# Correlation between the curvature and some properties of the neutron star

S. K. Biswal  H. C. Das,11footnotetext: Corresponding author. Ankit Kumar
Bharat Kumar
S. K. Patra

###### Abstract

We calculate neutron star (NS) properties like mass $M$, radius $R$,
compactness $C$ and surface curvature (SC) using relativistic mean-field (RMF)
and Skyrme-Hartree-Fock (SHF) models. Predictive competence of the various RMF
and SHF parameter sets are discussed and compared with the NICER and pulsar
observational data. We try to correlate between some properties of the NS like
$C$, $R$ and SC. To calculate the correlations coefficient, we employ the
Pearson formula. We substantiate a correlation between the SC and $C$ for
canonical NS, and it shows a strong correlation with a coefficient of 0.992.
Similarly, we find another correlation between the radius and SC with a
coefficient of 0.982 for the canonical star. The three-dimensional
correlations are studied for the $C$, $R$ and SC with varying the masses of
the NS. To visualise the correlation between these quantities as mentioned
above, both for maximum and canonical mass, a $7\times 7$ heat map is
constructed, which gives the correlations between each pair of quantities. We
find that there is a strong correlation between these pairs SC1.4–$R_{1.4}$,
SC1.4–$C_{1.4}$. The correlations become weaker for the maximum mass NS. To
find the correlation between the same quantities but for different masses of
the NS, we calculated the correlations coefficients for 1.5-1.8 $M_{\odot}$
NS. There are also we get strong correlations between $C$, $R$ and SC.

##  1 Introduction

Understanding the nature of the fundamental interaction at supra-saturation
density is currently considered as a prominent topic in fundamental physics.
In the laboratory, we can create the dense matter up to few times of the
saturation density [1, 2], which is not enough to understand the nuclear
interaction at high degree of density and isospin asymmetry. This experimental
inadequacy forces us to use neutron star (NS) as sole ingredient to study the
high dense nature of the nuclear interaction [3]. NS is one of the most
familiar members of the compact object family of the visible universe, having
central density 5–6 times the density of the matter at nuclear centre [4, 3].
Most of the terrestrial experiments and analysis of the finite nuclear data
give the information about the nature of the equation of state (EOS) around
saturation density, while the higher density region still remains unexplored.
Various theoretical models predict diverge behaviour for the EOSs in that
region, leading to completely different values for the global properties of
the NS. The global properties of the NS like maximum mass, radius, moment of
inertia are used as an effective tool to put the strong constraints on the
nature of the EOS [3].

In recent years, the tidal deformability from the first binary NS merger
event, GW170817 [5, 6] can also spotlight the nature of matter enclosed inside
the NS. The composition of the NS is not clear till now. In the conventional
models, the NS is populated by the neutron and admixture of the proton and
electron are inside the NS to maintain the $\beta$-equilibrium and charge
neutrality conditions. The extreme conditions inside the NS favor various
exotic phenomena to happen like hyperon production [7, 8, 9], kaon
condensation [8, 10, 11, 12, 13, 14], deconfinement of quark [15, 16, 17, 18,
19], and presence of DM particle [20, 21, 22, 23, 24, 25, 26, 27]. Recently,
the Neutron Star Interior Composition Explorer (NICER) data [28, 29, 30, 31,
32, 33] can put a strong constraints on the mass and radius of a NS. This
simultaneous measurement of the mass and radius of a NS can constraint the
nuclear EOS. The correlation between the tidal deformability and the radius of
the canonical star is now a settled issue [34, 35, 36, 37, 38, 39, 40, 41, 42,
2, 43]. But the value of the correlation coefficient is still a debatable
issue, various theoretical formalism give different ranges of the correlation
coefficients. Similarly, it is noticed that a correlation exists between the
skin thickness of the heavy neutron-rich nuclei ( 208 Pb) and NS properties
[44, 45]. It is the consequence of the fact that the slope of the symmetry
energy determine the pressure of the neutron-rich skin and radius of the NS.
Li et al. have showed that an unique relation between $K_{sym}$ and slope $L$
can constrain the high density behaviour of the $E_{sym}$ [46]. Along the same
path Alam et al. have shown that there exist a strong correlation between the
NS radii and slope of the incompressibility of the nuclear matter (NM) [47].
Using Brueckner-Hartree-Fock formalism, Wei et al. found a strong correlation
between NS radius, tidal deformability and pressure of the beta stable matter
[48]. Therefore, it is a common practice to look for a correlation between the
NM and NS properties. In this work, we try to find a new type of correlation
between the NS properties, i.e correlation between the surface curvature (SC)
and other bulk properties like $R$ and $C$.

According to the general theory of relativity, the energy and momentum of
whatsoever matter or radiation present in the universe is strongly correlated
with the curvature of space-time. The strength of the curvature depends on the
distortion originated by a massive object in space-time, which mechanically is
similar to the functioning of a trampoline. To unfold this unified theory of
gravitation in terms of simple geometric algebra, certain mathematical
quantities like compactness ($C\equiv M/R$), Riemann tensor, Ricci scalar,
Kretschmann scalar have been defined. The more detailed interpretation and
derivation of these mathematical quantities which holds a lot of information
about the curvature can be found in the Ref. [49]. Among these quantities, the
quantities $\cal{K}$ and $\cal{W}$ are more prominent to measure the space-
time curvature both inside and outside the star. Our previous analysis have
calculated all these defined curvatures with and without dark matter (DM)
inside the NS. We found that DM has very significant effects on the curvatures
and compactness of the NS. Hence, in this present work, we want to explore
more on this curvature and correlate with some NS properties because the
correlations between curvatures and some bulk properties of the NS gives a
comprehensive picture of their nature.

This paper is organised as follow: in Sec. 2, we discuss the theoretical
formalism of the relativistic mean-field formalism used to calculate the bulk
properties of the NS. The last subsection of the Sec. 2 is dedicated to
discuss the theoretical formalism various curvature of the NS. In Sec. 3, we
discuss our numerical results. Finally, Sec. 4 is devoted to a concluding
remarks of our results and discussion.

##  2 Framework

This section outlines some quantities to calculate the curvature both inside
and outside of the NS for different EOSs. To study the NS properties, we take
relativistic mean-field (RMF), Skyrme-Hartree-Fock (SHF) and density-dependent
RMF (DDRMF) EOSs. For the last few decades, the assumed models provided a
better platform to predict the finite and infinite NM properties. Unlike the
non-relativistic model, the RMF model obeys the casual limit up to very high-
density [50]. The casual nature of the RMF model provides a natural way to go
from finite nuclei to NS, which has a very high density. Moreover, the
considered SHF models do not become acausal for masses below $2M_{\odot}$.

###  2.1 Mathematical form for different curvature

In this Sub-Sec., we adopt the curvature quantities from the Refs. [49]. The
quantities are Ricci scalar, full contraction of Ricci tensor, Kretschmann
scalar (full contraction of the Riemann tensor) and the full contraction of
the Weyl tensor to measure the curvature of the space-time.

The Ricci scalar

${\cal R}(r)=8\pi\bigg{[}{\cal{E}}_{NS}(r)-3P_{NS}(r)\bigg{]},$ (2.1)

the full contraction of the Ricci tensor

${\cal J}(r)\equiv\sqrt{{\cal R}_{\mu\nu}{\cal
R}^{\mu\nu}}=8\pi\left[{\cal{E}}_{NS}^{2}(r)+3P_{NS}^{2}(r)\right]^{1/2},$
(2.2)

the Kretschmann scalar

$\displaystyle{\cal{K}}(r)$ $\displaystyle\equiv$
$\displaystyle\sqrt{{\cal{R}}^{\mu\nu\rho\sigma}{\cal{R}}_{\mu\nu\rho\sigma}}$
(2.3) $\displaystyle=$ $\displaystyle
8\pi\bigg{[}\left\\{3{\cal{E}}_{NS}^{2}(r)+3P_{NS}^{2}(r)+2P_{NS}(r){\cal{E}}_{NS}(r)\right\\}-\frac{128{\cal{E}}_{NS}(r)m(r)}{r^{3}}+\frac{48m^{2}(r)}{r^{6}}\bigg{]}^{1/2},$

and the full contraction of the Weyl tensor

${\cal W}(r)\equiv\sqrt{{\cal C}^{\mu\nu\rho\sigma}{\cal
C}_{\mu\nu\rho\sigma}}=\bigg{[}\frac{4}{3}\left(\frac{6m(r)}{r^{3}}-8\pi{\cal{E}}_{NS}(r)\right)^{2}\bigg{]}^{1/2}.$
(2.4)

At the surface $m\rightarrow M$ due to $r\rightarrow R$. The Ricci tensor and
Ricci scalar vanish outside the star because they depend on the
${\cal{E}}_{NS}(r)$, $P_{NS}(r)$, which are zero outside the star. But, there
is a non-vanishing component of the Riemann tensor which does not vanish;
$\tensor{{\cal R}}{{}^{1}_{010}}=-\frac{2M}{R^{3}}=-\xi$, even in the outside
of the star [49, 51]. So the Riemann tensor is the more relevant quantity to
measure the curvature of the stars than others. Kretschmann scalar is the
square root of the full contraction of the Riemann tensor. The vacuum value
for both $\cal{K}$ and $\cal{W}$ is $\frac{4\sqrt{3}M}{R^{3}}$ , one can
easily see from Eqs. (2.3) and (2.4). Therefore, one can take $\cal K$ and
$\cal W$ as two reasonable measures for the curvature within the star. The SC
is defined as the ratio of curvature at the surface of the NS ${\cal{K}}(R)$
to the curvature of the Sun ${\cal{K}}_{\odot}$, SC
$={\cal{K}}(R)/{\cal{K}}_{\odot}$ . This ratio
${\cal{K}}(R)/{\cal{K}}_{\odot}\approx 10^{14}$ i.e the NS curvature is
$10^{14}$ times more than the Sun. Hence, we calculate the correlations
between SC and some bulk properties such as $M$, $R$ and $C$ in the following
section.

##  3 Results and Discussions

###  3.1 Equation of state of the NS

The structure of an NS is divided into the four regions outer crust, inner
crust, outer core and inner core. The outer crust consists of nuclei
distributed in a solid body-centred-cubic (bcc) lattice filled by a free
electron gas. As we go from outer crust to inner crust, the density increases
and eventually the nuclei in the crust become so neutron-rich that neutrons
start to drip from them. In this situation, the inner crust contains the free
electron and neutron gases and formed different types of pasta structure. With
the help of nuclear models, the neutron drip density determined the boundary
between the outer and inner crust. But, the transition density from the crust
to the core is much more uncertain and strongly model-dependent. When the
average density reaches a value about half of the NM saturation density, the
lattice structure escapes due to energetic reasons and the system changes to a
liquid phase.

Figure 1: (color online) Some selected EOSs from RMF , SHF and DD-RMF sets are
shown to know its behaviour mainly at the core part.

In Fig. 1, we plot some selected EOSs from RMF and SHF as representative case.
The lowest density part of the EOS represents the outer crust of the NS. The
inner crust ranges from a density $\sim 3\times 10^{-4}$ to $\sim 8\times
10^{-2}$ fm-3. The core part starts from a density $\sim 2\times 10^{-2}$ fm-3
and it extends up to the centre of the NS, which is 5–6 times the density of
the NM. At the lower density part all the EOSs shows almost same in nature but
at the higher density part, all shows different behaviour. This is due to that
we take same crust EOS ( both for outer and inner crust ) which is BCPM EOSs
[52] for all assumed parameter sets. In the present context, we take 30 well-
known parameter sets of the RMF models HS [53], LA [54], H1 [55], LZ [56], NL3
[57], NL3* [58], NL-SH [59], NL1 [60], GM1 [9], GL85 [8], GL97 [61], NL3-II
[57], NLD [54], NL-RA1 [62], TM1 [63], TM2 [63], PK1 [64], FSU [65], FSU2
[66], IUFSU [67], IUFSU* [68], SINPA [69], SINPB [69], G1 [70], G2 [70], G3
[71], IOPB-I [72], FSUGarnet [73], FSU2R [74], and FSU2H [74], 15 SHF models
such as BSk20, BSk21 [75], BSk22, BSk23, BSk24, BSk25 [76], KDE0v1 [77], SkI2,
SkI3, SkI5 [78], SkI6 [79], SLY2 [80], SLY4 [81], SL230a [82], Rs [83] and 6
DDRMF sets DD2 [84], DD2Y [85], DDME1 [86], DDME2 [87], DDME2Y [85], DDLZ1
[48] to study various properties of the NS and investigate the existing
correlation between various quantities. Moreover, one can take unified EOSs as
given in Refs. [85]. The main idea to take a large sets of the parameter sets
is to cover the wide range of the NM parameter value and establish a
correlation with more accuracy.

###  3.2 Mass-radius of the NS

In Fig. 2, we show the mass-radius relation for RMF EOSs. We also put the
masses of pulsar like PSR J1614-2230 [88], PSR J0348+0432 [89] and PSR
J0740+6620 [90]. Recently, the secondary components of the GW190814 events
left us to speculate whether it is the lowest massive black hole (BH) or a
super heavy NS. The observed mass was 2.50–2.67 $M_{\odot}$. Many authors have
claimed that it was a binary BH merger [91, 92], heaviest NS [93, 94], super-
fast pulsar [95] etc. The NICER results are also put to constraint both mass-
radius from the x-ray study of the millisecond pulsars PSR J0030+0451 [29,
32]. The constraint on mass-radius are found to be
$M$=$1.44_{-0.14}^{+0.15}M_{\odot}$ ($M$=$1.34_{-0.16}^{+0.15}M_{\odot}$) and
$R$=$13.02_{-1.06}^{+1.24}$ km ($R$=$12.71_{-1.19}^{+1.14}$ km ) by Miller et
al. [29] (Riley et al. [32]) which are indicated in two boxes.

Figure 2: (colour online) Left: Mass and radius of the NS for 30 parameter
sets are depicted. Right: Mass and radius of the NS for 15 Skyrme and 6 DDRMF
parameter sets. The recent observational constraints from GW190814 along with
different pulsars J0740+6620, J0348+0432 and J1614-2230 are shown with
horizontal bars. The mass-radius relation observed by the NICER from two
different analysis of pulsar PSR J0030+0451 is also shown [29, 32] .

Few parameter sets such as GL97, GL85, TM2, FSU2, IFSU*, SINPA, SINPB, G1, G2,
G3, IOPB-I, FSUGarnet and FSU2R lie in the range of the observed maximum
masses. Most of the RMF parameter sets satisfy the mass-radius constraint from
the NICER observation. We can see from Fig. 2 that the NICER data can not
discard many EOSs based on the mass-radius measurement. The NICER data is
related to the radius measurement of the NS of mass around 1.4$M_{\odot}$,
which has not very high central density. The central density of the canonical
NS lies 2-3$\rho_{0}$. As all the EOSs are fitted to the saturation
properties, they show a convergent behaviour up to a few times the saturation
density. This is also a fact that the properties of the small NS have a strong
correlation with the NM properties due to their low central density [96]. Few
parameter sets like HS, LA, LZ, NL-SH, NL1 and IUFSU parameter sets do not
obey the NICER mass-radius constraint. However, only eight parameter sets like
GM1, GL85, FSU2, IUFSU*, G1, IOPB-I, FSUGarnet and FSU2R obey both the NICER
and recent maximum NS mass constraints.

In the case of SHF and DD-RMF, the mass and radius of the NS are also depicted
in Fig. 2. Except for DDLZ1, DDME1, DDME2, DD2, all satisfies the maximum mass
constraints given by different PSR measurements. The NICER limit is also
satisfied by all parameter sets except the KDE0v1 and SLY family. The maximum
mass predicted by DDLZ1, which lies in the limit given by GW190814.

###  3.3 Radius of the canonical NS

Along with the maximum mass, in recent years, the radius of the canonical star
is also used as an important constraint to control the nature of the EOS in
the high-density region [67]. It is now a well-known fact that the radius of
the canonical NS and the canonical tidal deformability are strongly correlated
[97, 98, 34]. Various models give a different form of correlation. Different
analysis of tidal deformability data of GW170817 suggest different range of
canonical radius [34, 35, 36, 37, 38, 98, 39, 40, 41, 42, 43, 99, 100, 101,
102, 103, 104]. We plot the ranges of the canonical radius in Fig. 3.

Figure 3: (color online) We compile the ranges of the canonical radius from
some refs. [34, 35, 36, 37, 38, 98, 39, 40, 41, 42, 43, 99, 100, 101, 102,
103, 104]. The left and right arrow represents no fixed lower and upper limit
for canonical NS as compare to others. The NICER radius range given by Miller
and Riley et al. [29, 32] are depicted with solid green and dark red lines.

In some cases, the analysis gives a very narrow range of the canonical radius,
for example, Most et al. [37]. However, in many cases, the acceptable range is
too wide, which is not much suitable to constraint the EOS. If we consider the
maximum and minimum radius predicted by the RMF parameter sets, we can find
the radius range of the canonical star is $\sim 11.4-14.3$ km, which entirely
lies in the range reported by the NICER results [29] except HS, LA, LZ, NL-SH,
NL1 and IUFSU. This shows that RMF formalism is good enough to reproduce the
NICER data. If we do not consider the maximum mass limit and stick to the
NICER constraint only, then almost all RMF parameter obey the mass-radius
constraint except a few. From Fig. 2, it is clear that too soft EOS (low
maximum mass) and too stiff EOS (high maximum mass) are discarded by both
NICER and maximum mass constraint. Both SHF and DDRMF sets also lie in the
limit given by the NICER.

In Fig. 3, we compile the canonical radius of the NS predicted from different
approaches. We present the NICER results on top of it with solid green and
dark red lines. The upper limit of the canonical radius from various
approaches lies in the range of NICER results. For Miller et al. limit is
fully satisfied by Most et al. and more than 50% limit is satisfied by Malik,
Fattoyev, Annala, Radice and Coughlin et al. as shown in Fig. 3. But in case
of Riley et al. limit, only Malik and Most et al. approaches are within the
range but other approaches also satisfy $\geq 50\%$ limit.

###  3.4 Correlation between compactness and curvature

The compactness of the NS is defined as the ratio of the mass and the
corresponding radius. In Fig. 4, we plot the $C$ with SC for assumed parameter
sets for the canonical star. The graph shows that there is a strong
correlation between them for the canonical star. The correlation looks cubic
and the value of the correlation coefficient 0.992 i.e these are strongly
correlated. The three-dimensional correlation between the SC and $C$ at
different masses of the NS are also studies. We use the Pearson formula to
calculate the three-dimensional correlation between some properties of the NS
although it is valid for linear correlation. Therefore, a linear correlation
between any two quantities $x$ and $y$ given by formula as [105]

$\xi=\frac{\Sigma_{xy}}{\sqrt{\Sigma_{xx}\Sigma_{yy}}},$ (3.1)

where

$\displaystyle\Sigma_{xy}=\frac{1}{N}\sum_{i=0}^{N}{x_{i}}{y_{i}}-\frac{1}{N^{2}}\Big{(}\sum_{i=0}^{N}{x_{i}}\Big{)}\Big{(}\sum_{i=0}^{N}{y_{i}}\Big{)},$
(3.3)
$\displaystyle\Sigma_{xx}=\frac{1}{N}\sum_{i=0}^{N}x_{i}^{2}-\frac{1}{N^{2}}\Big{(}\sum_{i=0}^{N}{x_{i}}\Big{)}^{2},$
$\displaystyle\mathrm{and}$ (3.5)
$\displaystyle\Sigma_{yy}=\frac{1}{N}\sum_{i=0}^{N}y_{i}^{2}-\frac{1}{N^{2}}\Big{(}\sum_{i=0}^{N}{y_{i}}\Big{)}^{2}.$

and $N$ is total number of models used and $i$ runs over N.

Figure 4: (color online) Left: We plot the SC with compactness for canonical
star for various parameter sets of the RMF model. We find correlation with co-
efficient $\zeta$= 0.992. Right: SC with radius and the correlation co-
efficient $\xi=0.982$.

The SC and radius of the different parameter set of the RMF model shown in
Fig. 4. Here, also exist a strong correlation between them, and it looks to be
inverse cubic. The correlation coefficient found to be 0.982. This correlation
is comparatively weaker than the SC and compactness.

To show more specifically the mass dependence, we plot the SC, $C$, and $R$ of
the NS for the different parameter sets for different masses of the NS in Fig.
5. One can see that there is correlation at each mass of the NS.

Figure 5: (color online) Left: The correlation between SC and compactness for
considered parameter sets is shown for different masses of the NS. Right:
Correlation between SC with radius. Figure 6: (color online) The heat map plot
represents the correlation between different quantities like $M_{max.}$,
$R_{1.4}$, $R_{max.}$, SC1.4, SCmax., $C_{1.4}$ and $C_{max.}$. Each number
inside the box represents the correlation co-efficients calculated using the
Pearson formula between that corresponding pair.

Figure 7: (color online) Left: The heat map represents the correlation between
SC and compactness of the NS with masses 1.4, 1.5, 1.6, 1.7 and 1.8
$M_{\odot}$. Right: Heat map for SC and radii of different masses of the NS.

We calculated the correlation between a pair of quantities using Eqs. (3.1)
and (3.5) and present in Fig. 6. The 7$\times$7 matrix representing the
correlations between a pair of quantities, and the correlations coefficient is
written inside the box. We find a noticeable correlation between SC with $R$
and $C$. There is a strong correlation between these pairs SC1.4–$R_{1.4}$,
SC1.4–$C_{1.4}$. But the correlation between $R_{max.}$ and SCmax. is around
85% but for $C_{max.}$ and SCmax. is very poor.

In a similar fashion, we also calculate the value of $\xi$ between each pair
of quantities such as SC, $C$ and $R$ for 1.4-1.8 $M_{\odot}$ and depicted in
Fig. 7. The value of $\xi$ is $>85\%$ between each pair for 1.5-1.8
$M_{\odot}$ NS. Hence we also find a strong correlation between SC, $C$ and
$R$ for these masses of the NS. Finally, we have tabulated the calculated
properties such as its mass, radius, central density, SC and compactness for
both canonical and maximum mass NS as given in Table 1.

##  4 Conclusions

In summary, we calculate some quantities such as mass, radius, curvatures and
compactness of NS obtained from RMF and SHF sets. For the last four decades,
the RMF and SHF formalism has been well suited for studying NM and NS
properties. To study the correlations, we have taken 30 different RMF, 15 SHF
and 6 DDRMF EOSs, which covers a broader range of nuclear saturation
properties. We have analysed the range of the canonical radius from different
approaches. We have also compared the RMF results with NICER data. We find
that the lower limit of the canonical radius from different approaches lies
completely, such as Most and Malik et al. data, and more than 50% is inside by
other approaches. Also, we see that only a few parameter sets can satisfy both
the maximum mass and NICER constraints. Fig. 2 shows the none of the parameter
sets can satisfy both the constraint from GW170817 and GW190814. Only a few
parameters sets satisfy the constraint from NICER, GW190814 and the observed
maximum masses of NSs. We can choose the most suitable parameter sets, which
obey the constraints from NICER, GW170817 and recent maximum mass limit
simultaneously. These parameter sets are SINPB, GL97, FSUGarnet, FSU2R,
IOPB-I, G1, GL85. This analysis shows that some parameter sets can reproduce
the maximum mass of the super-massive neutron star ( not confirmed yet super-
massive NS or smallest black hole ) but simultaneously unable to reproduce
other constraints. So it gives a hint that we can modify these equations of
state in the lower density region to satisfy the constraints from the GW170817
and NICER data. We calculate the curvature of the neutron star using RMF and
SHF EOSs. The interesting conclusion is that we find a correlation between
surface curvature and compactness at different masses of the NS. They follow a
cubic correlation between them. Using the Pearson formula, we have calculated
the correlation coefficient. We found the correlation coefficient between the
curvature and compactness is $\xi=0.992$ for the canonical star which
represents that the correlation is strong enough. Similarly, we find another
correlation between the curvature and the neutron star’s radius, having the
correlation coefficient, $\xi=0.982$ for the canonical star. The correlations
between surface curvature, compactness and radius are more stronger for
1.5-1.8 $M_{\odot}$.

Table 1: The properties of NS maximum mass $M_{max.}$, radius $R$, central density ${\cal{E}}_{c}$, surface curvature SC and compactness $C$. Parameter sets |  $M_{max.}$ ($M_{\odot}$) |  | $R$
---
(km)
| ${\cal{E}}_{c}$
---
(MeV fm-3)
| SC
---
| $C$
---
$R_{1.4}$ | $R_{max.}$ | ${\cal{E}}_{1.4}$ | ${\cal{E}}_{max.}$ | SC1.4 | SCmax. | $C_{1.4}$ | $C_{max.}$
HS | 2.980 | 14.31 | 14.03 | 226 | 750 | 1.414 | 3.183 | 0.144 | 0.313
LA | 2.981 | 14.32 | 14.04 | 228 | 755 | 1.416 | 3.185 | 0.144 | 0.313
H1 | 2.987 | 14.23 | 14.03 | 226 | 750 | 1.431 | 3.188 | 0.145 | 0.314
LZ | 2.981 | 14.76 | 14.16 | 226 | 740 | 1.285 | 3.095 | 0.140 | 0.311
NL3 | 2.774 | 14.08 | 13.16 | 270 | 870 | 1.477 | 3.584 | 0.147 | 0.311
NL3* | 2.760 | 14.03 | 13.11 | 276 | 870 | 1.492 | 3.610 | 0.147 | 0.311
NL1 | 2.845 | 14.56 | 13.51 | 254 | 830 | 1.338 | 3.397 | 0.142 | 0.310
NL-SH | 2.795 | 14.35 | 13.42 | 249 | 830 | 1.394 | 3.141 | 0.144 | 0.307
GM1 | 2.370 | 13.56 | 11.96 | 314 | 1100 | 1.654 | 4.085 | 0.152 | 0.292
GL85 | 2.168 | 14.17 | 11.93 | 311 | 1150 | 1.449 | 3.769 | 0.146 | 0.268
GL97 | 2.003 | 12.70 | 10.67 | 440 | 1440 | 2.012 | 4.865 | 0.162 | 0.277
NL3-II | 2.774 | 14.05 | 13.15 | 271 | 870 | 1.487 | 3.593 | 0.147 | 0.311
NLD | 2.425 | 13.65 | 12.28 | 302 | 1000 | 1.624 | 3.857 | 0.151 | 0.291
NL-RA1 | 2.785 | 14.11 | 13.23 | 265 | 860 | 1.467 | 3.548 | 0.146 | 0.310
TM1 | 1.865 | 13.70 | 11.50 | 332 | 1240 | 1.601 | 3.616 | 0.151 | 0.239
TM2 | 2.161 | 13.61 | 12.07 | 344 | 1100 | 1.632 | 3.619 | 0.152 | 0.264
PK1 | 2.314 | 13.83 | 12.48 | 304 | 1000 | 1.559 | 3.507 | 0.149 | 0.274
FSU | 1.722 | 11.94 | 10.62 | 540 | 1390 | 2.428 | 4.247 | 0.173 | 0.239
FSU2 | 2.161 | 13.61 | 12.07 | 344 | 1100 | 1.632 | 3.619 | 0.152 | 0.264
IUFSU | 1.898 | 15.47 | 12.54 | 310 | 1100 | 1.112 | 2.837 | 0.133 | 0.223
IUFSU* | 2.161 | 13.61 | 12.07 | 344 | 1100 | 1.632 | 3.619 | 0.152 | 0.264
SINPA | 2.002 | 12.51 | 11.37 | 405 | 1190 | 2.108 | 4.012 | 0.165 | 0.260
SINPB | 1.994 | 12.67 | 11.44 | 402 | 1180 | 2.027 | 3.930 | 0.163 | 0.257
G1 | 2.161 | 13.61 | 12.07 | 344 | 1100 | 1.632 | 3.619 | 0.152 | 0.264
G2 | 1.938 | 12.81 | 11.02 | 443 | 1342 | 1.956 | 4.286 | 0.161 | 0.260
G3 | 1.997 | 12.11 | 10.80 | 460 | 1325 | 2.320 | 4.726 | 0.171 | 0.273
IOPB-I | 2.149 | 12.78 | 11.76 | 366 | 1100 | 1.977 | 3.893 | 0.162 | 0.270
FSUGarnet | 2.066 | 12.59 | 11.57 | 384 | 1130 | 2.067 | 3.934 | 0.164 | 0.263
FSU2R | 2.063 | 12.72 | 11.61 | 375 | 1130 | 2.004 | 3.888 | 0.162 | 0.262
FSU2H | 2.379 | 13.14 | 12.32 | 327 | 1000 | 1.819 | 3.752 | 0.157 | 0.328
BSk20 | 2.167 | 11.60 | 10.15 | 519 | 1500 | 2.652 | 6.131 | 0.178 | 0.316
BSk21 | 2.278 | 12.39 | 11.03 | 411 | 1270 | 2.173 | 5.014 | 0.167 | 0.305
BSk22 | 2.265 | 12.81 | 11.00 | 390 | 1270 | 1.980 | 5.026 | 0.161 | 0.304
BSk23 | 2.272 | 12.12 | 10.95 | 398 | 1270 | 2.415 | 5.562 | 0.171 | 0.306
BSk24 | 2.279 | 12.41 | 11.02 | 410 | 1270 | 2.164 | 5.034 | 0.167 | 0.305
BSk25 | 2.224 | 12.19 | 10.99 | 418 | 1325 | 2.280 | 4.952 | 0.170 | 0.299
KDE0V1 | 1.969 | 11.49 | 09.74 | 596 | 1700 | 2.725 | 6.287 | 0.180 | 0.299
SkI2 | 2.163 | 13.30 | 11.06 | 382 | 1338 | 1.759 | 4.717 | 0.155 | 0.289
SkI3 | 2.240 | 13.37 | 11.27 | 366 | 1260 | 1.729 | 4.619 | 0.155 | 0.293
SkI5 | 2.239 | 13.79 | 11.23 | 339 | 1260 | 1.586 | 5.119 | 0.150 | 0.294
SkI6 | 2.189 | 12.32 | 10.72 | 438 | 1360 | 2.211 | 5.247 | 0.168 | 0.302
SLY2 | 2.053 | 11.64 | 09.96 | 544 | 1600 | 2.619 | 6.141 | 0.178 | 0.304
SLY4 | 2.050 | 11.57 | 09.95 | 552 | 1600 | 2.668 | 6.158 | 0.179 | 0.304
SL230a | 2.099 | 11.69 | 10.24 | 519 | 1480 | 2.589 | 5.776 | 0.177 | 0.303
Rs | 2.116 | 12.77 | 10.73 | 428 | 1400 | 1.986 | 5.069 | 0.162 | 0.291
DD2 | 2.418 | 13.04 | 11.84 | 352 | 1000 | 1.863 | 4.307 | 0.159 | 0.302
DD2Y | 2.092 | 13.02 | 11.66 | 353 | 1160 | 1.872 | 3.900 | 0.159 | 0.265
DDME1 | 2.395 | 11.90 | 11.41 | 370 | 1130 | 2.432 | 4.822 | 0.174 | 0.310
DDME2 | 2.482 | 13.08 | 11.96 | 340 | 1100 | 1.847 | 4.289 | 0.158 | 0.306
DDME2Y | 2.115 | 13.06 | 11.67 | 342 | 1160 | 1.856 | 3.933 | 0.158 | 0.268
DDLZ1 | 2.546 | 13.04 | 12.29 | 335 | 1000 | 1.615 | 3.888 | 0.159 | 0.306

## References

  * [1] P. Danielewicz and J. Lee, _Symmetry energy ii: Isobaric analog states_ , _Nucl. Phys. A_ 922 (2014) 1 .
  * [2] A.W. Steiner, J.M. Lattimer and E.F. Brown, _THE EQUATION OF STATE FROM OBSERVED MASSES AND RADII OF NEUTRON STARS_ , _The Astrophysical Journal_ 722 (2010) 33.
  * [3] J.M. Lattimer, _The physics of neutron stars_ , _Science_ 304 (2004) 536.
  * [4] G. Baym and C. Pethick, _Physics of neutron stars_ , _Annual Review of Astronomy and Astrophysics_ 17 (1979) 415.
  * [5] The LIGO Scientific Collaboration and the Virgo Collaboration collaboration, _Gw170817: Measurements of neutron star radii and equation of state_ , _Phys. Rev. Lett._ 121 (2018) 161101.
  * [6] LIGO Scientific Collaboration and Virgo Collaboration collaboration, _Gw170817: Observation of gravitational waves from a binary neutron star inspiral_ , _Phys. Rev. Lett._ 119 (2017) 161101.
  * [7] V.A. Ambartsumyan and G.S. Saakyan _Sov. Astron._ 4 (1960) .
  * [8] N.K. Glendenning, _Neutron stars are giant hypernuclei?_ , _Astrophys. J._ 293 (1985) 470.
  * [9] N.K. Glendenning and S.A. Moszkowski, _Reconciliation of neutron-star masses and binding of the $\Lambda$ in hypernuclei_, _Phys. Rev. Lett._ 67 (1991) 2414.
  * [10] N.K. Glendenning and J. Schaffner-Bielich, _Kaon condensation and dynamical nucleons in neutron stars_ , _Phys. Rev. Lett._ 81 (1998) 4564.
  * [11] N.K. Glendenning and J. Schaffner-Bielich, _First order kaon condensate_ , _Phys. Rev. C_ 60 (1999) 025803.
  * [12] M.B. Christiansen, N.K. Glendenning and J. Schaffner-Bielich, _Surface tension between a kaon condensate and the normal nuclear matter phase_ , _Phys. Rev. C_ 62 (2000) 025804.
  * [13] N. Gupta and P. Arumugam, _Role of higher order couplings in the presence of kaons in relativistic mean field description of neutron stars_ , _Phys. Rev. C_ 85 (2012) 015804.
  * [14] N. Gupta and P. Arumugam, _“pasta phases” in neutron stars studied with extended relativistic mean field models_ , _Phys. Rev. C_ 87 (2013) 028801.
  * [15] J.C. Collins and M.J. Perry, _Superdense matter: Neutrons or asymptotically free quarks?_ , _Physical Review Letters_ 34 (1975) 1353.
  * [16] C.-J. Xia, G.-X. Peng, E.-G. Zhao and S.-G. Zhou, _From strangelets to strange stars: a unified description_ , _Science Bulletin_ 61 (2016) 172.
  * [17] C.-J. Xia, G.-X. Peng, E.-G. Zhao and S.-G. Zhou, _Properties of strange quark matter objects with two types of surface treatments_ , _Phys. Rev. D_ 93 (2016) 085025.
  * [18] C.-J. Xia and S.-G. Zhou, _Stable strange quark matter objects with running masses and coupling constant_ , _Nucl. Phys. B_ 916 (2017) 669.
  * [19] V. Dexheimer, L.T.T. Soethe, J. Roark et al., _Phase transitions in neutron stars_ , _International Journal of Modern Physics E_ 27 (2018) 1830008.
  * [20] G. Panotopoulos and I. Lopes, _Dark matter effect on realistic equation of state in neutron stars_ , _Phys. Rev. D_ 96 (2017) .
  * [21] A. Das, T. Malik and A.C. Nayak, _Confronting nuclear equation of state in the presence of dark matter using gw170817 observation in relativistic mean field theory approach_ , _Phys. Rev. D_ 99 (2019) .
  * [22] A. Li, F. Huang and R.-X. Xu, _Too massive neutron stars: The role of dark matter?_ , _Astroparticle Physics_ 37 (2012) 70–74.
  * [23] H.C. Das, A. Kumar, B. Kumar et al., _Effects of dark matter on the nuclear and neutron star matter_ , _MNRAS_ 495 (2020) 4893.
  * [24] J. Ellis, G. Hütsi, K. Kannike et al., _Dark matter effects on neutron star properties_ , _Phys. Rev. D_ 97 (2018) .
  * [25] S.A. Bhat and A. Paul, _Cooling of dark-matter admixed neutron stars with density-dependent equation of state_ , _The European Physical Journal C_ 80 (2020) 544.
  * [26] P. Ciarcelluti and F. Sandin, _Have neutron stars a dark matter core?_ , _Phys. Lett. B_ 695 (2011) 19–21.
  * [27] S.-C. Leung, M.-C. Chu and L.-M. Lin, _Dark-matter admixed neutron stars_ , _Phys. Rev. D_ 84 (2011) .
  * [28] G. Raaijmakers, T.E. Riley, A.L. Watts et al., _A NICER view of PSR j0030+0451: Implications for the dense matter equation of state_ , _The Astrophysical Journal_ 887 (2019) L22.
  * [29] M.C. Miller, F.K. Lamb, A.J. Dittmann et al., _PSR j0030+0451 mass and radius from NICER data and implications for the properties of neutron star matter_ , _The Astrophysical Journal_ 887 (2019) L24.
  * [30] S. Bogdanov, F.K. Lamb, S. Mahmoodifar et al., _Constraining the neutron star mass–radius relation and dense matter equation of state with NICER. II. emission from hot spots on a rapidly rotating neutron star_ , _The Astrophysical Journal_ 887 (2019) L26.
  * [31] A.V. Bilous, A.L. Watts, A.K. Harding et al., _A NICER view of PSR j0030+0451: Evidence for a global-scale multipolar magnetic field_ , _The Astrophysical Journal_ 887 (2019) L23.
  * [32] T.E. Riley, A.L. Watts, S. Bogdanov et al., _A NICER view of PSR j0030+0451: Millisecond pulsar parameter estimation_ , _The Astrophysical Journal_ 887 (2019) L21.
  * [33] S. Guillot, M. Kerr, P.S. Ray et al., _NICER x-ray observations of seven nearby rotation-powered millisecond pulsars_ , _The Astrophysical Journal_ 887 (2019) L27.
  * [34] T. Malik, N. Alam, M. Fortin et al., _Gw170817: Constraining the nuclear matter equation of state from the neutron star tidal deformability_ , _Phys. Rev. C_ 98 (2018) 035804.
  * [35] K. Hebeler, J.M. Lattimer, C.J. Pethick and A. Schwenk, _Constraints on neutron star radii based on chiral effective field theory interactions_ , _Phys. Rev. Lett._ 105 (2010) 161102.
  * [36] Y. Lim and J.W. Holt, _Neutron star tidal deformabilities constrained by nuclear theory and experiment_ , _Phys. Rev. Lett._ 121 (2018) 062701.
  * [37] E.R. Most, L.R. Weih, L. Rezzolla and J. Schaffner-Bielich, _New constraints on radii and tidal deformabilities of neutron stars from gw170817_ , _Phys. Rev. Lett._ 120 (2018) 261103.
  * [38] F.J. Fattoyev, J. Piekarewicz and C.J. Horowitz, _Neutron skins and neutron stars in the multimessenger era_ , _Phys. Rev. Lett._ 120 (2018) 172702.
  * [39] I. Tews, J. Margueron and S. Reddy, _Critical examination of constraints on the equation of state of dense matter obtained from gw170817_ , _Phys. Rev. C_ 98 (2018) 045804.
  * [40] E. Annala, T. Gorda, A. Kurkela and A. Vuorinen, _Gravitational-wave constraints on the neutron-star-matter equation of state_ , _Phys. Rev. Lett._ 120 (2018) 172703.
  * [41] N.-B. Zhang, B.-A. Li and J. Xu, _Combined constraints on the equation of state of dense neutron-rich matter from terrestrial nuclear experiments and observations of neutron stars_ , _The Astrophysical Journal_ 859 (2018) 90.
  * [42] T. Dietrich, M.W. Coughlin et al., _Multimessenger constraints on the neutron-star equation of state and the hubble constant_ , _Science_ 370 (2020) 1450.
  * [43] C.D. Capano, I. Tews, S.M. Brown et al., _Stringent constraints on neutron-star radii from multimessenger observations and nuclear theory_ , _Nature Astron._ 4 (2020) 625.
  * [44] F.J. Fattoyev and J. Piekarewicz, _Neutron skins and neutron stars_ , _Phys. Rev. C_ 86 (2012) 015802.
  * [45] C.J. Horowitz and J. Piekarewicz, _Neutron radii of ${}^{208}\mathrm{Pb}$ and neutron stars_, _Phys. Rev. C_ 64 (2001) 062802.
  * [46] B.-A. Li and M. Magno, _Curvature-slope correlation of nuclear symmetry energy and its imprints on the crust-core transition, radius, and tidal deformability of canonical neutron stars_ , _Phys. Rev. C_ 102 (2020) 045807.
  * [47] N. Alam, B.K. Agrawal, M. Fortin et al., _Strong correlations of neutron star radii with the slopes of nuclear matter incompressibility and symmetry energy at saturation_ , _Phys. Rev. C_ 94 (2016) 052801.
  * [48] B. Wei, Q. Zhao, Z.-H. Wang, J. Geng, B.-Y. Sun, Y.-F. Niu et al., _Novel relativistic mean field lagrangian guided by pseudo-spin symmetry restoration_ , _Chinese Physics C_ 44 (2020) 074107.
  * [49] K.Y. Ekşi, C. Güngör and M.M. Türkoğlu, _What does a measurement of mass and/or radius of a neutron star constrain: Equation of state or gravity?_ , _Phys. Rev. D_ 89 (2014) 063003.
  * [50] M. Dutra, O. Lourenço, S.S. Avancini et al., _Relativistic mean-field hadronic models under nuclear matter constraints_ , _Phys. Rev. C_ 90 (2014) 055203.
  * [51] X.-T. He, F.J. Fattoyev, B.-A. Li and W.G. Newton, _Impact of the equation-of-state–gravity degeneracy on constraining the nuclear symmetry energy from astrophys.observables_ , _Phys. Rev. C_ 91 (2015) 015810.
  * [52] B.K. Sharma, Centelles, M., Viñas, X., Baldo, M. and Burgio, G. F., _Unified equation of state for neutron stars on a microscopic basis_ , _A &A_ 584 (2015) A103.
  * [53] C.J. Horowitz and B.D. Serot, _Self-consistent hartree description of finite nuclei in a relativistic quantum field theory_ , _Nucl. Phys. A_ 368 (1981) 503 .
  * [54] R.J. Furnstahl, C.E. Price and G.E. Walker, _Systematics of light deformed nuclei in relativistic mean-field models_ , _Phys. Rev. C_ 36 (1987) 2590.
  * [55] S. Haddad, _Density dependence of the nuclear symmetry energy in a relativistic mean-field approach_ , _Europhysics Letters (EPL)_ 48 (1999) 505.
  * [56] P.G. Reinhard, _The relativistic mean-field description of nuclei and nuclear dynamics_ , _Reports on Progress in Physics_ 52 (1989) 439.
  * [57] G.A. Lalazissis, J. König and P. Ring, _New parametrization for the lagrangian density of relativistic mean field theory_ , _Phys. Rev. C_ 55 (1997) 540.
  * [58] G.A. Lalazissis, S. Karatzikos, R. Fossion et al., _The effective force nl3 revisited_ , _Physics Letters B_ 671 (2009) 36 .
  * [59] M. Sharma, M. Nagarajan and P. Ring, _Rho meson coupling in the relativistic mean field theory and description of exotic nuclei_ , _Physics Letters B_ 312 (1993) 377 .
  * [60] P.G. Reinhard, M. Rufa, J. Maruhn, W. Greiner and J. Friedrich, _Nuclear ground-state properties in a relativistic meson-field theory_ , _Z. Phys. A Atomic Nuclei_ 323 (1986) 13.
  * [61] N.K. Glendenning, _Compact Stars : Nuclear Physics, particle Physics , and General Relativity_ , Spinger - Verlag, New York (1997).
  * [62] M. Rashdan, _Structure of exotic nuclei and superheavy elements in a relativistic shell model_ , _Phys. Rev. C_ 63 (2001) 044303.
  * [63] Y. Sugahara and H. Toki, _Relativistic mean-field theory for unstable nuclei with non-linear $\sigma$ and $\omega$ terms_, _Nucl. Phys. A_ 579 (1994) 557 .
  * [64] W. Long, J. Meng, N.V. Giai and S.-G. Zhou, _New effective interactions in relativistic mean field theory with nonlinear terms and density-dependent meson-nucleon coupling_ , _Phys. Rev. C_ 69 (2004) 034319.
  * [65] B.G. Todd-Rutel and J. Piekarewicz, _Neutron-rich nuclei and neutron stars: A new accurately calibrated interaction for the study of neutron-rich matter_ , _Phys. Rev. Lett._ 95 (2005) 122501.
  * [66] W.-C. Chen and J. Piekarewicz, _Building relativistic mean field models for finite nuclei and neutron stars_ , _Phys. Rev. C_ 90 (2014) 044305.
  * [67] F.J. Fattoyev, C.J. Horowitz, J. Piekarewicz and G. Shen, _Relativistic effective interaction for nuclei, giant resonances, and neutron stars_ , _Phys. Rev. C_ 82 (2010) 055803.
  * [68] F.J. Fattoyev and J. Piekarewicz, _Relativistic models of the neutron-star matter equation of state_ , _Phys. Rev. C_ 82 (2010) 025805.
  * [69] C. Mondal, B.K. Agrawal, J.N. De and S.K. Samaddar, _Sensitivity of elements of the symmetry energy of nuclear matter to the properties of neutron-rich systems_ , _Phys. Rev. C_ 93 (2016) 044328.
  * [70] R.J. Furnstahl, B.D. Serot and H.-B. Tang, _A chiral effective lagrangian for nuclei_ , _Nucl. Phys. A_ 615 (1997) 441 .
  * [71] B. Kumar, S.K. Biswal and S.K. Patra, _Tidal deformability of neutron and hyperon stars within relativistic mean field equations of state_ , _Phys. Rev. C_ 95 (2017) 015801.
  * [72] B. Kumar, S.K. Patra and B.K. Agrawal, _New relativistic effective interaction for finite nuclei, infinite nuclear matter, and neutron stars_ , _Phys. Rev. C_ 97 (2018) 045806.
  * [73] W.-C. Chen and J. Piekarewicz, _Searching for isovector signatures in the neutron-rich oxygen and calcium isotopes_ , _Physics Letters B_ 748 (2015) 284 .
  * [74] L. Tolos, M. Centelles and A. Ramos, _EQUATION OF STATE FOR NUCLEONIC AND HYPERONIC NEUTRON STARS WITH MASS AND RADIUS CONSTRAINTS_ , _The Astrophysical Journal_ 834 (2016) 3.
  * [75] S. Goriely, N. Chamel and J.M. Pearson, _Further explorations of skyrme-hartree-fock-bogoliubov mass formulas. xii. stiffness and stability of neutron-star matter_ , _Phys. Rev. C_ 82 (2010) 035804.
  * [76] S. Goriely, N. Chamel and J.M. Pearson, _Further explorations of skyrme-hartree-fock-bogoliubov mass formulas. xiii. the 2012 atomic mass evaluation and the symmetry coefficient_ , _Phys. Rev. C_ 88 (2013) 024308.
  * [77] B.K. Agrawal, S. Shlomo and V.K. Au, _Determination of the parameters of a skyrme type effective interaction using the simulated annealing approach_ , _Phys. Rev. C_ 72 (2005) 014310.
  * [78] P.-G. Reinhard and H. Flocard, _Nuclear effective forces and isotope shifts_ , _Nuclear Physics A_ 584 (1995) 467.
  * [79] W. Nazarewicz, J. Dobaczewski, T.R. Werner, J.A. Maruhn, P.-G. Reinhard, K. Rutz et al., _Structure of proton drip-line nuclei around doubly magic ${}^{48}\mathrm{Ni}$_, _Phys. Rev. C_ 53 (1996) 740.
  * [80] E. Chabanat, Ph.D. thesis, University Claude Bernard Lyon-1, Lyon, France, 1995\.
  * [81] E. Chabanat, P. Bonche, P. Haensel, J. Meyer and R. Schaeffer, _A skyrme parametrization from subnuclear to neutron star densities part ii. nuclei far from stabilities_ , _Nuclear Physics A_ 635 (1998) 231.
  * [82] E. Chabanat, P. Bonche, P. Haensel, J. Meyer and R. Schaeffer, _A skyrme parametrization from subnuclear to neutron star densities_ , _Nuclear Physics A_ 627 (1997) 710.
  * [83] J. Friedrich and P.-G. Reinhard, _Skyrme-force parametrization: Least-squares fit to nuclear ground-state properties_ , _Phys. Rev. C_ 33 (1986) 335.
  * [84] S. Banik, M. Hempel and D. Bandyopadhyay, _NEW HYPERON EQUATIONS OF STATE FOR SUPERNOVAE AND NEUTRON STARS IN DENSITY-DEPENDENT HADRON FIELD THEORY_ , _The Astrophysical Journal Supplement Series_ 214 (2014) 22.
  * [85] M. Fortin, C. Providência, A.R. Raduta, F. Gulminelli, J.L. Zdunik, P. Haensel et al., _Neutron star radii and crusts: Uncertainties and unified equations of state_ , _Phys. Rev. C_ 94 (2016) 035804.
  * [86] T. Nikšić, D. Vretenar, P. Finelli and P. Ring, _Relativistic hartree-bogoliubov model with density-dependent meson-nucleon couplings_ , _Phys. Rev. C_ 66 (2002) 024306.
  * [87] G.A. Lalazissis, T. Nikšić, D. Vretenar and P. Ring, _New relativistic mean-field interaction with density-dependent meson-nucleon couplings_ , _Phys. Rev. C_ 71 (2005) 024312.
  * [88] P.B. Demorest et al., _A two-solar-mass neutron star measured using shapiro delay_ , _Nature_ 467 (2010) 1081.
  * [89] J. Antoniadis et al., _A massive pulsar in a compact relativistic binary_ , _Science_ 340 (2013) .
  * [90] H.T. Cromartie, E. Fonseca, S.M. Ransom, P.B. Demorest, Z. Arzoumanian, H. Blumer et al., _Relativistic shapiro delay measurements of an extremely massive millisecond pulsar_ , _Nature Astronomy_ 4 (2019) 72–76.
  * [91] F.J. Fattoyev, C.J. Horowitz, J. Piekarewicz and B. Reed, _Gw190814: Impact of a 2.6 solar mass neutron star on the nucleonic equations of state_ , _Phys. Rev. C_ 102 (2020) 065805.
  * [92] H.C. Das, A. Kumar, B. Kumar, S.K. Biswal and S.K. Patra, 2020.
  * [93] H. Tan, J. Noronha-Hostler and N. Yunes, 2020.
  * [94] K. Huang, J. Hu, Y. Zhang and H. Shen, 2020.
  * [95] N.-B. Zhang and B.-A. Li, _GW190814’s secondary component with mass 2.50–2.67 m $\odot$ as a superfast pulsar_, _The Astrophysical Journal_ 902 (2020) 38.
  * [96] J. Carriere, C.J. Horowitz and J. Piekarewicz, _Low-mass neutron stars and the equation of state of dense matter_ , _The Astrophysical Journal_ 593 (2003) 463.
  * [97] R. Nandi, P. Char and S. Pal, _Constraining the relativistic mean-field model equations of state with gravitational wave observations_ , _Phys. Rev. C_ 99 (2019) 052802.
  * [98] O. Lourenço, M. Bhuyan, C. Lenzi et al., _Gw170817 constraints analyzed with gogny forces and momentum-dependent interactions_ , _Physics Letters B_ 803 (2020) 135306.
  * [99] S. De, D. Finstad, J.M. Lattimer, D.A. Brown, E. Berger and C.M. Biwer, _Tidal deformabilities and radii of neutron stars from the observation of gw170817_ , _Phys. Rev. Lett._ 121 (2018) 091102.
  * [100] S. Köppel, L. Bovard and L. Rezzolla, _A general-relativistic determination of the threshold mass to prompt collapse in binary neutron star mergers_ , _The Astrophysical Journal_ 872 (2019) L16.
  * [101] G. Montaña, L. Tolós, M. Hanauske and L. Rezzolla, _Constraining twin stars with gw170817_ , _Phys. Rev. D_ 99 (2019) 103009.
  * [102] D. Radice and L. Dai, _Multimessenger parameter estimation of gw170817_ , _The European Physical Journal A_ 55 (2019) .
  * [103] M.W. Coughlin, T. Dietrich, B. Margalit and B.D. Metzger, _Multimessenger bayesian parameter inference of a binary neutron star merger_ , _Monthly Notices of the Royal Astronomical Society: Letters_ 489 (2019) L91–L96.
  * [104] B. Kumar and P. Landry, _Inferring neutron star properties from gw170817 with universal relations_ , _Phys. Rev. D_ 99 (2019) 123026.
  * [105] J. Zimmerman, Z. Carson, K. Schumacher, A.W. Steiner and K. Yagi, 2020.