Separate Universe calibration of the dependence of halo bias on cosmic
  web anisotropy
  We use the Separate Universe technique to calibrate the dependence of linear
and quadratic halo bias $b_1$ and $b_2$ on the local cosmic web environment of
dark matter haloes. We do this by measuring the response of halo abundances at
fixed mass and cosmic web tidal anisotropy $\alpha$ to an infinite wavelength
initial perturbation. We augment our measurements with an analytical framework
developed in earlier work which exploits the near-Lognormal shape of the
distribution of $\alpha$ and results in very high precision calibrations. We
present convenient fitting functions for the dependence of $b_1$ and $b_2$ on
$\alpha$ over a wide range of halo mass for redshifts $0\leq z\leq1$. Our
calibration of $b_2(\alpha)$ is the first demonstration to date of the
dependence of non-linear bias on the local web environment. Motivated by
previous results which showed that $\alpha$ is the primary indicator of halo
assembly bias for a number of halo properties beyond halo mass, we then extend
our analytical framework to accommodate the dependence of $b_1$ and $b_2$ on
any such secondary property which has, or can be monotonically transformed to
have, a Gaussian distribution. We demonstrate this technique for the specific
case of halo concentration, finding good agreement with previous results. Our
calibrations will be useful for a variety of halo model analyses focusing on
galaxy assembly bias, as well as analytical forecasts of the potential for
using $\alpha$ as a segregating variable in multi-tracer analyses.
