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

TL;DR

This work evaluates photometric redshift performance for low-resolution spectrophotometric data anticipated from SPHEREx and 7DS. By applying six methods (four template-fitting codes and two ML-based approaches) to mock SPHEREx/7DS catalogs built from COSMOS/GAMA data with Brown+COSMOS templates, the authors quantify accuracy, bias, and outlier rates as functions of magnitude and redshift. They demonstrate that combining SPHEREx and 7DS yields substantial improvements over either survey alone, with sub-percent-level scatter for bright galaxies ($13<i<18$) and improved performance for fainter targets when using the joint dataset; PDFs are generally well-calibrated though confidence intervals are often underestimated, particularly for bright sources. The study also contrasts method-specific behaviors, noting, for example, that SPHEREx in-house templates perform well, while ML methods excel in certain regimes but face challenges with non-detections, and discusses implications for future large-scale redshift catalogs and science cases relying on accurate distance measurements.

Abstract

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.

Figures (10)

• Figure 1: The 5$\sigma$ point source detection limits of SPHEREx surveys and 7DS. The colored squares show the depths of the three layers of 7DS, with the RIS at the top, followed by the WTS and IMS layers. The circular markers show the depths of SPHEREx full-sky and deep surveys from the top. The blue, red, green, and pale blue triangles denote the 5$\sigma$ point source depths of other popular optical and NIR imaging surveys (SDSS york00_sdss, unWISE schlafly19_unwise, VHS mcmahon13_vhs, and Pan-STARRS chambers16). The shaded regions show the wavelength ranges of the plotted broadband filters (u, g, r, i, z, Y, J, H, $K_s$, W1, and W2) with the names indicated at the top.
• Figure 2: The redshift and $i$ magnitude distribution of GAMA and COSMOS galaxies used in this work. The GAMA data (bright blue) consists of brighter galaxies ($i \lesssim 18.5$) with low redshifts ($z \lesssim 0.4$) compared to COSMOS (maroon) galaxies with $18 \lesssim i \lesssim 25$ and $z \lesssim 6$.
• Figure 3: Simulated SPHEREx and 7DS data used in this study. The grey plot shows the mock SED from feder24. The left column of the figure shows the simulated photometry of the deep dataset (SPHEREx deep + 7DS IMS) and the right column shows that of the wide dataset (SPHEREx full-sky + 7DS WTS), with the same example galaxies sorted in ascending $i$ magnitudes. The blue markers show the mock datapoints from the 7DS, and the orange markers show the simulated SPHEREx datapoints.
• Figure 4: The measured photo-$z$ values as a function of true redshifts. GAMA galaxies with $13<i<18$ ($N=$ 5,961) in the wide dataset are shown in this figure. The colors show the magnitudes of the galaxies, binned by 1-magnitude intervals. From the first row, results from the SPHEREx full-sky data, 7DS WTS data, 7DS RIS data, and combined SPHEREx full-sky + 7DS WTS data are plotted. Each plot has a subplot showing $\Delta z/(1+z_{\rm true})$ as a function of $z_{\rm true}$. The statistics for measuring photo-z evaluation performances, NMAD ($\sigma$), bias ($b$), catastrophic failure ($\eta$, 10 % outlier rate), and their corresponding errors, are noted in each plot.
• Figure 5: Same as Figure \ref{['fig:zz_1318']}, but for COSMOS galaxies with $18<i<21$ ($N=$ 990) in the wide dataset. Note that the redshift and magnitude ranges of the sample are different from Figure \ref{['fig:zz_1318']}.