The Bispectrum of Intrinsic Alignments: II. Precision Comparison Against Dark Matter Simulations

TL;DR

This work tests a tree-level EFT for halo intrinsic alignments by measuring the IA–dark matter bispectrum in N-body simulations and projecting it into E- and B-mode multipoles. Using FFT-based estimators and a seven-multipole likelihood, the authors show that a five-parameter IA model (four deterministic second-order biases plus a stochastic amplitude) describes the data up to $k_ ext{max} o 0.11\,h\,\text{Mpc}^{-1}$, with parameters consistent with independent power-spectrum fits. Higher-order multipoles substantially improve constraints and break degeneracies among second-order IA biases, while parity-odd bispectra are detected at high significance and align with the parity-even sector. These results establish the IA bispectrum as a viable cosmological probe and framework for IA mitigation in weak lensing analyses, guiding future joint power–bispectrum analyses for realistic galaxy samples.

Abstract

We measure three-dimensional bispectra of halo intrinsic alignments (IA) and dark matter overdensities in real space from N-body simulations for halos of mass $10^{12}-10^{12.5} M_\odot /h$. We show that their multipoles with respect to the line of sight can be accurately described by a tree-level perturbation theory model on large scales ($k\lesssim 0.11\,h$/Mpc) at $z=0$. For these scales and in a simulation volume of 1 (Gpc/$h)^3$, we detect the bispectrum monopole $B_{δδE}^{00}$ at SNR $\sim 30$ and the two quadrupoles $B_{δδE}^{11}$ and $B_{δδE}^{20}$ at SNR $\sim 25$ and SNR $\sim 15$, respectively. We also report similar SNR for the lowest order multipoles of $B_{δEE}$ and $B_{EEE}$, although these are largely driven by stochastic contributions. We show that the first and second order EFT parameters are consistent with those obtained from fitting the IA power spectrum analysis at next-to-leading order, without requiring any priors to break degeneracies for the quadratic bias parameters. Moreover, the inclusion of higher multipole moments of $B_{δδE}$ greatly reduces the errors on second order bias parameters, by factors of 5 or more. The IA bispectrum thus provides an effective means of determining higher order shape bias parameters, thereby characterizing the scale dependence of the IA signal. We also detect parity-odd bispectra such as $B_{δδB}$ and $B_{δEB}$ at $\sim 10 σ$ significance or more for $k<0.15\,h$/Mpc and they are consistent with the parity-even sector. Furthermore, we check that the Gaussian covariance approximation works reasonably well on the scales we consider here. These results lay the groundwork for using the bispectrum of IA in cosmological analyses.

Figures (15)

• Figure 1: Ratio of diagonal sample covariance to the theoretical Gaussian prediction for several different multipoles. The grey shade indicates the region where $k_\text{max} < 0.05\,h/\text{Mpc}$ (this region was chosen somewhat artifically); deviations in this region are likely due to discretization effects and do not indicate model failure.
• Figure 2: SNR of the difference of the integral approximation (solid lines) and the effective wavenumber approximation (dashed lines) for three different multipoles of $B_{\delta \delta E}$. The black dashed horizontal line indicates an SNR of 3, which we take as a rough threshold for what is admissible.
• Figure 3: Top Panel: SNR for the lowest order multipoles of the parity-even bispectra from Eq. \ref{['eq:combs']} (with the exception of the matter bispectrum), as well as the two higher order multipoles of $B_{\delta \delta E}$ that were also considered in Paper I. Bottom Panel: same as top panel but for the parity-odd bispectra. The black dashed line indicates an SNR of 3.
• Figure 4: Results for the breakdown criterion from Eq. \ref{['eq:delta']} for all different cases considered in Section \ref{['sec:results']}. Solid lines indicate the use of the theoretical Gaussian covariance, while dashed lines indicate the use of the 'block diagonal sample variance' from Eq. \ref{['eq:covest']}. Blue, pink and green refer to at most one, two or three shape fields, as discussed in Sections \ref{['subsec:onefield']}, \ref{['subsec:twofield']} and \ref{['subsec:threefield']} respectively. The shades indicate $\Delta = 1.5$ and $\Delta = 2$ respectively and the vertical dotted line indicates $k_\text{max} = 0.11\,h/\text{Mpc}$, the maximum wavenumber at which we deem the tree-level EFT of IA model to be a good fit to the data.
• Figure 5: Comparison of the posteriors from bispectra with at most one (green), two (grey) or three (red) shape fields at $k_\text{max} = 0.11\,h/\text{Mpc}$. Also show is the (Gaussian) power spectrum posterior from bakx_eft, cf. Eq. \ref{['eq:b1fid']} and \ref{['eq:b2fid']} (where a prior on the sign of $b_{2,2}^\text{g}$ and $b_{2,3}^\text{g}$ had to be applied). Observe that the grey and red posteriors are almost identical. Here we used the Hartlap-corrected diagonal sample variance from Eq. \ref{['eq:covest']}