syren-baryon: Analytic emulators for the impact of baryons on the matter power spectrum

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Volume 701 (September 2025)

A&A, 701 (2025) A284

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Table 3.

Chosen models for the baryonic correction to the power spectrum log S (Eq. (2)) as a function of wavenumber k, redshift z and the cosmological and hydrodynamical parameters outlined in Tables 1 and 2.

Model	Fit for log P(k, z, θ)
Astrid	$\frac{α_{1} k {(α_{2} k)}^{α_{3}} (α_{4} - z)}{(α_{5} z - α_{6}^{- 2 z}) (α_{7} + α_{8} k + k^{2})} + (α_{9} k - 1 + e^{- α_{10} k}) e^{- α_{11} z}$ $\frac{ \alpha_1 k \left(\alpha_{2} k\right)^{\alpha_{3}} \left(\alpha_{4} - z\right)}{\left(\alpha_{5} z - \alpha_{6}^{- 2 z}\right) \left(\alpha_{7} + \alpha_{8} k + k^{2}\right)} + \left(\alpha_{9} k - 1 + e^{- \alpha_{10} k}\right) e^{- \alpha_{11} z}$
	$α_{1} = 7.9 \frac{A_{SN 2}}{Ω_{m}}$ $\alpha_1 = 7.9 \frac{A_{\mathrm{SN2}}}{\Omega_{\mathrm{m}}}$ , α₂ = 0.0014, α₃ = 0.937A_SN2,
	α₄ = 1.622A_AGN2 + 0.849A_SN1 + 5.092A_SN2²(0.23A_AGN1−A_AGN2−0.71A_SN1+3.107σ₈)
	α₅ = 0.78, α₆ = 0.677, α₇ = A_AGN2(19.756Ω_m+2.8478)
	α₈ = 1.7347A_AGN2 + 11.389Ω_m + 1.642 α₉ = 0.0224, α₁₀ = 0.029, α₁₁ = 0.063


IllustrisTNG	$- α_{1} α_{2}^{- α_{3} k - α_{4} z} k (1 + α_{5} (- α_{6} k + α_{7}^{z})) + α_{8} e^{- \frac{α_{9} e^{α_{10} z}}{k}}$ $- \alpha_{1} \alpha_{2}^{- \alpha_{3} k - \alpha_{4} z} k \left(1 + \alpha_{5} \left(- \alpha_{6} k + \alpha_{7}^{z}\right)\right) + \alpha_{8} e^{- \frac{\alpha_{9} e^{\alpha_{10} z}}{k}}$
	$α_{1} = 0.0109 \frac{A_{SN 2}}{Ω_{m}}, α_{2} = 3592.322 Ω_{m}, α_{3} = 0.0087, α_{4} = 0.059$ $\alpha_{1} = 0.0109 \frac{A_{\mathrm{SN2}}}{\Omega_{\mathrm{m}}}, \quad \alpha_{2} = 3592.322 \Omega_{\mathrm{m}}, \quad \alpha_{3} = 0.0087, \quad \alpha_{4} = 0.059$ ,
	$α_{5} = 0.9007 \frac{A_{AGN 2}}{A_{SN 2}} - 0.5901 \frac{A_{SN 1}}{A_{SN 2}} - 1.5576 + 2.6846 \frac{σ_{8}}{A_{SN 2}}$ $\alpha_{5} = 0.9007 \frac{A_{\mathrm{AGN2}}}{A_{\mathrm{SN2}}} - 0.5901 \frac{A_{\mathrm{SN1}}}{A_{\mathrm{SN2}}} - 1.5576 + 2.6846 \frac{\sigma_8}{A_{\mathrm{SN2}}}$ ,
	α₆ = 0.048, α₇ = (0.3Ω_m)^0.193, α₈ = 0.022, α₉ = 0.021, α₁₀ = 0.797



SIMBA	$- \frac{α_{1} k (k + α_{2})}{({(α_{3} k)}^{α_{4} z} + α_{5} z) (k^{α_{6}} + α_{7} z + α_{8})} + α_{9} e^{- \frac{α_{10} e^{- α_{11} z}}{k} - 2 z}$ $- \frac{ \alpha_{1} k \left(k + \alpha_{2}\right)}{\left( \left(\alpha_{3} k\right)^{\alpha_{4} z} + \alpha_{5} z\right) \left( k^{\alpha_{6}} + \alpha_{7} z + \alpha_{8}\right)} + \alpha_{9} e^{- \frac{\alpha_{10} e^{- \alpha_{11} z}}{k} - 2 z}$
	$α_{1} = \frac{0.00133}{Ω_{m}^{2}}, α_{2} = Ω_{m} (25.727 A_{AGN 1} + 153.382 A_{AGN 2} - 70.6363 A_{SN 1} + 260.812 σ_{8})$ $\alpha_{1} = \frac{0.00133}{\Omega_{\mathrm{m}}^{2}}, \quad \alpha_{2} = \Omega_{\mathrm{m}} \left(25.727 A_{\mathrm{AGN1}} + 153.382 A_{\mathrm{AGN2}} - 70.6363 A_{\mathrm{SN1}} + 260.812 \sigma_{8}\right)$ ,
	α₃ = 0.0553, α₄ = 0.79055, α₅ = 0.6024, α₆ = 1.594, α₇ = 16.01,
	α₈ = 12.0685(1.0047A_SN2)^0.6788A_SN1, α₉ = 4.4661, α₁₀ = 114.529, α₁₁ = 1.21


Swift-EAGLE	$α_{1}^{\frac{α_{2}}{k} + α_{3} k + α_{4} z} (- α_{5} k + α_{6} z + \frac{α_{7} k z + k^{2}}{α_{8} k + α_{9}} + \frac{α_{10} k + α_{11}}{α_{12} z + α_{13} + k} + α_{14}) + α_{15} e^{- \frac{α_{16} e^{- z}}{k} - e^{α_{17} z}}$ $\alpha_{1}^{\frac{\alpha_{2}}{k} + \alpha_{3} k + \alpha_{4} z} \left(- \alpha_{5} k + \alpha_{6} z + \frac{\alpha_{7} k z + k^{2}}{\alpha_{8} k + \alpha_{9}} + \frac{\alpha_{10} k + \alpha_{11}}{\alpha_{12} z + \alpha_{13} + k} + \alpha_{14}\right) + \alpha_{15} e^{- \frac{\alpha_{16} e^{- z}}{k} - e^{\alpha_{17} z}}$
	$α_{1} = 0.272 Ω_{m}, α_{2} = 0.22, α_{3} = 0.0168, α_{4} = 0.074, α_{5} = \frac{0.0204}{Ω_{m}^{1.625}}, α_{6} = \frac{0.004}{Ω_{m}^{1.625}}$ $\alpha_{1} = 0.272 \Omega_{\mathrm{m}}, \quad \alpha_{2} = 0.22, \quad \alpha_{3} = 0.0168, \quad \alpha_{4} = 0.074, \quad \alpha_{5} = \frac{0.0204}{\Omega_{\mathrm{m}}^{1.625}}, \quad \alpha_{6} = \frac{0.004}{\Omega_{\mathrm{m}}^{1.625}}$ ,
	$α_{7} = 1.1166, α_{8} = 54.3014 Ω_{m}^{1.625}, α_{9} = 0.12055 Ω_{m}^{1.625} (4822.2 A_{SN 1} + 8228.9 Ω_{m})$ $\alpha_{7} = 1.1166, \quad \alpha_{8} = 54.3014 \Omega_{\mathrm{m}}^{1.625}, \quad \alpha_{9} = 0.12055 \Omega_{\mathrm{m}}^{1.625} \left(4822.2 A_{\mathrm{SN1}} + 8228.9 \Omega_{\mathrm{m}}\right)$ ,
	$α_{10} = \frac{- 0.2588 A_{AGN 1} + 6.13845 A_{SN 1}}{Ω_{m}^{1.625} (6.528 A_{AGN 2} + 12.855 A_{SN 1})}, α_{11} = \frac{(0.9788 - 0.1659 A_{SN 1}) (- 0.3745 A_{AGN 1} + 8.877 A_{SN 1})}{Ω_{m}^{1.625} (6.528 A_{AGN 2} + 12.855 A_{SN 1})}, α_{12} = 9.2437$ $\alpha_{10} = \frac{- 0.2588 A_{\mathrm{AGN1}} + 6.13845 A_{\mathrm{SN1}}}{\Omega_{m}^{1.625} \left(6.528 A_{\mathrm{AGN2}} + 12.855 A_{\mathrm{SN1}}\right)}, \quad \alpha_{11} = \frac{\left(0.9788 - 0.1659 A_{\mathrm{SN1}}\right) \left(- 0.3745 A_{\mathrm{AGN1}} + 8.877 A_{\mathrm{SN1}}\right)}{\Omega_{\mathrm{m}}^{1.625} \left(6.528 A_{\mathrm{AGN2}} + 12.855 A_{\mathrm{SN1}}\right)}, \quad \alpha_{12} = 9.2437$ ,
	$α_{13} = 9.2965 A_{SN 2} + 18.4, α_{14} = \frac{0.034 Ω_{m} - 0.02 σ_{8}}{Ω_{m}^{1.625}}, α_{15} = 2.287, α_{16} = 130.0, α_{17} = 0.565$ $\alpha_{13} = 9.2965 A_{\mathrm{SN2}} + 18.4, \quad \alpha_{14} = \frac{0.034 \Omega_{\mathrm{m}} - 0.02 \sigma_{8}}{\Omega_{\mathrm{m}}^{1.625}}, \quad \alpha_{15} = 2.287, \quad \alpha_{16} = 130.0, \quad \alpha_{17} = 0.565$ ,

Baryonification	α₁α₂^α₃zk(α₄−(α₅k)^α₆)(α₇k+α₈^{(α₉+α₁₀z)^α₁₁})
	α₁ = 2.4663(5.823Ω_b)^3.23Ω_m, α₂ = 5.823Ω_b, α₃ = 0.4355,
	α₄ = 0.0495log₁₀(M₁), α₅ = 0.2479, α₆ = −0.27log₁₀(η),
	α₇ = 0.0015log₁₀(M_inn)+0.0176log₁₀(θ_inn)−0.0015(3.9144σ₈)^{0.2058log₁₀(M₁)},
	α₈ = 0.016log₁₀(M_c), α₉ = 0.0706log₁₀(M_c), α₁₀ = 0.0383, α₁₁ = −6.5log₁₀(β)−6.5

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