Constraints on the state of the intergalactic medium at z∼8 − 10 using redshifted 21 cm observations with LOFAR

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Volume 699 (July 2025)

A&A, 699 (2025) A109

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Table 4.

Constraints on the IGM parameters derived using the LOFAR upper limits from Mertens et al. (2025) for the A_r = 0 scenario.

IGM	Credible	z = 8.3	z = 9.1	z = 10.1
Parameters	intervals
(MCMC	[%]
Model)

${\bar{x}}_{HII}$ $\overline{x}_{\mathrm{HII}}$	68	[0, 0.15]	[0, 0.13]	[0, 0.2]
(Single-z)	95	[0, 0.57]	[0, 0.55]	[0, 0.47]

${\bar{x}}_{HII}$ ${\overline{x}_{\mathrm{HII}}}$	68	[0, 0.24]	[0, 0.06]	[0, 0.01]
(Joint-z)	95	[0, 0.85]	[0, 0.46]	[0, 0.17]

f_heat	68	[0, 0.21]	[0, 0.18]	[0, 0.22]
(Single-z)	95	[0, 1]	[0, 0.57]	[0, 0.47]

f_heat	68	[0, 0.49]	[0, 0.15]	[0, 0.05]
(Joint-z)	95	[0, 0.9]	[0, 0.54]	[0, 0.21]

${\bar{T}}_{K}$ ${\overline{T}_{\mathrm{K}}}$ (K)	68	[1.8, 7.7]	[2.2, 7.3]	[2.6, 12.8]
(Single-z)	95	[1.8, 50]	[2.2, 21]	[2.6, 22]

${\bar{T}}_{K}$ ${\overline{T}_{\mathrm{K}}}$ (K)	68	[1.8, 28.5]	[2.2, 7.2]	[2.6, 5]
(Joint-z)	95	[1.8, 977]	[2.2, 35.6]	[2.6, 15]

${\bar{δ T}}_{b}$ ${\overline{\delta T}_{\mathrm{b}}}$ (mK)	68	[–300, –124]	[–276, –123]	[–222, –113]
(Single-z)	95	[–345, –23]	[–317, –61]	[–283, –80]

${\bar{δ T}}_{b}$ ${\overline{\delta T}_{\mathrm{b}}}$ (mK)	68	[–264, –4]	[–308, –141]	[–308, –220]
(Joint-z)	95	[–313, 10]	[–337, –36]	[–289., –116]

$R_{peak}^{heat}$ ${R^{\mathrm{heat}}_{\mathrm{peak}}}$ (h⁻¹ Mpc)	68	[0, 26.3]	[0, 28.1]	[0, 20.6]
(Single-z)	95	[0, 56.4.]	[0, 39.5]	[0, 35.5]

$R_{peak}^{heat}$ ${R^{\mathrm{heat}}_{\mathrm{peak}}}$ (h⁻¹ Mpc)	68	[0, 68]	[0, 25]	[0, 14]
(Joint-z)	95	[0, 205]	[0, 41]	[0, 23]

$Δ R_{FWHM}^{heat}$ ${\Delta R^{\mathrm{heat}}_{\mathrm{FWHM}}}$ (h⁻¹ Mpc)	68	[6, 47]	[9, 46]	[11,38]
(Single-z)	95	[3, 118]	[4, 81]	[3.5, 79]

$Δ R_{FWHM}^{heat}$ ${\Delta R^{\mathrm{heat}}_{\mathrm{FWHM}}}$ (h⁻¹ Mpc)	68	[0, 135]	[0, 40]	[0, 21]
(Joint-z)	95	[0, 331]	[0, 85]	[0, 33]

Notes. The first column shows the list of IGM parameters derived from both the Single-z and Joint-z analysis, the second refers to the credible intervals of the disfavoured models, while the last three to the constraints obtained from the analysis at three redshifts.

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