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Rank-2 tensor fields of large-scale structure, e.g. a tensor field inferredfrom shapes of galaxies, open up a window to directly access 2-scalar, 2-vectorand 2-tensor modes, where the scalar fields can be measured independently fromthe standard density field that is traced by distribution of galaxies. Here wedevelop an estimator of the multipole moments of power spectra for thethree-dimensional tensor field, taking into account the projection onto planeperpendicular to the line-of-sight direction. To do this, we find that aconvenient representation of the power spectrum multipoles can be obtained bythe use of the associated Legendre polynomials in the form which allows for thefast Fourier transform estimations under the local plane-parallel (LPP)approximation. The formulation also allows us to obtain the Hankel transformsto connect the two-point statistics in Fourier and configuration space, whichare needed to derive theoretical templates of the power spectrum includingconvolution of a survey window. To validate our estimators, we use thesimulation data of the projected tidal field assuming a survey window thatmimics the BOSS-like survey footprint. We show that the LPP estimators fairlywell recover the multipole moments that are inferred from the globalplane-parallel approximation. We find that the survey window causes a moresignificant change in the multipole moments of projected tensor power spectrumat $k\lesssim 0.1\,h{\rm Mpc}^{-1}$ from the input power spectrum, than in thedensity power spectrum. Nevertheless, our method to compute the theory templateincluding the survey window effects successfully reproduces thewindow-convolved multipole moments measured from the simulations. The analysismethod presented here paves the way for a cosmological analysis usingthree-dimensional tensor-type tracers of large-scale structure for current andfuture surveys.

physical review. d/physical review. d.

Analysis method for 3D power spectrum of projected tensor field with  fast estimator and window convolution modelling: an application to intrinsic  alignments