2023AJ....165..210S

High-precision lightcurves combined with eclipse-mapping techniques can reveal the horizontal and vertical structure of a planet's thermal emission and the dynamics of hot Jupiters. Someday, they even may reveal the surface maps of rocky planets. However, inverting lightcurves into maps requires an understanding of the planet, star, and instrumental trends because they can resemble the gradual flux variations as the planet rotates (i.e., partial phase curves). In this work, we simulate lightcurves with baseline trends and assess the impact on planet maps. Baseline trends can be erroneously modeled by incorrect astrophysical planet map features, but there are clues to avoid this pitfall in both the residuals of the lightcurve during eclipse and sharp features at the terminator of the planet. Models that use a Gaussian process or polynomial to account for a baseline trend successfully recover the input map even in the presence of systematics but with worse precision for the m = 1 spherical harmonic terms. This is also confirmed with the ThERESA eigencurve method where fewer lightcurve terms can model the planet without correlations between the components. These conclusions help aid the decision on how to schedule observations to improve map precision. If the m = 1 components are critical, such as measuring the east/west hot-spot shift on a hot Jupiter, better characterization of baseline trends can improve the m = 1 terms' precision. For latitudinal north/south information from m ≠ 1 mapping terms, it is preferable to obtain high signal to noise at ingress/egress with more eclipses.