KiDS-Legacy: Redshift distributions and their calibration

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Table 5.

Redshift distribution estimates from simulations.

Simulation	Run	Desc.	Statistic	Tomographic Bin						Described
	ID			1	2	3	4	5	6	in:
			$⟨ {\hat{μ}}_{z} ⟩$ $\langle\hat\mu_z\rangle$	0.315	0.472	0.604	0.798	0.998	1.312
	[A]:	Fiducial (Pvol & Swgt)	⟨δ_z, 0⟩	0.026	0.038	0.006	−0.005	−0.095	−0.196	6.1.1
			⟨δ_z⟩	−0.026	0.014	−0.002	0.008	−0.011	−0.054
			σ_δz	0.002	0.001	0.002	0.001	0.002	0.004

			$⟨ {\hat{μ}}_{z} ⟩$ $\langle\hat\mu_z\rangle$	0.316	0.472	0.605	0.798	0.999	1.313
	[B]:	Single Shear Realisation	⟨δ_z⟩	−0.025	0.013	−0.001	0.008	−0.012	−0.053	6.1.2
			σ_δz	0.002	0.001	0.002	0.001	0.004	0.004
			Δ⟨δ_z⟩	0.001	−0.000	0.001	−0.001	0.000	0.002

	[C]:	Algor. var.	σ_δz	0.001	0.001	0.001	0.001	0.001	0.003	6.1.3

			$⟨ {\hat{μ}}_{z} ⟩$ $\langle\hat\mu_z\rangle$	0.314	0.470	0.603	0.798	0.999	1.313
	[D]:	z-dependant Shear	⟨δ_z⟩	−0.027	0.012	−0.003	0.008	−0.010	−0.051	6.1.4
			σ_δz	0.002	0.001	0.002	0.001	0.002	0.005
SKiLLS			Δ⟨δ_z⟩	0.001	0.002	0.001	0.000	−0.001	−0.003

			$⟨ {\hat{μ}}_{z} ⟩$ $\langle\hat\mu_z\rangle$	0.316	0.470	0.608	0.800	1.008	1.334
	[E]:	No stellar contam.	⟨δ_z, 0⟩	0.041	0.040	0.011	−0.003	−0.091	−0.171
			⟨δ_z⟩	−0.023	0.008	−0.001	0.006	−0.007	−0.039	6.1.5
			σ_δz	0.002	0.001	0.002	0.001	0.003	0.004
			Δ⟨δ_z⟩	0.0024	−0.005	0.001	−0.002	0.005	0.015

			$⟨ {\hat{μ}}_{z} ⟩$ $\langle\hat\mu_z\rangle$	0.346	0.497	0.637	0.803	0.982	1.302
	[F]:	No calib. weights	⟨δ_z, 0⟩	−0.004	0.035	0.006	−0.000	−0.087	−0.163	6.1.6
			⟨δ_z⟩	0.008	0.038	0.031	0.011	−0.029	−0.065
			σ_δz	0.003	0.000	0.002	0.000	0.002	0.005

			$⟨ {\hat{μ}}_{z} ⟩$ $\langle\hat\mu_z\rangle$	0.345	0.494	0.636	0.807	0.997	1.298
	[G]:	Swgt only (no prior volume weight)	⟨δ_z, 0⟩	−0.018	0.030	−0.002	−0.006	−0.096	−0.193	6.1.7
			⟨δ_z⟩	0.002	0.035	0.029	0.016	−0.014	−0.068
			σ_δz	0.003	0.001	0.002	0.001	0.003	0.005

		Pvol only (No calib. shape weight)	$⟨ {\hat{μ}}_{z} ⟩$ $\langle\hat\mu_z\rangle$	0.318	0.472	0.608	0.801	1.008	1.335
	[H]:		⟨δ_z, 0⟩	0.043	0.043	0.015	0.002	−0.086	−0.164	6.1.8
			⟨δ_z⟩	−0.020	0.013	0.004	0.011	−0.001	−0.032
			σ_δz	0.002	0.001	0.001	0.001	0.003	0.005

		Pvol only (no calib. shape weight)	$⟨ {\hat{μ}}_{z} ⟩$ $\langle\hat\mu_z\rangle$	0.320	0.469	0.604	0.798	0.983	1.110
SKiLLS trunc.	[I]:		⟨δ_z, 0⟩	0.032	0.041	0.022	0.001	−0.074	−0.091	6.1.9
			⟨δ_z⟩	0.001	0.015	0.017	0.014	−0.004	−0.014
			σ_δz	0.001	0.001	0.001	0.001	0.001	0.005

		Pvol only (no calib. shape weight)	$⟨ {\hat{μ}}_{z} ⟩$ $\langle\hat\mu_z\rangle$	0.304	0.468	0.593	0.796	0.965	1.097
MICE2	[J]:		⟨δ_z, 0⟩	0.048	0.042	0.021	0.024	−0.039	−0.074
			⟨δ_z⟩	0.010	0.020	0.009	0.034	0.014	−0.011	6.1.9
			σ_δz	0.002	0.002	0.002	0.001	0.002	0.007
			Δ⟨δ_z⟩	0.009	0.004	−0.008	0.020	0.017	0.003

Notes. Entries above include abbreviations for prior volume weights (‘Pvol’), lensfit shape weights (‘Swgt’), Statistics in the table include: $⟨ {\hat{μ}}_{z} ⟩$ $\langle\hat\mu_z\rangle$ : average of mean redshifts of all realisations of the calibration sample ⟨δ_z, 0⟩: average bias of the mean redshift prior to SOM ⟨δ_z⟩: average bias of the mean redshift after SOM weighting σ_δz: uncertainty of ⟨δ_z⟩, where values of ≤0.01 are considered negligible. Δ⟨δ_z⟩: difference in biases (after SOM weighting) between scenario and reference, i.e. ⟨δ_z⟩−⟨δ_z⟩_ref.

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