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

Abstract: 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, $\tau$, measured at redshift, $z_{i}=127$. From the TNG 300-1 galactic halos in logarithmic mass range of $10.5< m\equiv \log[M/(h^{-1}M_{\odot})]\le 13$ identified at $z=0,\ 0.5$ and $1$, a clear signal of $\tau$ bias is detected. For the case that $\tau$ is measured from the initial tidal field smoothed on the scale of $R_{f}/(h^{-1}\,{\rm Mpc})\lesssim 1$, the halo $\tau$ bias is found to be very similar in its tendency and amplitude to the spin bias at all of the three redshifts, if the effects of backsplash halos are properly eliminated. For the case of $R_{f}/(h^{-1}\,{\rm Mpc})=2$, the $\tau$ bias at $z=1$ turns out to behave like the age bias, diminishing rapidly in the range of $m> 12$. At $z=0$ and $0.5$, however, the $\tau$ 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 $\tau$ 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, $\tau$, and that the difference in the tendency between the two bias factors on the galactic mass scale reflects the multi-scale influence of $\tau$ on the halo secondary properties.