In 2019, Neutron star Interior Composition ExploreR (NICER) mission released its findings on the mass and radius of the isolated neutron star (INS) PSR J0030+0451, revealing a mass of approximately 1.4 solar masses ($M_{\odot}$) and a radius near 13 kilometers. However, the recent re-analysis by the NICER collaboration \citep{vinciguerra2024updated} suggests that the available data primarily yields a precise inference of the compactness for this source while the resulting mass and radius are strongly model-dependent and diverse (the 68.3\% confidence counters just overlap slightly for the ST+PDT and PDT-U models). By integrating this compactness data with the equation of state (EoS) refined by our latest investigations, we have deduced the mass and radius for PSR J0030+0451, delivering estimates of $M=1.48^{+0.09}_{-0.10}~M_\odot$ and $R=12.39_{-0.70}^{+0.50}~{\rm km}$ for the compactness found in ST+PDT model, alongside $M=1.47^{+0.14}_{-0.20}~M_\odot$ and $R=12.37_{-0.70}^{+0.50}~{\rm km}$ for the compactness in PDT-U model. These two groups of results are well consistent with each other and the direct X-ray data inference within the ST+PDT model seems to be favored. Additionally, we have calculated the tidal deformability, moment of inertia, and gravitational binding energy for this NS. Furthermore, employing these refined EoS models, we have updated mass-radius estimates for three INSs with established gravitational redshifts.
Abstract GW190425 is the second neutron star merger event detected by the Advanced LIGO/Virgo detectors. If interpreted as a double neutron star merger, the total gravitational mass is substantially larger than that of the binary systems identified in the Galaxy. In this work we analyze the gravitational-wave data within the neutron star–black hole merger scenario. For the black hole, we yield a mass of and an aligned spin of . As for the neutron star we find a mass of and the dimensionless tidal deformability of . These parameter ranges are for 90% credibility. The inferred masses of the neutron star and the black hole are not in tension with current observations and we suggest that GW190425 is a viable candidate of a neutron star–black hole merger event. Benefitting from the continual enhancement of the sensitivities of the advanced gravitational detectors and the increase of the number of the observatories, similar events are anticipated to be much more precisely measured in the future and the presence of black holes below the so-called mass gap will be unambiguously clarified. If confirmed, the mergers of neutron stars with (quickly rotating) low-mass black holes are likely important production sites of the heaviest r -process elements.
Gravitational-wave (GW) data can be used to test general relativity in the highly nonlinear and strong field regime. Modified gravity theories such as Einstein-dilation-Gauss-Bonnet and dynamical Chern-Simons can be tested with the additional GW signals detected in the first half of the third observing run of Advanced LIGO/Virgo. Specifically, we analyze gravitational-wave data of GW190412 and GW190814 to place constraints on the parameters of these two theories. Our results indicate that dynamical Chern-Simons gravity remains unconstrained. For Einstein-dilation-Gauss-Bonnet gravity, we find $\sqrt{\alpha_{\rm EdGB}}\lesssim 0.40\,\rm km$ when considering GW190814 data, assuming it is a black hole binary. Such a constraint is improved by a factor of approximately $10$ in comparison to that set by the first Gravitational-Wave Transient Catalog events.
Recently, the radius of neutron star (NS) PSR J0740+6620 was measured by NICER and an updated measurement of neutron skin thickness of ${}^{208}$Pb ($R_{\rm skin}^{208}$) was reported by the PREX-II experiment. These new measurements can help us better understand the unknown equation of state (EoS) of dense matter. In this work, we adopt a hybrid parameterization method, which incorporates the nuclear empirical parameterization and some widely used phenomenological parameterizations, to analyze the results of nuclear experiments and astrophysical observations. With the joint Bayesian analysis of GW170817, PSR J0030+0451, and PSR J0740+6620, the parameters that characterize the ultra dense matter EoS are constrained. We find that the slope parameter $L$ is approximately constrained to $70_{-18}^{+21}$ MeV, which predicts $R_{\rm skin}^{208}=0.204^{+0.030}_{-0.026}\,{\rm fm}$ by using the universal relation between $R_{\rm skin}^{208}$ and $L$. And the bulk properties of canonical $1.4\,M_\odot$ NS (e.g., $R_{1.4}$ and $\Lambda_{1.4}$) as well as the pressure ($P_{2\rho_{\rm sat}}$) at two times the nuclear saturation density are well constrained by the data, i.e., $R_{1.4}$, $\Lambda_{1.4}$, and $P_{2\rho_{\rm sat}}$ are approximately constrained to $12.3\pm0.7$ km, $330_{-100}^{+140}$, and $4.1_{-1.2}^{+1.5}\times10^{34}\,{\rm dyn\,cm^{-2}}$, respectively. Besides, we find that the Bayes evidences of the hybrid star and normal NS assumptions are comparable, which indicates that current observation data are compatible with quarkyonic matter existing in the core of massive star. Finally, in the case of normal NS assumption, we obtain a constraint for the maximum mass of nonrotating NS $M_{\rm TOV}=2.30^{+0.30}_{-0.18}$ $M_\odot$. All of the uncertainties reported above are for 68.3% credible levels.
Abstract We introduce a new nonparametric representation of the neutron star (NS) equation of state (EOS) by using the variational autoencoder (VAE). As a deep neural network, the VAE is frequently used for dimensionality reduction since it can compress input data to a low-dimensional latent space using the encoder component and then reconstruct the data using the decoder component. Once a VAE is trained, one can take the decoder of the VAE as a generator. We employ 100,000 EOSs that are generated using the nonparametric representation method based on Han et al. as the training set and try different settings of the neural network, then we get an EOS generator (the trained VAE’s decoder) with four parameters. We use the mass–tidal-deformability data of binary NS merger event GW170817, the mass–radius data of PSR J0030+0451, PSR J0740+6620, PSR J0437-4715, and 4U 1702-429, and the nuclear constraints to perform the Bayesian inference. The overall results of the analysis that includes all the observations are R1.4=12.59−0.42+0.36km , Λ1.4=489−110+114 , and Mmax=2.20−0.19+0.37M⊙ (90% credible levels), where R 1.4 /Λ 1.4 are the radius/tidal deformability of a canonical 1.4 M ⊙ NS, and Mmax is the maximum mass of a nonrotating NS. The results indicate that the implementation of these VAE techniques can obtain reasonable results, while accelerating calculation by a factor of ∼3–10 or more, compared with the original method.
In this work we parameterize the Equation of State of dense neutron star (NS) matter with four pressure parameters of $\{\hat{p}_1, \hat{p}_2, \hat{p}_3, \hat{p}_4\}$ and then set the combined constraints with the data of GW 170817 and the data of 6 Low Mass X-ray Binaries (LMXBs) with thermonuclear burst or alternatively the symmetry energy of the nuclear interaction. We find that the nuclear data effectively narrow down the possible range of $\hat{p}_1$, the gravitational wave data plays the leading role in bounding $\hat{p}_2$, and the LMXB data as well as the lower bound on maximal gravitational mass of non-rotating NSs govern the constraints on $\hat{p}_3$ and $\hat{p}_4$. Using posterior samples of pressure parameters and some universal relations, we further investigate how the current data sets can advance our understanding of tidal deformability ($\Lambda$), moment of inertia ($I$) and binding energy ($BE$) of NSs. For a canonical mass of $1.4M_\odot$, we have $I_{1.4} = {1.43}^{+0.30}_{-0.13} \times 10^{38}~{\rm kg \cdot m^2}$, $\Lambda_{1.4} = 390_{-210}^{+280}$ , $R_{1.4} = 11.8_{-0.7}^{+1.2}~{\rm km}$ and $BE_{1.4} = {0.16}^{+0.01}_{-0.02} M_{\odot}$ if the constraints from the nuclear data and the gravitational wave data have been jointly applied. For the joint analysis of gravitational wave data and the LMXB data, we have $I_{1.4} = {1.28}^{+0.15}_{-0.08} \times 10^{38}~{\rm kg \cdot m^2}$, $\Lambda_{1.4} = 220_{-90}^{+90}$, $R_{1.4} = 11.1_{-0.6}^{+0.7}~{\rm km}$ and $BE_{1.4} = {0.18}^{+0.01}_{-0.01} M_{\odot}$. These results suggest that the current constraints on $\Lambda$ and $R$ still suffer from significant systematic uncertainties, while $I_{1.4}$ and $BE_{1.4}$ are better constrained.
Abstract The discovery of gravitational waves from compact objects coalescence opens a brand-new window to observe the universe. With more events being detected in the future, statistical examinations would be essential to better understand the underlying astrophysical processes. In this work we investigate the prospect of measuring the mass function of black holes that are merging with the neutron stars. Applying Bayesian parameter estimation for hundreds of simulated neutron star–black hole (NSBH) mergers, we find that the parameters for most of the injected events can be well recovered. We also take a Bayesian hierarchical model to reconstruct the population properties of the masses of black holes, in the presence of a low mass gap, both the mass gap and power-law index ( α ) of black hole mass function can be well measured, thus we can reveal where the α is different for binary black hole (BBH) and NSBH systems. In the absence of a low mass gap, the gravitational wave data as well as the electromagnetic data can be used to pin down the nature of the merger event and then measure the mass of these very light black holes. However, as a result of the misclassification of BBH into NSBH, the measurement of α is more challenging and further dedicated efforts are needed.
Recently, the radius of neutron star (NS) PSR J0740+6620 was measured by NICER and an updated measurement of neutron skin thickness of ${}^{208}$Pb ($R_{\rm skin}^{208}$) was reported by the PREX-II experiment. These new measurements can help us better understand the unknown equation of state (EoS) of dense matter. In this work, we adopt a hybrid parameterization method, which incorporates the nuclear empirical parameterization and some widely used phenomenological parameterizations, to analyze the results of nuclear experiments and astrophysical observations. With the joint Bayesian analysis of GW170817, PSR J0030+0451, and PSR J0740+6620, the parameters that characterize the ultra dense matter EoS are constrained. We find that the slope parameter $L$ is approximately constrained to $70_{-18}^{+21}$ MeV, which predicts $R_{\rm skin}^{208}=0.204^{+0.030}_{-0.026}\,{\rm fm}$ by using the universal relation between $R_{\rm skin}^{208}$ and $L$. And the bulk properties of canonical $1.4\,M_\odot$ NS (e.g., $R_{1.4}$ and $\Lambda_{1.4}$) as well as the pressure ($P_{2\rho_{\rm sat}}$) at two times the nuclear saturation density are well constrained by the data, i.e., $R_{1.4}$, $\Lambda_{1.4}$, and $P_{2\rho_{\rm sat}}$ are approximately constrained to $12.3\pm0.7$ km, $330_{-100}^{+140}$, and $4.1_{-1.2}^{+1.5}\times10^{34}\,{\rm dyn\,cm^{-2}}$, respectively. Besides, we find that the Bayes evidences of the hybrid star and normal NS assumptions are comparable, which indicates that current observation data are compatible with quarkyonic matter existing in the core of massive star. Finally, in the case of normal NS assumption, we obtain a constraint for the maximum mass of nonrotating NS $M_{\rm TOV}=2.30^{+0.30}_{-0.18}$ $M_\odot$. All of the uncertainties reported above are for 68.3% credible levels.
Recently, an association of GW190425 and FRB 20190425A had been claimed and a highly magnetized neutron star (NS) remnant was speculated.Given the ∼ 2.5-h delay of the occurrence of FRB 20190425A, a uniformly rotating supramassive magnetar is favored since the differential rotation would have been promptly terminated by the magnetic braking.The required maximum gravitational mass (MTOV) of the nonrotating NS is ≈ 2.77M⊙, which is strongly in tension with the relatively low MTOV ≈ 2.25M⊙ obtained in current equation of state (EOS) constraints incorporating perturbative quantum chromodynamics (pQCD) information.However, the current mass-radius and mass-tidal deformability measurements of NSs alone do not convincingly exclude the high MTOV possibility.By performing EOS constraints with mock measurements, we find that with a 2% determination for the radius of PSR J0740+6620-like NS it is possible to distinguish between the low and high MTOV scenarios.We further explore the prospect to resolve the issue of the appropriate density to impose the pQCD constraints with future massive NS observations or determinations of MTOV and/or RTOV.It turns out that measuring the radius of a PSR J0740+6620-like NS is insufficient to probe the EOSs around 5 nuclear saturation density, where the information from pQCD becomes relevant.The additional precise MTOV measurements anyhow could provide insights into the EOS at such a density.Indeed, supposing the central engine of GRB 170817A is a black hole formed via the collapse of a supramassive NS, the resulting MTOV ≈ 2.2M⊙ considerably softens the EOS at the center of the most massive NS, which is in favor of imposing the pQCD constraint at density beyond the one achievable in the NSs.
Recently, the radius of neutron star (NS) PSR $\mathrm{J}0740+6620$ was measured by Neutron Star Interior Composition Explorer (NICER), and an updated measurement of neutron skin thickness of $^{208}\mathrm{Pb}$ (${R}_{\mathrm{skin}}^{208}$) was reported by the PREX-II experiment. These new measurements can help us better understand the unknown equation of state (EOS) of dense matter. In this work, we adopt a hybrid parameterization method, which incorporates the nuclear empirical parameterization and some widely used phenomenological parameterizations, to analyze the results of nuclear experiments and astrophysical observations. With the joint Bayesian analysis of GW170817, PSR $\mathrm{J}0030+0451$, and PSR $\mathrm{J}0740+6620$, the parameters that characterize the ultradense matter EOS are constrained. We find that the slope parameter $L$ is approximately constrained to ${70}_{\ensuremath{-}18}^{+21}\text{ }\text{ }\mathrm{MeV}$, which predicts ${R}_{\mathrm{skin}}^{208}=0.20{4}_{\ensuremath{-}0.026}^{+0.030}\text{ }\text{ }\mathrm{fm}$ by using the universal relation between ${R}_{\mathrm{skin}}^{208}$ and $L$. The bulk properties of canonical $1.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ NS (e.g., ${R}_{1.4}$ and ${\mathrm{\ensuremath{\Lambda}}}_{1.4}$) as well as the pressure (${P}_{2{\ensuremath{\rho}}_{\mathrm{sat}}}$) at two times the nuclear saturation density are well constrained by the data; i.e., ${R}_{1.4}$, ${\mathrm{\ensuremath{\Lambda}}}_{1.4}$, and ${P}_{2{\ensuremath{\rho}}_{\mathrm{sat}}}$ are approximately constrained to $12.3\ifmmode\pm\else\textpm\fi{}0.7\text{ }\text{ }\mathrm{km}$, ${330}_{\ensuremath{-}100}^{+140}$, and ${4.1}_{\ensuremath{-}1.2}^{+1.5}\ifmmode\times\else\texttimes\fi{}{10}^{34}\text{ }\text{ }\mathrm{dyn}\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$, respectively. Besides, we find that the Bayes evidences of the hybrid star and normal NS assumptions are comparable, which indicates that current observation data are compatible with quarkyonic matter existing in the core of massive star. Finally, in the case of normal NS assumption, we obtain a constraint for the maximum mass of nonrotating NS ${M}_{\mathrm{TOV}}=2.3{0}_{\ensuremath{-}0.18}^{+0.30}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. Based on this result and the current observational and theoretical knowledge about the NS population and its EOS, we find that a binary black hole merger scenario for GW190814 is more plausible. All of the uncertainties reported above are for 68.3% credible levels.
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