The Bispectrum of Intrinsic Alignments: Theory Modelling and Forecasts for Stage IV Galaxy Surveys

We present a complete treatment of the bispectrum of intrinsic alignments, both in three spatial dimensions and in projection in the flat-sky approximation. Since intrinsic alignment is a spin-2 observable, the bispectrum of intrinsic alignments contains a parity-even and a parity-odd part, the latter being nonzero even in the absence of parity violation. Moreover, all possible combinations of scalar, E- and B-mode bispectra are nonzero in the absence of parity violation. In analogy to the galaxy bispectrum in redshift space, we construct a complete set of multipoles for anisotropic bispectra of projected spin-2 fields. We then construct separable bispectrum estimators, both for parity-even and parity-odd bispectra, which can be computed by means of Fast Fourier Transforms (FFTs). We compare several different choices of angular weighting in terms of signal-to-noise ratios (SNR) for a Stage IV setup using luminous red galaxies (LRGs) from the Dark Energy Spectroscopic Instrument (DESI) with galaxy shapes measured by the Legacy Survey of Space and Time (LSST). Assuming an overlapping area of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>000</mml:mn> </mml:mrow> </mml:math> square degrees (yielding <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>1.3</mml:mn> </mml:mrow> </mml:math> million LRGs) and including scales up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mtext mathvariant="normal">max</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.14</mml:mn> <mml:mspace width="0.167em"/> <mml:mi>h</mml:mi> </mml:mrow> </mml:math> /Mpc, we find that the position-position-E-mode bispectrum <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi>D</mml:mi> <mml:mi>D</mml:mi> <mml:mi>E</mml:mi> </mml:mrow> </mml:msub> </mml:math> (which is parity-even) can be strongly detected at SNR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>30</mml:mn> </mml:mrow> </mml:math> , while detecting parity-odd bispectra (such as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi>D</mml:mi> <mml:mi>D</mml:mi> <mml:mi>B</mml:mi> </mml:mrow> </mml:msub> </mml:math> , SNR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> ) or bispectra with more than one shape field (such as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi>D</mml:mi> <mml:mi>E</mml:mi> <mml:mi>E</mml:mi> </mml:mrow> </mml:msub> </mml:math> , SNR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> ) may also be possible.