The Scale-Dependence of Halo Assembly Bias
  The two-point clustering of dark matter halos is influenced by halo
properties besides mass, a phenomenon referred to as halo assembly bias. Using
the depth of the gravitational potential well, $V_{\rm max}$, as our secondary
halo property, in this paper we present the first study of the scale-dependence
assembly bias. In the large-scale linear regime, $r\geq10h^{-1}{\rm Mpc},$ our
findings are in keeping with previous results. In particular, at the low-mass
end ($M_{\rm vir}<M_{\rm coll}\approx10^{12.5}{\rm M}_{\odot}$), halos with
high-$V_{\rm max}$ show stronger large-scale clustering relative to halos with
low-$V_{\rm max}$ of the same mass, this trend weakens and reverses for $M_{\rm
vir}\geq M_{\rm coll}.$ In the nonlinear regime, assembly bias in low-mass
halos exhibits a pronounced scale-dependent "bump" at $500h^{-1}{\rm
kpc}-5h^{-1}{\rm Mpc},$ a new result. This feature weakens and eventually
vanishes for halos of higher mass. We show that this scale-dependent signature
can primarily be attributed to a special subpopulation of ejected halos,
defined as present-day host halos that were previously members of a higher-mass
halo at some point in their past history. A corollary of our results is that
galaxy clustering on scales of $r\sim1-2h^{-1}{\rm Mpc}$ can be impacted by up
to $\sim15\%$ by the choice of the halo property used in the halo model, even
for stellar mass-limited samples.
