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 $b_\phi = 2\delta_c\left(b_1 - p\right)$ 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 $0.5\sigma$ to $1\sigma$; 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 $f_{\rm NL} \neq 0$ 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.

中文翻译：

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星系偏差不确定性对原始非高斯约束的影响

我们研究了星系偏差参数之间假设关系的不确定性对局部 PNG $f_{\rm NL}$ 参数约束的影响。我们在具有多示踪星系功率谱和双谱数据的理想化预测设置中关注线性密度星系偏差 $b_1$ 和局部 PNG 偏差 $b_\phi$ 之间的关系。我们考虑星系偏差的两种参数化：1）一种受到普遍性关系的启发，其中 $b_\phi = 2\delta_c\left(b_1 - p\right)$ 和 $p$ 是一个自由参数；和 2) 另一个直接拟合偏置参数和 $f_{\rm NL}$ 的乘积，如 $f_{\rm NL} b_\phi$。$f_{\rm NL}-p$ 平面上的约束明显是双峰的，并且 $f_{\rm NL}$ 上边缘化约束的中心值和宽度都敏感地依赖于 $p$ 上的先验。假设在具有 $p=0.55$ 基准值的约束中固定 $p=1$ 可以将推断的 $f_{\rm NL}$ 偏差 $0.5\sigma$ 到 $1\sigma$；然而，在我们的设置中，这个基准值周围的先验 $\Delta p \approx 0.5$ 足以返回无偏约束。在功率谱分析中，对 $b_\phi$ 不做任何假设的参数化 2 可以区分 $f_{\rm NL} \neq 0$，其重要性与参数化 1 假设完全了解 $b_\phi$（然而 $f_{\rm NL}$ 的值未知）。参数化 2 的一个缺点是双谱信息的添加不像参数化 1 那样有益。我们的结果强烈地激发了在 PNG 约束分析中纳入针对偏差不确定性的缓解策略，