, when we translate the depth measurement into a radius measurement of the planet, we find a much larger radius uncertainty of 3.6 per cent. This is due to a degeneracy between the transit radius ratio, the limb darkening, and the impact parameter caused by the inability to constrain the transit impact parameter in the presence of stellar variability. We find that surface brightness inhomogeneity due to photospheric granulation contributes a lower limit of only 2 ppm to the photometry in-transit. The radius uncertainty due to granulation and oscillations, combined with the degeneracy with the transit impact parameter, accounts for a significant fraction of the error budget of the PLATO mission, before detector or observational noise is introduced to the light curve. If it is possible to constrain the impact parameter or to obtain follow-up observations at longer wavelengths where limb darkening is less significant, this may enable higher precision radius measurements.

Current Population Statistics Do Not Favor Photoevaporation over Core-powered Mass Loss as the Dominant Cause of the Exoplanet Radius Gap

Abstract We search for evidence of the cause of the exoplanet radius gap, i.e., the dearth of planets with radii near 1.8 R ⊕. If the cause were photoevaporation, the radius gap should trend with proxies for the early-life high-energy emission of the planet-hosting stars. If, alternatively, the cause were core-powered mass loss, no such trends should exist. Critically, spurious trends between the radius gap and stellar properties arise from an underlying correlation with instellation. After accounting for this underlying correlation, we find that no trends remain between the radius gap and stellar mass or present-day stellar activity as measured by near-UV emission. We dismiss the nondetection of a radius gap trend with near-UV emission because present-day near-UV emission is unlikely to trace early-life high-energy emission, but we provide a catalog of Galaxy Evolution Explorer near-UV and far-UV emission measurements for general use. We interpret the nondetection of a radius gap trend with stellar mass by simulating photoevaporation with mass-dependent evolution of stellar high-energy emission. The simulation produces an undetectable trend between the radius gap and stellar mass under realistic sources of error. We conclude that no evidence, from this analysis or others in the literature, currently exists that clearly favors either photoevaporation or core-powered mass loss as the primary cause of the exoplanet radius gap. However, repeating this analysis once the body of well-characterized <4 R ⊕ planets has roughly doubled could confirm or rule out photoevaporation.

Revisited mass-radius relations for exoplanets below 120 M⊕

The masses and radii of exoplanets are fundamental quantities needed for their characterisation. Studying the different populations of exoplanets is important for understanding the demographics of the different planetary types, which can then be linked to planetary formation and evolution. We present an updated exoplanet catalogue based on reliable, robust, and, as much as possible accurate mass and radius measurements of transiting planets up to 120 M⊕. The resulting mass-radius (M-R) diagram shows two distinct populations, corresponding to rocky and volatile-rich exoplanets which overlap in both mass and radius. The rocky exoplanet population shows a relatively small density variability and ends at mass of ~25 M⊕, possibly indicating the maximum core mass that can be formed. We use the composition line of pure water to separate the two populations, and infer two new empirical M-R relations based on this data: M = (0.9 ± 0.06) R(3.45±0.12) for the rocky population, and M = (1.74 ± 0.38) R(1.58±0.10) for the volatile-rich population. While our results for the two regimes are in agreement with previous studies, the new M-R relations better match the population in the transition region from rocky to volatile-rich exoplanets, which correspond to a mass range of 5–25 M⊕, and a radius range of 2–3 R⊕.

Searching for Planets Orbiting α Cen A with the James Webb Space Telescope

α Centauri A is the closest solar-type star to the Sun and offers an excellent opportunity to detect the thermal emission of a mature planet heated by its host star. The MIRI coronagraph on the James Webb Space Telescope can search the 1–3 au (1″–2″) region around α Cen A which is predicted to be stable within the α Cen AB system. We demonstrate that with reasonable performance of the telescope and instrument, a 20 hr program combining on-target and reference star observations at 15.5 μm could detect thermal emission from planets as small as ∼5 R⊕. Multiple visits every 3–6 months would increase the geometrical completeness, provide astrometric confirmation of detected sources, and push the radius limit down to ∼3 R⊕. An exozodiacal cloud only a few times brighter than our own should also be detectable, although a sufficiently bright cloud might obscure any planet present in the system. While current precision radial velocity (PRV) observations set a limit of 50–100 M⊕ at 1–3 au for planets orbiting α Cen A, there is a broad range of exoplanet radii up to 10 R⊕ consistent with these mass limits. A carefully planned observing sequence along with state-of-the-art post-processing analysis could reject the light from α Cen A at the level of ∼10−5 at 1″–2″ and minimize the influence of α Cen B located 7″–8″ away in the 2022–2023 timeframe. These space-based observations would complement on-going imaging experiments at shorter wavelengths as well as PRV and astrometric experiments to detect planets dynamically. Planetary demographics suggest that the likelihood of directly imaging a planet whose mass and orbit are consistent with present PRV limits is small, ∼5%, and possibly lower if the presence of a binary companion further reduces occurrence rates. However, at a distance of just 1.34 pc, α Cen A is our closest sibling star and certainly merits close scrutiny.

Growth model interpretation of planet size distribution

The radii and orbital periods of 4,000+ confirmed/candidate exoplanets have been precisely measured by the Kepler mission. The radii show a bimodal distribution, with two peaks corresponding to smaller planets (likely rocky) and larger intermediate-size planets, respectively. While only the masses of the planets orbiting the brightest stars can be determined by ground-based spectroscopic observations, these observations allow calculation of their average densities placing constraints on the bulk compositions and internal structures. However, an important question about the composition of planets ranging from 2 to 4 Earth radii (R⊕) still remains. They may either have a rocky core enveloped in a H2-He gaseous envelope (gas dwarfs) or contain a significant amount of multicomponent, H2O-dominated ices/fluids (water worlds). Planets in the mass range of 10-15 M⊕, if half-ice and half-rock by mass, have radii of 2.5 R⊕, which exactly match the second peak of the exoplanet radius bimodal distribution. Any planet in the 2- to 4-R⊕ range requires a gas envelope of at most a few mass percentage points, regardless of the core composition. To resolve the ambiguity of internal compositions, we use a growth model and conduct Monte Carlo simulations to demonstrate that many intermediate-size planets are "water worlds."

The Effects of Stellar Companions on the Observed Transiting Exoplanet Radius Distribution

Abstract Understanding the distribution and occurrence rate of small planets was a fundamental goal of the Kepler transiting exoplanet mission, and could be improved with K2 and Transiting Exoplanet Survey Satellite (TESS). Deriving accurate exoplanetary radii requires accurate measurements of the host star radii and the planetary transit depths, including accounting for any “third light” in the system due to nearby bound companions or background stars. High-resolution imaging of Kepler and K2 planet candidate hosts to detect very close (within ∼0.″5) background or bound stellar companions has been crucial for both confirming the planetary nature of candidates, and the determination of accurate planetary radii and mean densities. Here we present an investigation of the effect of close companions, both detected and undetected, on the observed (raw count) exoplanet radius distribution. We demonstrate that the recently detected “gap” in the observed radius distribution (also seen in the completeness-corrected distribution) is fairly robust to undetected stellar companions, given that all of the systems in the sample have undergone some kind of vetting with high-resolution imaging. However, while the gap in the observed sample is not erased or shifted, it is partially filled in after accounting for possible undetected stellar companions. These findings have implications for the most likely core composition, and thus formation location, of super-Earth and sub-Neptune planets. Furthermore, we show that without high-resolution imaging of planet candidate host stars, the shape of the observed exoplanet radius distribution will be incorrectly inferred, for both Kepler- and TESS-detected systems.

Revised Exoplanet Radii and Habitability Using Gaia Data Release 2

Accurate stellar properties are crucial for determining exoplanet characteristics. Gaia DR2 presents revised distances, luminosities, and radii for 1.6 billion stars. Here, we report the calculation of revised radii and densities for 320 exoplanets using this data and present updated calculations of the incident flux received by 690 known exoplanets. This allows the likelihood that those planets orbit in the habitable zone of their host stars to be reassessed. As a result of this analysis, three planets can be added to the catalogue of potentially habitable worlds: HIP~67537~b, HD~148156~b, and HD~106720~b. In addition, the changed parameterisation of BD~+49~898 means that its planet, BD~+49~898~b, now receives an incident flux that places it outside the optimistic habitable zone region, as defined by \citep{Kopparapu2013,Kopparapu2014}. We find that use of the new \textit{Gaia} data results in a mean increase in calculated exoplanet radius of 3.76\%. Previously, CoRoT-3 b had been reported as having the highest density of all known exoplanets. Here, we use updated information to revise the calculated density of CoRoT-3~b from 26.4$g\:cm^{-3}$ to 17.3$\pm2.9g\:cm^{-3}$. We also report the densest exoplanet in our dataset, KELT-1~b, with a density of 23.7$\pm4.0g\:cm^{-3}$. Overall, our results highlight the importance of ensuring the the parameterisation of known exoplanets be revisited whenever significant improvements are made to the precision of the stellar parameters upon which they are based.

Exoplanet Science in the Classroom: Learning Activities for an Introductory Physics Course

Discovery of planets outside our solar system, known as extra-solar planets or exoplanets for short, has been at the forefront of astronomical research for over 25 years. Reports of new discoveries have almost become routine; however, the excitement surrounding them has not. Amazingly, as groundbreaking as exoplanet science is, the basic physics is quite accessible to first-year physics students, as discussed in previous TPT articles. To further illustrate this point, we developed an iOS application that generates synthetic exoplanet data to provide students and teachers with interactive learning activities. Using introductory physics concepts, we demonstrate how to estimate exoplanet mass, radius, and density from the app output. These calculations form the basis for a diverse range of classroom activities. We conclude with a summary of exoplanet science resources for teachers.

A cautionary tale: limitations of a brightness-based spectroscopic approach to chromatic exoplanet radii

Determining wavelength-dependent exoplanet radii measurements is an excellent way to probe the composition of exoplanet atmospheres. In light of this, Borsa et al. (2016) sought to develop a technique to obtain such measurements by comparing ground-based transmission spectra to the expected brightness variations during an exoplanet transit. However, we demonstrate herein that this is not possible due to the transit light curve normalisation necessary to remove the effects of the Earth's atmosphere on the ground-based observations. This is because the recoverable exoplanet radius is set by the planet-to-star radius ratio within the transit light curve; we demonstrate this both analytically and with simulated planet transits, as well as through a reanalysis of the HD 189733b data.

EVOLUTIONARY MODELS OF SUPER-EARTHS AND MINI-NEPTUNES INCORPORATING COOLING AND MASS LOSS

We construct models of the structural evolution of super-Earth- and mini-Neptune-type exoplanets with hydrogen-helium envelopes, incorporating radiative cooling and XUV-driven mass loss. We conduct a parameter study of these models, focusing on initial mass, radius, and envelope mass fractions, as well as orbital distance, metallicity, and the specific prescription for mass loss. From these calculations, we investigate how the observed masses and radii of exoplanets today relate to the distribution of their initial conditions. Orbital distance and initial envelope mass fraction are the most important factors determining planetary evolution, particular radius evolution. Initial mass also becomes important below a "turnoff mass," which varies with orbital distance, with mass-radius curves being approximately flat for higher masses. Initial radius is the least important parameter we study, with very little difference between the hot start and cold start limits after an age of 100 Myr. Model sets with no mass loss fail to produce results consistent with observations, but a plausible range of mass loss scenarios is allowed. In addition, we present scenarios for the formation of the Kepler-11 planets. Our best fit to observations Kepler-11b and Kepler-11c involves formation beyond the snow line, after which they moved inward, circularized, and underwent a reduced degree mass loss.

The effect of stellar limb darkening values on the accuracy of the planet radii derived from photometric transit observations

We study how the precision of the exoplanet radius determination is affected by our present knowledge of limb darkening in two cases: when we fix the limb darkening coefficients and when we adjust them. We also investigate the effects of spots in one-colour photometry. We study the effect of limb darkening on the planetary radius determination both via analytical expressions and by numerical experiments. We also compare some of the existing limb darkening tables. When stellar spots affect the fit, we replace the limb darkening coefficients, calculated for the unspotted cases, with effective limb darkening coefficients to describe the effect of the spots. There are two important cases. (1) When one fixes the limb darkening values according to some theoretical predictions, the inconsistencies of the tables do not allow us to reach accuracy in the planetary radius of better than 1-10% (depending on the impact parameter) if the host star's surface effective temperature is higher than 5000 K. Below 5000 K the radius ratio determination may contain even 20% error. (2) When one allows adjustment of the limb darkening coefficients, the a/Rs ratio, the planet-to-stellar radius ratio, and the impact parameter can be determined with sufficient accuracy (<1%), if the signal-to-noise ratio is high enough. However, the presence of stellar spots and faculae can destroy the agreement between the limb darkening tables and the fitted limb darkening coefficients, but this does not affect the precision of the planet radius determination. We also find that it is necessary to fit the contamination factor, too. We conclude that the present inconsistencies of theoretical stellar limb darkening tables suggests one should not fix the limb darkening coefficients. When one allows them to be adjusted, then the planet radius, impact parameter, and the a/Rs can be obtained with the required precision.