We use the IllustrisTNG300 hydrodynamical simulation to study the dependence of the galaxy two-point correlation function on a broad range of secondary halo and galactic properties. We construct galaxy mock catalogues using a standard sub-halo abundance matching scheme coupled with a secondary assignment between galaxy colour or specific star formation rate and the following halo properties: starvation redshift z$_{rm starve}$, concentration at infall, dark matter density contrast $delta_R^{rm env}$, tidal anisotropy $alpha_R$, and tidal overdensity $delta_R$. The last two quantities allow us to fully characterise the tidal field of our haloes, acting as mediators between their internal and large-scale properties. The resulting mock catalogues return different levels of agreement with the IllustrisTNG300 measurements and strongly depend on the secondary halo property employed. Among all the secondary halo properties tested, we find that z$_{rm starve}$ and $delta_R$ are the ones that best trace the large-scale structure, producing reliable clustering predictions for different samples of red/blue and quenched/star-forming galaxies.
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