On the challenge of interpreting the morphology and color maps of high-z starburst galaxies with the JWST and Euclid

Morphology and color patterns hold fundamental insights into the early formation history of high-z galaxies. However, 2D reconstruction of rest-frame (RF) color maps of such systems from imaging data is a non-trivial task. This is mainly because the spectral energy distribution (SED) of high-sSFR (starburst) galaxies near and far is spatially inhomogeneous and thus the common practice of applying a spatially constant "morphological" k-correction can lead to serious observational biases. In this study we use the nearby blue compact galaxy Haro11 to illustrate how the spatial inhomogeneity of the SED impacts the morphology and color maps in the observer's frame (ObsF) visual and NIR, and potentially affects the physical characterization of distant starburst galaxies with the JWST and Euclid. Based on MUSE spectroscopy and spectral modeling, we first examine the elements shaping the spatially varying optical SED of Haro11, namely intrinsic stellar age gradients, strong nebular emission and its spatial decoupling from the ionizing stellar background, and differing extinction patterns in the stellar and nebular component both spatially and in their amount. Our simulations show, inter alia, that an optically bright yet dusty star-forming (SF) region may evade detection whereas a gas-evacuated (thus, potentially Lyman continuum photon-leaking) region with weaker SF activity can dominate the ObsF (RF UV) morphology of a high-z galaxy. We also show that ObsF color maps are affected by strong emission lines moving in and out of filter passbands depending on z, and, if taken at face value, can lead to erroneous conclusions about the nature, evolutionary status and dust content of a galaxy. A significant additional problem stems from the uncertain prominence of the 2175 {\AA} extinction bump that translates to appreciable inherent uncertainties in RF color maps of high-z galaxies. (abridged)