  New statistical properties of dark matter halos in Lagrangian space are
presented. Tracing back the dark matter particles constituting bound halos
resolved in a series of N-body simulations, we measure quantitatively the
correlations of the proto-halo's inertia tensors with the local tidal tensors
and investigate how the correlation strength depends on the proto-halo's
sphericity, local density and filtering scale. It is shown that the majority of
the proto-halos exhibit strong correlations between the two tensors provided
that the tidal field is smoothed on the proto-halo's mass scale. The
correlation strength is found to increase as the proto-halo's sphericity
increases, as the proto-halo's mass increases, and as the local density becomes
close to the critical value, delta_{ec}. It is also found that those peculiar
proto-halos which exhibit exceptionally weak correlations between the two
tensors tend to acquire higher specific angular momentum in Eulerian space,
which is consistent with the linear tidal torque theory. In the light of our
results, it is intriguing to speculate a hypothesis that the low surface
brightness galaxies observed at present epoch correspond to the peculiar
proto-halos with extreme low-sphericity whose inertia tensors are weakly
correlated with the local tidal tensors.
