Validating and improving two-fluid simulations of the magnetic field evolution in neutron star cores

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Volume 701 (September 2025)

A&A, 701 (2025) A71

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Table 1.

Normalization of the relevant variables.

Variable	Unit
B	B₀ = ⟨B(t = 0)⟩
r	R (core radius)
$\nabla$ $\boldsymbol\nabla$	1/R
α	B₀R² (see Eq. (16))
β	B₀R (see Eq. (16))
μ	μ₀ ≡ μ(r = 0)
n_n, n_c	n₀ ≡ n_c(r = 0)
χ_n, χ_c	χ₀ ≡ B₀²/4πn₀μ₀
K_nn, K_cc, K	μ₀/n₀
γ_cn	γ₀ ≡ γ_cn(r = 0, T = 10⁸ K)
ζ	γ₀n₀
t	t₀ = 4πγ₀n₀²R²/B₀²
v_c, v_n	R/t₀

Notes. Here, ⟨a⟩ denotes the rms of a vector field a in the volume of the core, 𝒱_core, $⟨ a ⟩ = \sqrt{\frac{1}{V_{core}} \int_{V_{core}} {| a |}^{2} d V}$ $\langle \boldsymbol{a}\rangle=\sqrt{\frac{1}{\mathcal{V}_\text{core}}\int_{\mathcal{V}_\text{core}}|\boldsymbol{a}|^2\,d\mathcal{V}}$ . The core radius R and the different quantities evaluated at the center of the star (n₀, μ₀, and γ₀) are dependent on the stellar model (see Sect. 5). Their values are given in Table 2.

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