Knot a Bad Idea: Testing BLISS Mapping for Spitzer Space Telescope Photometry

Much of transiting exoplanet science relies on high-precision photometry. The current generation of instruments can exhibit sensitivity variations greater than the astrophysical signals. For the InfraRed Array Camera (IRAC) on the Spitzer Space Telescope, a popular way to handle this is BiLinearly-Interpolated Subpixel Sensitivity (BLISS) mapping. As part of a Markov Chain Monte Carlo (MCMC), BLISS mapping estimates the sensitivity at many locations (knots) on the pixel, then interpolates to the target star's centroids. We show that such embedded optimization schemes can misfit or bias parameters. Thus, we construct a model of $\textit{Spitzer}$ eclipse light curves to test the accuracy and precision of BLISS mapping. We compare standard BLISS mapping to a variant where the knots are fit during the MCMC, as well as to a polynomial model. Both types of BLISS mapping give similar eclipse depths, and we find that standard knots behave like real parameters. Standard BLISS mapping is therefore a reasonable shortcut to fitting for knots in an MCMC. BLISS maps become inaccurate when the photon noise is low, but typically approximate the real sensitivity well. We also find there is no perfect method for choosing the ideal number of BLISS knots to use on given data. BLISS mapping gives fits that are usually more accurate than precise (i.e. they are overly conservative), and the routine is more precise than polynomial models for significant eclipses or pixels with more varied sensitivities. BLISS mapping has better predictive power for most of these particular synthetic data, depending on how one treats time-correlated residuals. Overall, we conclude that BLISS mapping can be a reasonable sensitivity model for IRAC photometry.