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

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Volume 692 (December 2024)

A&A, 692 (2024) A186

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Table 1.

Summary of the meaning of the key notations used in Sect. 2.1.

Notation	Meaning
Latin index, e.g. i	The index for spec-z sample bin i.
Latin index with a prime, e.g. i′	The index for photo-z sample bin i′.
M_i′ (M_i)	The angular galaxy number density of the photo-z sample in photo-z bin i′ (spec-z bin i).
N_i	The angular galaxy number density of the spec-z sample in spec-z bin i.
${\bar{M}}_{i'}$ $\bar{M}_{i\prime}$ ( ${\bar{M}}_{i}$ $\bar{M}_i$ )	The mean galaxy number density of the photo-z sample in photo-z bin i′ (spec-z bin i).
${\bar{N}}_{i}$ $\bar{N}_{i}$	The mean galaxy number density of the spec-z sample in spec-z bin i.
δ_i′ (δ_i)	The angular density fluctuation of the photo-z sample in photo-z bin i′ (spec-z bin i).
ϵ_i	The angular density fluctuation of the spec-z sample in spec-z bin i.
Q_ki′	The probability that a galaxy in spec-z bin k leaks to photo-z bin i′.
P_ki′	The fraction of galaxies in photo-z bin i′ originating from spec-z bin k.
C_i^′j^′	The correlation function of the photo-z sample between bin i′ and j′.
C_ij′	The cross correlation function between the spec-z sample in bin i with the photo-z sample in bin j′.
$C_{kk}'$ $C_{kk}\prime$	The correlation function of the photo-z sample in the spec-z bin k.
$C_{kk}^{x}$ $C_{kk}^{\mathrm{x}}$	The cross correlation function between the spec-z sample in bin k with the photo-z sample in spec-z bin k.
$C_{kk}^{m}$ $C_{kk}^{\mathrm{m}}$	The matter correlation function in spec-z bin k.
b_k′	The galaxy bias parameter of the photo-z sample in spec-z bin k (no photo-z bin dependence).
b_ki′	The galaxy bias parameter of the photo-z sample from photo-z bin i′ in spec-z bin k.
b_k	The galaxy bias parameter of the spec-z sample in spec-z bin k.
R_ki′	b_k′P_ki′, the quantity directly constrained by CZ.

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