The Aemulus Project IV: Emulating Halo Bias
  Models of the spatial distribution of dark matter halos must achieve new
levels of precision and accuracy in order to satisfy the requirements of
upcoming experiments. In this work, we present a halo bias emulator for
modeling the clustering of halos on large scales. It incorporates the
cosmological dependence of the bias beyond the mapping of halo mass to peak
height. The emulator makes substantial improvements in accuracy compared to the
widely used Tinker et al. (2010) model. Halos in this work are defined using an
overdensity criteria of 200 relative to the mean background density. Halo
catalogs are produced for 40 N-body simulations as part of the Aemulus project
at snapshots from z=3 to z=0. The emulator is trained over the mass range
$6\times10^{12}-7\times10^{15}\ h^{-1}M_{\odot}$. Using an additional suite of
35 simulations, we determine that the precision of the emulator is redshift
dependent, achieving sub-percent levels for a majority of the redshift range.
Two additional simulation suites are used to test the ability of the emulator
to extrapolate to higher and lower masses. Our high-resolution simulation suite
is used to develop an extrapolation scheme in which the emulator asymptotes to
the Tinker et al. (2010) model at low mass, achieving ~3% accuracy down to
$10^{11}\ h^{-1}M_{\odot}$. Finally, we present a method to propagate emulator
modeling uncertainty into an error budget. Our emulator is made publicly
available at \url{https://github.com/AemulusProject/bias_emulator}.
