Measuring the intergalactic medium correlation length at 5 < z < 6.1: A fast change at the end of reionization

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Volume 706 (February 2026)

A&A, 706 (2026) A273

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Table 1.

Summary of models and their best-fit parameters.

Observations	Model	Functional form	Best fit	minχ²/N_d.o.f. = χ_{N_d.o.f.}²; AIC

	ℳ1: constant	ℳ1(z₁, z₂) = A	$A = 0 . 09_{- 0.01}^{+ 0.01}$ $A = 0.09^{+0.01}_{-0.01}$	298.4/220 = 1.35; 300.4

	ℳ2: Gaussian, constant amplitude and width	$M 2 (z_{1}, z_{2}) = A exp [- \frac{1}{2} {(\frac{χ (z_{1}) - χ (z_{2})}{L})}^{2}]$ $\mathcal{M}2(z_1,z_2) = A\,\exp\left[-\dfrac{1}{2}\left(\dfrac{\chi(z_1)-\chi(z_2)}{L}\right)^2\right]$	$A = 0 . 22_{- 0.03}^{+ 0.03}$ $A = 0.22^{+0.03}_{-0.03}$ , $L = 86 . 16_{- 11.52}^{+ 16.42} Mpc$ $L = 86.16^{+16.42}_{-11.52}\,\mathrm{Mpc}$	256.6/219 = 1.17; 260.6
	ℳ3: Gaussian, redshift-dependent amplitude and width	$M 3 (z_{1}, z_{2}) = A (z_{1}, z_{2}) exp [- \frac{1}{2} {(\frac{χ (z_{1}) - χ (z_{2})}{L (z_{1}, z_{2})})}^{2}]$ $\mathcal{M}3(z_1,z_2) = A(z_1,z_2)\,\exp\left[-\dfrac{1}{2}\left(\dfrac{\chi(z_1)-\chi(z_2)}{L(z_1,z_2)}\right)^2\right]$ , A(z₁, z₂) = A₀ + A₁ ⋅ (z₂ − 5), L(z₁, z₂) = L₀ + L₁ ⋅ (z₂ − 5)	$A_{0} = - 0 . 10_{- 0.05}^{+ 0.05}$ $A_0 = -0.10^{+0.05}_{-0.05}$ , $A_{1} = 0 . 58_{- 0.09}^{+ 0.10}$ $A_1 = 0.58^{+0.10}_{-0.09}$ , L₀ ≤ 76.45 Mpc, $L_{1} = 283 . 77_{- 117.45}^{+ 176.24} Mpc$ $L_1 = 283.77^{+176.24}_{-117.45}\,\mathrm{Mpc}$	202.9/217 = 0.94; 210.9

	constλ	—————–	———	392.3/221 = 1.76; 392.3

	evolvλ	—————–	———	278.8/221 = 1.26; 278.8

	SCRIPT	—————–	———	274.6/221 = 1.24; 274.6



	Model	Best fit		minχ²/N_d.o.f. = χ_{N_d.o.f.}²; AIC

BIBORTON	ℳ3, constλ	$A_{0} = 0 . 78_{- 0.02}^{+ 0.04}, A_{1} = - 0 . 36_{- 0.06}^{+ 0.02}, L_{0} = 37 . 81_{- 1.56}^{+ 0.47} Mpc, L_{1} \leq 3.86 Mpc$ $A_0 = 0.78^{+0.04}_{-0.02},\,A_1 = -0.36^{+0.02}_{-0.06},\, L_0 = 37.81^{+0.47}_{-1.56}\,\mathrm{Mpc},\, L_1 \leq 3.86 \,\mathrm{Mpc}$		265.8/217 = 1.23; 269.8

	ℳ3, evolvλ	$A_{0} = 0 . 20_{- 0.02}^{+ 0.03}, A_{1} = 0 . 17_{- 0.05}^{+ 0.02}, L_{0} = 46 . 14_{- 4.56}^{+ 0.72} Mpc, L_{1} \leq 10.80 Mpc$ $A_0 = 0.20^{+0.03}_{-0.02},\,A_1 = 0.17^{+0.02}_{-0.05},\, L_0 = 46.14^{+0.72}_{-4.56}\,\mathrm{Mpc},\, L_1 \leq 10.80\,\mathrm{Mpc}$		315.4/217 = 1.45; 323.4

	ℳ3, SCRIPT	$A_{0} = 0 . 11_{- 0.02}^{+ 0.02}, A_{1} = 0 . 19_{- 0.05}^{+ 0.03}, L_{0} = 42 . 72_{- 4.83}^{+ 3.11} Mpc, L_{1} \leq 8.28 Mpc$ $A_0 = 0.11^{+0.02}_{-0.02},\,A_1 = 0.19^{+0.03}_{-0.05},\, L_0 = 42.72^{+3.11}_{-4.83}\,\mathrm{Mpc},\, L_1 \leq 8.28\,\mathrm{Mpc}$		294.8/217 = 1.36; 302.8

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