Full calibration of the tomographic redshift distribution from the HSC PDR3 Shape Catalog with DESI

J. Choppin de Janvry, S. Gontcho A Gontcho, U. Seljak, A. Baleato Lizancos, E. Chaussidon, W. d'Assignies, J. DeRose, S. Heydenreich, E. Paillas, D. Valcin, T. Zhang, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, F. J. Castander, T. Claybaugh, A. Cuceu, A. de la Macorra, P. Doel, S. Ferraro, A. Font-Ribera, J. E. Forero-Romero, E. Gaztañaga, G. Gutierrez, H. K. Herrera-Alcantar, K. Honscheid, M. Ishak, R. Joyce, S. Juneau, R. Kehoe, D. Kirkby, T. Kisner, A. Kremin, O. Lahav, C. Lamman, M. Landriau, L. Le Guillou, M. Manera, A. Meisner, R. Miquel, S. Nadathur, N. Palanque-Delabrouille, W. J. Percival, C. Poppett, F. Prada, I. Pérez-Ràfols, G. Rossi, E. Sanchez, D. Schlegel, M. Schubnell, J. Silber, D. Sprayberry, G. Tarlé, B. A. Weaver, R. Zhou

First listed 2025-11-22 | Last updated 2026-03-30

Abstract

The calibration of tomographic redshift distributions is essential for cosmological analysis of weak lensing data. In this work, we calibrate all four tomographic bins of the Hyper Suprime Camera (HSC) weak lensing catalog with the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 and 2 using the clustering redshifts technique. We include z > 1.2 redshift sources such as emission line galaxies (ELG) and quasars (QSO) sources in our calibration, which were not available in the previous HSC calibration (Rau et al. 2022), allowing a complete calibration of all the redshift bins. We find the first tomographic bin exhibits a small shift towards low redshifts. The second bin is in good agreement with the photometric calibration, while third and fourth bin exhibit a shift towards higher redshifts. However, these shifts are considerably smaller than the shifts obtained in the HSC Year 3 cosmic shear analyses. We evaluate the impact of galaxy bias and magnification effects from all the samples on the measurements, finding them to be small, and we propose corrections to reduce them further. Specifically, we relax the assumption of linear bias and only assume no redshift evolution of the cross-correlation coefficient, allowing us to leverage smaller clustering scales. We model the redshift distributions with splines and compare our results to previous analyses as well as to other parameterizations found in literature. For the two high-redshift tomographic bins, we find the shifts to higher redshifts with respect to the measurements performed in Rau+2022 to be $Δz_3=-0.039^{+0.020}_{-0.021}$ and $Δz_4=-0.048^{+0.012}_{-0.012}$.

Short digest

Using DESI DR1/DR2 as the spectroscopic reference, this paper fully calibrates the tomographic redshift distributions n(z) of the four HSC PDR3 shape bins via clustering redshifts, crucially adding ELG and QSO at z>1.2 to cover the high-z tails. Bin 1 is slightly shifted to lower z, Bin 2 matches the photometric calibration, and Bins 3–4 move to higher z, with high-z-bin shifts relative to Rau+2022 of Δz3=-0.039(+0.020/-0.021) and Δz4=-0.048(±0.012). The authors model n(z) with splines, relax linear-bias assumptions by requiring only a non-evolving cross-correlation coefficient to leverage smaller scales, and show galaxy-bias and magnification systematics are small with proposed corrections. The result is a complete, better-controlled n(z) for HSC cosmic-shear work, with shifts smaller than those adopted in HSC Year 3 analyses, tightening cosmological inferences.

Key figures to inspect

• Compare the spline-modeled n(z) for each tomographic bin against the stacked photo-z PDFs and the Rau+2022 calibration; read off mean Δz and uncertainties per bin, especially the quoted Δz3 and Δz4 values.
• Cross-correlation amplitude versus spectroscopic redshift for each bin split by DESI tracer (BGS/LRG/ELG/QSO); verify how ELG/QSO at z>1.2 anchor the tails of Bin 3–4 and enable full-bin calibration.
• Scale-dependence tests showing the effect of relaxing linear-bias assumptions (constant cross-correlation coefficient with redshift) and including smaller angular scales; check stability of recovered n(z).
• Systematics validation panels for galaxy bias and magnification (e.g., with/without magnification terms or tracer splits); confirm reported small impact and the efficacy of the proposed corrections.
• Comparison of this work’s n(z) shifts to those used in HSC Year 3 cosmic-shear analyses; assess expected change in lensing amplitude constraints when adopting the new calibration.