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A. Claret - One of the best experts on this subject based on the ideXlab platform.
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gravity and Limb Darkening coefficients for compact stars da db and dba eclipsing white dwarfs
arXiv: Solar and Stellar Astrophysics, 2020Co-Authors: A. Claret, Elena Cukanovaite, Kevin B Burdge, P E Tremblay, S G Parsons, T R MarsAbstract:The main objective of the present work is to extend these investigations by computing the gravity and Limb-Darkening coefficients for white dwarf atmosphere models with hydrogen, helium, or mixed compositions (types DA, DB, and DBA). We computed gravity and Limb-Darkening coefficients for DA, DB, and DBA white dwarfs atmosphere models, covering the transmission curves of the Sloan, UBVRI, Kepler, TESS, and Gaia photometric systems. Specific calculations for the HiPERCAM instrument were also carried out. For all calculations of the Limb-Darkening coefficients we used the least-squares method. Concerning the effects of tidal and rotational distortions, we also computed for the first time the gravity-Darkening coefficients $y(\lambda)$ for white dwarfs using the same models of stellar atmospheres as in the case of Limb-Darkening. A more general differential equation was introduced to derive these quantities, including the partial derivative $\left(\partial{\ln I_o(\lambda)}/{\partial{\ln g}}\right)_{T_{\rm eff}}$. Six laws were adopted to describe the specific intensity distribution: linear, quadratic, square root, logarithmic, power-2, and a more general one with four coefficients. The computations are presented for the chemical compositions log[H/He] = $-$10.0 (DB), $-$2.0 (DBA) and He/H = 0 (DA), with log g varying between 5.0 and 9.5 and effective temperatures between 3750 K-100\,000 K. For effective temperatures higher than 40\,000 K, the models were also computed adopting nonlocal thermal equilibirum (DA). The adopted mixing-length parameters are ML2/$\alpha = 0.8$ (DA case) and 1.25 (DB and DBA). The results are presented in the form of 112 tables. Additional calculations, such as for other photometric systems and/or different values of log[H/He], $\log g,$ and T$_{\rm eff}$ can be performed upon request.
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theoretical gravity and Limb Darkening coefficients for the most satellite photometric system
Astronomy and Astrophysics, 2014Co-Authors: A. Claret, D Dragomir, J M MatthewsAbstract:Aims. We present new calculations of Limb and gravity-Darkening coefficients to be used as input in many fields of stellar physics such as synthetic light curves of double-lined eclipsing binaries and planetary transits, studies of stellar diameters or line profiles in rotating stars. Methods. We compute the Limb-Darkening coefficients specifically for the photometric system of the satellite MOST (Microvariability and Oscillations in STars). All computations were performed by adopting the least-square method, but for completeness we also performed calculations for the linear and bi-parametric approaches by adopting the flux conservation method. The passband gravityDarkening coefficients y(λ) were computed by adopting a more general differential equation, which also takes the effects of convection into account. Results. We used two stellar atmosphere models: ATLAS (plane-parallel) and PHOENIX (spherical and quasi-spherical). We adopted six laws to describe the specific intensity distribution: linear, quadratic, square root, logarithmic, exponential, and a more general one with four terms. The covered ranges of Teff ,l ogg, metallicities, and microturbulent velocities are (1500–50 000 K, 0–5.5, −5.0–+1.0, 0–8 km s −1 ), respectively.
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new Limb Darkening coefficients for phoenix 1d model atmospheres ii calculations for 5000 k teff 10 000 k kepler corot spitzer uvby ubvrijhk sloan and 2mass photometric systems
Astronomy and Astrophysics, 2012Co-Authors: A. Claret, P H Hauschildt, S WitteAbstract:Aims. The knowledge of how the specific intensity is distributed over the stellar disk is crucial for interpreting the light curves of extrasolar transiting planets, double-lined eclipsing binaries, and other astrophysical phenomena. To provide theoretical inputs for light curve modelling codes, we present new calculations of Limb-Darkening coefficients for the spherically symmetric phoenix models. Methods. The Limb-Darkening coefficients were computed by covering the transmission curves of Kepler, CoRoT, and Spitzer space missions, as well as the passbands of the Stromgren, Johnson-Cousins, Sloan, and 2MASS. These computations adopted the leastsquare method. In addition, we also calculated the linear and bi-parametric approximations by adopting the flux conservation method as an additional tool for estimating the theoretical error bars in the Limb-Darkening coefficients. Results. Six laws were used to describe the specific intensity distribution: linear, quadratic, square root, logarithmic, exponential, and a more general one with 4 terms. The computations are presented for the solar chemical composition, with log g varying between 2.5 and 5.5 and effective temperatures between 1500−4800 K. The adopted microturbulent velocity and the mixing-length parameters are 2.0 km s −1 and 2.0, respectively.
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gravity and Limb Darkening coefficients for the kepler corot spitzer uvby ubvrijhk and sloan photometric systems
Astronomy and Astrophysics, 2011Co-Authors: A. Claret, Steven BloemenAbstract:Aims. The complex physics of close binary stars is made even more challenging by the proximity effects that affect it. Understanding the influence of these proximity effects is one of the most important tasks in theoretical stellar astrophysics. It is crucial to know how the specific intensity is distributed over the stellar disk for a correct modelling of the light curves of eclipsing binaries and planetary transits. To provide theoretical input for light curve modelling codes, we present new calculations of gravity- and Limb-Darkening coefficients for a wide range of effective temperatures, gravities, metallicities, and microturbulent velocities. Methods. We computed Limb-Darkening coefficients for several atmosphere models, which cover the transmission curves of the Kepler, CoRoT, and Spitzer space missions as well as more widely used passbands (Stromgren, Johnson-Cousins, Sloan). In addition to these computations, which were made adopting the least-square method, we also performed calculations for the bi-parametric approximations by adopting the flux conservation method to provide users with an additional tool to estimate the theoretical error bars. To facilitate the modelling of the effects of tidal and rotational distortions, we computed the gravity-Darkening coefficients y(λ) using the same models of stellar atmospheres as for the Limb-Darkening. Compared to previous work, a more general differential equation was used, which now takes into account local gravity variations and the effects of convection. Results. The Limb-Darkening coefficients were computed with a higher numerical resolution (100 μ points instead of 15 or 17, as is often used in the ATLAS models), and five equations were used to describe the specific intensities (linear, quadratic, root-square, logarithmic, and a 4-coefficient law). Concerning the gravity-Darkening coefficients, the influence of the local gravity on y(λ) is shown as well as the effects of convection, which turn out to be very significant for cool stars. The results are tabulated for log g's ranging from 0.0 to 5.0, -5.0 ≤ log [M/H] < +1, 2000 K ≤ T eff ≤ 50 000 K and for five values of the microturbulent velocity. ATLAS and PHOENIX plane-parallel atmosphere models were used for all computations.
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testing the Limb Darkening coefficients measured from eclipsing binaries
Astronomy and Astrophysics, 2008Co-Authors: A. ClaretAbstract:Aims. The numerical methods used to compute Limb-Darkening coefficients (LDCs) are still a matter of discussion. To improve this scenario, we have revised our earlier calculations and compare the new LDCs with previous theoretical ones, as well as with empirical values measured from eclipsing binaries. Methods. We present new LDCs, based on the least-squares method but computed with higher numerical resolution (100 µ points instead of 11). The LDCs are computed for the following photometric bands: Johnson-Cousins, Stromgren, Geneva, and Walraven systems. Bolometric and monochromatic calculations are also available on request. The computations are presented for 19 metallicities ranging from 10 −5 up to 10 +1 times the solar abundance, with log g values between 0.0 and 5.0, effective temperatures between 2000 K and 50 000 K, and microturbulent velocities from 0 km s −1 to 8 km s −1 . Results. The new theoretical LDCs provide better fits to the calculated specific intensities than those derived by adopting the r-integration. The improvement is approximately one order of magnitude. When compared with empirical linear LDCs measured for nine eclipsing binaries, it was not possible to distinguish our results from those provided by the r-integration method. However, this comparison also reveals that the theoretical atmosphere models are unable to give a satisfactory fit to the observations. This result is supported by a recent investigation of transiting extrasolar planets. These discrepancies may also be related to problems with the empirical LDC values themselves.
John B Lester - One of the best experts on this subject based on the ideXlab platform.
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Limb Darkening and Planetary Transits: Testing Center-to-Limb Intensity Variations and Limb-Darkening Directly from Model Stellar Atmospheres
The Astrophysical Journal, 2017Co-Authors: Hilding R Neilson, Joseph T. Mcneil, Richard Ignace, John B LesterAbstract: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 simple parameterization with two coefficients that are derived from stellar atmosphere models or fit directly. In this work, we revisit this assumption and compute synthetic planetary transit light curves directly from model stellar atmosphere center-to-Limb intensity variations (CLIV) using the plane-parallel \textsc{Atlas} and spherically symmetric \textsc{SAtlas} codes. We compare these light curves to those constructed using best-fit Limb-Darkening parameterizations. We find that adopting parametric stellar Limb-Darkening laws lead to systematic differences from the more geometrically realistic model stellar atmosphere CLIV of about 50 -- 100 ppm at the transit center and up to 300 ppm at ingress/egress. While these errors are small they are systematic, and appear to limit the precision necessary to measure secondary effects. Our results may also have a significant impact on transit spectra.
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spherically symmetric model stellar atmospheres and Limb Darkening i Limb Darkening laws gravity Darkening coefficients and angular diameter corrections for red giant stars
arXiv: Solar and Stellar Astrophysics, 2013Co-Authors: Hilding R Neilson, John B LesterAbstract:Model stellar atmospheres are fundamental tools for understanding stellar observations from interferometry, microlensing, eclipsing binaries and planetary transits. However, the calculations also include assumptions, such as the geometry of the model. We use intensity profiles computed for both plane-parallel and spherically symmetric model atmospheres to determine fitting coefficients in the BVRIHK, CoRot and Kepler wavebands for Limb Darkening using several different fitting laws, for gravity-Darkening and for interferometric angular diameter corrections. Comparing predicted variables for each geometry, we find that the spherically symmetric model geometry leads to different predictions for surface gravities log g < 3. In particular, the most commonly used Limb-Darkening laws produce poor fits to the intensity profiles of spherically symmetric model atmospheres, which indicates the need for more sophisticated laws. Angular diameter corrections for spherically symmetric models range from 0.67 to 1, compared to the much smaller range from 0.95 to 1 for plane-parallel models.
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Using Limb Darkening to measure fundamental parameters of stars
Astronomy & Astrophysics, 2012Co-Authors: Hilding R Neilson, John B LesterAbstract:Context. Limb Darkening is an important tool for understanding stellar atmospheres, but most observations measuring Limb Darkening assume various parameterizations that yield no significant information about the structure of stellar atmospheres. Aims. We use a specific Limb-Darkening relation to study how the best-fit coefficients relate to fundamental stellar parameters from spherically symmetric model stellar atmospheres. Methods. Using a grid of spherically symmetric Atlas model atmospheres, we compute Limb-Darkening coefficients, and develop a novel method to predict fundamental stellar parameters. Results. We find our proposed method predicts the mass of stellar atmosphere models given only the radius and Limb-Darkening coefficients, suggesting that microlensing, interferometric, transit and eclipse observations can constrain stellar masses. Conclusions. This novel method demonstrates that Limb-Darkening parameterizations contain important information about the structure of stellar atmospheres, with the potential to be a valuable tool for measuring stellar masses.
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Weighing Betelgeuse: Measuring the mass of alpha Orionis from stellar Limb-Darkening
arXiv: Solar and Stellar Astrophysics, 2011Co-Authors: Hilding R Neilson, John B Lester, Xavier HauboisAbstract:Stellar Limb-Darkening is an important tool for constraining the properties of a stellar atmosphere. We present a novel method for relating the fundamental stellar parameters mass and radius to Limb-Darkening laws using grids of spherical model stellar atmospheres. This method is applied to interferometric observations of the red supergiant Betelgeuse, where an unique measure of the stellar mass is determined.
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Limb Darkening in spherical stellar atmospheres
Astronomy and Astrophysics, 2011Co-Authors: Hilding R Neilson, John B LesterAbstract:Context. Stellar Limb Darkening, I(μ = cos θ), is an important constraint for microlensing, eclipsing binary, planetary transit, and interferometric observations, but is generally treated as a parameterized curve, such as a linear-plus-square-root law. Many analyses assume Limb-Darkening coefficients computed from model stellar atmospheres. However, previous studies, using I(μ) from planeparallel models, have found that fits to the flux-normalized curves pass through a fixed point, a common μ location on the stellar disk, for all values of Teff ,l ogg and wavelength. Aims. We study this fixed μ-point to determine if it is a property of the model stellar atmospheres or a property of the Limb-Darkening laws. Furthermore, we use this Limb-Darkening law as a tool to probe properties of stellar atmospheres for comparison to LimbDarkening observations. Methods. Intensities computed with plane-parallel and spherically-symmetric Atlas models (characterized by the three fundamental
Hilding R Neilson - One of the best experts on this subject based on the ideXlab platform.
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Limb Darkening and Planetary Transits: Testing Center-to-Limb Intensity Variations and Limb-Darkening Directly from Model Stellar Atmospheres
The Astrophysical Journal, 2017Co-Authors: Hilding R Neilson, Joseph T. Mcneil, Richard Ignace, John B LesterAbstract: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 simple parameterization with two coefficients that are derived from stellar atmosphere models or fit directly. In this work, we revisit this assumption and compute synthetic planetary transit light curves directly from model stellar atmosphere center-to-Limb intensity variations (CLIV) using the plane-parallel \textsc{Atlas} and spherically symmetric \textsc{SAtlas} codes. We compare these light curves to those constructed using best-fit Limb-Darkening parameterizations. We find that adopting parametric stellar Limb-Darkening laws lead to systematic differences from the more geometrically realistic model stellar atmosphere CLIV of about 50 -- 100 ppm at the transit center and up to 300 ppm at ingress/egress. While these errors are small they are systematic, and appear to limit the precision necessary to measure secondary effects. Our results may also have a significant impact on transit spectra.
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spherically symmetric model stellar atmospheres and Limb Darkening i Limb Darkening laws gravity Darkening coefficients and angular diameter corrections for red giant stars
arXiv: Solar and Stellar Astrophysics, 2013Co-Authors: Hilding R Neilson, John B LesterAbstract:Model stellar atmospheres are fundamental tools for understanding stellar observations from interferometry, microlensing, eclipsing binaries and planetary transits. However, the calculations also include assumptions, such as the geometry of the model. We use intensity profiles computed for both plane-parallel and spherically symmetric model atmospheres to determine fitting coefficients in the BVRIHK, CoRot and Kepler wavebands for Limb Darkening using several different fitting laws, for gravity-Darkening and for interferometric angular diameter corrections. Comparing predicted variables for each geometry, we find that the spherically symmetric model geometry leads to different predictions for surface gravities log g < 3. In particular, the most commonly used Limb-Darkening laws produce poor fits to the intensity profiles of spherically symmetric model atmospheres, which indicates the need for more sophisticated laws. Angular diameter corrections for spherically symmetric models range from 0.67 to 1, compared to the much smaller range from 0.95 to 1 for plane-parallel models.
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Using Limb Darkening to measure fundamental parameters of stars
Astronomy & Astrophysics, 2012Co-Authors: Hilding R Neilson, John B LesterAbstract:Context. Limb Darkening is an important tool for understanding stellar atmospheres, but most observations measuring Limb Darkening assume various parameterizations that yield no significant information about the structure of stellar atmospheres. Aims. We use a specific Limb-Darkening relation to study how the best-fit coefficients relate to fundamental stellar parameters from spherically symmetric model stellar atmospheres. Methods. Using a grid of spherically symmetric Atlas model atmospheres, we compute Limb-Darkening coefficients, and develop a novel method to predict fundamental stellar parameters. Results. We find our proposed method predicts the mass of stellar atmosphere models given only the radius and Limb-Darkening coefficients, suggesting that microlensing, interferometric, transit and eclipse observations can constrain stellar masses. Conclusions. This novel method demonstrates that Limb-Darkening parameterizations contain important information about the structure of stellar atmospheres, with the potential to be a valuable tool for measuring stellar masses.
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Weighing Betelgeuse: Measuring the mass of alpha Orionis from stellar Limb-Darkening
arXiv: Solar and Stellar Astrophysics, 2011Co-Authors: Hilding R Neilson, John B Lester, Xavier HauboisAbstract:Stellar Limb-Darkening is an important tool for constraining the properties of a stellar atmosphere. We present a novel method for relating the fundamental stellar parameters mass and radius to Limb-Darkening laws using grids of spherical model stellar atmospheres. This method is applied to interferometric observations of the red supergiant Betelgeuse, where an unique measure of the stellar mass is determined.
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Limb Darkening in spherical stellar atmospheres
Astronomy and Astrophysics, 2011Co-Authors: Hilding R Neilson, John B LesterAbstract:Context. Stellar Limb Darkening, I(μ = cos θ), is an important constraint for microlensing, eclipsing binary, planetary transit, and interferometric observations, but is generally treated as a parameterized curve, such as a linear-plus-square-root law. Many analyses assume Limb-Darkening coefficients computed from model stellar atmospheres. However, previous studies, using I(μ) from planeparallel models, have found that fits to the flux-normalized curves pass through a fixed point, a common μ location on the stellar disk, for all values of Teff ,l ogg and wavelength. Aims. We study this fixed μ-point to determine if it is a property of the model stellar atmospheres or a property of the Limb-Darkening laws. Furthermore, we use this Limb-Darkening law as a tool to probe properties of stellar atmospheres for comparison to LimbDarkening observations. Methods. Intensities computed with plane-parallel and spherically-symmetric Atlas models (characterized by the three fundamental
David K. Sing - One of the best experts on this subject based on the ideXlab platform.
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Limb Darkening laws for two exoplanet host stars derived from 3d stellar model atmospheres comparison with 1d models and hst light curve observations
2014Co-Authors: W Hayek, David K. Sing, F Pont, Martin AsplundAbstract:We compare Limb Darkening laws derived from 3D hydrodynamical model atmospheres and 1D hydrostatic MARCS models for the host stars of two well-studied transiting exoplanet systems, the late-type dwarfs HD 209458 and HD 189733. The surface brightness distribution of the stellar disks is calculated for a wide spectral range using 3D LTE spectrum formation and opacity sampling ? . We test our theoretical predictions using least-squares fits of model light curves to wavelength-integrated primary eclipses that were observed with the Hubble Space Telescope (HST). The Limb Darkening law derived from the 3D model of HD 209458 in the spectral region between 2900 A and 5700 A produces significantly better fits to the HST data, removing systematic residuals that were previously observed for model light curves based on 1D Limb Darkening predictions. This di erence arises mainly from the shallower mean temperature structure of the 3D model, which is a consequence of the explicit simulation of stellar surface granulation where 1D models need to rely on simplified recipes. In the case of HD 189733, the model atmospheres produce practically equivalent Limb Darkening curves between 2900 A and 5700 A, partly due to obstruction by spectral lines, and the data are not su cient to distinguish between the light curves. We also analyze HST observations between 5350 A and 10500 A for this star; the 3D model leads to a better fit compared to 1D Limb Darkening predictions. The significant improvement of fit quality for the HD 209458 system demonstrates the higher degree of realism of 3D hydrodynamical models and the importance of surface granulation for the formation of the atmospheric radiation field of late-type stars. This result agrees well with recent investigations of Limb Darkening in the solar continuum and other observational tests of the 3D models. The case of HD 189733 is no contradiction as the model light curves are less sensitive to the temperature stratification of the stellar atmosphere and the observed data in the 2900 A - 5700 A region are not su cient to distinguish more clearly between the 3D and 1D Limb Darkening predictions.
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Limb Darkening laws for two exoplanet host stars derived from 3d stellar model atmospheres
arXiv: Solar and Stellar Astrophysics, 2012Co-Authors: W Hayek, David K. Sing, F Pont, Martin AsplundAbstract:We compare Limb Darkening laws derived from 3D hydrodynamical model atmospheres and 1D hydrostatic MARCS models for the host stars of the two transiting exoplanet systems HD 209458 and HD 189733. The surface brightness distribution of the stellar disks is calculated using 3D LTE spectrum formation and opacity sampling. We test our predictions using least-squares fits of model light curves to primary eclipses that were observed with the Hubble Space Telescope (HST). The Limb Darkening law derived from the 3D model of HD 209458 between 2900 A and 5700 A produces significantly better fits to the HST data, removing systematic residuals that were previously observed for model light curves based on 1D predictions. This difference arises mainly from the shallower mean temperature structure of the 3D model, which is a consequence of the explicit simulation of surface granulation. In the case of HD 189733, the model atmospheres produce practically equivalent Limb Darkening curves between 2900 A and 5700 A, partly due to obstruction by spectral lines, and the data are not sufficient to distinguish between the light curves. We also analyze HST observations between 5350 A and 10500 A for this star; the 3D model leads to a better fit compared to 1D predictions. The significant improvement of fit quality for the HD 209458 system demonstrates the higher degree of realism of 3D models and the importance of surface granulation for the formation of the atmospheric radiation field of late-type stars. This result agrees well with recent investigations of Limb Darkening in the solar continuum and other observational tests. The case of HD 189733 is no contradiction as the model light curves are less sensitive to the temperature stratification of the atmosphere and the observed data in the 2900 A - 5700 A region are not sufficient to distinguish more clearly between 3D and 1D Limb Darkening.
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Stellar Limb-Darkening Coefficients for CoRot and Kepler
Astronomy and Astrophysics, 2010Co-Authors: David K. SingAbstract:Transiting exoplanets provide unparalleled access to the fundamental parameters of both extrasolar planets and their host stars. We present Limb-Darkening coefficients (LDCs) for the exoplanet hunting CoRot and Kepler missions. The LDCs are calculated with ATLAS stellar atmospheric model grids and span a wide range of Teff, log g, and metallically [M/H]. Both CoRot and Kepler contain wide, nonstandard response functions, and are producing a large inventory of high-quality transiting lightcurves, sensitive to stellar Limb Darkening. Comparing the stellar model Limb Darkening to results from the first seven CoRot planets, we find better fits are found when two model intensities at the Limb are excluded in the coefficient calculations. This calculation method can help to avoid a major deficiency present at the Limbs of the 1D stellar models.
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stellar Limb Darkening coefficients for corot and kepler
Astronomy and Astrophysics, 2010Co-Authors: David K. SingAbstract:Transiting exoplanets provide unparalleled access to the fundamental parameters of both extrasolar planets and their host stars. We present Limb-Darkening coefficients (LDCs) for the exoplanet hunting CoRot and Kepler missions. The LDCs are calculated with ATLAS stellar atmospheric model grids and span a wide range of Teff , log g, and metallically [M/H]. Both CoRot and Kepler use wide nonstandard photometric filters, and are producing a large inventory of high-quality transiting lightcurves, sensitive to stellar Limb Darkening. Comparing the stellar model Limb Darkening to results from the first seven CoRot planets, we find better fits are found when two model intensities at the Limb are excluded in the coefficient calculations. This calculation method can help to avoid a major deficiency present at the Limbs of the 1D stellar models.
Heike Rauer - One of the best experts on this subject based on the ideXlab platform.
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the effect of stellar Limb Darkening values on the accuracy of the planet radii derived from photometric transit observations
Astronomy and Astrophysics, 2013Co-Authors: Sz Csizmadia, T Pasternacki, C Dreyer, J Cabrera, A Erikson, Heike RauerAbstract:Context. The radius of an exoplanet is one of its most important parameters. Studies of planetary interiors and their evolution require 1% precision in the radius determination. Transiting exoplanets offer a unique oppurtunity to measure the radius of exoplanets in stellar units. These radius measurements and their precision are strongly affected by our knowledge of Limb Darkening. Aims. 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. Methods. 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. Results. 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. Conclusions. 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.
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the effect of stellar Limb Darkening values on the accuracy of the planet radii derived from photometric transit observations
arXiv: Earth and Planetary Astrophysics, 2012Co-Authors: Sz Csizmadia, T Pasternacki, C Dreyer, J Cabrera, A Erikson, Heike RauerAbstract: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.