The Anisotropic Two-Point Correlation Functions of the Nonlinear
  Traceless Tidal Field in the Principal-Axis Frame
  Galaxies on the largest scales of the Universe are observed to be embedded in
the filamentary cosmic web which is shaped by the nonlinear tidal field. As an
efficient tool to quantitatively describe the statistics of this cosmic web, we
present the anisotropic two-point correlation functions of the nonlinear
traceless tidal field in the principal-axis frame, which are measured using
numerical data from an N-body simulation. We show that both of the nonlinear
density and traceless tidal fields are more strongly correlated along the
directions perpendicular to the eigenvectors associated with the largest
eigenvalues of the local tidal field. The correlation length scale of the
traceless tidal field is found to be ~20 Mpc/h, which is much larger than that
of the density field ~5 Mpc/h. We also provide analytic fitting formulae for
the anisotropic correlation functions of the traceless tidal field, which turn
out to be in excellent agreement with the numerical results. We expect that our
numerical results and analytic formula are useful to disentangle cosmological
information from the filamentary network of the large-scale structures.
