Is binning always sinning? The impact of time-averaging for exoplanet phase curves

TL;DR

This paper investigates how temporal binning affects exoplanet phase-curve analysis, providing formulas to correct biases and improve parameter estimation, with tests on synthetic and real datasets including Spitzer data.

Contribution

It introduces analytical formulas to account for the effects of time-averaging on phase-curve analysis and offers guidelines to optimize data binning without biasing results.

Findings

Binning can be safely applied to phase curves with minimal bias if corrected properly.

Analytical formulas accurately predict amplitude reduction due to binning.

Binning may influence parameter estimates beyond theoretical predictions in real data.

Abstract

We explore how finite integration time or temporal binning can affect the analysis of exoplanet phase-curves. We provide analytical formulae to account for this effect or, if neglected, to estimate the potential biases in the retrieved parameters. As expected, due to their smoother variations over longer time-scales, phase curves can be binned more heavily than transits without causing severe biases. In the simplest case of a sinusoidal phase curve with period $P$, the integration time $\Delta t$ reduces its amplitude by the scaling factor $\text{sinc}{ \left ( \pi \Delta t / P \right ) }$, without altering its phase or shape. We also provide formulae to predict reasonable parameter error bars from phase-curve observations. Our findings are tested with both synthetic and real datasets, including unmodelled astrophysical signals and/or instrumental systematic effects. Tests with the Spitzer data show that binning can affect the best-fitting parameters beyond predictions, due to the correction of high-frequency correlated noise. Finally, we summarize key guidelines for speeding up the analysis of exoplanet phase curves without introducing significant biases in the retrieved parameters.