Halo assembly bias in the early Universe: a clustering probe of the origin of the Little Red Dots

Abstract

The clustering of galaxies encodes key information about the structure and assembly history of their host dark matter (DM) haloes, providing a powerful probe of the origin of extreme high-redshift systems. While halo assembly bias has been extensively studied at low redshift, its behavior in the early Universe remains poorly explored. Using the large-volume, high-resolution Shin-Uchuu cosmological $N$-body simulation, we characterize halo assembly bias associated with formation time, concentration, and angular momentum across a wide range of halo masses and redshifts. We find that the sign and amplitude of assembly bias depend on halo mass for both concentration and spin. High-concentration and low-spin haloes are more strongly clustered below characteristic peak heights of $ν\sim 1.5$ and $\sim 0.75$, respectively, while the trends weaken or reverse at higher masses. Halo age bias persists at all redshifts but decreases toward higher masses and earlier cosmic times. We apply these results to assess whether clustering can distinguish competing formation scenarios for the Little Red Dots (LRDs). We find that the direct-collapse-black-hole (DCBH) scenario predicts the strongest large-scale bias and enhanced pair fractions, the self-interacting-dark-matter (SIDM) core-collapse scenario and low-spin compact-galaxy scenarios yield weaker clustering due to lower characteristic halo masses and spin-related secondary bias, and a primordial-black-hole (PBH) scenario predicts unbiased clustering. Our results demonstrate that halo assembly bias and characteristic host masses provide powerful diagnostics for constraining the physical origin of LRDs, offering testable predictions for upcoming clustering measurements with JWST and future deep surveys.

Figures (8)

• Figure 1: Mass functions at $z\simeq5$ for distinct haloes in Shin-Uchuu (blue circles) and galaxies from the UniverseMachine catalogue (yellow squares). The halo mass function is in good agreement with theoretical expectations from Sheth2001 (blue solid), while the galaxy mass function exhibits a good agreement at the low-mass end and a deficit at the massive end relative to recent JWST results from Wang2025MIRI (gray).
• Figure 2: Distributions of halo properties examined in this study, at $z\simeq 5$ in the Shin-Uchuu simulation. From top to bottom, the panels display halo concentration, spin, and formation redshift as functions of halo mass. The colour indicates number density, while the solid curves indicate the median relation. The thicker and thinner error bars denote the $1\sigma$ and $4\sigma$ intervals, respectively. Side panels show the corresponding one-point distributions. For concentration, the histogram of the subsample of relaxed haloes is included for comparison, as indicated by the dashed grey line. At high redshift, halo concentration exhibits no clear dependence on mass. Spin is nearly mass-independent. Lower-mass haloes tend to form earlier than more massive ones.
• Figure 3: Auto-correlation functions (ACFs) of haloes from the Shin-Uchuu simulation at $z \simeq 5$. haloes are grouped into mass bins of width 0.25 dex, and we show three representative cases: low mass ($\log( M_{\rm vir}\,[h^{-1}\rm M_\odot])\simeq8$), intermediate mass ($\log( M_{\rm vir}\,[h^{-1}\rm M_\odot])\simeq9.5$), and high mass ($\log( M_{\rm vir}\,[h^{-1}\rm M_\odot])\simeq11$). The dashed black curves denote the ACFs of the full populations in each mass bin, while the colored curves correspond to subsamples selected by percentiles of concentration, spin, or formation time, as indicated. The three parameters exhibit distinct assembly-bias behaviors and mass trends. Concentration shows weak bias at the low-mass end and a reversal at high masses, where low-$c$ haloes cluster more strongly. Spin exhibits a mass-independent trend in which low-spin haloes are more strongly clustered. Formation time shows enhanced clustering for the oldest haloes, with the strength of this trend weakening towards higher masses.
• Figure 4: Redshift evolution of secondary bias as a function of halo mass for concentration (top), spin (middle), and formation time (bottom), from $z=0$ to $z\simeq8$. In each panel, the left-hand column shows the bias factors for the upper 25% of the parameter distribution, and the right-hand column shows the corresponding lower 25%. Curves are evaluated over scales of $5-15\,h^{-1}\,\,{\rm Mpc}$. At $z=0$, we assess consistency by comparing our measurements with results from Sato-Polito2019. The amplitudes of all the secondary biases here exhibit dependence on halo mass and clear evolution with redshift.
• Figure 5: Redshift evolution of the critical mass, $M_{\rm c}$, at which the assembly-bias signals reverses sign for high-concentration (left) and low-spin (right) haloes. The critical masses are extracted from Fig. \ref{['fig:bias_z_evo']} as the halo-mass intervals within which the relative bias (Eq. (\ref{['eq:RelativeBias']})) of the top 25% highest-$c$ or bottom 25% lowest-$\lambda$ haloes crosses unity. Overlaid for comparison are the contours of peak height ($\nu$), measurements at low redshift from previous studies (grey symbols or band), and the atomic-cooling threshold, which serves as a proxy for the minimum halo mass for galaxy formation. A red (blue) background colour indicates the regimes of more (less) strong clustering, with the colour saturation schematically illustrates the strength of deviating from a relative bias of unity. The critical masses for high-$c$ bias and low-$\lambda$ bias broadly correspond to $1.5-1.75\sigma$ and $0.75\sigma$ density peaks, respectively.