Photometric Redshift Forecast for 7-Dimensional Sky Survey

We investigate the expected accuracy of redshifts that can be obtained using low-resolution spectroscopic (medium-band) data from the 7-Dimensional Sky Survey (7DS). By leveraging 40 densely sampled filters with widths of full width at half maximum (FWHM) = 25 nm, we create 7DS mock catalogs and estimate the redshift accuracy for three 7DS main surveys: Wide-field Time-Domain Survey (WTS), Intensive Monitoring Survey (IMS), and Reference Image Survey (RIS). Using photometric redshifts calculated from EAZY, we find that the five-year WTS provides reliable photometric redshifts with an normalized median absolute deviation ($σ_{\text{NMAD}}$) ranging from 0.003 to 0.007 and a catastrophic failure fraction (η) from 0.8% to 8.1% at $19 \leq m_{625} < 22$. The spectral resolution R ~ 50 of the medium-band dataset effectively captures the 4000 Å break and various emission lines. We also explore the synergy with data obtained from Pan-STARRS1, VIKING, and SPHEREx surveys. Combining the SPHEREx all-sky data with WTS significantly improves the accuracy of photometric redshift estimates, achieving η = 0.4% and $σ_{\text{NMAD}}$ = 0.004 for fainter sources at higher redshifts. The additional near-IR information provided by SPHEREx and VIKING plays an essential role in resolving degeneracies between low and high redshifts. We also observe color excesses by subtracting adjacent broad-band data, which improves the confinement of photometric redshifts and aids in the detection of strong emission line galaxies.