Constrained cosmological simulations of the Local Group using Bayesian hierarchical field-level inference

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Volume 691 (November 2024)

A&A, 691 (2024) A348

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Table 2.

Summary of our adopted observational constraints and of the parameter values that are used in building the likelihood, as described in Section 2.3.

Constraint	Functional form	Values
Milky Way filtered mass	ln(M(x_obs, w)) ∼ 𝒩(ln(M_obs),σ_rel²)	x_obs = ( − 3.9, −6.9, −1.8) kpc, w = 100 kpc, M_obs = 1.085 × 10¹² M_⊙, $σ_{rel} = \sqrt{0 . 05^{2} + 0 . 1291^{2}}$ $\sigma_\text{rel} = \sqrt{0.05^2+0.1291^2}$
Milky Way centre of mass	Δx_CoM(x_obs)∼𝒩(0, Σ = Σ_x,res)	$Σ_{x,res} = {(30 kpc)}^{2} 1$ ${{\boldsymbol{\Sigma}}}_\text{x,res} = ({30}\,\mathrm{kpc})^2 {{{\mathbb{1}}}}$

M31 filtered mass	ln(M(x_obs, w)) ∼ 𝒩(ln(M_obs),σ_rel²)	x_obs = (780, 0, 0) kpc, w = 100 kpc, M_obs = 1.288 × 10¹² M_⊙, $σ_{rel} = \sqrt{0 . 05^{2} + 0 . 167^{2}}$ $\sigma_\text{rel} = \sqrt{0.05^2+0.167^2}$
M31 centre of mass	Δx_CoM(x_obs)∼𝒩(0, Σ = Σ_x,res)	$Σ_{x,res} = {(30 kpc)}^{2} 1$ ${{\boldsymbol{\Sigma}}}_\text{x,res} = ({30}\,\mathrm{kpc})^2 {{{\mathbb{1}}}}$

M31-MW velocity	Equation (20)	$Δ v / (km s^{- 1}) = (- 114.7, 39.8, - 59.8), Σ_{meas} / {(km s^{- 1})}^{2} = (0 . 9^{2}, 39 . 2^{2}, 30 . 2^{2}) 1, Σ_{v,res} = {(10 km s^{- 1})}^{2} 1$ $\Delta {{\boldsymbol{v}}}/(\mathrm{km}\,\mathrm{s}^{-1}) = (-114.7, 39.8, -59.8), {{\boldsymbol{\Sigma}}}_\text{meas}/(\mathrm{km}\,\mathrm{s}^{-1})^2 = (0.9^2,39.2^2,30.2^2){{{\mathbb{1}}}}, {{\boldsymbol{\Sigma}}}_\text{v,res}=({10}\,\mathrm{km}\,\mathrm{s}^{-1})^2{{{\mathbb{1}}}}$

Local Hubble flow	Equation (21)	31 galaxies, σ_int = 35 km s⁻¹, w = 250 kpc ⋅ (d/Mpc)

Notes. The final likelihood also assumes an isotropic Gaussian uncertainty with dispersion 10 km s⁻¹ per component in the reference frame corresponding to the velocity of the MW halo (see Section 2.3.6).

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