The SPHEREx View of Galaxy Clusters: A Simulation-based Validation of the Forced Photometry Pipeline for Extended Sources

Technical Summary: The SPHEREx View of Galaxy Clusters

Problem Statement
Galaxy clusters are critical probes for cosmology and galaxy evolution, requiring large, homogeneously selected samples with accurately measured member properties, particularly redshifts and spectral energy distributions (SEDs). While spectroscopic surveys provide precise redshifts, they are observationally prohibitive for the vast number of member galaxies in large cluster catalogs (e.g., from eROSITA, SPT, and future surveys like Euclid and Rubin/LSST). Photometric redshifts offer a solution but require stringent control over systematic biases and scatter to meet cosmological requirements (bias $\lesssim 0.003$ and scatter $\sim 0.03$).

The SPHEREx mission, an all-sky near-infrared spectrophotometric survey, promises dense sampling of rest-frame optical and NIR features. However, its large pixel scale ($6.15'' \times 6.15''$) introduces significant challenges for cluster science, specifically source blending in dense cluster cores and the accurate photometry of intrinsically extended sources that are undersampled by the pixels. Previous studies have addressed blending in general fields or extragalactic settings, but the performance of forced photometry in the extreme overdensities of galaxy cluster cores, and its ability to recover fluxes for extended sources, remained unexplored. Furthermore, the effective survey depth for characterizing faint cluster members within the nominal 2-year mission required dedicated investigation.

Methodology
The authors present an end-to-end simulation-driven assessment of the SPHEREx pipeline for galaxy cluster science. The methodology involves:

1. Sample Selection: A working sample of eight galaxy clusters spanning a redshift range of $z \approx 0.02$ to $1.1$ (including Coma, Abell clusters, and SPT-selected clusters) was selected from the HeCS-omnibus, SPT-SZ, and GOGREEN catalogs. The COSMOS field served as a low-density field reference.
2. Source Characterization: Ancillary data from the DESI Legacy Survey and COSMOS2025 were used to derive initial SEDs and morphological parameters (Sérsic index, effective radius, ellipticity) for sources. Star-galaxy separation was performed using morphological types, spectroscopic redshifts, and template fitting goodness-of-fit.
3. Mock Observation Generation: Realistic mock SPHEREx images were generated using the SPHEREx Sky Simulator. The pipeline integrated the GalSim library to render high-resolution (oversampled by 5x) light profiles of extended sources based on their morphological parameters. These were convolved with position- and wavelength-dependent PSF models and downsampled to the SPHEREx pixel scale. A pixel-by-pixel response model accounted for the chromatic effects of the Linear Variable Filters (LVFs).
4. Forced Photometry: The Tractor software was used to perform forced photometry on the simulated images. Source positions and shapes were fixed to their known input values, and only fluxes were fitted using SPHEREx-optimized Mixture-of-Gaussians (MoG) models for Sérsic profiles.
5. Catalog Construction and Redshift Estimation: Individual flux measurements were compiled into a Primary Catalog and binned into a Secondary Catalog (102 spectral channels). Photometric redshifts ($z_{phot}$) were derived using eazy-py on the Secondary Catalog spectrophotometry.
6. Performance Metrics: The study quantified photometric bias, scatter, source blending effects (using neighbor flux ratios and counts), effective survey depth, and photometric redshift accuracy ($\sigma_{NMAD}$, bias, and outlier fractions).

Key Contributions

• First End-to-End Cluster Simulation: This work provides the first quantitative assessment of the SPHEREx forced photometry pipeline specifically tailored to the extreme source densities of galaxy cluster cores.
• Extended Source Modeling: Unlike previous studies that treated sources as unresolved, this pipeline explicitly models intrinsically extended sources (cluster members) using Sérsic profiles, addressing the challenge of undersampling by large pixels.
• Blending Analysis in Clusters: The study isolates the impact of source blending in cluster environments, distinguishing between the effects of neighbor flux ratios and neighbor counts, and comparing these against low-density field environments.
• Depth and Redshift Validation: The paper establishes the effective depth for member detection relative to the Brightest Cluster Galaxy (BCG) and validates photometric redshift precision for cluster members across a wide redshift range.

Results

• Photometry Performance: The pipeline recovers fluxes with minimal bias (typically $< 2\%$) for most magnitudes. A small positive bias ($\sim 2\%$) appears at the faintest magnitudes, primarily driven by compact extended sources ($r_e < 1''$) where the MoG model mismatches the input Sérsic profile. Binning into the Secondary Catalog reduces scatter by $\sim 50\%$.
• Source Blending: Source blending is identified as the primary driver of catastrophic photometric outliers. While the mean bias remains small, the scatter increases dramatically when the combined flux of neighbors is comparable to the target flux. Blending suppresses the extended tails of the residual distribution, reducing the fraction of catastrophic outliers from $\sim 0.4\%$ in blended runs to $< 0.01\%$ in single-source runs.
• Survey Depth: SPHEREx detects members down to $K_s \approx 20$ AB ($5\sigma$). In nearby clusters (e.g., Coma), this allows detection of members 7–9 magnitudes fainter than the BCG. At $z \sim 1$, where the BCG itself fades to $K_s \approx 18$, the detection limit is only 1–2 magnitudes fainter than the BCG.
• Photometric Redshift Accuracy:
  • For the full sample, performance is dominated by faint, low-S/N sources.
  • With brightness cuts ($K_s < 19$), the scatter improves to $\sigma_{NMAD} \approx 0.016$.
  • For the highest-quality sample ($K_s < 17.5$ or detected in all 102 channels), $\sigma_{NMAD}$ reaches $\approx 0.002$.
  • Passive (quiescent) galaxies show significantly better performance than star-forming galaxies, particularly at faint magnitudes, due to the constraining power of the 1.6 $\mu$m stellar bump.
• Cluster Redshift Estimation: Combining the photometric redshifts of quality-selected members yields cluster redshifts with a bias of $|\Delta z|/(1+z) < 0.002$ and a scatter of $\sigma \approx 0.002$ at $z \lesssim 0.5$. This meets the precision requirements for cluster cosmology. At higher redshifts ($z \sim 1$), the precision is limited by the number of members above the detection threshold rather than the intrinsic redshift precision of individual galaxies.

Significance
The paper claims that despite the large pixel scale of SPHEREx, the forced photometry pipeline can deliver reliable photometry and photometric redshifts for cluster galaxies, provided appropriate sample selection based on brightness or signal-to-noise is applied. The results demonstrate that SPHEREx is well-suited for assembling large, well-characterized cluster samples for cosmological analyses, particularly at $z \lesssim 0.5$. The study establishes that the pipeline is robust to the cluster environment at the field-averaged level, though high-density cores require careful handling of blending. These findings serve as a foundational validation for the development of Level 4 legacy science products, such as a SPHEREx Galaxy Cluster Catalog, and highlight the potential of SPHEREx's rich NIR spectrophotometry to improve mass-observable scaling relations and self-calibration techniques in cluster cosmology. The authors emphasize that their results represent a best-case scenario regarding morphological priors and that future work must address membership selection and cluster detection algorithms tailored to SPHEREx data.