Optimizing redshift distribution inference through joint self-calibration and clustering-redshift synergy

¹ School of Physics and Astronomy, Sun Yat-Sen University, 2 Daxue Road, Tangjia, Zhuhai 519082, China
² CSST Science Center for the Guangdong-Hongkong-Macau Greater Bay Area, SYSU, Zhuhai 519082, China
³ Shanghai Astronomical Observatory, Chinese Academy of Sciences, Nandan Road 80, Shanghai 200240, China
⁴ Department of Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
⁵ Key Laboratory for Particle Astrophysics and Cosmology (MOE)/Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai 200240, China
⁶ Peng Cheng Laboratory, No. 2, Xingke 1st Street, Shenzhen 518000, China

^⋆ Corresponding author; chankc@mail.sysu.edu.cn

Received: 21 September 2024
Accepted: 12 November 2024

Abstract

Context. Accurately characterizing the true redshift (true-z) distribution of a photometric redshift (photo-z) sample is critical for cosmological analyses in imaging surveys. Clustering-based techniques, which include clustering-redshift (CZ) and self-calibration (SC) methods–depending on whether external spectroscopic data are used–offer powerful tools for this purpose.

Aims. In this study, we explore the joint inference of the true-z distribution by combining SC and CZ (denoted as SC+CZ).

Methods. We derived simple multiplicative update rules to perform the joint inference. By incorporating appropriate error weighting and an additional weighting function, our method shows significant improvement over previous algorithms. We validated our approach using a DES Y3 mock catalog.

Results. The true-z distribution estimated through the combined SC+CZ method is generally more accurate than using SC or CZ alone. To account for the different constraining powers of these methods, we assigned distinct weights to the SC and CZ contributions. The optimal weights, which minimize the distribution error, depend on the relative constraining strength of the SC and CZ data. Specifically, for a spectroscopic redshift sample that amounts to 1% of the photo-z sample, the optimal combination reduces the total error by 20% (40%) compared to using CZ (SC) alone, and it keeps the bias in mean redshift [Δ͞z/(1+z)] at the level of 0.003. Furthermore, when CZ data are only available in the low-z range and the high-z range relies solely on SC data, SC+CZ enables consistent estimation of the true-z distribution across the entire redshift range.

Conclusions. Our findings demonstrate that SC+CZ is an effective tool for constraining the true-z distribution, paving the way for clustering-based methods to be applied at z ≳ 1.