  The galaxy intrinsic alignment (IA) is a major challenge of weak lensing
cosmology. To alleviate this problem, Zhang (2010, MNRAS, 406, L95) proposed a
self-calibration method, independent of IA modeling. This proposal relies on
several scaling relations between two-point clustering of IA and matter/galaxy
fields, which were previously only tested with analytical IA models. In this
paper, these relations are tested comprehensively with an $N$-body simulation
of $3072^3$ simulation particles and boxsize 600 $h^{-1} \, \mathrm{Mpc}$. They
are verified at the accuracy level of $\mathcal{O}(1)\%$ over angular scales
and source redshifts of interest. We further confirm that these scaling
relations are generic, insensitive to halo mass, weighting in defining halo
ellipticities, photo-$z$ error, and misalignment between galaxy ellipticities
and halo ellipticities. We also present and verify three new scaling relations
on the B-mode IA. These results consolidate and complete the theory side of the
proposed self-calibration technique.
