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

TL;DR

This paper delivers a full calibration of the Hyper Suprime-Cam (HSC) tomographic redshift distributions by leveraging clustering redshifts from DESI DR1/DR2, including high-redshift tracers ($z>1.2$) to complete all bins. The authors model $n(z)$ with splines (and alternative parametrizations) while accounting for galaxy bias evolution in both photometric and spectroscopic samples and magnification effects, validating results against previous calibrations. They report small redshift-shift corrections, with the two highest-redshift bins shifting toward higher redshift by approximately $\ Delta z_3=-0.039^{+0.020}_{-0.021}$ and $\Delta z_4=-0.048^{+0.012}_{-0.012}$, and they demonstrate consistency across scale cuts, reducing tensions with prior cosmic shear analyses. The work provides public code and data to reproduce the results and paves the way for robust cosmological inferences with upcoming Stage IV surveys by mitigating key clustering-redshift systematics.

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, arXiv:2211.16516), 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. 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 $Δz_4=-0.048^{+0.012}_{-0.012}$.

Figures (9)

• Figure 1: Sky coverage of DESI DR2 DESI.DR2.Presentation.InPrep (dark blue), DR1 DESI.DR1.I.Presentation (light blue, overlapping DR2) and HSC Year 3 Shape Catalog HSCShapeCataloguePDR3Li2022 (red outline), with the galactic plane (gray line). An area centered around $\mathrm{RA}\sim355^\circ$, $\mathrm{DEC}\sim0^\circ$ is highlighted with density maps to compare the coverage of DESI DR1 and DR2 of the same area covering a chunk of the footprint of HSC Y3's VVDS field. The HSC data lands in areas of high overall completeness for DESI, as these areas were targeted in priority. DESI DR2 improves over DR1 with better overall completeness, especially for the ELGs and in the northern HECTOMAP field (roughly $\mathrm{RA}\sim40^\circ$, $\mathrm{DEC}\sim240^\circ$).
• Figure 2: Upper panel: N(z) angular density per redshift from the HSC catalog, using photometric redshifts from the DNNz algorithm DNNZHSCNishizawa2020. The effect of the calibration cut on HSC is displayed, removing problematic sources up to $z_{\mathrm{best}}^{\mathtt{DNNz}}\leq0.9$ (dotted histogram), as well as HSC's four tomographic bin selections (shaded colors, including the calibration cut). Lower panel: N(z) angular density per redshift of the DESI Large Scale Structure clustering catalogs DESIConstructionLSS2024, showcasing the combined tracers distribution (light blue) in the HSC footprint and individual tracers (BGS, ELG, LRG and QSOs). DR1 is represented in dotted lines and DR2 is represented in full lines. In this figure, ELGs are distinguished between ELG-LOP (DR1 analysis) and ELG-LOP+VLO (DR2 analysis). Since most of the HSC footprint is already included in DR1, adding DR2 does not provide an improvement as big as one could expect, though there still are density differences as showcased in Figure \ref{['fig:footprint']}. Per tomographic bin, the effective number density counts of photometric sources are 3.77, 5.07, 4.00 and 2.12 arcmin$^{-2}$PSFModellingHSCZhang2023 after applying the calibration cut.
• Figure 3: Example cross-correlation measurements for small spectroscopic slices with HSC bins. Here, the spectroscopic sources are DR1 LRGs, cross-correlated with the first two HSC tomographic bins. Comoving distance is computed at the redshift highlighted in the top left corner of each plot. As the redshift increases, one can see the weaker integrated signal for cross correlations with the first tomographic bin (purple), since the $n(z)$ decreases when far away from the photo-$z$ boundaries, and the stronger signal for the second tomographic bin as the redshifts reaches $z\sim0.6-0.9$ (orange).
• Figure 4: Top panel: $\sqrt{\bar{\omega}_{pp}^{\mathrm{true}}}$ and $\sqrt{\bar{\omega}_{pp}^{\mathrm{photo}-z}}$ with the power law fit through the corrected measurements. This showcases the importance of the correction, as the $\sqrt{\bar{\omega}_{pp}^{\mathrm{photo}-z}}$ alone does not capture significant galaxy bias evolution, whereas the correction captures a general evolution trend. Middle panel: Clustering redshifts measurements for a few of the intermediate small tomographic bins ($n_{p_k}(z)$ distributions), highlighting the tomographic bin ranges with the dotted lines. The $n_{p_k}(z)$ are modeled with splines, described further in section \ref{['sec:parametrization:bspline']}. Nonetheless, the photometric redshift spread and the gradual expectation shift can be seen increasing with redshift, compared to the midpoint of the bins (between the dotted lines). Bottom panel: Comparing $b_p(z)$ computed with the corrections to $\bar{\omega}_{pp}$ and a "passive evolution" galaxy sample where the linear bias follows $b_p(z)\propto1/D(z)$ with $D(z)$ the growth factor of the universe.
• Figure 5: Top panel: Bin 2 data (as presented in section \ref{['sec:results']} with all corrections) underlaid with the spline distribution (red, posterior median and $1\sigma$ contour) and some example samples from the spline modeling (indigo). Position of interior knots are shown in gray dotted lines. The NNLS result of equation \ref{['eq:model_nz_bspline']} is shown in dashed navy. Bottom left panel: B-spline functions $(B_i)_{i\in\llbracket 1,n\rrbracket}$ over the redshift range. Bottom right panel: In the bottom plot, we show the posterior median coefficient distribution over the samples with associated standard deviations, where $c_i$ coefficients are constrained to be positive. Above, the $\mathbf{Dir}(\alpha)$ prior is showcased, per expression \ref{['eq:dir_prior']}.