The dependence of halo bias on the protohalo shape alignment with the initial tidal field

We present a numerical evidence supporting the primordial origin of secondary halo bias even on the galactic mass scale. Analyzing the data from the IllustrisTNG 300-1 simulations, we investigate the dependence of halo bias on the degree of misalignment between the protohalo inertia and initial tidal tensors, , measured at redshift, z₈=127. From the TNG 300-1 galactic halos in logarithmic mass range of 10. 5 12. At z=0 and 0. 5, however, the and age bias factors show large differences in their overall strengths, which is attributed to the dominant nonlinear effects that undermine the former but enhance the latter. Given these numerical results along with the previous finding that shares a large amount of mutual information with the formation epochs and spin parameters of galactic halos, it is concluded that the origins of halo age and spin bias must be closely linked with the primordial factor, , and that the difference in the tendency between the two bias factors on the galactic mass scale reflects the multi-scale influence of on the halo secondary properties.