Neutron Star Mass Distribution Research Articles

Impact of lensing of gravitational waves on the observed distribution of neutron star masses

The distribution of masses of neutron stars, particularly the maximum mass value, is considered a probe of their formation, evolution and internal physics (i.e., equation of state). This mass distribution could in principle be inferred from the detection of gravitational waves from binary neutron star mergers. Using mock catalogues of 105 dark sirens events, expected to be detected by Einstein Telescope over an operational period of , we show how the biased luminosity distance measurement induced by gravitational lensing affects the inferred redshift and mass of the merger. This results in higher observed masses than expected. Up to 2% of the events are predicted to fall above the maximum allowed neutron star mass depending on the intrinsic mass distribution and signal-to-noise ratio threshold adopted. The underlying true mass distribution and maximum mass could still be approximately recovered in the case of bright standard sirens.

A targeted radio pulsar survey of redback candidates with MeerKAT

ABSTRACT Redbacks are millisecond pulsar binaries with low-mass, irradiated companions. These systems have a rich phenomenology that can be used to probe binary evolution models, pulsar wind physics, and the neutron star mass distribution. A number of high-confidence redback candidates have been identified through searches for variable optical and X-ray sources within the localization regions of unidentified but pulsar-like Fermi-LAT gamma-ray sources. However, these candidates remain unconfirmed until pulsations are detected. As part of the TRAPUM project, we searched for radio pulsations from six of these redback candidates with MeerKAT. We discovered three new radio millisecond pulsars, PSRs J0838−2827, J0955−3947, and J2333−5526, confirming their redback nature. PSR J0838−2827 remained undetected for 2 yr after our discovery despite repeated observations, likely due to evaporated material absorbing the radio emission for long periods of time. While, to our knowledge, this system has not undergone a transition to an accreting state, the disappearance, likely caused by extreme eclipses, illustrates the transient nature of spider pulsars and the heavy selection bias in uncovering their radio population. Radio timing enabled the detection of gamma-ray pulsations from all three pulsars, from which we obtained 15-yr timing solutions. All of these sources exhibit complex orbital period variations consistent with gravitational quadrupole moment variations in the companion stars. These timing solutions also constrain the binary mass ratios, allowing us to narrow down the pulsar masses. We find that PSR J2333−5526 may have a neutron star mass in excess of 2 M⊙.

Mass Distribution and Maximum Mass of Neutron Stars: Effects of Orbital Inclination Angle

Matter at ultra-high densities finds a physical realization inside neutron stars. One key property is their maximum mass, which has far-reaching implications for astrophysics and the equation of state of ultra dense matter. In this work, we employ Bayesian analysis to scrutinize the mass distribution and maximum mass threshold of galactic neutron stars. We compare two distinct models to assess the impact of assuming a uniform distribution for the most important quantity, the cosine of orbital inclination angles (i), which has been a common practice in previous analyses. This prevailing assumption yields a maximum mass of 2.25 M⊙ (2.15–3.32 M⊙ within 90% confidence), with a strong peak around the maximum value. However, in the second model, which indirectly includes observational constraints of i, the analysis supports a mass limit of 2.56−0.58+0.87M⊙ (2σ uncertainty), a result that points in the same direction as some recent results gathered from gravitational wave observations, although their statistics are still limited. This work stresses the importance of an accurate treatment of orbital inclination angles, and contributes to the ongoing debate about the maximum neutron star mass, further emphasizing the critical role of uncertainties in the individual neutron star mass determinations.

An optimal envelope ejection efficiency for merging neutron stars

ABSTRACT We use the rapid binary stellar evolution code binary_c to estimate the rate of merging neutron stars with numerous combinations of envelope ejection efficiency and natal kick dispersion. We find a peak in the local rate of merging neutron stars around α ≈ 0.3–0.4, depending on the metallicity, where α is the efficiency of utilizing orbital energy to unbind the envelope. The peak height decreases with increasing electron-capture supernova kick dispersion σECSN. We explain the peak as a competition between the total number of systems that survive the common-envelope phase increasing with α and their separation, which increases with α as well. Increasing α reduces the fraction of systems that merge within a time shorter than the age of the Universe and results in different mass distributions for merging and non-merging double neutron stars. This offers a possible explanation for the discrepancy between the Galactic double neutron star mass distribution and the observed massive merging neutron star event GW190425. Within the α–σECSN parameter space that we investigate, the rate of merging neutron stars spans several orders of magnitude up to more than $1\times 10^{3} \, \mathrm{Gpc}^{-3}\, \mathrm{yr}^{-1}$ and can be higher than the observed upper limit or lower than the observed lower limit inferred thus far from merging neutron stars detected by gravitational waves. Our results stress the importance of common-envelope physics for the quantitative prediction and interpretation of merging binary neutron star events in this new age of gravitational wave astronomy.

Population of Merging Compact Binaries Inferred Using Gravitational Waves through GWTC-3

We report on the population properties of compact binary mergers inferred from gravitational-wave observations of these systems during the first three LIGO-Virgo observing runs. The Gravitational-Wave Transient Catalog 3 (GWTC-3) contains signals consistent with three classes of binary mergers: binary black hole, binary neutron star, and neutron star–black hole mergers. We infer the binary neutron star merger rate to be between 10 and 1700 Gpc−3 yr−1 and the neutron star–black hole merger rate to be between 7.8 and 140 Gpc−3 yr−1, assuming a constant rate density in the comoving frame and taking the union of 90% credible intervals for methods used in this work. We infer the binary black hole merger rate, allowing for evolution with redshift, to be between 17.9 and 44 Gpc−3 yr−1 at a fiducial redshift (z=0.2). The rate of binary black hole mergers is observed to increase with redshift at a rate proportional to (1+z)κ with κ=2.9−1.8+1.7 for z≲1. Using both binary neutron star and neutron star–black hole binaries, we obtain a broad, relatively flat neutron star mass distribution extending from 1.2−0.2+0.1 to 2.0−0.3+0.3M⊙. We confidently determine that the merger rate as a function of mass sharply declines after the expected maximum neutron star mass, but cannot yet confirm or rule out the existence of a lower mass gap between neutron stars and black holes. We also find the binary black hole mass distribution has localized over- and underdensities relative to a power-law distribution, with peaks emerging at chirp masses of 8.3−0.5+0.3 and 27.9−1.8+1.9M⊙. While we continue to find that the mass distribution of a binary’s more massive component strongly decreases as a function of primary mass, we observe no evidence of a strongly suppressed merger rate above approximately 60M⊙, which would indicate the presence of a upper mass gap. Observed black hole spins are small, with half of spin magnitudes below χi≈0.25. While the majority of spins are preferentially aligned with the orbital angular momentum, we infer evidence of antialigned spins among the binary population. We observe an increase in spin magnitude for systems with more unequal-mass ratio. We also observe evidence of misalignment of spins relative to the orbital angular momentum.22 MoreReceived 4 February 2022Revised 28 October 2022Accepted 19 December 2022DOI:https://doi.org/10.1103/PhysRevX.13.011048Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGravitational wave sourcesGravitational wavesTechniquesGravitational wave detectionGravitation, Cosmology & Astrophysics

Investigating the distribution of double neutron stars and unconventional component mass

ABSTRACTThe mass distribution of double neutron stars (DNSs) can help us to understand the evolution of binary systems, which can also contain information about DNSs induced by gravitational wave radiation. Henceforth, for the 25 pairs of DNS systems so far discovered by radio observations, we have only statistically analysed 13 systems with precisely measured masses of two-component NSs, by employing the classical Gaussian mixture models based on the Akaike and Bayesian information criteria. The result infers that the mass distributions for recycled and non-recycled NSs follow a double-Gaussian and single-Gaussian distribution, respectively. In the conventional scenario of DNS formation, the mass of the first formed recycled NS is higher than that of the second-formed companion NS. However, there exist some unconventional cases with a reverse mass ratio. To explore the phenomenon of this ‘unconventional component mass’ of DNSs, we employed Monte Carlo sampling. We find that the unconventional DNS systems occupy about 27.7 per cent of all DNSs, which could be a useful reference for the future gravitational wave detection by LIGO/Virgo. Furthermore, we discuss a possible explanation for the unconventional DNS mass ratio, which involves the recycling process and its birth rate. This also has an implication for the mass distribution of the DNS progenitors.

Constraints on the merging binary neutron star mass distribution and equation of state based on the incidence of jets in the population

A relativistic jet has been produced in the single well-localised binary neutron star (BNS) merger detected to date in gravitational waves (GWs), and the local rates of BNS mergers and short gamma-ray bursts are of the same order of magnitude. This suggests that jet formation is not a rare outcome for BNS mergers, and we show that this intuition can be turned into a quantitative constraint: at least about one-third of GW-detected BNS mergers and at least about one-fifth of all BNS mergers should produce a successful jet (90% credible level). Whether a jet is launched depends on the properties of the merger remnant and of the surrounding accretion disc, which in turn are a function of the progenitor binary masses and equation of state (EoS). The incidence of jets in the population therefore carries information about the binary component mass distribution and EoS. Under the assumption that a jet can only be produced by a black hole remnant surrounded by a non-negligible accretion disc, we show how the jet incidence can be used to place a joint constraint on the space of BNS component mass distributions and EoS. The result points to a broad mass distribution, with particularly strong support for masses in the 1.3 − 1.6 M⊙ range. The constraints on the EoS are shallow, but we show how they will tighten as the knowledge on the jet incidence improves. We also discuss how to extend the method to include future BNS mergers, with possibly uncertain jet associations.

Inferring the Neutron Star Maximum Mass and Lower Mass Gap in Neutron Star–Black Hole Systems with Spin

Gravitational-wave (GW) detections of merging neutron star–black hole (NSBH) systems probe astrophysical neutron star (NS) and black hole (BH) mass distributions, especially at the transition between NS and BH masses. Of particular interest are the maximum NS mass, minimum BH mass, and potential mass gap between them. While previous GW population analyses assumed all NSs obey the same maximum mass, if rapidly spinning NSs exist, they can extend to larger maximum masses than nonspinning NSs. In fact, several authors have proposed that the ∼2.6 M ⊙ object in the event GW190814—either the most massive NS or least massive BH observed to date—is a rapidly spinning NS. We therefore infer the NSBH mass distribution jointly with the NS spin distribution, modeling the NS maximum mass as a function of spin. Using four LIGO–Virgo NSBH events including GW190814, if we assume that the NS spin distribution is uniformly distributed up to the maximum (breakup) spin, we infer the maximum nonspinning NS mass is (90% credibility), while assuming only nonspinning NSs, the NS maximum mass must be >2.53 M ⊙ (90% credibility). The data support the mass gap’s existence, with a minimum BH mass at . With future observations, under simplified assumptions, 150 NSBH events may constrain the maximum nonspinning NS mass to ±0.02 M ⊙, and we may even measure the relation between the NS spin and maximum mass entirely from GW data. If rapidly rotating NSs exist, their spins and masses must be modeled simultaneously to avoid biasing the NS maximum mass.

Modified gravitational wave propagation and the binary neutron star mass function

Modified gravitational wave (GW) propagation is a generic phenomenon in modified gravity. It affects the reconstruction of the redshift of coalescing binaries from the luminosity distance measured by GW detectors, and therefore the reconstruction of the actual masses of the component compact stars from the observed (`detector-frame') masses. We show that, thanks to the narrowness of the mass distribution of binary neutron stars, this effect can provide a clear signature of modified gravity, particularly for the redshifts explored by third generation GW detectors such as Einstein Telescope and Cosmic Explorer.

The effect of spin mismodelling on gravitational-wave measurements of the binary neutron star mass distribution

Abstract The binary neutron star (BNS) mass distribution measured with gravitational-wave observations has the potential to reveal information about the dense matter equation of state, supernova physics, the expansion rate of the Universe, and tests of general relativity. As most current gravitational-wave analyses measuring the BNS mass distribution do not simultaneously fit the spin distribution, the implied population-level spin distribution is the same as the spin prior applied when analysing individual sources. In this work, we demonstrate that introducing a mismatch between the implied and true BNS spin distributions can lead to biases in the inferred mass distribution. This is due to the strong correlations between the measurements of the mass ratio and spin components aligned with the orbital angular momentum for individual sources. We find that applying a low-spin prior that excludes the true spin magnitudes of some sources in the population leads to significantly overestimating the maximum neutron star mass and underestimating the minimum neutron star mass at the population level with as few as six BNS detections. The safest choice of spin prior that does not lead to biases in the inferred mass distribution is one that allows for high spin magnitudes and tilts misaligned with the orbital angular momentum.

Hierarchical Inference of Binary Neutron Star Mass Distribution and Equation of State with Gravitational Waves

Abstract Gravitational-wave observations of binary neutron star mergers provide valuable information about neutron star structure and the equation of state of dense nuclear matter. Numerous methods have been proposed to analyze the population of observed neutron stars, and previous work has demonstrated the necessity of jointly fitting the astrophysical distribution and the equation of state in order to accurately constrain the equation of state. In this work, we introduce a new framework to simultaneously infer the distribution of binary neutron star masses and the nuclear equation of state using Gaussian mixture model density estimates, which mitigates some of the limitations previously used methods suffer from. Using our method, we reproduce previous projections for the expected precision of our joint mass distribution and equation-of-state inference with tens of observations. We also show that mismodeling the equation of state can bias our inference of the neutron star mass distribution. While we focus on neutron star masses and matter effects, our method is widely applicable to population inference problems.

Population Properties of Neutron Stars in the Coalescing Compact Binaries

Abstract We perform a hierarchical Bayesian inference to investigate the population properties of the coalescing compact binaries involving at least one neutron star (NS). With the current gravitational-wave (GW) observation data, we can rule out none of the double Gaussian, single Gaussian, and uniform NS mass distribution models, though a specific double Gaussian model inferred from the Galactic NSs is found to be slightly more preferred. The mass distribution of black holes (BHs) in the neutron star–black hole (NSBH) population is found to be similar to that in the Galactic X-ray binaries. Additionally, the ratio of the merger rate densities between NSBHs and BNSs is estimated to be ∼3:7. The spin properties of the binaries, though constrained relatively poorly, play a nontrivial role in reconstructing the mass distribution of NSs and BHs. We find that a perfectly aligned spin distribution can be ruled out, while a purely isotropic distribution of spin orientation is still allowed. To evaluate the feasibility of reliably determining the population properties of NSs in the coalescing compact binaries with upcoming GW observations, we perform simulations with a mock population. We find that with 100 detections (including BNSs and NSBHs) the mass distribution of NSs can be well determined, and the fraction of BNSs can also be accurately estimated.

The Mass Distribution of Neutron Stars in Gravitational-wave Binaries

Abstract The discovery of two neutron star–black hole coalescences by LIGO and Virgo brings the total number of likely neutron stars observed in gravitational waves to six. We perform the first inference of the mass distribution of this extragalactic population of neutron stars. In contrast to the bimodal Galactic population detected primarily as radio pulsars, the masses of neutron stars in gravitational-wave binaries are thus far consistent with a uniform distribution, with a greater prevalence of high-mass neutron stars. The maximum mass in the gravitational-wave population agrees with that inferred from the neutron stars in our Galaxy and with expectations from dense matter.

Dispersion of pressure at the inner edge of the neutron star crust

This paper presents a method for estimating the pressure variance at the inner edge of a neutron star crust. The obtained results quantify uncertainty in the estimation of pressure at the core-crust interface, implying that they depend on the selected equation of state and the neutron star's mass distribution function. The quality of the transition pressure determination depends on the neutron star's mass, with a significant decrease in accuracy for configurations with masses close to $2\mathrm{M}\ensuremath{\bigodot}$. The method used makes it possible to control the theoretical part of the core-crust pressure dispersion in determining the observational quantities.

Discriminating between Neutron Stars and Black Holes with Imperfect Knowledge of the Maximum Neutron Star Mass

Abstract Although gravitational-wave signals from exceptional low-mass compact binary coalescences, like GW170817, may carry matter signatures that differentiate the source from a binary black hole system, only one out of every eight events detected by the current Advanced LIGO and Virgo observatories are likely to have signal-to-noise ratios large enough to measure matter effects, even if they are present. Nonetheless, the systems’ component masses will generally be constrained precisely. Constructing an explicit mixture model for the total rate density of merging compact objects, we develop a hierarchical Bayesian analysis to classify gravitational-wave sources according to the posterior odds that their component masses are drawn from different subpopulations. Accounting for current uncertainty in the maximum neutron star mass and adopting a power-law mass distribution with or without a mass gap and either random or mass-ratio-dependent pairing, we examine two recent events from the LIGO–Virgo Collaboration’s third observing run, GW190425 and GW190814. For population models with no overlap between the neutron star and black hole mass distributions, we typically find that there is a chance, depending on the exact population model, that GW190425 was a binary neutron star merger rather than a neutron-star–black-hole merger. On the other hand, we find that there is a chance that GW190814 involved a slowly spinning neutron star, regardless of our assumed population model.

Neural network reconstruction of the dense matter equation of state derived from the parameters of neutron stars

Context. Neutron stars are currently studied with an rising number of electromagnetic and gravitational-wave observations, which will ultimately allow us to constrain the dense matter equation of state and understand the physical processes at work within these compact objects. Neutron star global parameters, such as the mass and radius, can be used to obtain the equation of state by directly inverting the Tolman-Oppenheimer-Volkoff equations. Here, we investigate an alternative approach to this procedure. Aims. The aim of this work is to study the application of the artificial neural networks guided by the autoencoder architecture as a method for precisely reconstructing the neutron star equation of state, using their observable parameters: masses, radii, and tidal deformabilities. In addition, we study how well the neutron star radius can be reconstructed using only the gravitational-wave observations of tidal deformability, that is, using quantities that are not related in any straightforward way. Methods. The application of an artificial neural network in the equation-of-state reconstruction exploits the non-linear potential of this machine learning model. Since each neuron in the network is basically a non-linear function, it is possible to create a complex mapping between the input sets of observations and the output equation-of-state table. Within the supervised training paradigm, we construct a few hidden-layer deep neural networks on a generated data set, consisting of a realistic equation of state for the neutron star crust connected with a piecewise relativistic polytropes dense core, with its parameters representative of state-of-the art realistic equations of state. Results. We demonstrate the performance of our machine-learning implementation with respect to the simulated cases with a varying number of observations and measurement uncertainties. Furthermore, we study the impact of the neutron star mass distributions on the results. Finally, we test the reconstruction of the equation of state trained on parametric polytropic training set using the simulated mass–radius and mass–tidal-deformability sequences based on realistic equations of state. Neural networks trained with a limited data set are capable of generalising the mapping between global parameters and equation-of-state input tables for realistic models.

Maximum mass cutoff in the neutron star mass distribution and the prospect of forming supramassive objects in the double neutron star mergers

The sample of neutron stars with a measured mass is growing quickly. With the latest sample, we adopt both a flexible Gaussian mixture model and a Gaussian plus Cauchy-Lorentz component model to infer the mass distribution of neutron stars and use the Bayesian model selection to explore evidence for multimodality and a sharp cutoff in the mass distribution. The two models yield rather similar results. Consistent with previous studies, we find evidence for a bimodal distribution together with a cutoff at a mass of $M_{\rm max}=2.26_{-0.05}^{+0.12}M_\odot$ (68% credible interval; for the Gaussian mixture model). If such a cutoff is interpreted as the maximum gravitational mass of nonrotating cold neutron stars, the prospect of forming supramassive remnants is found to be quite promising for the double neutron star mergers with a total gravitational mass less than or equal to 2.7$M_\odot$ unless the thermal pions could substantially soften the equation of state for the very hot neutron star matter. These supramassive remnants have a typical kinetic rotational energy of approximately $1-2\times 10^{53}$ ergs. Together with a high neutron star merger rate approximately $10^{3}~{\rm Gpc^{-3}~yr^{-3}}$, the neutron star mergers are expected to be significant sources of EeV($10^{18}$eV) cosmic-ray protons.

Nuclear Pairing Gaps and Neutron Star Cooling

We study the cooling of isolated neutron stars with particular regard to the importance of nuclear pairing gaps. A microscopic nuclear equation of state derived in the Brueckner-Hartree-Fock approach is used together with compatible neutron and proton pairing gaps. We then study the effect of modifying the gaps on the final deduced neutron star mass distributions. We find that a consistent description of all current cooling data can be achieved and a reasonable neutron star mass distribution can be predicted employing the (slightly reduced by about 40%) proton 1S0 Bardeen-Cooper-Schrieffer (BCS) gaps and no neutron 3P2 pairing.

Gravitational waves or deconfined quarks: What causes the premature collapse of neutron stars born in short gamma-ray bursts?

We infer the collapse times of long-lived neutron stars into black holes using the X-ray afterglows of 18 short gamma-ray bursts. We then apply hierarchical inference to infer properties of the neutron star equation of state and dominant spin-down mechanism. We measure the maximum non-rotating neutron star mass $M_\mathrm{TOV} = 2.31 ^{+0.36}_{-0.21} M_{\odot}$ and constrain the fraction of remnants spinning down predominantly through gravitational-wave emission to $\eta = 0.69 ^{+0.21}_{-0.39}$ with $68 \%$ uncertainties. In principle, this method can determine the difference between hadronic and quark equation of states. In practice, however, the data is not yet informative with indications that these neutron stars do not have hadronic equation of states at the $1\sigma$ level. These inferences all depend on the underlying progenitor mass distribution for short gamma-ray bursts produced by binary neutron star mergers. The recently announced gravitational-wave detection of GW190425 suggests this underlying distribution is different from the locally-measured population of double neutron stars. We show that $M_\mathrm{TOV}$ and $\eta$ constraints depend on the fraction of binary mergers that form through a distribution consistent with the locally-measured population and a distribution that can explain GW190425. The more binaries that form from the latter distribution, the larger $M_\mathrm{TOV}$ needs to be to satisfy the X-ray observations. Our measurements above are marginalised over this unknown fraction. If instead, we assume GW190425 is not a binary neutron star merger, i.e the underlying mass distribution of double neutron stars is the same as observed locally, we measure $M_\mathrm{TOV} = 2.26 ^{+0.31}_{-0.17} M_{\odot}$.

PUSHing Core-collapse Supernovae to Explosions in Spherical Symmetry. IV. Explodability, Remnant Properties, and Nucleosynthesis Yields of Low-metallicity Stars*

Abstract In this fourth paper of the series, we use the parameterized, spherically symmetric explosion method PUSH to perform a systematic study of two sets of nonrotating stellar progenitor models. Our study includes pre-explosion models with metallicities Z = 0 and Z = Z ⊙ × 10−4 and covers a progenitor mass range from 11 to 75 M ⊙. We present and discuss the explosion properties of all models and predict remnant (neutron star or black hole) mass distributions within this approach. We also perform systematic nucleosynthesis studies and predict detailed isotopic yields as a function of the progenitor mass and metallicity. We present a comparison of our nucleosynthesis results with observationally derived 56Ni ejecta from normal core-collapse supernovae (CCSNe) and with iron-group abundances for metal-poor star HD 84937. Overall, our results for explosion energies, remnant mass distribution, 56Ni mass, and iron-group yields are consistent with observations of normal CCSNe. We find that stellar progenitors at low and zero metallicity are more prone to black hole formation than those at solar metallicity, which allows for the formation of black holes in the mass range observed by LIGO/VIRGO.