Constraining nuclear EOSs with massive neutron stars in the framework of RMF models

Wenjie XIE; Chengjun XIA

doi:10.11889/j.0253-3219.2025.hjs.48.250167

NUCLEAR TECHNIQUES, Volume. 48, Issue 5, 050007(2025)

Constraining nuclear EOSs with massive neutron stars in the framework of RMF models

Wenjie XIE^1,2,3 and Chengjun XIA^4、*

Author Affiliations

¹Department of Physics, Yuncheng University, Yuncheng 044000, China

²Shanxi Province Intelligent Optoelectronic Sensing Application Technology, Innovation Center, Yuncheng University, Yuncheng 044000, China

³Guangxi Key Laboratory of Nuclear Physics and Nuclear Technology, Guangxi Normal University, Guilin 541004, China

⁴Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China

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Fig. 1. The effective density-dependent coupling constants in the isoscalar-scalar ( $α_{S} = g_{σ}^{2} / m_{σ}^{2}$ ), isoscalar-vector ( $α_{V} = g_{ω}^{2} / m_{ω}^{2}$ ), and isovector-vector ( $α_{T V} = g_{ρ}^{2} / m_{ρ}^{2}$ ) channels in symmetric nuclear matter predicted by various relativistic density functionals

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Fig. 2. The potential energy per baryon in symmetric nuclear matter predicted by various relativistic density functionals

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Fig. 3. Posterior probability distribution functions of the squared speed of sound, central energy densities for neutron stars with M=1.4 M_⊙ and 2.0 M_⊙

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Fig. 4. The nucleon effective masses in neutron star matter within their 90% credible intervals

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Fig. 5. Posterior probability distribution functions of the tidal deformability for neutron stars with M=1.4 M_⊙ (a) and 2.0 M_⊙ (b)

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Fig. 6. Posterior probability distribution functions of the energy per nucleon in symmetry nuclear matter E₀, the nuclear symmetry energy E_sym, pressure p and the speed of sound v_s as functions of the reduced density n_V/n₀ at 68% credible level using n_crit=2n₀ (red region) and n_crit=3n₀ (blue region) (color online)

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Fig. 7. Posterior probability distribution functions of the maximum masses of neutron stars

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Table 1. The adopted zeroth, first, and second order derivatives for the coupling constants in Eqs.(17)~(19) at subsaturation density n_on≤n_V≤n₀, which are fixed by the relativistic density functional DD-ME2^[32]
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Table 1. The adopted zeroth, first, and second order derivatives for the coupling constants in Eqs.(17)~(19) at subsaturation density n_on≤n_V≤n₀, which are fixed by the relativistic density functional DD-ME2^[32]
Coupling
Zeroth order
/ 10^-4 MeV^-2
First order
/ 10^-10 MeV^-5
Second order
/ 10^-16 MeV^-8
α_S (n_on) 4.068 95 -1.316 29 1.949 90
α_V (n_on) 3.077 85 -1.018 83 1.408 85
α_TV (n_on) 0.342 884 -0.331 735 0.320 949

Table 2. Dataset for neutron stars' radii adopted in the present work

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Table 2. Dataset for neutron stars' radii adopted in the present work

Mass / M_⊙	Radius R / km	Source and Ref.
1.4	11.9 $_{- 1.4}^{+ 1.4}$ (90% CFL)	GW 170817^[25]
1.4	10.8 $_{- 1.6}^{+ 2.1}$ (90% CFL)	GW 170817^[43]
1.4	11.7 $_{- 1.1}^{+ 1.1}$ (90% CFL)	QLMXBs^[44]
1.34 $_{- 0.16}^{+ 0.15}$	12.71 $_{- 1.29}^{+ 1.14}$ (68% CFL)	PSR J0030+0451^[14]
1.44 $_{- 0.16}^{+ 0.15}$	13.0 $_{- 1.0}^{+ 1.2}$ (68% CFL)	PSR J0030+0451^[45]
2.08 $_{- 0.07}^{+ 0.07}$	13.7 $_{- 1.5}^{+ 2.6}$ (68% CFL)	PSR J0740+6620^[17]
0.77 $_{- 0.17}^{+ 0.20}$	10.4 $_{- 0.78}^{+ 0.86}$ (68% CFL)	HESS J1731-347^[46]

Table 3. Most probable values and their corresponding credible intervals (68% and 90%) for the derived central energy densities, tidal deformability corresponding to the neutron stars with masses of 1.4 and 2.0 solar masses, and the squared speed of sound as well as the maximum mass

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Table 3. Most probable values and their corresponding credible intervals (68% and 90%) for the derived central energy densities, tidal deformability corresponding to the neutron stars with masses of 1.4 and 2.0 solar masses, and the squared speed of sound as well as the maximum mass

Quantities	n₁=2n₀		n₁=3n₀
Quantities	68%	90%	68%	90%
$ε_{1.4}^{c}$ / MeV∙fm^-3	344.6 $_{- 13.8}^{+ 41.4}$	344.6 $_{- 13.8}^{+ 110.3}$	510.1 $_{- 96.5}^{+ 41.3}$	510.1 $_{- 179.3}^{+ 55.1}$
$ε_{2.0}^{c}$ / MeV∙fm^-3	399.8 $_{- 27.6}^{+ 220.5}$	399.8 $_{- 27.6}^{+ 454.9}$	758.2 $_{- 82.7}^{+ 317.1}$	758.2 $_{- 220.6}^{+ 372.2}$
$υ_{S}^{2}$	0.54 $_{- 0.26}^{+ 0.04}$	0.54 $_{- 0.31}^{+ 0.23}$	0.51 $_{- 0.3}^{+ 0.05}$	0.51 $_{- 0.33}^{+ 0.27}$
$Λ$ _1.4	600 $_{- 85}^{+ 80}$	600 $_{- 175}^{+ 125}$	425 $_{- 125}^{+ 190}$	425 $_{- 140}^{+ 350}$
$Λ$ _2.0	75 $_{- 33}^{+ 6}$	75 $_{- 54}^{+ 12}$	21 $_{- 9}^{+ 12}$	21 $_{- 9}^{+ 36}$
Mass / M_⊙	2.0 $_{- 0.0}^{+ 0.4}$	2.0 $_{- 0.0}^{+ 0.65}$	2.0 $_{- 0.0}^{+ 0.15}$	2.0 $_{- 0.0}^{+ 0.3}$

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Wenjie XIE, Chengjun XIA. Constraining nuclear EOSs with massive neutron stars in the framework of RMF models[J]. NUCLEAR TECHNIQUES, 2025, 48(5): 050007

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Paper Information

Category: Special Topics on Applications of Machine Learning in Nuclear Physics and Nuclear Data

Received: Apr. 12, 2025

Accepted: --

Published Online: Jun. 26, 2025

The Author Email: Chengjun XIA (夏铖君)

DOI:10.11889/j.0253-3219.2025.hjs.48.250167

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Instrumentation, Measurement and Metrology

Table 1. The adopted zeroth, first, and second order derivatives for the coupling constants in Eqs.(17)~(19) at subsaturation density n_on≤n_V≤n₀, which are fixed by the relativistic density functional DD-ME2^[32]

Table 1. The adopted zeroth, first, and second order derivatives for the coupling constants in Eqs.(17)~(19) at subsaturation density n_on≤n_V≤n₀, which are fixed by the relativistic density functional DD-ME2^[32]

Table 2. Dataset for neutron stars' radii adopted in the present work

Table 2. Dataset for neutron stars' radii adopted in the present work

Table 3. Most probable values and their corresponding credible intervals (68% and 90%) for the derived central energy densities, tidal deformability corresponding to the neutron stars with masses of 1.4 and 2.0 solar masses, and the squared speed of sound as well as the maximum mass

Table 3. Most probable values and their corresponding credible intervals (68% and 90%) for the derived central energy densities, tidal deformability corresponding to the neutron stars with masses of 1.4 and 2.0 solar masses, and the squared speed of sound as well as the maximum mass

Table 1. The adopted zeroth, first, and second order derivatives for the coupling constants in Eqs.(17)~(19) at subsaturation density non≤nV≤n0, which are fixed by the relativistic density functional DD-ME2[32]

Table 1. The adopted zeroth, first, and second order derivatives for the coupling constants in Eqs.(17)~(19) at subsaturation density non≤nV≤n0, which are fixed by the relativistic density functional DD-ME2[32]

Table 2. Dataset for neutron stars' radii adopted in the present work

Table 2. Dataset for neutron stars' radii adopted in the present work

Table 3. Most probable values and their corresponding credible intervals (68% and 90%) for the derived central energy densities, tidal deformability corresponding to the neutron stars with masses of 1.4 and 2.0 solar masses, and the squared speed of sound as well as the maximum mass

Table 3. Most probable values and their corresponding credible intervals (68% and 90%) for the derived central energy densities, tidal deformability corresponding to the neutron stars with masses of 1.4 and 2.0 solar masses, and the squared speed of sound as well as the maximum mass

Table 1. The adopted zeroth, first, and second order derivatives for the coupling constants in Eqs.(17)~(19) at subsaturation density n_on≤n_V≤n₀, which are fixed by the relativistic density functional DD-ME2^[32]

Table 1. The adopted zeroth, first, and second order derivatives for the coupling constants in Eqs.(17)~(19) at subsaturation density n_on≤n_V≤n₀, which are fixed by the relativistic density functional DD-ME2^[32]