Towards optimal and robust f_nl constraints with multi-tracer analyses

We discuss the potential of the multi-tracer technique to improve observational constraints of the local primordial non-Gaussianity (PNG) parameter f _nl from the galaxy power spectrum. For two galaxy samples A and B, the constraining power is ∝ |b^B₁ b^A_ϕ - b^A₁ b^B_ϕ |, where b ₁ and b_ϕ are the linear and PNG galaxy bias parameters. We show this allows for significantly improved constraints compared to the traditional expectation ∝ |b^A - b^B | based on naive universality-like relations where b_ϕ ∝ b ₁. Using IllustrisTNG galaxy simulation data, we find that different equal galaxy number splits of the full sample lead to different |b^B₁ b^A_ϕ - b^A₁ b^B_ϕ |, and thus have different constraining power. Of all of the strategies explored, splitting by g-r color is the most promising, more than doubling the significance of detecting f _nl b_ϕ ≠ 0. Importantly, since these are constraints on f _nl b_ϕ and not f _nl , they do not require priors on the b_ϕ (b ₁) relation. For direct constraints on f _nl , we show that multi-tracer constraints can be significantly more robust than single-tracer to b_ϕ misspecifications and uncertainties; this relaxes the precision and accuracy requirements for b_ϕ priors. Our results present new opportunities to improve our chances to detect and robustly constrain f _nl , and strongly motivate galaxy formation simulation campaigns to calibrate the b_ϕ (b ₁) relation.