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

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.

💡 Research Summary

This paper presents a comprehensive measurement and theoretical interpretation of the three‑point statistics (bispectrum) of intrinsic alignments (IA) of dark‑matter halos and the underlying matter density field, using a large‑volume N‑body simulation. The authors focus on halos with masses $10^{12}$–$10^{12.5},M_\odot/h$ at redshift $z=0$ in a $1,$(Gpc/$h$)$^{3}$ box, and analyse the bispectra in real space.

The theoretical framework is the Effective Field Theory of Intrinsic Alignments (EFT‑IA) at tree‑level. The IA tensor field $g_{ij}$ is decomposed into a deterministic part built from bias operators $\Pi^{