We study the impact that uncertainties on assumed relations between galaxy bias parameters have on constraints of the local PNG $f_{rm NL}$ parameter. We focus on the relation between the linear density galaxy bias $b_1$ and local PNG bias $b_phi$ in an idealized forecast setup with multitracer galaxy power spectrum and bispectrum data. We consider two parametrizations of galaxy bias: 1) one inspired by the universality relation where $b_phi = 2delta_cleft(b_1 - pright)$ and $p$ is a free parameter; and 2) another in which the product of bias parameters and $f_{rm NL}$, like $f_{rm NL} b_phi$, is directly fitted for. The constraints on the $f_{rm NL}-p$ plane are markedly bimodal, and both the central value and width of marginalized constraints on $f_{rm NL}$ depend sensitively on the priors on $p$. Assuming fixed $p=1$ in the constraints with a fiducial value of $p=0.55$ can bias the inferred $f_{rm NL}$ by $0.5sigma$ to $1sigma$; priors $Delta p approx 0.5$ around this fiducial value are however sufficient in our setup to return unbiased constraints. In power spectrum analyses, parametrization 2, that makes no assumptions on $b_phi$, can distinguish $f_{rm NL} eq 0$ with the same significance as parametrization 1 assuming perfect knowledge of $b_phi$ (the value of $f_{rm NL}$ is however left unknown). A drawback of parametrization 2 is that the addition of the bispectrum information is not as beneficial as in parametrization 1. Our results motivate strongly the incorporation of mitigation strategies for bias uncertainties in PNG constraint analyses, as well as further theoretical studies on the relations between bias parameters to better inform those strategies.
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