Predictions for local PNG bias in the galaxy power spectrum and bispectrum and the consequences for f_NL constraints

We use hydrodynamical separate universe simulations with the IllustrisTNG model to predict the local primordial non-Gaussianity (PNG) bias parameters b_ϕ and b_ϕδ, which enter at leading order in the galaxy power spectrum and bispectrum. This is the first time that b_ϕδ is measured from either gravity-only or galaxy formation simulations. For dark matter halos, the popular assumption of universality overpredicts the b_ϕδ(b₁) relation in the range 1 ≲ b₁ ≲ 3 by up to Δ b_ϕδ ∼ 3 (b₁ is the linear density bias). The adequacy of the universality relation is worse for the simulated galaxies, with the relations b_ϕ(b₁) and b_ϕδ(b₁) being generically redshift-dependent and very sensitive to how galaxies are selected (we test total, stellar and black hole mass, black hole mass accretion rate and color). The uncertainties on b_ϕ and b_ϕδ have a direct, often overlooked impact on the constraints of the local PNG parameter f_NL, which we study and discuss. For a survey with V = 100 Gpc³/h³ at z=1, uncertainties Δ b_ϕ ≲ 1 and Δ b_ϕδ ≲ 5 around values close to the fiducial can yield relatively unbiased constraints on f_NL using power spectrum and bispectrum data. We also show why priors on galaxy bias are useful even in analyses that fit for products f_NLb_ϕ and f_NLb_ϕδ. The strategies we discuss to deal with galaxy bias uncertainties can be straightforwardly implemented in existing f_NL constraint analyses (we provide fits for some of the bias relations). Our results motivate more works with galaxy formation simulations to refine our understanding of b_ϕ and b_ϕδ towards improved constraints on f_NL.