Limb darkening and exoplanets: testing stellar model atmospheres and identifying biases in transit parameters

By Néstor Espinoza, A. Jord'an. 2015

152 citations recorded by the source corpus.

Limb-darkening is fundamental in determining transit lightcurve shapes, and is typically modeled by a variety of laws that parametrize the intensity profile of the star that is being transited. Confronted with a transit lightcurve, some authors fix the parameters of these laws, the so-called limb-darkening coefficients (LDCs), while others prefer to let them float in the lightcurve fitting procedure. Which of these is the best strategy, however, is still unclear, as well as how and by how much each of these can bias the retrieved transit parameters. In this work we attempt to clarify those points by first re-calculating these LDCs, comparing them to measured values from Kepler transit lightcurves using an algorithm that takes into account uncertainties in both the geometry of the transit and the parameters of the stellar host. We show there are significant departures from predicted model values, suggesting that our understanding of limb-darkening still needs to improve. Then, we show through simulations that if one uses the quadratic limb-darkening law to parametrize limb-darkening, fixing and fitting the LDCs can lead to significant biases -up to $\sim 3\%$ and $\sim 1\%$ in $R_p/R_*$, respectively-, which are important for several confirmed and candidate exoplanets. We conclude that, in this case, the best approach is to let the LDCs be free in the fitting procedure. Strategies to avoid biases in data from present and future missions involving high precision measurements of transit parameters are described.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/a6dda600ae5fe22e2905e6f994d84fcb04fbebe3

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Citations in the corpus

The JWST Early Release Observations (2022, methodology): “…law, but using as priors limb-darkening coefficients obtained through the limb-darkening software combined with the SPAM algorithm, as described in Espinoza & Jordán (2015); the priors were set on the transformed coefficients (q1, q2), with truncated normal distributions centered on these…”
Limb and gravity-darkening coefficients for the TESS satellite at several metallicities, surface gravities, and microturbulent velocities (2016, methodology): “Based on the work by Wittkowskii, Aufdenberg, & Kervella (2004), Espinoza & Jordan (2015) used r = (1 − µ 2 ), instead of µ . p They derive the LDC by searching for the maximum of the derivative of the speciﬁc intensity with respect to r and shifting the proﬁle to this point (hereafter referred as…”
A NEW APPROACH TO ANALYZING HST SPATIAL SCANS: THE TRANSMISSION SPECTRUM OF HD 209458 b (2015, methodology): “It returns the relative flux, F (t), as a function of the limb darkening coefficients, an, the Rp/R∗ ratio and all the orbital parameters (T0, P, i, a/R∗, e, ω), based on the nonlinear limb darkening model (Claret 2000) for the host star: I(an, r) = 1− n=4∑ n=1 an(1− (1− r2)n/4) (11) We calculate th”
Disentangling the Planet from the Star in Late-Type M Dwarfs: A Case Study of TRAPPIST-1g (2018, methodology): “The 4-parameter limbdarkening law is chosen in this analysis as this has been demonstrated to avoid biases in the data better than the quadratic law (Espinoza & Jordán 2015).”