Improving $z\sim7-11$ Galaxy Property Estimates with JWST/NIRCam Medium-Band Photometry

The past decade has seen impressive progress in the detection of $z>7$ galaxies with the Hubble Space Telescope, however little is known about their properties. The James Webb Space Telescope will revolutionise the high-$z$ field by providing NIR (i.e., rest-frame optical) data of unprecedented depth and spatial resolution. Measuring galaxy quantities such as resolved stellar ages or gas metallicity gradients traditionally requires spectroscopy, as broad-band imaging filters are generally too coarse to fully isolate diagnostics such as the 4000 \r{A} (rest-frame) break, continuum emission from aged stars, and key emission lines (e.g., [OII], [OIII], H$\beta$). However, in this paper, we show that adding NIRCam images through a strategically chosen medium-band filter to common wide-band filters sets adopted by ERS and GTO programs delivers tighter constraints on these galactic properties. To constrain the choice of filter, we perform a systematic investigation of which combinations of wide-band filters from ERS and GTO programs and single medium-band filters offer the tightest constraints on several galaxy properties at redshifts $z\sim7-11$. We employ the JAGUAR extragalactic catalogs to construct statistical samples of physically-motivated mock photometry and conduct SED-fitting procedures to evaluate the accuracy of galaxy property (and photo-$z$) recovery with a simple star-formation history model. We find that adding $>4.1 \mu$m medium filters at comparable depth to the broad-band filters can significantly improve photo-$z$s and yield close to order-of-magnitude improvements in the determination of quantities such as stellar ages, metallicities, SF-related quantities and emission line fluxes at $z\sim8$. For resolved sources, the proposed approach enables spatially-resolved determination of these quantities that would be prohibitive with slit spectroscopy.