Comparison of Limb-Darkening Laws from Plane-Parallel and Spherically-Symmetric Model Stellar Atmospheres

Neilson, Hilding R.

doi:10.1017/s174392131102744x

Cited by 2 publications

(2 citation statements)

References 13 publications

(17 reference statements)

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“…This effect gives rise to the well known differences in limb darkening behaviour for plane-parallel and spherical models in stellar atmospheres (e.g. Neilson 2012). Since the T-p profiles used in Sect.…”

Section: D Geometric Effectsmentioning

confidence: 90%

Exoplanetary Monte Carlo radiative transfer with correlated-k – I. Benchmarking transit and emission observables

Lee

Taylor

Grimm

et al. 2019

Monthly Notices of the Royal Astronomical Society

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Current observational data of exoplanets are providing increasing detail of their 3D atmospheric structures. As characterisation efforts expand in scope, the need to develop consistent 3D radiative-transfer methods becomes more pertinent as the complex atmospheric properties of exoplanets are required to be modelled together consistently. We aim to compare the transmission and emission spectra results of a 3D Monte Carlo Radiative Transfer (MCRT) model to contemporary radiative-transfer suites. We perform several benchmarking tests of a MCRT code, Cloudy Monte Carlo Radiative Transfer (CMCRT), to transmission and emission spectra model output.We add flexibility to the model through the use of k-distribution tables as input opacities. We present a hybrid MCRT and ray tracing methodology for the calculation of transmission spectra with a multiple scattering component. CMCRT compares well to the transmission spectra benchmarks at the 10s of ppm level. Emission spectra benchmarks are consistent to within 10% of the 1D models. We suggest that differences in the benchmark results are likely caused by geometric effects between plane-parallel and spherical models. In a practical application, we post-process a cloudy 3D HD 189733b GCM model and compare to available observational data. Our results suggest the core methodology and algorithms of CMCRT produce consistent results to contemporary radiative transfer suites. 3D MCRT methods are highly suitable for detailed post-processing of cloudy and non-cloudy 1D and 3D exoplanet atmosphere simulations in instances where atmospheric inhomogeneities, significant limb effects/geometry or multiple scattering components are important considerations.

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Section: D Geometric Effectsmentioning

confidence: 90%

Exoplanetary Monte Carlo radiative transfer with correlated-k – I. Benchmarking transit and emission observables

Lee

Taylor

Grimm

et al. 2019

Monthly Notices of the Royal Astronomical Society

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“…[3][4][5] The mass affects the depth of the atmosphere, an effect that is not present in plane-parallel models. The Neilson models are given for 1000 values of μ, so no interpolation was needed, but with a wavelength resolution of 10 nm in the visual range.…”

Section: Npoi Data and Model Calculationsmentioning

confidence: 99%

Precise stellar diameters from coherently averaged visibilities

Armstrong

Jorgensen

Neilson

et al. 2012

Optical and Infrared Interferometry III

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Optical interferometry is the only means of directly measuring the sizes of stars. The most precise angular diameter measurements, however, depend on measuring complex fringe visibilities V at spatial frequencies where Re(V ) crosses zero. We can then use the spatial frequency B ⊥ /λ 0 of the zero crossing as a measure of the stellar diameter via θ UD,0 ≈ 1.22λ 0 /B ⊥ , where λ 0 and is the wavelength at which Re(V ) = 0 when observed with a baseline length B ⊥ projected toward the star, and θ UD,0 is the equivalent uniform disk diameter. The variation in limb darkening with wavelength leads to a corresponding variation in θ UD,0 with λ, even at fixed B, which allows us to measure the limb darkening in detail and probe the structure of the atmosphere. However, in order to take meaningful data at those spatial frequencies, we need some form of bootstrapping, in wavelength, baseline length, or both. Reduction of these bootstrapped data benefits greatly from the increase in SNR offered by coherent averaging. We demonstrate the effect of limb darkening on θ UD,0 (λ) with simulated observations based on model atmospheres, and compare them to coherently averaged NPOI data. THE ZERO-CROSSING IDEAThe majority of interferometric stellar diameter measurements are made at spatial frequencies u within the first null of the V 2 (θ, u) visibility curve. Within this range, the difference between the best-fit uniform disk curve and a curve that takes limb darkening into account is small. Therefore, the usual method of determining a diameter from these data is to fit a uniform-disk model to the observed visibilities, and multiply the resulting uniform-disk diameter θ UD by a correction factor appropriate to the stellar type to obtain the limb-darkened diameter θ LD .In principle, we could make more-detailed diameter measurements by fitting a uniform disk curve through each measured V 2 (u) point. If the data were from several wavelength channels on the same baseline, we would obtain a set of uniform disk diameters θ UD (λ) resulting from the individual uniform-disk V 2 (B ⊥ /λ) curves (B ⊥ is the baseline length projected toward the star). In practice, the visibility calibration is usually not accurate enough to give an interesting degree of precision for θ UD (λ): when V 2 ≈ 0.6, a 1% error in V 2 corresponds to a 1% error in θ UD (λ), while at V 2 ≈ 0.4, a 1% error in V 2 corresponds to a 0.5% error in θ UD (λ).However, we can make a much more precise determination of θ UD (λ) if we have data that straddles Re [V (u)] = 0 -for this discussion, it is more useful to look at Re(V ) than at V 2 -because any (multiplicative) calibration * tom.armstrong@nrl.navy.mil; phone 1 202 767 0669; fax 1 202 404 8894Optical and Infrared Interferometry III, edited by Françoise Delplancke, Jayadev K. Rajagopal, Fabien Malbet, Proc. of SPIE Vol. 8445, 84453K · © 2012 SPIE · CCC code: 0277-786/12/$18 ·

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Comparison of Limb-Darkening Laws from Plane-Parallel and Spherically-Symmetric Model Stellar Atmospheres

Cited by 2 publications

References 13 publications

Exoplanetary Monte Carlo radiative transfer with correlated-k – I. Benchmarking transit and emission observables

Exoplanetary Monte Carlo radiative transfer with correlated-k – I. Benchmarking transit and emission observables

Precise stellar diameters from coherently averaged visibilities

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