Analytic Approximations for Transit Light-Curve Observables, Uncertainties, and Covariances

By J. Carter, Jennifer C. Yee, Jason Eastman, B. Gaudi, J. Winn. 2008

136 citations recorded by the source corpus.

The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a nonanalytic and computationally intensive problem, it is often useful to have analytic approximations for the parameters as well as their uncertainties and covariances. Here, we give such formulae, for the case of an exoplanet transiting a star with a uniform brightness distribution. We also assess the advantages of some relatively uncorrelated parameter sets for fitting actual data. When limb darkening is significant, our parameter sets are still useful, although our analytic formulae underpredict the covariances and uncertainties.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/180cbd8257e8c2e6144b80a9a578f19296f6e11c

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In Applied Mathematics

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Citations in the corpus

THE FLAT TRANSMISSION SPECTRUM OF THE SUPER-EARTH GJ1214b FROM WIDE FIELD CAMERA 3 ON THE HUBBLE SPACE TELESCOPE (2011, background): “1 to ensure uniform priors for the physical parameters Rp, R?, and i (see Burke et al. 2007; Carter et al. 2008, for detailed discussions).”
Transits and Occultations (2010, unknown): “A Fisher information nalysis (essentially a glorified error propagation) leadsto estimates for the 1σ uncertainties in the transit parameters (Carter et al. 2008): σδ ≈ Q−1δ, (43) σtc ≈ Q−1T √ τ/2T , (44) σT ≈ Q−1T √ 2τ/T , (45) στ ≈ Q−1T √ 6τ/T , (46) which are valid whenδ ≪ 1, limb darkening is…”
HAT-P-11b: A SUPER-NEPTUNE PLANET TRANSITING A BRIGHT K STAR IN THE KEPLER FIELD (2009, background): “We chose these parameters because of their simple geometric meanings and the fact that these show negligible correlations (see Carter et al. 2008; Bakos et al. 2007b; Pál 2008b).”
Accurate Empirical Radii and Masses of Planets and Their Host Stars with Gaia Parallaxes (2016, background): “The eccentricity of the orbit can be determined from the precise shape of the Doppler reflex (radial velocity, or RV) motion of the star, and the inclination can be measured from the relative duration of the ingress/egress τ and full-width half-maximum T of the transit (Carter et al. 2008).”
Morphological Lightcurve Distortions due to Finite Integration Time (2010, background): “The simplest way to understand the effect on this parameter is to appreciate that b and aR exhibit an extremely strong negative correlation, as demonstrated by Carter et al. (2008).”
OBLIQUITIES OF HOT JUPITER HOST STARS: EVIDENCE FOR TIDAL INTERACTIONS AND PRIMORDIAL MISALIGNMENTS (2012, methodology): “By choosing those particular parameters we minimized the correlations among their uncertainties (Carter et al. 2008), consistent with our treatment of the priors as independent Gaussian functions.”
The prevalence of dust on the exoplanet HD 189733b from Hubble and Spitzer observations (2012, methodology): “In the Spitzer bands where the effects of limb-darkening are small, we corrected the values calculated with other parameters using the first-order expressions of the relation between orbital parameters and transit shape given in Carter et al. (2008).”
ARCHITECTURE OF KEPLER'S MULTI-TRANSITING SYSTEMS. II. NEW INVESTIGATIONS WITH TWICE AS MANY CANDIDATES (2012, background): “With respect to photometric noise, the error on a duration measurement is σdur ' Tdur √ 2r/SNR (Carter et al. 2008), typically ∼ 1%.”
PLANETARY CANDIDATES OBSERVED BY KEPLER. VI. PLANET SAMPLE FROM Q1–Q16 (47 MONTHS) (2015, background): “Rp/R∗ is strongly correlated with b, and the local linearized uncertainty estimate employed by DV becomes ill-conditioned (see Table 2 of Carter et al. 2008), resulting in an overestimate of the uncertainty of b.”