Power spectrum of halo intrinsic alignments in simulations
  We use a suite of $N$-body simulations to study intrinsic alignments (IA) of
halo shapes with the surrounding large-scale structure in the $\Lambda$CDM
model. For this purpose, we develop a novel method to measure multipole moments
of the three-dimensional power spectrum of the $E$-mode field of halo shapes
with the matter/halo distribution, $P_{\delta E}^{(\ell)}(k)$ (or
$P^{(\ell)}_{{\rm h}E}$), and those of the auto-power spectrum of the $E$ mode,
$P^{(\ell)}_{EE}(k)$, based on the $E$/$B$-mode decomposition. The IA power
spectra have non-vanishing amplitudes over the linear to nonlinear scales, and
the large-scale amplitudes at $k\lesssim 0.1~h~{\rm Mpc}^{-1}$ are related to
the matter power spectrum via a constant coefficient ($A_{\rm IA}$), similar to
the linear bias parameter of galaxy or halo density field. We find that the
cross- and auto-power spectra $P_{\delta E}$ and $P_{EE}$ at nonlinear scales,
$k\gtrsim 0.1~h~{\rm Mpc}^{-1}$, show different $k$-dependences relative to the
matter power spectrum, suggesting a violation of the nonlinear alignment model
commonly used to model contaminations of cosmic shear signals. The IA power
spectra exhibit baryon acoustic oscillations, and vary with halo samples of
different masses, redshifts and cosmological parameters ($\Omega_{\rm m},
S_8$). The cumulative signal-to-noise ratio for the IA power spectra is about
60% of that for the halo density power spectrum, where the super-sample
covariance is found to give a significant contribution to the total covariance.
Thus our results demonstrate that the IA power spectra of galaxy shapes,
measured from imaging and spectroscopic surveys for an overlapping area of the
sky, can be used to probe the underlying matter power spectrum, the primordial
curvature perturbations, and cosmological parameters, in addition to the
standard galaxy density power spectrum.
