The dependence of assembly bias on the cosmic web

For low-mass haloes, the physical origins of halo assembly bias have been linked to the slowdown of accretion due to tidal forces, which are expected to be more dominant in some cosmic-web environments as compared to others. In this work, we use publicly available data from the application of the Discrete Persistent Structures Extractor (DisPerSE) to the IllustrisTNG magnetohydrodynamical simulation to investigate the dependence of the related galaxy assembly bias effect on the cosmic web. We first show that, at fixed halo mass, the galaxy population displays significant low-mass secondary bias when split by distance to DisPerSE critical points representing nodes ($d_{\rm node}$), filaments ($d_{\rm skel}$), and saddles ($d_{\rm sadd}$), with objects closer to these features being more tightly clustered. The secondary bias produced by some of these parameters exceeds the assembly bias signal considerably at some mass ranges, particularly for $d_{\rm sadd}$. We also demonstrate that the assembly bias signal is reduced significantly when clustering is conditioned to galaxies being close or far from these critical points. The maximum attenuation is measured for galaxies close to saddle points, where less than 35$\%$ of the signal remains. Conversely, objects near voids preserve a fairly pristine effect (almost 85$\%$ of the signal). Our analysis confirms the important role played by the tidal field in shaping assembly bias, but they are also consistent with the signal being the result of different physical mechanisms. Our work introduces some new aspects of secondary bias where the predictions from hydrodynamical simulations can be directly tested with observational data.