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

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 $\mathrm{\Delta }t$ reduces its amplitude by the scaling factor $\text{sinc}\left(\pi \mathrm{\Delta }t\mathrm{/}P\right)$, 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.