  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.
