Interpreting the strong clustering of ultra-diffuse galaxies by halo spin bias

TL;DR

This work shows that the interpretation of halo spin bias for low-mass halos hinges on whether unbound particles are included in the spin calculation. Using IllustrisTNG-ODM, the authors demonstrate that $λ_{ m a}$ (including unbound particles) yields stronger clustering for high-spin halos across masses, while $λ_{ m b}$ (bound-only) exhibits an inversion below $M_{ m h} \\sim 10^{11} h^{-1} M_\odot$, driven by a subset of high-$λ_{ m a}$ but low-$λ_{ m b}$ halos in dense environments. They construct SDSS-like mocks and an empirical $Σ_*$–$λ_{ m a}$ model with a correlation coefficient $R$ (best-fit $R \\\approx -0.54$), establishing a robust anti-correlation where more diffuse dwarfs reside in higher-spin halos. The model reproduces the observed strong clustering of UDGs within ΛCDM without exotic physics, suggesting that unbound halo material and tidal environments can transfer angular momentum to gas and drive UDG formation; this provides a practical observational handle on halo secondary bias and informs how SAMs and hydrodynamic simulations treat halo spin and galaxy sizes.

Abstract

We use the IllustrisTNG300-ODM simulation to investigate the spin bias of low-mass halos and its connection to the strong clustering of ultra-diffuse galaxies (UDGs) reported by Zhang et al. (2025). By comparing two halo spin definitions-one using only bound particles ($λ_{\rm b}$) and another including unbound particles ($λ_{\rm a}$)-we demonstrate that the spin bias of low-mass halos critically depends on the definition. While $λ_{\rm a}$ yields stronger clustering for higher-spin halos at all masses, $λ_{\rm b}$ produces an inverted trend below $M_{\rm h}\sim 10^{11} \rm M_{\odot}/h$. This discrepancy is driven by a subset of halos in high-density environments that have large $λ_{\rm a}$ but small $λ_{\rm b}$. Using an empirical model implemented in SDSS-like mocks, we link the stellar surface-mass-density ($Σ_\ast$) of a galaxy to $λ_{\rm a}$ of its host halo and find an anti-correlation that more diffuse dwarfs tend to reside in higher-spin halos. The model naturally reproduces the observed strong clustering of UDGs within the standard $Λ$CDM framework without invoking exotic assumptions such as self-interacting dark matter. The high fraction of unbound particles in UDG hosts likely originates from tidal fields in dense regions, an effect particularly significant for low-mass halos. We discuss how the angular momentum of a halo represented by $λ_{\rm a}$ may be transferred to the gas to affect size and surface density of the galaxy that forms in the halo.

Figures (8)

• Figure 1: The possibility distribution (PDF) of halo spin in different mass bins. The black dashed lines are for $\lambda_{\rm b}$ and solid lines are for $\lambda_{\rm a}$. The red lines correspond to the culmulative distribution (CDF) of those two definitions, with the y-axis on the right.
• Figure 2: Spin bias as a function of halo mass. Dashed lines are for $\lambda_{\rm b}$ and solid lines are for $\lambda_{\rm a}$. The blue and red color corresponds to top 20% and bottom 20% in spin, respectively, with the error estimated by 100 bootstrap resamplings.
• Figure 3: The distinction of halo spin in different definitions.Top panels: The spin calculated by all particles ($\lambda_{\rm a}$) versus that calculated by bound particles ($\lambda_{\rm b}$) across different halo mass bins from left to the right panel. The contours cover 75%, 95%, and 99% of the distribution, respectively. The gray shade regions indicate the top $25^{\rm th}$ in $\lambda_{\rm a}$ and $\lambda_{\rm b}$ in each mass bin, respectively. The black line is the one to one line as a reference. Bottom panels: The ranking percentile of halo spin calculated by all particles ($\lambda_{\rm a}$) versus that calculated by bound particles ($\lambda_{\rm b}$) for different halo mass bins from left to the right panel. The color indicates the relative density, defined by the ratio of the number density of this halo with $r \sim 10 h^{-1}$Mpc ($\rho$) to the averaged number density of the whole sample in this mass bin ($\hat{\rho}(M_{\rm h})$), smoothed by the LOESS method Cleveland01091988, using the Python package Cappellari2013. The black line is the one to one line as a reference.
• Figure 4: The projected cross-correlation functions for mock catalogs and SDSS galaxies in different absolute magnitudes from left to the right panels. For both the SDSS galaxies and our mock catalog, we select the galaxies in given magnitude bin, including the centrals and satellites as the main sample, and utilize the whole sample as the reference sample to calculate the projected cross-correlation function. The error for the SDSS galaxies is estimated by 100 bootstrap resamplings, while error of the mock catalog, showed as the filling lines, represents the 1$\sigma$ scatter between 10 mock catalogs constructed from the TNG300-ODM simulation using the same sky mask and magnitude and redshift limits as for the real sample.
• Figure 5: The main results of the empirical model. Panel a: The normalization distribution (left y-axis) and cumulative distribution (right y-axis) of the surface mass density $\Sigma_{*}$ of the mock catalog (orange) compared to the SDSS (black). Panel b: the MCMC best-fitting possibility distribution of the correlation coefficient $\mathcal{R}$ between the surface mass density $\Sigma_{*}$ and the spin $\lambda_{\rm a}$, with the black arrow indicating the median value. The labeled number is the median and 25-75 percentile of $\mathcal{R}$. Panel c: The $\Sigma_{*}$-$\lambda_{\rm a}$ relation for dwarf galaxies in the best-fit model. The contours enclose 25%, 50%, 75% and 95% of the entire sample. The red dots correspond to results without adding scatter ($\mathcal{R} = -1$).