Angular correlation functions of bright Lyman-break galaxies at $\mathbf{3 \lesssim z \lesssim 5}$

TL;DR

The study measures the angular clustering of bright Lyman-break galaxies at $z\sim3$–$5$ in the COSMOS field using $w(\theta)$ and fits a five-parameter halo-occupation distribution (HOD) model via Bayesian MCMC to infer halo masses, galaxy bias, and duty cycle. The analysis finds a rising galaxy bias with redshift for UV-limited samples ($b_g\approx3.18$ at $z\sim3$ to $b_g\approx4.27$ at $z\sim5$) and typical host halos of $M_{\min}\sim10^{11}M_\odot$ and $M_1\sim10^{12}M_\odot$, with a modest, roughly constant duty cycle $f_c$ across $z\sim3$–$5$. The results imply a decrease in the effective halo mass for a fixed UV luminosity threshold as redshift increases and suggest shorter star-formation timescales at higher $z$, consistent with rapid early assembly. The work demonstrates the viability of HOD modelling for high-$z$ photometric samples and sets the stage for LSST-scale clustering studies of early galaxy populations.

Abstract

We investigate the clustering of Lyman-break galaxies at redshifts of 3 $\lesssim z \lesssim$ 5 within the COSMOS field by measuring the angular two-point correlation function. Our robust sample of $\sim$60,000 bright ($m_{\rm UV}\lesssim 27$) Lyman-break galaxies was selected based on spectral energy distribution fitting across 14 photometric bands spanning optical and near-infrared wavelengths. We constrained both the 1- and 2-halo terms at separations up to 300 arcsec, finding an excess in the correlation function at scales corresponding to $<20$ kpc, consistent with enhancement due to clumps in the same galaxy or interactions on this scale. We then performed Bayesian model fits on the correlation functions to infer the Halo Occupation Distribution parameters, star formation duty cycle, and galaxy bias in three redshift bins. We examined several cases where different combinations of parameters were varied, showing that our data can constrain the slope of the satellite occupation function, which previous studies have fixed. For an $M_{\rm{UV}}$-limited sub-sample, we found galaxy bias values of $b_g=3.18^{+0.14}_{-0.14}$ at $z\simeq3$, $b_g=3.58^{+0.27}_{-0.29}$ at $z\simeq4$, $b_g=4.27^{+0.25}_{-0.26}$ at $z\simeq5$. The duty cycle values are $0.62^{+0.25}_{-0.26}$, $0.40^{+0.34}_{-0.22}$, and $0.39^{+0.31}_{-0.20}$, respectively. These results suggest that, as the redshift increases, there is a slight decrease in the host halo masses and a shorter timescale for star formation in bright galaxies, at a fixed rest-frame UV luminosity threshold.

Figures (12)

• Figure 1: The redshift distribution of galaxies in the COSMOS field across our three photometric $z$ bins selected in adams2023total. The total galaxy counts for the full samples are 44,132 ($z\simeq 3$), 13,407 ($z\simeq 4$), and 7,861 ($z\simeq 5$). The galaxy counts for the $M_{\rm{UV}}$-limited samples are 16,033 ($z\simeq 3$), 13,118 ($z\simeq 4$), and 7,800 ($z\simeq 5$).
• Figure 2: Angular correlation function for all galaxies in our sample of LBGs (left) and with an absolute magnitude cut of $M_{\rm{UV}}\le-20.0$ (right), shown at three redshift bins. The data points for higher redshifts are shifted slightly to the right for clarity.
• Figure 3: Measured correlation matrices for our $z\simeq3$, $z\simeq4$, and $z\simeq5$ full sample respectively, illustrating the correlation coefficients between different angular bins. The color scale represents the strength of correlation, with values ranging from -1 to 1. Each matrix is structured with axes representing angular separations $\theta$ in a logarithmic scale from 1 to $10^3$ arcsec. The correlation coefficients are computed from the covariance matrix using $\rho_{ij} = C_{ij} / \sqrt{C_{ii} \cdot C_{jj}}$ where $C$ is the covariance matrix, and $i,j$ are the angular bin indices.
• Figure 4: Halo model fitting results for the angular correlation function $w(\theta)$ at $z\simeq3$, comparing the observational data (dots with error bars) to several theoretical models (solid lines) with different combinations of free parameters. The different colours correspond to different sets of free parameters used in the fits. If the parameter is not free, it is fixed to 1. The solid lines represent the model fits, and the shaded regions and error bars correspond to the $1\sigma$ uncertainties in the model predictions. We apply small horizontal shifts in the lower panel for clarity. The lower panel shows the z-score, defined as the difference between the model and the data, normalised by the error bars. The horizontal dashed lines indicate the $1\sigma$ and $3\sigma$ significance levels, with the triangular markers indicating data points that exceed a $3\sigma$ deviation.
• Figure 5: The same as Fig. \ref{['fig:halo_model_z3']}, but excluding the first three data points (displayed as open squares) at the smallest angular scales for the $M_{\rm{UV}}$-limited sample at $z\simeq3$.