Assembly bias in the local PNG halo bias and its implication for $f_{\rm NL}$ constraints

We use $N$-body simulations to study halo assembly bias (i.e., the dependence of halo clustering on properties beyond total mass) in the density and primordial non-Gaussianity (PNG) linear bias parameters $b_1$ and $b_\phi$, respectively. We consider concentration, spin and sphericity as secondary halo properties, for which we find a clear detection of assembly bias for $b_1$ and $b_\phi$. At fixed total mass, halo spin and sphericity impact $b_1$ and $b_\phi$ in a similar manner, roughly preserving the shape of the linear $b_\phi(b_1)$ relation satisfied by the global halo population. Halo concentration, however, drives $b_1$ and $b_\phi$ in opposite directions. This induces significant changes to the $b_\phi(b_1)$ relation, with higher concentration halos having higher amplitude of $b_\phi(b_1)$. For $z=0.5$ and $b_1 \approx 2$ in particular, the population comprising either all halos, those with the $33\%$ lowest or those with the $33\%$ highest concentrations have a PNG bias of $b_\phi \approx 3$, $b_\phi \approx -1$ and $b_\phi \approx 9$, respectively. Varying the halo concentration can make $b_\phi$ very small and even change its sign. These results have important ramifications for galaxy clustering constraints of the local PNG parameter $f_{\rm NL}$ that assume fixed forms for the $b_\phi(b_1)$ relation. We illustrate the significant impact of halo assembly bias in actual data using the BOSS DR12 galaxy power spectrum: assuming that BOSS galaxies are representative of all halos, the $33\%$ lowest or the $33\%$ highest concentration halos yields $\sigma_{f_{\rm NL}} = 44, 165, 19$, respectively. Our results suggest taking host halo concentration into account in galaxy selection strategies to maximize the signal-to-noise on $f_{\rm NL}$. They also motivate more simulation-based efforts to study the $b_\phi(b_1)$ relation of halos and galaxies.