Neutron Star Mass Distribution Research Articles

The distribution of neutron star masses

AbstractFrom the beginning of current century to the present, the sample of observed neutron star (NS) with measured masses grew owing to the great effort in the observational field, and the so‐called “canonical” unique value formerly attributed to NS at birth was put into question. Different groups pointed out the existence of different channels for a NS formation, possibly leading to a multimodal distribution. We employ in the present work tools from frequentist and Bayesian analysis to test some inferences about the mass distribution of neutron stars, in order to clarify if the observed objects belong to the same populations or show differences at the birth/evolutionary history.

The mass distribution of Galactic double neutron stars: constraints on the gravitational-wave sources like GW170817

ABSTRACT The merger event of double neutron star (DNS) system (GW170817) was detected by the gravitational-wave (GW) detectors (Advanced LIGO and Advanced Virgo) in 2017 for the first time, so their mass distribution has become a significant topic with the new round GW hunting (O3) in 2019. A few models (e.g. Gaussian, two-Gaussian, or mixture-Gaussian) were adopted to draw the mass distribution of observed Galactic DNS systems, however, there is no a confirmed model now due to the small size of DNS samples (N < 20). Here we focus on determining the most probable distribution ranges of DNS masses without model selection by assuming the neutron star masses to be uniformly distributed between the lower and upper bounds. We apply a Bayesian analysis and Markov chain Monte Carlo simulation to 15 Galactic DNS systems, and obtain that the component masses of DNS systems should mainly fall in the range of 1.165–1.590 M⊙, and the predominant ranges for the total mass, mass ratio, and chirp mass lie in 2.535–2.867 M⊙, 0.741–0.995, and 1.115–1.237 M⊙, respectively. Our results are in agreement with the properties of DNS in GW170817, whose 90 per cent credible intervals for the component masses, total masses, mass ratio, and chirp masses are 1.16–1.60 M⊙, $2.73_{-0.01}^{+0.04}\, \mathrm{ M}_\odot$, 0.73–1.00, and $1.186_{-0.001}^{+0.001}\, \mathrm{ M}_\odot$, respectively. The above similarity is an important indicator that reveals the source of GW170817 to be a DNS system from the galaxy NGC 4993, and our results can be tested by the forthcoming GW hunting O3.

The Multi-messenger Matrix: The Future of Neutron Star Merger Constraints on the Nuclear Equation of State

Abstract The electromagnetic (EM) signal of a binary neutron star (BNS) merger depends sensitively on the total binary mass, M tot, relative to various threshold masses set by the neutron star (NS) equation of state (EOS), parameterized through the neutron star (NS) maximum mass, M TOV, and characteristic radius, R 1.6. EM observations of a BNS merger detected through its gravitational-wave (GW) emission, which are of sufficient quality to ascertain the identity of the merger remnant, can therefore constrain the values of M TOV and R 1.6, given the tight connection between M tot and the well-measured chirp mass. We elucidate the present and future landscape of EOS constraints from BNS mergers, introducing the “Multi-Messenger Matrix,” a mapping between GW and EM measurables that defines the ranges of event chirp masses that provide the most leverage on constraining the EOS. By simulating a population of BNS mergers drawn from the Galactic double NS mass distribution we show that ∼10 joint detections can constrain M TOV and R 1.6 to several percent level where systematic uncertainties may become significant. Current EOS constraints imply that most mergers will produce supramassive or hypermassive remnants, a smaller minority (possibly zero) will undergo prompt collapse, while at most only a few percent of events will form indefinitely stable NSs. In support of the envisioned program, we advocate in favor of Laser Interferometer Gravitational-Wave Observatory (LIGO)/Virgo releasing chirp mass estimates as early as possible to the scientific community, enabling observational resources to be allocated in the most efficient way to maximize the scientific gain from multi-messenger discoveries.

Nucleosynthesis and Kilonovae from Strange Star Mergers

In this talk, we summarize the work in progress toward a full characterization of strange star–strange star (SS–SS) mergers related to the GW/GRB/kilonova events. In addition, we show that the a priori probability constructed from the observed neutron star mass distribution points toward an asymmetric binary system as the progenitor of the GW170817 event.

The Mass Distribution of Galactic Double Neutron Stars

Abstract The conventional wisdom, dating back to 2012, is that the mass distribution of Galactic double neutron stars (DNSs) is well-fit by a Gaussian distribution with a mean of 1.33 M ⊙ and a width of 0.09 M ⊙. With the recent discovery of new Galactic DNSs and GW170817, the first neutron star merger event to be observed with gravitational waves, it is timely to revisit this model. In order to constrain the mass distribution of DNSs, we perform Bayesian inference using a sample of 17 Galactic DNSs, effectively doubling the sample used in previous studies. We expand the space of models so that the recycled neutron star need not be drawn from the same distribution as the nonrecycled companion. Moreover, we consider different functional forms including uniform, single-Gaussian, and two-Gaussian distributions. While there is insufficient data to draw firm conclusions, we find positive support (a Bayes factor (BF) of 9) for the hypothesis that recycled and nonrecycled neutron stars have distinct mass distributions. The most probable model—preferred with a BF of 29 over the conventional model—is one in which the recycled neutron star mass is distributed according to a two-Gaussian distribution, and the nonrecycled neutron star mass is distributed uniformly. We show that precise component mass measurements of ≈20 DNSs are required in order to determine with high confidence (a BF of 150) whether recycled and nonrecycled neutron stars come from a common distribution. Approximately 60 DNSs are needed in order to establish the detailed shape of the distributions.

Neutron star cooling with microscopic equations of state

We model neutron star cooling with several microscopic nuclear equations of state based on different nucleon-nucleon interactions and three-body forces, and compatible with the recent GW170817 neutron star merger event. They all feature strong direct Urca processes. We find that all models are able to describe well the current set of cooling data for isolated neutron stars, provided that large and extended proton 1S0 gaps and no neutron 3PF2 gaps are active in the stellar matter. We then analyze the neutron star mass distributions predicted by the different models and single out the preferred ones.

Evidence for a maximum mass cut-off in the neutron star mass distribution and constraints on the equation of state

We infer the mass distribution of neutron stars in binary systems using a flexible Gaussian mixture model and use Bayesian model selection to explore evidence for multi-modality and a sharp cut-off in the mass distribution. We find overwhelming evidence for a bimodal distribution, in agreement with previous literature, and report for the first time positive evidence for a sharp cut-off at a maximum neutron star mass. We measure the maximum mass to be $2.0M_\odot < m_\mathrm{max} < 2.2M_\odot$ (68\%), $2.0M_\odot < m_\mathrm{max}< 2.6M_\odot$ (90\%), and evidence for a cut-off is robust against the choice of model for the mass distribution and to removing the most extreme (highest mass) neutron stars from the dataset. If this sharp cut-off is interpreted as the maximum stable neutron star mass allowed by the equation of state of dense matter, our measurement puts constraints on the equation of state. For a set of realistic equations of state that support $>2M_\odot$ neutron stars, our inference of $m_\mathrm{max}$ is able to distinguish between models at odds ratios of up to $12:1$, whilst under a flexible piecewise polytropic equation of state model our maximum mass measurement improves constraints on the pressure at $3-7\times$ the nuclear saturation density by $\sim 30-50\%$ compared to simply requiring $m_\mathrm{max}> 2M_\odot$. We obtain a lower bound on the maximum sound speed attained inside the neutron star of $c_s^\mathrm{max} > 0.63c$ (99.8\%), ruling out $c_s^\mathrm{max} < c/\sqrt{3}$ at high significance. Our constraints on the maximum neutron star mass strengthen the case for neutron star-neutron star mergers as the primary source of short gamma-ray bursts.

Confronting Models of Massive Star Evolution and Explosions with Remnant Mass Measurements

Abstract The mass distribution of compact objects provides a fossil record that can be studied to uncover information on the late stages of massive star evolution, the supernova explosion mechanism, and the dense matter equation of state. Observations of neutron star masses indicate a bimodal Gaussian distribution, while the observed black hole mass distribution decays exponentially for stellar-mass black holes. We use these observed distributions to directly confront the predictions of stellar evolution models and the neutrino-driven supernova simulations of Sukhbold et al. We find strong agreement between the black hole and low-mass neutron star distributions created by these simulations and the observations. We show that a large fraction of the stellar envelope must be ejected, either during the formation of stellar-mass black holes or prior to the implosion through tidal stripping due to a binary companion, in order to reproduce the observed black hole mass distribution. We also determine the origins of the bimodal peaks of the neutron star mass distribution, finding that the low-mass peak (centered at ∼1.4 M ⊙) originates from progenitors with M ZAMS ≈ 9–18 M ⊙. The simulations fail to reproduce the observed peak of high-mass neutron stars (centered at ∼1.8 M ⊙) and we explore several possible explanations. We argue that the close agreement between the observed and predicted black hole and low-mass neutron star mass distributions provides new, promising evidence that these stellar evolution and explosion models capture the majority of relevant stellar, nuclear, and explosion physics involved in the formation of compact objects.

Constraining the mass and radius of neutron stars in globular clusters

We analyze observations of eight quiescent low-mass X-ray binaries in globular clusters and combine them to determine the neutron star mass-radius curve and the equation of state of dense matter. We determine the effect that several uncertainties may have on our results, including uncertainties in the distance, the atmosphere composition, the neutron star maximum mass, the neutron star mass distribution, the possible presence of a hotspot on the neutron star surface, and the prior choice for the equation of state of dense matter. We find that the radius of a 1.4 solar mass neutron star is most likely from 10 to 14 km and that tighter constraints are only possible with stronger assumptions about the nature of the neutron stars, the systematics of the observations, or the nature of dense matter. Strong phase transitions are preferred over other models and interpretations of the data with a Bayes factor of 8 or more, and in this case, the radius is likely smaller than 12 km. However, radii larger than 12 km are preferred if the neutron stars have uneven temperature distributions.

The X-ray binary system in the EP era

Searching for X-ray binaries and establishing a large sample are the foundation of answering many scientific problems, such as, how many BH X-ray binaries are there within our Milky Way galaxy? Does there exist a real gap between the mass distribution of neutron stars and black holes? Is there any black hole system within globular clusters? The planned mission Einstein Probe (EP) has a much better sensitivity compared to the past missions, so it is expected to discover many new X-ray binary systems over its operating period, which will play a key role in helping solve the problems above then.

Thermal states of neutron stars with a consistent model of interior

We model the thermal states of both isolated neutron stars and accreting neutron stars in X-ray transients in quiescence and confront them with observations. We use an equation of state and superfluid baryon gaps, which are consistently calculated. We conclude that the direct Urca process is required to be consistent with low-luminous accreting neutron stars. In addition, proton superfluidity and sufficiently weak neutron superfluidity are necessary to explain the cooling of middle-aged neutron stars and to obtain a realistic distribution of neutron star masses.

THE NANOGRAV NINE-YEAR DATA SET: MASS AND GEOMETRIC MEASUREMENTS OF BINARY MILLISECOND PULSARS

ABSTRACT We analyze 24 binary radio pulsars in the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) nine-year data set. We make 14 significant measurements of the Shapiro delay, including new detections in four pulsar-binary systems (PSRs J0613−0200, J2017+0603, J2302+4442, and J2317+1439), and derive estimates of the binary-component masses and orbital inclination for these MSP-binary systems. We find a wide range of binary pulsar masses, with values as low as for PSR J1918−0642 and as high as for PSR J1614−2230 (both 68.3% credibility). We make an improved measurement of the Shapiro timing delay in the PSR J1918−0642 and J2043+1711 systems, measuring the pulsar mass in the latter system to be (68.3% credibility) for the first time. We measure secular variations of one or more orbital elements in many systems, and use these measurements to further constrain our estimates of the pulsar and companion masses whenever possible. In particular, we used the observed Shapiro delay and periastron advance due to relativistic gravity in the PSR J1903+0327 system to derive a pulsar mass of (68.3% credibility). We discuss the implications that our mass measurements have on the overall neutron-star mass distribution, and on the “mass/orbital-period” correlation due to extended mass transfer.

Masses, Radii, and the Equation of State of Neutron Stars

We summarize our current knowledge of neutron-star masses and radii. Recent instrumentation and computational advances have resulted in a rapid increase in the discovery rate and precise timing of radio pulsars in binaries in the past few years, leading to a large number of mass measurements. These discoveries show that the neutron-star mass distribution is much wider than previously thought, with three known pulsars now firmly in the 1.9–2.0-M⊙ mass range. For radii, large, high-quality data sets from X-ray satellites as well as significant progress in theoretical modeling led to considerable progress in the measurements, placing them in the 10–11.5-km range and shrinking their uncertainties, owing to a better understanding of the sources of systematic errors. The combination of the massive-neutron-star discoveries, the tighter radius measurements, and improved laboratory constraints of the properties of dense matter has already made a substantial impact on our understanding of the composition and bulk properties of cold nuclear matter at densities higher than that of the atomic nucleus, a major unsolved problem in modern physics.

Beyond the Horizon Distance: LIGO-Virgo can Boost Gravitational-Wave Detection Rates by Exploiting the Mass Distribution of Neutron Stars.

The masses of neutron stars in neutron star binaries are observed to fall in a narrow mass range around ∼1.33M_{⊙}. We explore the advantage of focusing on this region of the parameter space in gravitational-wave searches. We find that an all-sky (externally triggered) search with an optimally reduced template bank is expected to detect 14% (61%) more binary mergers than without the reduction. A reduced template bank can also represent significant improvement in technical cost. We also develop a more detailed search method using binary mass distribution, and find a sensitivity increase similar to that due to the reduced template bank.

PULSAR J0453+1559: A DOUBLE NEUTRON STAR SYSTEM WITH A LARGE MASS ASYMMETRY

To understand the nature of supernovae and neutron star (NS) formation, as well as binary stellar evolution and their interactions, it is important to probe the distribution of NS masses. Until now, all double NS (DNS) systems have been measured to have a mass ratio close to unity (q $\geq$ 0.91). Here we report the measurement of the individual masses of the 4.07-day binary pulsar J0453+1559 from measurements of the rate of advance of periastron and Shapiro delay: The mass of the pulsar is 1.559(5) $M_{\odot}$ and that of its companion is 1.174(4) $M_{\odot}$; q = 0.75. If this companion is also a neutron star (NS), as indicated by the orbital eccentricity of the system (e=0.11), then its mass is the smallest precisely measured for any such object. The pulsar has a spin period of 45.7 ms and a spin derivative of 1.8616(7) x$10^-19$; from these we derive a characteristic age of ~ 4.1 x $10^9$ years and a magnetic field of ~ 2.9 x $10^9$ G,i.e, this pulsar was mildly recycled by accretion of matter from the progenitor of the companion star. This suggests that it was formed with (very approximately) its current mass. Thus NSs form with a wide range of masses, which is important for understanding their formation in supernovae. It is also important for the search for gravitational waves released during a NS-NS merger: it is now evident that we should not assume all DNS systems are symmetric.

THE NEUTRON STAR MASS DISTRIBUTION

In recent years, the number of pulsars with secure mass measurements has increased to a level that allows us to probe the underlying neutron star (NS) mass distribution in detail. We critically review the radio pulsar mass measurements. For the first time, we are able to analyze a sizable population of NSs with a flexible modeling approach that can effectively accommodate a skewed underlying distribution and asymmetric measurement errors. We find that NSs that have evolved through different evolutionary paths reflect distinctive signatures through dissimilar distribution peak and mass cutoff values. NSs in double neutron star and neutron star-white dwarf systems show consistent respective peaks at 1.33 Msun and 1.55 Msun suggesting significant mass accretion (delta m~0.22 Msun) has occurred during the spin-up phase. The width of the mass distribution implied by double NS systems is indicative of a tight initial mass function while the inferred mass range is significantly wider for NSs that have gone through recycling. We find a mass cutoff at ~2.1 Msun for NSs with white dwarf companions which establishes a firm lower bound for the maximum NS mass. This rules out the majority of strange quark and soft equation of state models as viable configurations for NS matter. The lack of truncation close to the maximum mass cutoff along with the skewed nature of the inferred mass distribution both enforce the suggestion that the 2.1 Msun limit is set by evolutionary constraints rather than nuclear physics or general relativity, and the existence of rare super-massive NSs is possible.

ADVANCED BURNING STAGES AND FATE OF 8-10M☉STARS

The stellar mass range 8<M/Mo<12 corresponds to the most massive AGB stars and the most numerous massive stars. It is host to a variety of supernova progenitors and is therefore very important for galactic chemical evolution and stellar population studies. In this paper, we study the transition from super-AGB star to massive star and find that a propagating neon-oxygen burning shell is common to both the most massive electron capture supernova (EC-SN) progenitors and the lowest mass iron-core collapse supernova (FeCCSN) progenitors. Of the models that ignite neon burning off-center, the 9.5Mo model would evolve to an FeCCSN after the neon-burning shell propagates to the center, as in previous studies. The neon-burning shell in the 8.8Mo model, however, fails to reach the center as the URCA process and an extended (0.6 Mo) region of low Ye (0.48) in the outer part of the core begin to dominate the late evolution; the model evolves to an EC-SN. This is the first study to follow the most massive EC-SN progenitors to collapse, representing an evolutionary path to EC-SN in addition to that from SAGB stars undergoing thermal pulses. We also present models of an 8.75Mo super-AGB star through its entire thermal pulse phase until electron captures on 20Ne begin at its center and of a 12Mo star up to the iron core collapse. We discuss key uncertainties and how the different pathways to collapse affect the pre-supernova structure. Finally, we compare our results to the observed neutron star mass distribution.

On the gravitational wave background from compact binary coalescences in the band of ground-based interferometers

This paper reports a comprehensive study on the gravitational wave (GW) background from compact binary coalescences. We consider in our calculations newly available observation-based neutron star and black hole mass distributions and complete analytical waveforms that include post-Newtonian amplitude corrections. Our results show that: (i) post-Newtonian effects cause a small reduction in the GW background signal; (ii) below 100 Hz the background depends primarily on the local coalescence rate $r_0$ and the average chirp mass and is independent of the chirp mass distribution; (iii) the effects of cosmic star formation rates and delay times between the formation and merger of binaries are linear below 100 Hz and can be represented by a single parameter within a factor of ~ 2; (iv) a simple power law model of the energy density parameter $\Omega_{GW}(f) ~ f^{2/3}$ up to 50-100 Hz is sufficient to be used as a search template for ground-based interferometers. In terms of the detection prospects of the background signal, we show that: (i) detection (a signal-to-noise ratio of 3) within one year of observation by the Advanced LIGO detectors (H1-L1) requires a coalescence rate of $r_0 = 3 (0.2) Mpc^{-3} Myr^{-1}$ for binary neutron stars (binary black holes); (ii) this limit on $r_0$ could be reduced 3-fold for two co-located detectors, whereas the currently proposed worldwide network of advanced instruments gives only ~ 30% improvement in detectability; (iii) the improved sensitivity of the planned Einstein Telescope allows not only confident detection of the background but also the high frequency components of the spectrum to be measured. Finally we show that sub-threshold binary neutron star merger events produce a strong foreground, which could be an issue for future terrestrial stochastic searches of primordial GWs.

Massive star evolution and nucleosynthesis: Lower end of Fe-core-collapse supernova progenitors and remnant neutron star mass distribution

In order to explore various aspects of stellar evolution, supernovae, gamma ray bursts, and nucleosynthesis, we have developed a new efficient stellar evolution code. In this paper, we describe this new code and compare the results with those calculated by the previous code. Specifically, we focus on the progenitor evolution of the lower end of Fe-core-collapse supernovae, and the mass distribution of remnant neutron stars. We describe how different assumptions will lead to different neutron star mass distributions. We also review some of the recent work by our research group.

ON THE MASS DISTRIBUTION AND BIRTH MASSES OF NEUTRON STARS

We investigate the distribution of neutron star masses in different populations of binaries, employing Bayesian statistical techniques. In particular, we explore the differences in neutron star masses between sources that have experienced distinct evolutionary paths and accretion episodes. We find that the distribution of neutron star masses in non-recycled eclipsing high-mass binaries as well as of slow pulsars, which are all believed to be near their birth masses, has a mean of 1.28 M_solar and a dispersion of 0.24 M_solar. These values are consistent with expectations for neutron star formation in core-collapse supernovae. On the other hand, double neutron stars, which are also believed to be near their birth masses, have a much narrower mass distribution, peaking at 1.33 M_solar but with a dispersion of only 0.05 M_solar. Such a small dispersion cannot easily be understood and perhaps points to a particular and rare formation channel. The mass distribution of neutron stars that have been recycled has a mean of 1.48 M_solar and a dispersion of 0.2 M_solar, consistent with the expectation that they have experienced extended mass accretion episodes. The fact that only a very small fraction of recycled neutron stars in the inferred distribution have masses that exceed ~2 M_solar suggests that only a few of these neutron stars cross the mass threshold to form low mass black holes.