Three-point intrinsic alignments of dark matter halos in the
  IllustrisTNG simulation
  We use the IllustrisTNG suite of cosmological simulations to measure
intrinsic alignment (IA) bispectra of dark matter subhalos between redshifts 0
and 1. We decompose the intrinsic shear field into E- and B-modes and find that
the bispectra $B_{\delta\delta\mathrm{E}}$ and $B_{\delta\mathrm{EE}}$, between
the matter overdensity field, $\delta$, and the E-mode field, are detected with
high significance. We also model the IA bispectra analytically using a method
consistent with the two-point non-linear alignment model. We use this model and
the simulation measurements to infer the intrinsic alignment amplitude
$A_\mathrm{IA}$ and find that values of $A_\mathrm{IA}$ obtained from IA power
spectra and bispectra agree well at scales up to $k_\mathrm{max}= 2 \, h
\mathrm{Mpc}^{-1}$, for example at $z=1$ $A_\mathrm{IA} = 2.13 \pm$ 0.02 from
the cross power spectrum between the matter overdensity and E-mode fields and
$A_\mathrm{IA} =2.11 \pm$ 0.03 from $B_{\delta\delta \mathrm{E}}$. This
demonstrates that a single physically motivated model can jointly model
two-point and three-point statistics of intrinsic alignments, thus enabling a
cleaner separation between intrinsic alignments and cosmological weak lensing
signals.
