Simulating Spectral Confusion in SPHEREx Photometry and Redshifts

We model the impact of source confusion on photometry and the resulting spectrophotometric redshifts for SPHEREx, a NASA Medium-Class Explorer that is carrying out an all-sky near-infrared spectral survey. Spectral confusion from untargeted background galaxies degrades sensitivity and introduces a spectral bias. Using interpolated spectral energy distributions (SEDs) from the COSMOS2020 catalog, we construct a Monte Carlo library of confusion spectra that captures the cumulative impact from faint galaxies. By injecting confusion realizations into galaxy SEDs and performing forced photometry at known source positions, we quantify photometric and redshift error and bias. For our current expected selection of sources for the cosmology analysis, we find typical 1-$σ$ confusion levels range from $0.8-3.8\ μ\mathrm{Jy}$ across $0.75-5.0\ μ\mathrm{m}$. While negligible at full-sky survey depth, spectral confusion becomes significant in the SPHEREx deep fields, reducing the number of intermediate-precision redshifts and inducing a small systematic overestimation in redshift. In parallel, we also model targeted source blending from beam overlaps, which contributes additional photometric noise without systematic redshift bias, provided that positions are known exactly. Together, confusion and blending vary with the depth of the selected reference sample, revealing a trade-off, where deeper selections reduce confusion but increase blending-induced noise. Our methodology informs optimization of the SPHEREx deep-field selection strategy and future treatments of stellar source blending and confusion.