The Redshifts from 122 Bands: Comparative Redshift Forecast for Low-Resolution Spectra from SPHEREx and 7-Dimensional Sky Survey (7DS)

The recently initiated SPHEREx and 7DS surveys will deliver low-resolution spectra ($R\approx 30-130$) for hundreds of millions of galaxies over the optical to near-infrared range ($0.4-5.0μm$), covering a wide sky area without sample selection. These unique datasets will improve redshift estimation and provide a rich redshift catalog for the community. In this study, we forecast the performance of widely-used photometric redshift estimation methods using simulated SPHEREx and 7DS data. Four template-fitting approaches and two machine-learning (ML) methods are used to derive photometric redshifts from low-resolution spectrophotometric data. We measure redshifts using mock catalogs based on the GAMA and COSMOS galaxy samples and achieve high precision for bright (13 < i < 18) galaxies, with $σ_{NMAD}\lesssim 0.005$, bias $\lesssim 0.005$, and a catastrophic failure rate $\lesssim 0.005$ for all methods employed. We find that the combined SPHEREx + 7DS dataset significantly improves redshift estimation compared to using either the SPHEREx or 7DS datasets alone, highlighting the synergy between the two surveys. Moreover, we compare the redshift estimation performance across magnitude ranges for the different methods and examine the probability distribution functions (PDFs) produced by the template-fitting approaches. As a result, we identify some factors that can affect the redshift measurements, like treatments on dust extinction or inclusion of flux uncertainty in the ML model. We also show that the PDFs are relatively well calibrated, although the confidence intervals are generally underestimated, particularly for bright galaxies in the template-fitting methods. This study demonstrates the strong potential of SPHEREx and 7DS to deliver improved redshift measurements from low-resolution spectrophotometric data, underscoring the scientific value of jointly utilizing both datasets.