Reconstructing the epoch of reionisation with Planck PR4

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Table 2.

Constraints on the optical depth, τ, for the reionisation models considered.

Model		d.o.f.	τ 68% constraints

			Raw posterior	Posterior with flat-τ prior	Profile likelihood
Hyperbolic tangent	`tanh`	1	0.0576 ± 0.0061	$0 . 0578_{- 0.0064}^{+ 0.0059}$ $0.0578^{+0.0059}_{-0.0064}$	$0 . 0581_{- 0.0063}^{+ 0.0062}$ $0.0581_{-0.0063}^{+0.0062}$
	`tanhdz`	2	0.0564 ± 0.0063	0.0567 ± 0.0063	$0 . 0576_{- 0.0058}^{+ 0.0067}$ $0.0576_{-0.0058}^{+0.0067}$

Power-law	`2-pow`	2	$0 . 0580_{- 0.0061}^{+ 0.0060}$ $0.0580^{+0.0060}_{-0.0061}$	$0 . 0576_{- 0.0062}^{+ 0.0061}$ $0.0576^{+0.0061}_{-0.0062}$	$0 . 0584_{- 0.0066}^{+ 0.0060}$ $0.0584_{-0.0066}^{+0.0060}$
	`3-pow`	3	$0 . 0576_{- 0.0061}^{+ 0.0062}$ $0.0576^{+0.0062}_{-0.0061}$	0.0577 ± 0.0062	$0 . 0580_{- 0.0061}^{+ 0.0064}$ $0.0580_{-0.0061}^{+0.0064}$

Step-based	`2-steps`	3	$0 . 0583_{- 0.0062}^{+ 0.0057}$ $0.0583^{+0.0057}_{-0.0062}$	$0 . 0578_{- 0.0063}^{+ 0.0058}$ $0.0578^{+0.0058}_{-0.0063}$	$0 . 0592_{- 0.0060}^{+ 0.0061}$ $0.0592_{-0.0060}^{+0.0061}$
	`3-steps`	5	$0 . 0593_{- 0.0057}^{+ 0.0056}$ $0.0593^{+0.0056}_{-0.0057}$	$0 . 0580_{- 0.0059}^{+ 0.0058}$ $0.0580^{+0.0058}_{-0.0059}$	$0 . 0585_{- 0.0056}^{+ 0.0062}$ $0.0585_{-0.0056}^{+0.0062}$

Interpolation-based	`2-knots`	2	$0 . 0586_{- 0.0063}^{+ 0.0057}$ $0.0586^{+0.0057}_{-0.0063}$	$0 . 0576_{- 0.0063}^{+ 0.0058}$ $0.0576^{+0.0058}_{-0.0063}$	$0 . 0582_{- 0.0064}^{+ 0.0061}$ $0.0582_{-0.0064}^{+0.0061}$
	`3-knots`	4	$0 . 0592_{- 0.0062}^{+ 0.0056}$ $0.0592^{+0.0056}_{-0.0062}$	0.0584 ± 0.0060	$0 . 0585_{- 0.0061}^{+ 0.0059}$ $0.0585_{-0.0061}^{+0.0059}$
	`2-flex`	2	0.0587 ± 0.0060	0.0577 ± 0.0061	$0 . 0578_{- 0.0059}^{+ 0.0065}$ $0.0578_{-0.0059}^{+0.0065}$
	`3-flex`	4	$0 . 0593_{- 0.0062}^{+ 0.0057}$ $0.0593^{+0.0057}_{-0.0062}$	0.0579 ± 0.0061	$0 . 0582_{- 0.0064}^{+ 0.0060}$ $0.0582_{-0.0064}^{+0.0060}$

Binned	`10-bins`	10	$0 . 0641_{- 0.0054}^{+ 0.0047}$ $0.0641^{+0.0047}_{-0.0054}$	$0 . 0562_{- 0.0053}^{+ 0.0047}$ $0.0562^{+0.0047}_{-0.0053}$	0.0580 ± 0.0059

PCA	`pca-5`	5	0.0590 ± 0.0060	0.0581 ± 0.0060	$0 . 0570_{- 0.0055}^{+ 0.0062}$ $0.0570_{-0.0055}^{+0.0062}$

Average				0.0576 ± 0.0060 ± 0.0006	0.0581 ± 0.0061 ± 0.0005

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