Using N -body simulations for the first time , we show that the anisotropic primordial non-Gaussianity ( PNG ) causes a scale-dependent modification , given by 1 / k ^ { 2 } at small k limit , in the three-dimensional power spectra of halo shapes ( intrinsic alignments ) , whilst the conventional power spectrum of halo number density field remains unaffected .
We discuss that wide-area imaging and spectroscopic surveys observing the same region of the sky allow us to constrain the quadrupole PNG coefficient f _ { NL } ^ { s = 2 } at a precision comparable with that of the cosmic microwave background .