Halo assembly bias from Separate Universe simulations
  We present a calibration of halo assembly bias using the Separate Universe
technique. Specifically, we measure the response of halo abundances at fixed
mass and concentration to the presence of an infinite-wavelength initial
perturbation. We develop an analytical framework for describing the
concentration dependence of this peak-background split halo bias -- a measure
of assembly bias -- relying on the near-Lognormal distribution of halo
concentration at fixed halo mass. The combination of this analytical framework
and the Separate Universe technique allows us to achieve very high precision in
the calibration of the linear assembly bias $b_1$, and qualitatively reproduces
known trends such as the monotonic decrease (increase) of $b_1$ with halo
concentration at large (small) masses. The same framework extends to the
concentration dependence of higher order bias parameters $b_n$, and we present
the first calibration of assembly bias in $b_2$. Our calibrations are directly
applicable in analytical Halo Model calculations that seek to robustly detect
galaxy assembly bias in observational samples. We detect a non-universality in
the $b_1 - b_2$ relation arising from assembly bias, and suggest that
simultaneous measurements of these bias parameters could be used to both detect
the signature of assembly bias as well as mitigate its effects in cosmological
analyses.
