Neutron Star Mass Research Articles

Ultrawide Black Hole—Neutron Star Binaries as a Possible Source for Gravitational Waves and Short Gamma-Ray Bursts

The third observing run of the LIGO/Virgo/KARGA collaboration reported a few neutron star–black hole (NSBH) merger events. While NSBH mergers have yet to receive extensive theoretical attention, they may have a promising electromagnetic signature in the form of short gamma-ray bursts. Here we show that NSBH dynamical mergers can naturally form from ultrawide binaries in the field. Flyby gravitational interactions with other neighbors in the galaxy in these ultrawide systems may result in high eccentricity that drives the binary into a merger. We show that this process can result in a merger rate at the order of ∼10 Gpc−3 yr−1 (∼1 Gpc−3 yr−1) for elliptical (spiral) galaxies. This channel predicts a higher merger rate with a higher velocity dispersion of the host galaxy, a delay time distribution that is steeper than uniform but shallower than 1/t, and a higher merger rate for a lower black hole to neutron star mass ratio.

The role of supernova convection for the lower mass gap in the isolated binary formation of gravitational wave sources

ABSTRACT Understanding the astrophysical phenomena involving compact objects requires an insight about the engine behind the core-collapse supernovae (SNe) and the fate of the stellar collapse of massive stars. In particular, this insight is crucial in developing an understanding of the origin and formation channels of the growing populations of the detected black hole–black hole, black hole–neutron star, and neutron star–neutron star mergers. The time-scale of convection growth may have a large effect on the strength of SN explosion and therefore also on the mass distribution of stellar remnants. We adopt new formulas for the relation between the pre-SN star properties and their remnants and check how they impact the population of double compact object (DCO) mergers formed via the isolated binary evolution. The new formulas give one the ability to test a wide spectrum of assumptions on the convection growth time. In particular, the different variants allow for a smooth transition between having a deep mass gap and a remnant mass distribution filled by massive neutron stars and low-mass black holes. We present the distribution of masses, mass ratios, and the local merger rate densities of DCO for the different variants of new formulas and test them together with different approaches to other highly uncertain processes. We find that the mass distribution of DCO mergers is sensitive to the adopted assumption on the SN convection growth time-scale up to $m_1+m_2 \lesssim 35 \, \mathrm{M}_{\odot }$. Between the two extreme tested variants the probability of compact object formation within the mass gap may differ by up to approximately two orders of magnitude.

Kaon–baryon coupling schemes and kaon condensation in hyperon-mixed matter

Abstract The possible coexistence of kaon condensation and hyperons in highly dense matter [the (Y + K) phase] is investigated on the basis of the relativistic mean-field theory combined with the effective chiral Lagrangian. Two coupling schemes for the s-wave kaon–baryon interaction are compared regarding the onset density of kaon condensation in hyperon-mixed matter and the equation of state for the developed (Y + K) phase. One is the contact interaction scheme related to the nonlinear effective chiral Lagrangian. The other is the meson exchange scheme, where the interaction vertices between the kaon field and baryons are described by an exchange of mesons (σ, σ* mesons for scalar coupling, and ω, ρ, ϕ mesons for vector coupling). It is shown that in the meson exchange scheme, the contribution from the nonlinear scalar self-interaction gives rise to a repulsive effect for the kaon effective energy, pushing up the onset density of kaon condensation as compared with the contact interaction scheme. In general, the difference in kaon–baryon dynamics between the contact interaction scheme and the meson exchange scheme relies on the specific forms of the nonlinear self-interacting meson terms. They generate many-baryon forces through the equations of motion for the meson mean fields. However, they should have a definite effect on the ground state properties of nuclear matter only around the saturation density. It is shown that the nonlinear self-interacting term is not relevant to repulsive energy leading to stiffening of the equation of state at high densities, and that it cannot be compensated with a large attractive energy due to the appearance of the (Y + K) phase in the case of the contact interaction scheme. We also discuss what effects are necessary in the contact interaction scheme to make the equation of state with (Y + K) phase stiff enough to be consistent with recent observations of massive neutron stars.

Nearly model-independent constraints on dense matter equation of state in a Bayesian approach

We apply a Bayesian approach to construct a large number of minimally constrained equations of state (EOSs) and study their correlations with a few selected properties of a neutron star (NS). Our set of minimal constraints includes a few basic properties of saturated nuclear matter and low-density pure neutron matter EOS which is obtained from a precise next-to-next-to-next-to-leading-order (${\mathrm{N}}^{3}\mathrm{LO}$) calculation in chiral effective field theory. The tidal deformability and radius of a NS with mass $1--2\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ are found to be strongly correlated with the pressure of $\ensuremath{\beta}$-equilibrated matter at densities higher than the saturation density (${\ensuremath{\rho}}_{0}=0.16\text{ }\text{ }{\mathrm{fm}}^{\ensuremath{-}3}$) in a nearly model-independent manner. These correlations are employed to parametrize the pressure for $\ensuremath{\beta}$-equilibrated matter, around $2{\ensuremath{\rho}}_{0}$, as a function of neutron star mass and the corresponding tidal deformability. The maximum mass of the neutron star is also found to be strongly correlated with the pressure of $\ensuremath{\beta}$-equilibrated matter at densities $\ensuremath{\sim}4.5{\ensuremath{\rho}}_{0}$.

Relativistic mean field model parametrizations in the light of GW170817, GW190814, and PSR J0740+6620

Three parametrizations DOPS1, DOPS2, and DOPS3 (named after the Department of Physics Shimla) of the relativistic mean field model have been proposed with the inclusion of all possible self and mixed interactions between the scalar-isoscalar ($\ensuremath{\sigma}$), vector-isoscalar ($\ensuremath{\omega}$), and vector-isovector ($\ensuremath{\rho}$) mesons up to quartic order. The generated parameter sets are in harmony with the finite and bulk nuclear matter properties. A set of equations of state (EOSs) composed of pure hadronic (nucleonic) matter and nucleonic with quark matter (hybrid EOSs) for superdense hadron-quark matter in $\ensuremath{\beta}$ equilibrium is obtained. The quark matter phase is calculated by using the three-flavor Nambu-Jona-Lasinio (NJL) model. The maximum mass of a nonrotating neutron star with DOPS1 parametrization is found to be around $2.6M\ensuremath{\bigodot}$ for the pure nucleonic matter, which satisfies the recent gravitational wave analysis of GW190814 [Abbott et al., Astrophys. J. Lett. 896, L44 (2020)] with possible maximum mass constraint indicating that the secondary component of GW190814 could be a nonrotating heaviest neutron star composed of pure nucleonic matter. EOSs computed with the DOPS2 and DOPS3 parametrizations satisfy the x-ray observational data [Steiner et al., Astrophys. J. 722, 33 (2010)] and the recent observations of GW170817 maximum mass constraint of a stable nonrotating neutron star in the range $2.01\ifmmode\pm\else\textpm\fi{}0.04--2.16\ifmmode\pm\else\textpm\fi{}0.03M\ensuremath{\bigodot}$ [Rezzolla et al., Astrophys. J. Lett. 852, L25 (2018)] and also in good agreement with constraints on mass and radius measurement for PSR $\mathrm{J}0740+6620$ (NICER) [Riley et al., Astrophys. J. Lett. 918, L27 (2021); Miller et al., Astrophys. J. Lett. 918, L28 (2021)]. The hybrid EOSs obtained with the NJL model also satisfy astrophysical constraints on the maximum mass of a neutron star from PSR J1614-2230 [Demorest et al., Nature (London) 467, 1081 (2010)]. We also present the results for dimensionless tidal deformability, $\mathrm{\ensuremath{\Lambda}}$ which are consistent with the waveform models analysis of GW170817.

MAXI J1957+032: a new accreting millisecond X-ray pulsar in an ultra-compact binary

ABSTRACT The detection of coherent X-ray pulsations at ∼314 Hz (3.2 ms) classifies MAXI J1957+032 as a fast-rotating, accreting neutron star. We present the temporal and spectral analysis performed using NICER observations collected during the latest outburst of the source. Doppler modulation of the X-ray pulsation revealed the ultra-compact nature of the binary system characterized by an orbital period of ∼1 h and a projected semimajor axis of 14 lt-ms. The neutron star binary mass function suggests a minimum donor mass of 1.7 × 10−2 M⊙, assuming a neutron star mass of 1.4 M⊙ and a binary inclination angle lower than 60 deg. This assumption is supported by the lack of eclipses or dips in the X-ray light curve of the source. We characterized the 0.5–10 keV energy spectrum of the source in outburst as the superposition of a relatively cold black-body-like thermal emission compatible with the emission from the neutron star surface and a Comptonization component with photon index consistent with a typical hard state. We did not find evidence for iron K α lines or reflection components.

Unified neutron star EOSs and neutron star structures in RMF models

In the framework of the Thomas-Fermi approximation, we systematically study the EOSs and microscopic structures of neutron star matter in a vast density range with n b ≈ 10−10-2 fm−3, where various covariant density functionals are adopted, i.e., those with nonlinear self couplings (NL3, PK1, TM1, GM1, MTVTC) and density-dependent couplings (DD-LZ1, DDME-X, PKDD, DD-ME2, DD2, TW99). It is found that the EOSs generally coincide with each other at n b ≲ 10−4 fm−3 and 0.1 fm−3 ≲ n b ≲ 0.3 fm−3, while in other density regions they are sensitive to the effective interactions between nucleons. By adopting functionals with a larger slope of symmetry energy L, the curvature parameter K sym and neutron drip density generally increases, while the droplet size, proton number of nucleus, core-crust transition density, and onset density of non-spherical nuclei, decrease. All functionals predict neutron stars with maximum masses exceeding the two-solar-mass limit, while those of DD2, DD-LZ1, DD-ME2, and DDME-X predict optimum neutron star radii according to the observational constraints. Nevertheless, the corresponding skewness coefficients J are much larger than expected, while only the functionals MTVTC and TW99 meet the start-of-art constraints on J. More accurate measurements on the radius of PSR J0740 + 6620 and the maximum mass of neutron stars are thus essential to identify the functional that satisfies all constraints from nuclear physics and astrophysical observations. Approximate linear correlations between neutron stars’ radii at M = 1.4M ⊙ and 2M ⊙, the slope L and curvature parameter K sym of symmetry energy are observed as well, which are mainly attributed to the curvature-slope correlations in the functionals adopted here. The results presented here are applicable for investigations of the structures and evolutions of compact stars in a unified manner.

Constraining neutron star properties with a new equation of state insensitive approach

Instead of parameterizing the pressure-density relation of a neutron star (NS), one can parameterize its macroscopic properties such as mass ($M$), radius ($R$), and dimensionless tidal deformability ($\Lambda$) to infer the equation of state (EoS) combining electromagnetic and gravitational wave (GW) observations. We present a new method to parameterize $R(M)$ and $\Lambda(M)$ relations, which approximate the candidate EoSs with accuracy better than 5\% for all masses and span a broad region of $M-R-\Lambda$ plane. Using this method we combine the $M-\Lambda$ measurement from GW170817 and GW190425, and simultaneous $M-R$ measurement of PSR J0030+0451 and PSR J0740+6620 to place joint constraints on NS properties. At 90 \% confidence, we infer $R_{1.4}=12.05_{-0.87}^{+0.98}$ km and $\Lambda_{1.4}=372_{-150}^{+220}$ for a $1.4 M_{\odot}$ NS, and $R_{2.08}=12.65_{-1.46}^{+1.36}$ km for a $2.08 M_{\odot}$ NS. Furthermore, we use the inferred values of the maximum mass of a nonrotating NS $M_{\rm max}=2.52_{-0.29}^{+0.33} M_{\odot}$ to investigate the nature of the secondary objects in three potential neutron star-black hole merger (NSBH) system.

Solving Tolman–Oppenheimer–Volkoff equations in f(T) gravity: A novel approach applied to some realistic equations of state

There are many ways to probe alternative theories of gravity, namely, via experimental tests at solar system scale, cosmological data and models, gravitational waves and compact objects. In this paper, we consider a model of gravity with torsion [Formula: see text] applied to compact objects such as neutron stars (NSs) for a couple of realistic equations of state (EOS). To do so, we follow our previous articles, in which we show how to model compact stars in [Formula: see text] gravity by obtaining its corresponding Tolman–Oppenheimer–Volkof equations. In this modeling of NS in [Formula: see text] gravity presented here, we calculate, among other things, the maximum mass allowed for a given realistic EOS, which would also allow us to evaluate which models are in accordance with the observations. The results already known to General Relativity must be reproduced to some extent and, eventually, we can find models that allow higher maximum masses for NSs than Relativity itself, which could explain, for example, the secondary component of the event GW190814, if this star is a massive NS.

The Hadron-quark Crossover in Neutron Star within Gaussian Process Regression Method

The equations of state of the neutron star at the hadron-quark crossover region are interpolated with the Gaussian process regression (GPR) method, which can reduce the randomness of present interpolation schemes. The relativistic mean-field (RMF) model and Nambu–Jona-Lasinio (NJL) model are employed to describe the hadronic phase and quark phase, respectively. In the RMF model, the coupling term between ω and ρ mesons is considered to control the density-dependent behaviors of symmetry energy, i.e., the slope of symmetry energy L. Furthermore, the vector interaction between quarks is included in the NJL model to obtain the additional repulsive contributions. Their coupling strengths and the crossover windows are discussed in the present framework under the constraints on the neutron star from gravitational-wave detections, massive neutron star measurements, mass–radius simultaneous observation of the NICER Collaboration, and the neutron skin thickness of 208Pb from PREX-II. It is found that the slope of symmetry energy, L, should be around 50−90 MeV and the crossover window is (0.3, 0.6) fm−3 with these observables. Furthermore, the uncertainties of neutron star masses and radii in the hadron-quark crossover regions are also predicted by the GPR method.

Neural network reconstruction of the dense matter equation of state from neutron star observables

The Equation of State (EoS) of strongly interacting cold and hot ultra-dense QCD matter remains a major challenge in the field of nuclear astrophysics. With the advancements in measurements of neutron star masses, radii, and tidal deformabilities, from electromagnetic and gravitational wave observations, neutron stars play an important role in constraining the ultra-dense QCD matter EoS. In this work, we present a novel method that exploits deep learning techniques to reconstruct the neutron star EoS from mass-radius (M-R) observations. We employ neural networks (NNs) to represent the EoS in a model-independent way, within the range of ∼1-7 times the nuclear saturation density. The unsupervised Automatic Differentiation (AD) framework is implemented to optimize the EoS, so as to yield through TOV equations, an M-R curve that best fits the observations.We demonstrate that this method works by rebuilding the EoS on mock data, i.e., mass-radius pairs derived from a randomly generated polytropic EoS. The reconstructed EoS fits the mock data with reasonable accuracy, using just 11 mock M-R pairs observations, close to the current number of actual observations.

Upgraded GMRT survey for pulsars in globular clusters

Context. Globular clusters (GCs) contain a unique pulsar population, with many exotic systems that can form only in their dense stellar environments. Such systems are potentially very interesting for new tests of gravity theories and neutron-star mass measurements. Aims. The leap in sensitivity of the upgraded Giant Metrewave Radio Telescope (uGMRT) in India, especially at low radio frequencies (< 1 GHz), motivated a new search for radio pulsars in a group of eight southern GCs. We aim to image these clusters in order to have independent measurements of the radio fluxes of known pulsars and the identification of bright radio sources that could be pulsars missed by pulsation search pipelines due to their inherent limitations. Methods. The observations were conducted at 650 MHz (Band 4 receivers) on Terzan 5, NGC 6441, NGC 6440, and NGC 6544, and at 400 MHz (Band 3 receivers) on NGC 6652, NGC 6539, NGC 1851, and M 30. Segmented acceleration and jerk searches were performed on the data. Simultaneously, we obtained interferometric data on these clusters, which were later converted into radio images. Results. We discovered PSR J1835−3259B, a 1.83-ms pulsar in NGC 6652; this is in a near-circular wide orbit of 28.7-h with an unidentified low-mass (∼0.2 M⊙) companion, likely a helium white dwarf. We derived a ten-year timing solution for this system. We also present measurements of scattering, flux densities, and spectral indices for some of the previously known pulsars in these GCs. Conclusions. A significant fraction of the pulsars in these clusters have steep spectral indices. Additionally, we detected eight radio point sources not associated with any known pulsar positions in the radio images. There are four newly identified sources, three in NGC 6652 and one in NGC 6539, as well as one previously identified source in NGC 1851, NGC 6440, NGC 6544, and Terzan 5. Surprisingly, our images show that our newly discovered pulsar, PSR J1835−3259B, is the brightest pulsar in all GCs we have imaged; like other pulsars with broad profiles (Terzan 5 C and O), its flux density in the radio images is much larger than in its pulsations. This indicates that their pulsed emission is only a fraction of their total emission. The detection of radio sources outside the core radii but well within the tidal radii of these clusters show that future GC surveys should complement the search analysis by using the imaging capability of interferometers, and preferentially synthesise large number of search beams in order to obtain a larger field of view.

Thermodynamics of Hot Neutron Stars and Universal Relations

Over the last few years, the detection of gravitational waves from binary neutron star systems has rekindled our hopes for a deeper understanding of the unknown nature of ultradense matter. In particular, gravitational wave constraints on the tidal deformability of a neutron star can be translated into constraints on several neutron star properties using a set of universal relations. Apart from binary neutron star mergers, supernova explosions are also important candidates for the detection of multimessenger signals. Such observations may allow us to impose significant constraints on the binding energy of neutron stars. The purpose of the present study is twofold. Firstly, we investigate the agreement of finite temperature equations of state with established universal relations. Secondly, we examine the possible existence of a universal relation between the binding energy and the dimensionless tidal deformability, which are the bulk properties connected to the most promising sources for multimessenger signals. We find that hot equations of state are not always compatible with accepted universal relations. Therefore, the use of such expressions for probing general relativity or imposing constraints on the structure of neutron stars would be inconclusive (when thermal effects are present). Additionally, we show that the binding energy and the dimensionless tidal deformability exhibit a universal trend at least for moderate neutron star masses. The latter allows us to set bounds on the binding energy of a 1.4 M⊙ neutron star using data from the GW170817 event. Finally, we provide a relation between the compactness, the binding energy and the dimensionless tidal deformability of a neutron star that is accurate for cold and hot isentropic equations of state.

PSR J0952−0607: The Fastest and Heaviest Known Galactic Neutron Star

We describe Keck-telescope spectrophotometry and imaging of the companion of the “black widow” pulsar PSR J0952−0607, the fastest known spinning neutron star (NS) in the disk of the Milky Way. The companion is very faint at minimum brightness, presenting observational challenges, but we have measured multicolor light curves and obtained radial velocities over the illuminated “day” half of the orbit. The model fits indicate system inclination i = 59.°8 ± 1.°9 and a pulsar mass M NS = 2.35 ± 0.17 M ⊙, the largest well-measured mass found to date. Modeling uncertainties are small, since the heating is not extreme; the companion lies well within its Roche lobe and a simple direct-heating model provides the best fit. If the NS started at a typical pulsar birth mass, nearly 1 M ⊙ has been accreted; this may be connected with the especially low intrinsic dipole surface field, estimated at 6 × 107 G. Joined with reanalysis of other black widow and redback pulsars, we find that the minimum value for the maximum NS mass is (2.09 M ⊙) at 1σ (3σ) confidence. This is ∼ 0.15 M ⊙ heavier than the lower limit on implied by the white dwarf–pulsar binaries measured via radio Shapiro-delay techniques.

Massive Neutron Stars and White Dwarfs as Noncommutative Fuzzy Spheres

Over the last couple of decades, there have been direct and indirect evidences for massive compact objects than their conventional counterparts. A couple of such examples are super-Chandrasekhar white dwarfs and massive neutron stars. The observations of more than a dozen peculiar over-luminous type Ia supernovae predict their origins from super-Chandrasekhar white dwarf progenitors. On the other hand, recent gravitational wave detection and some pulsar observations provide arguments for massive neutron stars, lying in the famous mass-gap between lowest astrophysical black hole and conventional highest neutron star masses. We show that the idea of a squashed fuzzy sphere, which brings in noncommutative geometry, can self-consistently explain either of the massive objects as if they are actually fuzzy or squashed fuzzy spheres. Noncommutative geometry is a branch of quantum gravity. If the above proposal is correct, it will provide observational evidences for noncommutativity.

Probing the Incompressibility of Nuclear Matter at Ultrahigh Density through the Prompt Collapse of Asymmetric Neutron Star Binaries.

Using 250 neutron star merger simulations with microphysics, we explore for the first time the role of nuclear incompressibility in the prompt collapse threshold for binaries with different mass ratios. We demonstrate that observations of prompt collapse thresholds, either from binaries with two different mass ratios or with one mass ratio but combined with the knowledge of the maximum neutron star mass or compactness, will constrain the incompressibility at the maximum neutron star density K_{max} to within tens of percent. This otherwise inaccessible measure of K_{max} can potentially reveal the presence of hyperons or quarks inside neutron stars.

General-relativistic neutrino-radiation magnetohydrodynamic simulation of seconds-long black hole-neutron star mergers

Seconds-long numerical-relativity simulations for black hole-neutron star mergers are performed for the first time to obtain a self-consistent picture of the merger and post-merger evolution processes. To investigate the case that tidal disruption takes place, we choose the initial mass of the black hole to be $5.4M_\odot$ or $8.1M_\odot$ with the dimensionless spin of 0.75. The neutron-star mass is fixed to be $1.35M_\odot$. We find that after the tidal disruption, dynamical mass ejection takes place spending $\lesssim 10$ ms together with the formation of a massive accretion disk. Subsequently, the magnetic field in the disk is amplified by the magnetic winding and magnetorotational instability, establishing a turbulent state and inducing the angular momentum transport. The post-merger mass ejection by the magnetically-induced viscous effect sets in at $\sim 300$-500\,ms after the tidal disruption, at which the neutrino luminosity drops below $\sim 10^{51.5}\,{\rm erg/s}$, and continues for several hundreds ms. A magnetosphere near the rotational axis of the black hole is developed after the matter and magnetic flux fall into the black hole from the accretion disk, and high-intensity Poynting flux generation sets in at a few hundreds ms after the tidal disruption. The intensity of the Poynting flux becomes low after the significant post-merger mass ejection, because the opening angle of the magnetosphere increases. The lifetime for the stage with the strong Poynting flux is $1$-2 s, which agrees with the typical duration of short-hard gamma-ray bursts.

Observing Supernova Neutrino Light Curves with Super-Kamiokande. III. Extraction of Mass and Radius of Neutron Stars from Synthetic Data

Neutrinos are guaranteed to be observable from the next Galactic supernova (SN). Optical light and gravitational waves are also observable, but may be difficult to observe if the location of the SN in the Galaxy or the details of the explosion are unsuitable. The key to observing the next SN is to first use neutrinos to understand various physical quantities and then link them to other signals. In this paper, we present Monte Carlo sampling calculations of neutrino events from Galactic SN explosions observed with Super-Kamiokande. The analytical solution of neutrino emission, which represents the long-term evolution of the neutrino light curve from SNe, is used as a theoretical template. It gives the event rate and event spectrum through inverse beta decay interactions with explicit model parameter dependence. Parameter estimation is performed on these simulated sample data by fitting least squares using the analytical solution. The results show that the mass, radius, and total energy of a remnant neutron star produced by an SN can be determined with an accuracy of ∼ 0.1 M ⊙, ∼1 km, and ∼ 1051 erg, respectively, for a Galactic SN at 8 kpc.

X-Ray Observations of the Isolated Black Hole Candidate OGLE-2011-BLG-0462 and Other Collapsed Objects Discovered through Gravitational Microlensing

Isolated black holes and neutron stars can be revealed through the observation of long-duration gravitational microlensing events. A few candidates have been found in surveys of stars in the direction of the Galactic bulge. Recently, thanks to the addition of astrometric information at milliarcsecond level, it has been possible to reduce the uncertainties in the masses and distances for some of these “dark” gravitational lenses and select the most promising candidates. These isolated compact objects might emit X-rays powered by accretion from the interstellar medium. Using data of the Chandra, XMM-Newton, and INTEGRAL satellites, we searched for X-ray emission in the isolated black hole candidate OGLE-2011-BLG-0462, and in several other putative collapsed objects found with gravitational microlensing. OGLE-2011-BLG-0462 has been recently interpreted as a 7.1 M ⊙ black hole at a distance of 1.6 kpc, although a different group obtained a mass range (1.6–4.4 M ⊙) that cannot exclude a massive neutron star. We have derived upper limits on the flux from OGLE-2011-BLG-0462 of 9 × 10−15 erg cm−2 s−1 in the 0.5–7 keV range and ∼2 × 10−12 erg cm−2 s−1 in the 17–60 keV range. The implied X-ray luminosity is consistent with the small radiative efficiency expected for a black hole and disfavors a neutron star interpretation. Limits down to a factor of about five lower are obtained for the soft X-ray flux of other candidates, but their interpretation is affected by larger uncertainties in the masses, distances, and spatial velocities.

Constraining properties of massive neutron star through R-mode

Constraining properties of massive neutron star through R-mode