Probabilistic Lagrangian bias estimators and the cumulant bias expansion

Open Access

Table 2.

Sets of bias parameters that are shown in Figure 15.

Parameter	10¹⁴ h⁻¹ M_⊙	10¹⁵ h⁻¹ M_⊙	Unit
b₁	0.54	3.08
b₂	−0.89	7.20
b₃	−1.93	7.81
b₄	7.81	−32.30
b_L	−13.92	17.76	h⁻²Mpc²
b_K²	0.04	−0.17
b_(∇δ)²	−13.81	22.87	h⁻²Mpc²
$\frac{1}{2} b_{3 \equiv 3}$ $\frac{1}{2} b_{3 \equiv 3}$	2.10	−1.08	h⁻²Mpc²

β₂	−1.13	−2.25
β₃	−0.33	−0.66
β₄	0.19	−1.11

Notes. The first set corresponds to M ∼ 10¹⁴ h⁻¹ M_⊙ and has moderate bias values, whereas the second set with 10¹⁵ h⁻¹ M_⊙ is strongly biased. The last two lines show cumulant bias parameters that can be used instead of b₃ and b₄.

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