Simulating Spectral Confusion in SPHEREx Photometry and Redshifts

TL;DR

This work develops a rigorous framework to quantify how blending of targeted sources and spectral confusion from faint background galaxies affect SPHEREx photometry and spectrophotometric redshifts. By combining Tractor-based forced photometry with Fisher-information covariance corrections and a Monte Carlo spectral confusion library built from COSMOS2020 data, the authors quantify how these effects degrade redshift precision, induce color biases, and alter outlier rates across full-sky and deep-field depths. They find blending dominates photometric noise at full-sky depth while spectral confusion becomes significant in deep fields, introducing a modest high-redshift bias, and that an optimal deep-field selection balances both effects to maximize reliable redshifts. The results inform SPHEREx deep-field optimization, stellar contamination handling, and methodologies for treating confusion and blending in future spectrophotometric surveys, with implications for cross-field cosmology analyses and LSS studies.

Abstract

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.

Figures (19)

• Figure 1: Color–magnitude diagram (LS-$z$ – WISE-1 vs. LS-$z$) for COSMOS and GAMA galaxies cross-matched to the LS catalog, resampled according to their survey footprints (1.27 and 217 deg$^2$, respectively). Points are color-coded by redshift. The solid black lines show the fiducial cosmology selection defined in Equation \ref{['eq:cut']}. Vertical dashed lines indicate candidate constant $z$-band magnitude cuts at 21.3, 22.0, 22.7, and 23.4, which will be explored in following blending and confusion analyses.
• Figure 2: Tractor photometry including flux covariance. The top left panel shows a pair of blended sources in a high-resolution noiseless scene upsampled by a factor of 5 from the SPHEREx resolution $6\farcs15$. Sources are separated by 3 oversampled pixels ($3\farcs69$) and have an intrinsic flux ratio of 2:1. The image is downsampled to SPHEREx resolution with simulated noise added, as shown on the top right panel. The bottom row displays the unbiased photometric z-score based on a locally modified implementation of Tractor with covariance (light green) performed on the blended pair simultaneously, with fitted Gaussian statistics (dark green) and an ideal distribution (black dashed curve), for each source in the blended pair. This is compared with the z-score distribution from the original nominal Tractor results (blue).
• Figure 3: Fractional excess in flux uncertainty for a pair of blended sources (flux ratio 2:1) as a function of their separation. Photon noise and readout noise are included, with subpixel sampling achieved by averaging over PSF orientations. Both sources are below the ZL photon noise floor, so the choice of which source to show is unimportant; here we show the fainter one. At shorter wavelengths (top), the PSF is more asymmetric, resulting in a broader 16–84% variation band (shaded light green) around the median curve. At longer wavelengths (bottom), the median flux inflation (black) is higher due to larger diffraction and thus greater PSF overlap. The fractional increase in flux uncertainty, $\delta f$, for separations of 1.0, 0.6, and 0.2 SPHEREx pixels is labeled.
• Figure 4: Ensemble flux error inflation among targeted galaxies. For each $z$-magnitude cut (LS-$z<21.3,\ 22.0,\ 22.7,\ 23.4$) that corresponds to a target number density (color-coded), we compare the true photometric error from the covariance mode $\hat{F}_B$ to the naive isolated flux error $\hat{\sigma}_{\mathrm{iso}}$. Distributions of $(\hat{F}_B - F_{\text{true}})/\hat{\sigma}_{\mathrm{iso}}$ are shown, with a standard normal (black) for reference. The broadening is quantified by the NMAD, labeled as $\overline{\sigma_{F,B} / \sigma_{\mathrm{F, iso}}}$ for each sample of galaxies. Results are shown for two SPHEREx channels: 0.76 (left) and $4.98\ \mu \mathrm{m}$ (right).
• Figure 5: Fractional increase in flux error due to blending vs. target number density. Each set of points corresponds to a $z$-magnitude cut, with associated number densities on the lower $x$-axis (navy) and $z$-magnitude on the upper axis. The LS-$z < 22.3$ cut matches the number density of our fiducial cosmology sample ($\sim\!7.0$ arcmin$^{-2}$).