Analysis method for 3D power spectrum of projected tensor fields with fast estimator and window convolution modeling: An application to intrinsic alignments

Rank-2 tensor fields of large-scale structure, e.g. a field inferred from shapes galaxies, open up window to directly access 2-scalar, 2-vector and 2-tensor modes, where the scalar can be measured independently standard density that is traced by distribution galaxies. Here we develop an estimator multipole moments power spectra for three-dimensional field, taking into account projection onto plane perpendicular line-of-sight direction. To do this, find convenient representation spectrum multipoles obtained use associated Legendre polynomials in form which allows fast Fourier transform estimations under local plane-parallel (LPP) approximation. The formulation also us obtain Hankel transforms connect two-point statistics configuration space, are needed derive theoretical templates including convolution survey window. validate our estimators, simulation data projected tidal assuming mimics BOSS-like footprint. We show LPP estimators fairly well recover global causes more significant change at $k\lesssim 0.1\,h{\rm Mpc}^{-1}$ input spectrum, than spectrum. Nevertheless, method compute theory template effects successfully reproduces window-convolved simulations. analysis presented here paves way cosmological using tensor-type tracers structure current future surveys.