Exploring the cosmic microwave background dipole direction using gamma-ray bursts

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Volume 703 (November 2025)

A&A, 703 (2025) A115

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Table 1.

Best-fit parameters and 1σ errors for a, b, σ_ex, and Ω_m for both GRB correlations in different directions across the sky.

Correlation	Direction	(α, δ)	Hemisphere	a	b	σ_ex	Ω_m	σ
E_p − E_iso	Whole sky		−	$50 . 07_{- 0.39}^{+ 0.37}$ $50.07_{-0.39}^{+0.37}$	$1 . 11_{- 0.13}^{+ 0.12}$ $1.11_{-0.13}^{+0.12}$	$0 . 41_{- 0.04}^{+ 0.05}$ $0.41_{-0.04}^{+0.05}$	$0 . 61_{- 0.32}^{+ 0.33}$ $0.61_{-0.32}^{+0.33}$	−
	Δa_max	(144° , − 54° )	N	$50 . 22_{- 0.18}^{+ 0.18}$ $50.22^{+0.18}_{-0.18}$	1.11	0.41	$0 . 31_{- 0.22}^{+ 0.22}$ $0.31^{+0.22}_{-0.22}$	0.79
			S	$50 . 04_{- 0.18}^{+ 0.18}$ $50.04^{+0.18}_{-0.18}$	1.11	0.41	$0 . 53_{- 0.26}^{+ 0.26}$ $0.53^{+0.26}_{-0.26}$
	CMB	(168° , − 7° )	N	$50 . 09_{- 0.18}^{+ 0.18}$ $50.09^{+0.18}_{-0.18}$	1.11	0.41	$0 . 78_{- 0.24}^{+ 0.24}$ $0.78^{+0.24}_{-0.24}$	−0.03
			S	$50 . 10_{- 0.20}^{+ 0.20}$ $50.10^{+0.20}_{-0.20}$	1.11	0.41	$0 . 39_{- 0.26}^{+ 0.26}$ $0.39^{+0.26}_{-0.26}$

L₀ − E_p − T	Whole sky		−	$49 . 55_{- 0.24}^{+ 0.29}$ $49.55_{-0.24}^{+0.29}$	$0 . 79_{- 0.12}^{+ 0.09}$ $0.79_{-0.12}^{+0.09}$	$0 . 37_{- 0.04}^{+ 0.04}$ $0.37_{-0.04}^{+0.04}$	$0 . 93_{- 0.24}^{+ 0.07}$ $0.93_{-0.24}^{+0.07}$	−
	Δa_max	(270° , − 6° )	N	$49 . 64_{- 0.13}^{+ 0.13}$ $49.64^{+0.13}_{-0.13}$	0.79	0.37	$0 . 70_{- 0.20}^{+ 0.20}$ $0.70^{+0.20}_{-0.20}$	0.42
			S	$49 . 65_{- 0.14}^{+ 0.14}$ $49.65^{+0.14}_{-0.14}$	0.79	0.37	$0 . 84_{- 0.21}^{+ 0.21}$ $0.84^{+0.21}_{-0.21}$
	CMB	(168° , − 7° )	N	$49 . 65_{- 0.13}^{+ 0.13}$ $49.65^{+0.13}_{-0.13}$	0.79	0.37	$0 . 72_{- 0.18}^{+ 0.18}$ $0.72^{+0.18}_{-0.18}$	0.13
			S	$49 . 50_{- 0.14}^{+ 0.14}$ $49.50^{+0.14}_{-0.14}$	0.79	0.37	$0 . 89_{- 0.21}^{+ 0.21}$ $0.89^{+0.21}_{-0.21}$

Notes. Best-fit parameters and 1σ errors are obtained for the following directions: the whole sky, the maximum Δa, and the CMB dipole. For the last two directions, we indicated the equatorial coordinates (α, δ) and the associated significance σ only for the N hemisphere. The parameters b and σ_ex exhibit errors only in the whole-sky fits, when determined for the first time; in the other cases these parameters are fixed to the whole-sky values, as the correlation of the whole sample holds in each hemisphere.

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