我們利用 Hyper Suprime-Cam Subaru Strategic Program（HSC-SSP）的光學測光資料，以及 eROSITA Final Equatorial-Depth Survey（eFEDS）中 X-ray 選取的星系團樣本，量測並分析星系團星系的條件光度函數（conditional luminosity functions, CLFs）。我們的最終樣本包含 346 個星系團，這些星系團是從原始的 542 個 eFEDS 星系團中篩選而得，涵蓋紅移範圍 0.1 < z < 1.2，以及質量範圍 10^13 < M500c/(M⊙/h) < 10^15。星系團質量直接採用 Chiu et al. 的結果，該研究利用弱重力透鏡與 X-ray 可觀測量進行校準。CLF 的建構僅考慮位於 r500c 內的星系，並以統計方式扣除前景與背景星系的貢獻。我們將 CLFs 依紅移分群堆疊，並在每一個紅移區間中進一步考慮兩類星系族群：完整樣本（紅色加藍色星系）以及透過事先校準的紅序模型（Chiu in prep.）進行紅–藍分離後所選取的紅序星系樣本。CLFs 以 Schechter 函數進行擬合，其中三個自由參數 (ϕ∗, α, m∗) 重新參數化為 (ϕ′, α, ∆m)。在此， ϕ′ ≡ ϕ∗M500c/Mpiv 為基準質量 Mpiv = 10^14M⊙/h 正規化後的歸一化參數，而 ∆m ≡ m∗ − m∗model 則表示特徵星等相對於紅序模型預測值的偏移量。我們使用馬可夫鏈蒙地卡羅（MCMC）方法來探索參數空間。我們的主要結果如下：（1）紅序星系族群每單位質量得歸一化參數ϕ′ 隨紅移增加呈現微弱（1.5σ）的下降趨勢；（2）完整星系族群的 m∗ 值傾向於比紅序族群更為負值；以及（3）在目前的堆疊策略下，紅序模型能夠良好地描述觀測資料。

We measure and analyze the conditional luminosity functions (CLFs) of cluster galaxies using photometric data from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) and a sample of X-ray–selected galaxy clusters from the eROSITA Final Equatorial-Depth Survey (eFEDS). Our final sample consists of 346 clusters selected from an initial catalog of 542 eFEDS systems, spanning the redshift range 0.1 < z < 1.2 and halo masses 10^13 < M500c/(M⊙/h) < 10^15. The cluster masses are adopted directly from Chiu et al. , where they are calibrated using weak-lensing and X-ray observables. The CLFs are constructed using galaxies within r500c, with the fore- and background galaxy populations statistically subtracted. We stack the CLFs in redshift bins and, within each bin, consider two galaxy populations: the full (red + blue) sample and a red-sequence–selected sample obtained through red–blue separation using a pre-calibrated red-sequence model (Chiu in prep.). The CLFs are modeled with a Schechter function, in which the three free parameters (ϕ∗, α, m∗) are reparameterized as (ϕ′, α, ∆m). Here, ϕ′ ≡ ϕ∗M500c/Mpiv represents the normalization per pivot halo mass Mpiv = 10^14M⊙/h, and ∆m ≡ m∗ − m∗ model denotes the deviation of the characteristic magnitude from the value predicted by the red-sequence model. We explore the parameter space using a Markov chain Monte Carlo method. As a result, we find that (1) The normalization per pivotal mass ϕ′ of the red population has a weak (1.5σ) declining trend toward higher redshift; (2) the m∗ values of the full populations tend to be more negative than those of the red populations; and (3) the RS model provides a good description of the data under our current stacking strategy.

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