Multi-Wavelength Photometry Derived from Monochromatic Kepler Data

The Kepler mission has provided a wealth of data, revealing new insights in time-domain astronomy. However, Kepler's single band-pass has limited studies to a single wavelength. In this work we build a data-driven, pixel-level model for the Pixel Response Function (PRF) of Kepler targets, modeling the image data from the spacecraft. Our model is sufficiently flexible to capture known detector effects, such as non-linearity, intra-pixel sensitivity variations, and focus change. In theory, the shape of the Kepler PRF should also be weakly wavelength dependent, due to optical chromatic aberration and wavelength dependent detector response functions. We are able to identify these predicted shape changes to the PRF using the residuals between Kepler data and our model. In this work, we show that these PRF changes correspond to wavelength variability in Kepler targets using a small sample of eclipsing binaries. Using our model, we demonstrate that pixel-level light curves of eclipsing binaries show variable eclipse depths, ellipsoidal modulation and limb darkening. These changes at the pixel level are consistent with multi-wavelength photometry. Our work suggests each pixel in the Kepler data of a single target has a different effective wavelength, ranging from $\approx$ 550-750 $nm$. In this proof of concept, we demonstrate our model, and discuss possible use cases for the wavelength dependent Pixel Response Function of Kepler. These use cases include characterizing variable systems, and vetting exoplanet discoveries at the pixel level. The chromatic PRF of Kepler is due to weak wavelength dependence in the optical systems and detector of the telescope, and similar chromatic PRFs are expected in other similar telescopes, notably the NASA TESS telescope.