X-ray luminosity function of Compton-thick active galactic nuclei in the early Universe (z ≥ 3) - Robustness and biases of the CTK population

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Volume 712 (August 2026)

A&A, 712 (2026) A20

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Table A.1.

Prior limits and best-fitting values for the free parameters of the X-ray luminosity and absorption functions.

	Parameter	Prior limits	Best-fit value

			X-ray	X-ray and IR
Luminosity function	log A	[-5, -3]	$- 4 . 25_{- 0.10}^{+ 0.10}$ $Mathematical equation: $ -4.25^{+0.10}_{-0.10} $$	$- 4 . 03_{- 0.10}^{+ 0.09}$ $Mathematical equation: $ -4.03^{+0.09}_{-0.10} $$
	log L_*	[42, 46]	$44 . 60_{- 0.07}^{+ 0.08}$ $Mathematical equation: $ 44.60^{+0.08}_{-0.07} $$	$44 . 36_{- 0.07}^{+ 0.08}$ $Mathematical equation: $ 44.36^{+0.08}_{-0.07} $$
	γ₁	[-2, 2]	$0 . 25_{- 0.09}^{+ 0.09}$ $Mathematical equation: $ 0.25^{+0.09}_{-0.09} $$	$0 . 13_{- 0.10}^{+ 0.10}$ $Mathematical equation: $ 0.13^{+0.10}_{-0.10} $$
	γ₂	[1, 6]	$2 . 35_{- 0.16}^{+ 0.17}$ $Mathematical equation: $ 2.35^{+0.17}_{-0.16} $$	$2 . 16_{- 0.12}^{+ 0.13}$ $Mathematical equation: $ 2.16^{+0.13}_{-0.12} $$
	p_den	[-10, -3]	$- 8 . 53_{- 0.47}^{+ 0.49}$ $Mathematical equation: $ -8.53^{+0.49}_{-0.47} $$	$- 8 . 32_{- 0.46}^{+ 0.47}$ $Mathematical equation: $ -8.32^{+0.47}_{-0.46} $$

Absorption function	ε	[0, 10]	$2 . 841_{- 0.31}^{+ 0.37}$ $Mathematical equation: $ 2.841^{+0.37}_{-0.31} $$	$2 . 14_{- 0.27}^{+ 0.29}$ $Mathematical equation: $ 2.14^{+0.29}_{-0.27} $$
	f_CTK, r	[0, 10]	$0 . 35_{- 0.25}^{+ 0.28}$ $Mathematical equation: $ 0.35^{+0.28}_{-0.25} $$	< 0.32
	ψ₃	[0, 1]	$0 . 60_{- 0.25}^{+ 0.39}$ $Mathematical equation: $ 0.60^{+0.39}_{-0.25} $$	$0 . 99_{- 0.98}^{+ 0.29}$ $Mathematical equation: $ 0.99^{+0.29}_{-0.98} $$
	C	[-10, 10]	$- 3 . 0_{- 6.8}^{+ 6.0}$ $Mathematical equation: $ -3.0^{+6.0}_{-6.8} $$	$- 2 . 4_{- 4.2}^{+ 8.9}$ $Mathematical equation: $ -2.4^{+8.9}_{-4.2} $$
	a₂	[0, 15]	$10 . 6_{- 5.3}^{+ 3.6}$ $Mathematical equation: $ 10.6^{+3.6}_{-5.3} $$	$12 . 1_{- 6.0}^{+ 2.7}$ $Mathematical equation: $ 12.1^{+2.7}_{-6.0} $$

Notes. The normalisation, A, and the break luminosity, L_*, are given in units of Mpc⁻³ and erg s⁻¹, respectively. The quoted best-fitting values and uncertainties correspond to the mode of the posterior distribution and the 1σ credible intervals around the mode. Results are shown for both cases: using X-ray–only posteriors for the individual sources, and using posteriors updated with infrared (IR) information.

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