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

We use the TNG300-1-Dark simulation to investigate the spin bias of low-mass haloes and its connection to the strong clustering of ultra-diffuse galaxies (UDGs) reported by Zhang et al. 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 haloes critically depends on the definition. While $\lambda _{\rm a}$ yields stronger clustering for higher-spin haloes at all masses, $\lambda _{\rm b}$ produces an inverted trend below $M_{\rm h}\sim 10^{11} \rm {\rm M}_{\odot }\, h^{-1}$. This discrepancy is driven by a subset of haloes 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 that more diffuse dwarfs tend to reside in higher-spin haloes. 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 haloes. We discuss how the angular momentum of a halo represented by $\lambda _{\rm a}$ may be transferred to the gas through ram-pressure torquing to affect the size and surface density of the galaxy.