Short gamma-ray burst progenitors have short delay times

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Volume 710 (June 2026)

A&A, 710 (2026) A267

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Table 2.

Constraints on population parameters.

Empirical luminosity function			Quasi-universal structured jet

Parameter	Power-law DTD	Log-normal DTD	Parameter	Power-law DTD	Log-normal DTD	S23
α_BPL	${0.90}_{- 0.36}^{+ 0.38}$ $Mathematical equation: $ {0.90}_{-0.36}^{+0.38} $$	${0.81}_{- 0.32}^{+ 0.38}$ $Mathematical equation: $ {0.81}_{-0.32}^{+0.38} $$	α_L	${4.93}_{- 1.29}^{+ 0.96}$ $Mathematical equation: $ {4.93}_{-1.29}^{+0.96} $$	${5.01}_{- 1.20}^{+ 0.90}$ $Mathematical equation: $ {5.01}_{-1.20}^{+0.90} $$	$4 . 9_{- 1.7}^{+ 1.0}$ $Mathematical equation: $ 4.9^{+1.0}_{-1.7} $$
β_BPL	${2.18}_{- 0.99}^{+ 2.14}$ $Mathematical equation: $ {2.18}_{-0.99}^{+2.14} $$	${2.40}_{- 1.06}^{+ 2.24}$ $Mathematical equation: $ {2.40}_{-1.06}^{+2.24} $$	β_L	${1.95}_{- 4.49}^{+ 3.64}$ $Mathematical equation: $ {1.95}_{-4.49}^{+3.64} $$	${1.57}_{- 4.14}^{+ 4.00}$ $Mathematical equation: $ {1.57}_{-4.14}^{+4.00} $$	$1 . 9_{- 4.4}^{+ 3.7}$ $Mathematical equation: $ 1.9^{+3.7}_{-4.4} $$
γ_BPL	${- 2.37}_{- 2.32}^{+ 2.22}$ $Mathematical equation: $ {-2.37}_{-2.32}^{+2.22} $$	${- 1.90}_{- 2.64}^{+ 2.97}$ $Mathematical equation: $ {-1.90}_{-2.64}^{+2.97} $$	A	${2.78}_{- 0.40}^{+ 0.67}$ $Mathematical equation: $ {2.78}_{-0.40}^{+0.67} $$	${2.80}_{- 0.40}^{+ 0.65}$ $Mathematical equation: $ {2.80}_{-0.40}^{+0.65} $$	$2 . 9_{- 0.4}^{+ 0.7}$ $Mathematical equation: $ 2.9^{+0.7}_{-0.4} $$
log₁₀(L_*/erg s⁻¹)	${53.08}_{- 0.86}^{+ 2.26}$ $Mathematical equation: $ {53.08}_{-0.86}^{+2.26} $$	${52.99}_{- 1.03}^{+ 1.48}$ $Mathematical equation: $ {52.99}_{-1.03}^{+1.48} $$	log₁₀(L_c^★/erg s⁻¹)	${51.74}_{- 0.23}^{+ 0.46}$ $Mathematical equation: $ {51.74}_{-0.23}^{+0.46} $$	${51.75}_{- 0.25}^{+ 0.43}$ $Mathematical equation: $ {51.75}_{-0.25}^{+0.43} $$	$51 . 70_{- 0.10}^{+ 0.38}$ $Mathematical equation: $ 51.70^{+0.38}_{-0.10} $$
log₁₀(L_**/erg s⁻¹)	${49.07}_{- 2.15}^{+ 0.86}$ $Mathematical equation: $ {49.07}_{-2.15}^{+0.86} $$	${47.67}_{- 2.16}^{+ 1.98}$ $Mathematical equation: $ {47.67}_{-2.16}^{+1.98} $$	log₁₀(E_p, c^★/keV)	${3.50}_{- 0.28}^{+ 0.26}$ $Mathematical equation: $ {3.50}_{-0.28}^{+0.26} $$	${3.52}_{- 0.27}^{+ 0.27}$ $Mathematical equation: $ {3.52}_{-0.27}^{+0.27} $$	$3 . 65_{- 0.31}^{+ 0.38}$ $Mathematical equation: $ 3.65^{+0.38}_{-0.31} $$
log₁₀(L₀/erg s⁻¹)	${45.60}_{- 1.40}^{+ 1.26}$ $Mathematical equation: $ {45.60}_{-1.40}^{+1.26} $$	${47.67}_{- 2.16}^{+ 1.98}$ $Mathematical equation: $ {47.67}_{-2.16}^{+1.98} $$	α_{E_p}	${1.37}_{- 0.75}^{+ 0.85}$ $Mathematical equation: $ {1.37}_{-0.75}^{+0.85} $$	${1.44}_{- 0.79}^{+ 0.83}$ $Mathematical equation: $ {1.44}_{-0.79}^{+0.83} $$	$1 . 5_{- 0.9}^{+ 1.0}$ $Mathematical equation: $ 1.5^{+1.0}_{-0.9} $$
log₁₀(E_p^★/keV)	${3.59}_{- 0.23}^{+ 0.38}$ $Mathematical equation: $ {3.59}_{-0.23}^{+0.38} $$	${3.58}_{- 0.23}^{+ 0.26}$ $Mathematical equation: $ {3.58}_{-0.23}^{+0.26} $$	β_{E_p}	${0.74}_{- 3.39}^{+ 4.53}$ $Mathematical equation: $ {0.74}_{-3.39}^{+4.53} $$	${0.71}_{- 3.37}^{+ 4.70}$ $Mathematical equation: $ {0.71}_{-3.37}^{+4.70} $$	$1 . 5_{- 4.1}^{+ 4.0}$ $Mathematical equation: $ 1.5^{+4.0}_{-4.1} $$
			θ_c/deg	${2.87}_{- 1.59}^{+ 2.23}$ $Mathematical equation: $ {2.87}_{-1.59}^{+2.23} $$	${3.01}_{- 1.39}^{+ 2.22}$ $Mathematical equation: $ {3.01}_{-1.39}^{+2.22} $$	$3 . 0_{- 2.1}^{+ 2.4}$ $Mathematical equation: $ 3.0^{+2.4}_{-2.1} $$
			θ_w/deg	${61.39}_{- 38.05}^{+ 27.35}$ $Mathematical equation: $ {61.39}_{-38.05}^{+27.35} $$	${62.82}_{- 40.53}^{+ 23.90}$ $Mathematical equation: $ {62.82}_{-40.53}^{+23.90} $$	$64 . 5_{- 42.5}^{+ 23.2}$ $Mathematical equation: $ 64.5^{+23.2}_{-42.5} $$
log₁₀(σ_c)	${- 0.07}_{- 0.11}^{+ 0.09}$ $Mathematical equation: $ {-0.07}_{-0.11}^{+0.09} $$	${- 0.07}_{- 0.11}^{+ 0.09}$ $Mathematical equation: $ {-0.07}_{-0.11}^{+0.09} $$	log₁₀(σ_c)	${- 0.06}_{- 0.08}^{+ 0.08}$ $Mathematical equation: $ {-0.06}_{-0.08}^{+0.08} $$	${- 0.06}_{- 0.09}^{+ 0.08}$ $Mathematical equation: $ {-0.06}_{-0.09}^{+0.08} $$	$- 0 . 40_{- 0.12}^{+ 0.10}$ $Mathematical equation: $ -0.40^{+0.10}_{-0.12} $$
y	${0.21}_{- 0.18}^{+ 0.13}$ $Mathematical equation: $ {0.21}_{-0.18}^{+0.13} $$	${0.21}_{- 0.16}^{+ 0.15}$ $Mathematical equation: $ {0.21}_{-0.16}^{+0.15} $$	y	${0.06}_{- 0.29}^{+ 0.32}$ $Mathematical equation: $ {0.06}_{-0.29}^{+0.32} $$	${0.04}_{- 0.30}^{+ 0.30}$ $Mathematical equation: $ {0.04}_{-0.30}^{+0.30} $$	$0 . 0_{- 0.3}^{+ 0.3}$ $Mathematical equation: $ 0.0^{+0.3}_{-0.3} $$
τ_d^min/Gyr	${0.03}_{- 0.02}^{+ 0.28}$ $Mathematical equation: $ {0.03}_{-0.02}^{+0.28} $$		τ_d^min/Gyr	${0.04}_{- 0.03}^{+ 0.33}$ $Mathematical equation: $ {0.04}_{-0.03}^{+0.33} $$
α_τ	${3.20}_{- 1.55}^{+ 1.60}$ $Mathematical equation: $ {3.20}_{-1.55}^{+1.60} $$		α_τ	${3.33}_{- 1.59}^{+ 1.48}$ $Mathematical equation: $ {3.33}_{-1.59}^{+1.48} $$
μ_τ/Gyr		${0.08}_{- 0.07}^{+ 0.55}$ $Mathematical equation: $ {0.08}_{-0.07}^{+0.55} $$	μ_τ/Gyr		${0.09}_{- 0.07}^{+ 0.57}$ $Mathematical equation: $ {0.09}_{-0.07}^{+0.57} $$
σ_τ		${0.11}_{- 0.10}^{+ 1.71}$ $Mathematical equation: $ {0.11}_{-0.10}^{+1.71} $$	σ_τ		${0.14}_{- 0.12}^{+ 1.86}$ $Mathematical equation: $ {0.14}_{-0.12}^{+1.86} $$
log₁₀(R₀/Gpc⁻³yr⁻¹)	${1.92}_{- 0.92}^{+ 1.50}$ $Mathematical equation: $ {1.92}_{-0.92}^{+1.50} $$	${2.60}_{- 1.49}^{+ 1.23}$ $Mathematical equation: $ {2.60}_{-1.49}^{+1.23} $$	log₁₀(R₀/Gpc⁻³yr⁻¹)	${2.57}_{- 0.63}^{+ 0.67}$ $Mathematical equation: $ {2.57}_{-0.63}^{+0.67} $$	${2.25}_{- 0.50}^{+ 0.53}$ $Mathematical equation: $ {2.25}_{-0.50}^{+0.53} $$	$2 . 26_{- 0.71}^{+ 0.67}$ $Mathematical equation: $ 2.26^{+0.67}_{-0.71} $$

Notes. The S23 results refer to their ‘flux-limited sample’ analysis. All constraints are represented by their medians and 90% posterior credible intervals.

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