Binning is sinning: morphological light-curve distortions due to finite integration time

Abstract

We explore how finite integration times or equivalently temporal binning induces morphological distortions to the transit light curve. These distortions, if uncorrected for, lead to the retrieval of erroneous system parameters and may even lead to some planetary candidates being rejected as ostensibly unphysical. We provide analytic expressions for estimating the disturbance to the various light-curve parameters as a function of the integration time. These effects are particularly crucial in light of the long-cadence photometry often used for discovering new exoplanets by, for example, Convection Rotation and Planetary Transits (CoRoT) and the Kepler Missions (8.5 and 30 min). One of the dominant effects of long integration times is a systematic underestimation of the light-curve-derived stellar density, which has significant ramifications for transit surveys. We present a discussion of numerical integration techniques to compensate for the effects and produce expressions to quickly estimate the errors of such methods, as a function of integration time and numerical resolution. This allows for an economic choice of resolution before attempting fits of long-cadence light-curves. We provide a comparison of the short-and long-cadence light curves of TrES-2b and show that the retrieved transit parameters are consistent using the techniques discussed here.

Light Curve Solutions of Ten Eccentric Kepler Binaries, Three of them with Tidally Induced Humps

“…Similar behaviour could be seen also for other Kepler binaries (Hambleton et al 2013;Lehmann et al 2013;Maceroni et al 2014). We attributed them to the effects of finite integration time studied by Kipping (2010): (i) the large integration times smear out the light curve signal into a broader shape (see Figure 1 of Kipping 2010): the detected ingress and egress durations are bigger than their natural values (introducing an additional curvature into the eclipse wings) and the apparent positions of the contact points are temporally shifted from their true value; (ii) the large integration times smear out the curvature of the eclipse Table 4. Masses M i , radii R i , and luminosities L i of the target components (in solar units) according to the empirical relations.…”

SOPHIE velocimetry ofKeplertransit candidates

“…Basically, we modeled the light curves with the EBOP code (Etzel 1981;Popper & Etzel 1981) using a quadratic limb-darkening law with coefficients interpolated from the tables of Claret & Bloemen (2011). To deal with the distortion of the transit shape arising from the finite integration time (Kipping 2010) of LC data, we oversampled the model to five times the original sampling rate and re-binned to the LC sampling rate before comparing them to the data. The radial velocities were fitted to a Keplerian orbit.…”

Photospheric activity, rotation, and magnetic interaction in LHS 6343 A

“…This combines a Markov chain Monte Carlo (MCMC) technique to fit light curves and a wavelet-based likelihood function (Carter & Winn 2009), which is used to compute parameter uncertainties. The model light curve is resampled and rebinned according to the Kepler long-cadence (∼29.4 min) data sampling to avoid systematic deviations, in particular during the ingress and egress phases (Kipping 2010). The orbital period is fixed to 12.71382 days (Johnson et al 2011), and the adjusted parameters are the inclination i, the ratio of the companion and primary radii R C /R A , the scaled semimajor axis (a/R A ), and the time of mid-transit T 0 .…”