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

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 ($\lambda_{\rm b}$) and another including unbound particles ($\lambda_{\rm a}$)-we demonstrate that the spin bias of low-mass halos critically depends on the definition. While $\lambda_{\rm a}$ yields stronger clustering for higher-spin halos at all masses, $\lambda_{\rm b}$ 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 $\lambda_{\rm a}$ but small $\lambda_{\rm b}$. Using an empirical model implemented in SDSS-like mocks, we link the stellar surface-mass-density ($\Sigma_\ast$) of a galaxy to $\lambda_{\rm a}$ 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 $\Lambda$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 $\lambda_{\rm a}$ may be transferred to the gas to affect size and surface density of the galaxy that forms in the halo.