Bayesian inference of multi-messenger astrophysical data: Joint and coherent inference of gravitational waves and kilonovae

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Volume 689 (September 2024)

A&A, 689 (2024) A51

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Table 2

EOS constraints obtained from our multi-messenger PEs.

Data	$R_{1.4}^{TOV}$ $R_{1.4}^{{\rm{TOV}}}$	Λ_1,4	$M_{\max}^{TOV}$ $M_{\max }^{{\rm{TOV}}}$	$R_{\max}^{TOV}$ $R_{\max }^{{\rm{TOV}}}$	log₁₀ P(2ρ_sat)	log₁₀ P(4ρ_sat)
	(km)		(M_⊙)	(km)
Prior	${12.95}_{- 1.65}^{+ 3.10}$ $12.95_{ - 1.65}^{ + 3.10}$	$540_{- 310}^{+ 1410}$ $540_{ - 310}^{ + 1410}$	${2.27}_{- 0.26}^{+ 0.52}$ $2.27_{ - 0.26}^{ + 0.52}$	${11.90}_{- 1.54}^{+ 2.80}$ $11.90_{ - 1.54}^{ + 2.80}$	${34.72}_{- 0.29}^{+ 0.35}$ $34.72_{ - 0.29}^{ + 0.35}$	${35.50}_{- 0.18}^{+ 0.27}$ $35.50_{ - 0.18}^{ + 0.27}$
$M_{\max}^{TOV}$ $M_{\max }^{{\rm{TOV}}}$	${13.23}_{- 1.73}^{+ 2.98}$ $13.23_{ - 1.73}^{ + 2.98}$	$620_{- 350}^{+ 1470}$ $620_{ - 350}^{ + 1470}$	${2.32}_{- 0.22}^{+ 0.50}$ $2.32_{ - 0.22}^{ + 0.50}$	${12.15}_{- 1.62}^{+ 2.72}$ $12.15_{ - 1.62}^{ + 2.72}$	${34.76}_{- 0.29}^{+ 0.32}$ $34.76_{ - 0.29}^{ + 0.32}$	${35.54}_{- 0.20}^{+ 0.26}$ $35.54_{ - 0.20}^{ + 0.26}$

$M_{\max}^{TOV} + {NICER}^{ST + PDT}$ $M_{\max }^{{\rm{TOV}}} + {\rm{NICE}}{{\rm{R}}^{{\rm{ST}} + {\rm{PDT}}}}$	${12.08}_{- 0.7}^{+ 0.93}$ $12.08_{ - 0.7}^{ + 0.93}$	$360_{- 110}^{+ 190}$ $360_{ - 110}^{ + 190}$	${2.25}_{- 0.15}^{+ 0.26}$ $2.25_{ - 0.15}^{ + 0.26}$	${11.30}_{- 0.82}^{+ 1.32}$ $11.30_{ - 0.82}^{ + 1.32}$	${34.61}_{- 0.18}^{+ 0.18}$ $34.61_{ - 0.18}^{ + 0.18}$	${35.53}_{- 0.12}^{+ 0.14}$ $35.53_{ - 0.12}^{ + 0.14}$
$M_{\max}^{TOV} + {NICER}^{ST + PDT} + GW$ $M_{\max }^{{\rm{TOV}}} + {\rm{NICE}}{{\rm{R}}^{{\rm{ST}} + {\rm{PDT}}}} + {\rm{GW}}$	${11.86}_{- 0.66}^{+ 0.95}$ $11.86_{ - 0.66}^{ + 0.95}$	$330_{- 100}^{+ 180}$ $330_{ - 100}^{ + 180}$	${2.25}_{- 0.14}^{+ 0.23}$ $2.25_{ - 0.14}^{ + 0.23}$	${11.15}_{- 0.74}^{+ 1.23}$ $11.15_{ - 0.74}^{ + 1.23}$	${34.56}_{- 0.17}^{+ 0.18}$ $34.56_{ - 0.17}^{ + 0.18}$	${35.53}_{- 0.10}^{+ 0.13}$ $35.53_{ - 0.10}^{ + 0.13}$
$M_{\max}^{TOV} + {NICER}^{ST + PDT} + GW + kN$ $M_{\max }^{{\rm{TOV}}} + {\rm{NICE}}{{\rm{R}}^{{\rm{ST}} + {\rm{PDT}}}} + {\rm{GW}} + {\rm{kN}}$	${12.33}_{- 0.81}^{+ 0.84}$ $12.33_{ - 0.81}^{ + 0.84}$	$410_{- 130}^{+ 180}$ $410_{ - 130}^{ + 180}$	${2.27}_{- 0.15}^{+ 0.25}$ $2.27_{ - 0.15}^{ + 0.25}$	${11.48}_{- 0.90}^{+ 1.30}$ $11.48_{ - 0.90}^{ + 1.30}$	${34.65}_{- 0.17}^{+ 0.16}$ $34.65_{ - 0.17}^{ + 0.16}$	${35.54}_{- 0.12}^{+ 0.14}$ $35.54_{ - 0.12}^{ + 0.14}$
$M_{\max}^{TOV} + {NICER}^{ST + PDT} + GW + kN (NRI)$ $M_{\max }^{{\rm{TOV}}} + {\rm{NICE}}{{\rm{R}}^{{\rm{ST}} + {\rm{PDT}}}} + {\rm{GW}} + {\rm{kN}}({\rm{NRI}})$	${12.30}_{- 0.56}^{+ 0.81}$ $12.30_{ - 0.56}^{ + 0.81}$	$400_{- 100}^{+ 180}$ $400_{ - 100}^{ + 180}$	${2.28}_{- 0.16}^{+ 0.25}$ $2.28_{ - 0.16}^{ + 0.25}$	${11.53}_{- 0.90}^{+ 1.15}$ $11.53_{ - 0.90}^{ + 1.15}$	${34.64}_{- 0.12}^{+ 0.16}$ $34.64_{ - 0.12}^{ + 0.16}$	${35.54}_{- 0.12}^{+ 0.14}$ $35.54_{ - 0.12}^{ + 0.14}$

$M_{\max}^{TOV} + {NICER}^{PDT - U}$ $M_{\max }^{{\rm{TOV}}} + {\rm{NICE}}{{\rm{R}}^{{\rm{PDT}} - {\rm{U}}}}$	${13.64}_{- 1.18}^{+ 1.60}$ $13.64_{ - 1.18}^{ + 1.60}$	$740_{- 300}^{+ 670}$ $740_{ - 300}^{ + 670}$	${2.35}_{- 0.24}^{+ 0.40}$ $2.35_{ - 0.24}^{ + 0.40}$	${12.54}_{- 1.45}^{+ 1.77}$ $12.54_{ - 1.45}^{ + 1.77}$	${34.61}_{- 0.18}^{+ 0.18}$ $34.61_{ - 0.18}^{ + 0.18}$	${35.53}_{- 0.12}^{+ 0.14}$ $35.53_{ - 0.12}^{ + 0.14}$
$M_{\max}^{TOV} + {NICER}^{PDT - U} + GW$ $M_{\max }^{{\rm{TOV}}} + {\rm{NICE}}{{\rm{R}}^{{\rm{PDT}} - {\rm{U}}}} + {\rm{GW}}$	${12.86}_{- 0.83}^{+ 0.90}$ $12.86_{ - 0.83}^{ + 0.90}$	$540_{- 190}^{+ 230}$ $540_{ - 190}^{ + 230}$	${2.30}_{- 0.17}^{+ 0.31}$ $2.30_{ - 0.17}^{ + 0.31}$	${12.08}_{- 1.24}^{+ 1.54}$ $12.08_{ - 1.24}^{ + 1.54}$	${34.74}_{- 0.15}^{+ 0.20}$ $34.74_{ - 0.15}^{ + 0.20}$	${35.53}_{- 0.21}^{+ 0.18}$ $35.53_{ - 0.21}^{ + 0.18}$
$M_{\max}^{TOV} + {NICER}^{PDT - U} + GW + kN$ $M_{\max }^{{\rm{TOV}}} + {\rm{NICE}}{{\rm{R}}^{{\rm{PDT}} - {\rm{U}}}} + {\rm{GW}} + {\rm{kN}}$	${13.30}_{- 0.81}^{+ 0.87}$ $13.30_{ - 0.81}^{ + 0.87}$	$640_{- 190}^{+ 280}$ $640_{ - 190}^{ + 280}$	${2.30}_{- 0.20}^{+ 0.30}$ $2.30_{ - 0.20}^{ + 0.30}$	${12.33}_{- 1.28}^{+ 1.55}$ $12.33_{ - 1.28}^{ + 1.55}$	${34.77}_{- 0.11}^{+ 0.20}$ $34.77_{ - 0.11}^{ + 0.20}$	${35.54}_{- 0.22}^{+ 0.17}$ $35.54_{ - 0.22}^{ + 0.17}$
$M_{\max}^{TOV} + {NICER}^{PDT - U} + GW + kN (NRI)$ $M_{\max }^{{\rm{TOV}}} + {\rm{NICE}}{{\rm{R}}^{{\rm{PDT}} - {\rm{U}}}} + {\rm{GW}} + {\rm{kN}}({\rm{NRI}})$	${13.20}_{- 0.90}^{+ 0.91}$ $13.20_{ - 0.90}^{ + 0.91}$	$620_{- 200}^{+ 270}$ $620_{ - 200}^{ + 270}$	${2.32}_{- 0.19}^{+ 0.30}$ $2.32_{ - 0.19}^{ + 0.30}$	${12.21}_{- 1.24}^{+ 1.61}$ $12.21_{ - 1.24}^{ + 1.61}$	${34.76}_{- 0.12}^{+ 0.21}$ $34.76_{ - 0.12}^{ + 0.21}$	${35.54}_{- 0.22}^{+ 0.17}$ $35.54_{ - 0.22}^{ + 0.17}$

Notes. Starting from our agnostic prior set of 10 million EOS, we progressively added the information coming from PSR J0952+0607 ( $M_{\max}^{TOV} > 2.09 M_{⊙}$ $M_{\max }^{{\rm{TOV}}} > 2.09{M_ \odot }$ ), PSR J0030+0451 and PSR J0740+6620 (NICER), and GW170817 (GW) and AT2017gfo (kN). We report the median and 90% credible intervals of the relevant EOS-dependent properties.

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