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Universal relations for neutron star 𝑓-mode and 𝑔-mode oscillations

Among the various oscillation modes of neutron stars, 𝑓- and 𝑔- modes are the most likely to be ultimately observed in binary neutron star mergers due to their relatively large coupling and shared frequencies with tidal excitations. The 𝑓-mode frequency and damping time are known to correlate in normal neutron stars with their compactness, and previous fits to hadronic stars are extended and shown to be valid for an extremely broad sampling of equations of state using a piecewise polytropic parametrization scheme for hadrons and a constant sound-speed parametrization for quark matter. Separate fits applicable to quark (self-bound) stars are improved. Much more significant correlations exist with tidal deformability, and therefore with moment of inertia and quadrupole moment. It is conclusively demonstrated that these correlations are the same for all types of stars, whether hadronic, hybrid, or pure quark, and its accuracy is quantified. A novel 1-node branch of the 𝑓-mode that occurs in low-mass hybrid stars in a narrow mass range just beyond the critical mass necessary for a phase transition to appear is identified. This 1-node branch shows the largest, but still small, deviations from the universal correlation for any configuration. It is characterized by a nonmonotonic relation between neutron star mass and 𝑓-mode frequency, in contrast to the behavior otherwise observed in normal, quark and hybrid stars. The 𝑔-mode only exists in matter with a nonbarotropic equation of state involving temperature, chemical potential or composition (such as being out of beta equilibrium), or a phase transition in barotropic matter. Here, the 𝑔-mode therefore could serve as a probe for studying phase transitions in hybrid stars. In contrast with the 𝑓-mode, 𝑔-mode frequencies do not correlate well with tidal deformability, but depend strongly on properties of the transition (the density and the magnitude of the discontinuity) at the transition. Imposing causality and maximum mass constraints, a fit involving neutron star and phase transition properties is found and the 𝑔-mode frequency is determined to have an upper bound of about 1.25 kHz. However, if the sound speed 𝑐𝑠 in the inner core at densities above the phase transition density is restricted to 𝑐$^{2}_{𝑠}$ ≤1/3, 𝑔-mode frequencies can only reach about 0.8 kHz, which are significantly lower than 𝑓-mode frequencies (1.3–2.8 kHz). 𝑔-mode gravitational wave damping times are found to be extremely long, >10 4 s (102 s) in the inner core with 𝑐$^{2}_{𝑠}$ ≤1/3 (1), in comparison with 𝑓-mode damping times (0.1–1 s).

Composition of astronomical objects↗

Hard X-Ray Excess from the Magnificent Seven Neutron Stars

We report significant hard X-ray excesses in the energy range 2–8 keV for two nearby isolated neutron stars: RX J1856.6-3754 and RX J0420.0-5022. These neutron stars have previously been observed in soft X-rays to have nearly thermal spectra at temperatures ~100 eV, which are thought to arise from the warm neutron star surfaces. We find nontrivial hard X-ray spectra well above the thermal surface predictions with archival data from the XMM-Newton and Chandra X-ray telescopes. We analyze possible systematic effects that could generate such spurious signals, such as nearby X-ray point sources and pileup of soft X-rays, but we find that the hard X-ray excesses are robust to these systematics to the extent that is possible to test. We also investigate possible sources of hard X-ray emission from the neutron stars and find no satisfactory explanation with known mechanisms, suggesting that a novel source of X-ray emission is at play. Here, we do not find high-significance hard X-ray excesses from the other five Magnificent Seven isolated neutron stars.

79 ASTRONOMY AND ASTROPHYSICS↗

Unified nonparametric equation-of-state inference from the neutron-star crust to perturbative-QCD densities

Perturbative quantum chromodynamics (pQCD), while valid only at densities exceeding those found in the cores of neutron stars, could provide constraints on the dense-matter equation of state (EOS). Here, in this work, we examine the impact of pQCD information on the inference of the EOS using a nonparametric framework based on Gaussian processes (GPs). We examine the application of pQCD constraints through a ``pQCD likelihood,'' and verify the findings of previous works; namely, a softening of the EOS at the central densities of the most massive neutron stars and a reduction in the maximum neutron-star mass. Although the pQCD likelihood can be easily integrated into existing EOS inference frameworks, this approach requires an arbitrary selection of the density at which the constraints are applied. The EOS behavior is also treated differently on either side of the chosen density. To mitigate these issues, we extend the EOS model to higher densities, thereby constructing a ``unified'' description of the EOS from the neutron-star crust to densities relevant for pQCD. In this approach the pQCD constraints effectively become part of the prior. Since the EOS is unconstrained by any calculation or data between the densities applicable to neutron stars and pQCD, we argue for maximum modeling flexibility in that regime. We compare the unified EOS with the traditional pQCD likelihood, and although we confirm the EOS softening, we do not see a reduction in the maximum neutron-star mass or any impact on macroscopic observables. Though residual model dependence cannot be ruled out, we find that pQCD suggests the speed of sound in the densest neutron-star cores has already started decreasing toward the asymptotic limit; we find that the speed of sound squared at the center of the most massive neutron star has an upper bound of $\sim 0.5$ at the 90% level.

equations of state of nuclear matter↗

Detectability of subsolar mass neutron stars through a template bank search

Here, we study the detectability of gravitational-wave signals from subsolar-mass binary neutron star systems by the current generation of ground-based gravitational-wave detectors. We find that finite size effects from large tidal deformabilities of the neutron stars and lower merger frequencies can significantly impact the sensitivity of the detectors to these sources. By simulating a matched-filter based search using injected binary neutron star signals with tidal deformabilities derived from physically motivated equations of state, we calculate the reduction in sensitivity of the detectors. We conclude that the loss in sensitive volume can be as high as 78.4% for an equal mass binary system of chirp mass 0.17M ⊙ , in a search conducted using binary black hole template banks. We use this loss in sensitive volume, in combination with the results from the search for subsolar-mass binaries conducted on data collected by the LIGO-Virgo observatories during their first three observing runs, to obtain a conservative upper limit on the merger rate of subsolar-mass binary neutron stars. Since the discovery of a low-mass neutron star would provide new insight into formation mechanisms of neutron stars and further constrain the equation of state of dense nuclear matter, our result merits a dedicated search for subsolar-mass binary neutron star signals.

79 ASTRONOMY AND ASTROPHYSICS↗

Neutron stars and the dense matter equation of state

The past two decades have witnessed tremendous progress in understanding the properties of neutron stars, their maximum mass and radii, and the properties of the dense matter in their cores, made possible by electromagnetic observations of neutron stars and the detection of gravitational waves from their mergers. These observations have provided novel constraints on neutron-star structure that are intimately related to the properties of dense neutron-rich matter described by the nuclear equation of state. Nevertheless, constraining the equation of state over the wide range of densities probed by astrophysical observations is still challenging, as the physics involved is broad and the system spans many orders of magnitude in density. Here, theoretical approaches to calculate and model the neutron-star equation of state in various regimes of densities are reviewed, and the related consequent properties of neutron stars are discussed. How the equation of state at low densities can be calculated from nuclear interactions that are constrained and benchmarked by nuclear experiments is described. Neutron-star observations, with a particular emphasis on information provided by gravitational-wave signals and electromagnetic observations, are reviewed. Finally, future challenges and opportunities in the field are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Source term method for binary neutron stars initial data

The initial condition problem for a binary neutron star system requires a Poisson equation solver for the velocity potential with a Neumann-like boundary condition on the surface of the star. Difficulties that arise in this boundary value problem are: (a) the boundary is not known a priori, but constitutes part of the solution of the problem; (b) various terms become singular at the boundary. In this work, we present a new method to solve the fluid Poisson equation for irrotational/spinning binary neutron stars. The advantage of the new method is that it does not require complex fluid surface fitted coordinates and it can be implemented in a Cartesian grid, which is a standard choice in numerical relativity calculations. This is accomplished by employing the source term method proposed by Towers, where the boundary condition is treated as a jump condition and is incorporated as additional source terms in the Poisson equation, which is then solved iteratively. The issue of singular terms caused by vanishing density on the surface is resolved with an additional separation that shifts the computation boundary to the interior of the star. We present two-dimensional tests to show the convergence of the source term method, and we further apply this solver to a realistic three-dimensional binary neutron star problem. By comparing our solution with the one coming from the initial data solver cocal, we demonstrate agreement to approximately 1%. We report our method can be used in other problems with non-smooth solutions like in magnetized neutron stars.

79 ASTRONOMY AND ASTROPHYSICS↗

Assessing equation of state-independent relations for neutron stars with nonparametric models

Relations between neutron star properties that do not depend on the nuclear equation of state offer insights on neutron star physics and have practical applications in data analysis. Such relations are obtained by fitting to a range of phenomenological or nuclear physics equation of state models, each of which may have varying degrees of accuracy. In this study we revisit commonly used relations and reassess them with a very flexible set of phenomenological nonparametric equation of state models that are based on Gaussian processes. Our models correspond to two sets: equations of state which mimic hadronic models, and equations of state with rapidly changing behavior that resemble phase transitions. Here we quantify the accuracy of relations under both sets and discuss their applicability with respect to expected upcoming statistical uncertainties of astrophysical observations. We further propose a goodness-of-fit metric which provides an estimate for the systematic error introduced by using the relation to model a certain equation-of-state set. Overall, the nonparametric distribution is more poorly fit with existing relations, with the I–Love–Q relations retaining the highest degree of universality. Fits degrade for relations involving the tidal deformability, such as the binary-Love and compactness-Love relations, and when introducing phase transition phenomenology. For most relations, systematic errors are comparable to current statistical uncertainties under the nonparametric equation of state distributions.

79 ASTRONOMY AND ASTROPHYSICS↗

Shedding far-ultraviolet light on the donor star and evolutionary state of the neutron-star LMXB Swift J1858.6−0814

ABSTRACT The evolution of accreting X-ray binary systems is closely coupled to the properties of their donor stars. Consequently, we can constrain the evolutionary track a system is by establishing the nature of its donor. Here, we present far-ultraviolet (far-UV) spectroscopy of the transient neutron-star low-mass X-ray binary J1858 in different accretion states (low-hard, high-hard, and soft). All of these spectra exhibit anomalous N v, C iv, Si iv, and He ii lines, suggesting that its donor star has undergone CNO processing. We also determine the donor’s effective temperature, Td ≃ 5700 K, and radius, Rd ≃ 1.7 R⊙, based on photometric observations obtained during quiescence. Lastly, we leverage the transient nature of the system to set an upper limit of $\dot{M}_{\rm acc} \lesssim 10^{-8.5}~{\rm M}_{\odot }~\mathrm{ yr}^{-1}$ on the present-day mass-transfer rate. Combining these with the orbital period of the system, Porb = 21.3 h, we search for viable evolution paths. The initial donor masses in the allowed solutions span the range 1 M⊙ ≲ Md,i ≲ 3.5 M⊙. All but the lowest masses in this range are consistent with the strong CNO-processing signature in the UV line ratios. The present-day donor mass in the permitted tracks are 0.5 M⊙ ≲ Md,obs ≲ 1.3 M⊙, higher than suggested by eclipse modelling. Since Porb is close to the so-called bifurcation period, both converging and diverging binary tracks are permitted. If the former is confirmed, J1858 will end its life as an ultracompact system with a substellar donor.

Castro Segura, N. (ORCID:0000000258700443)↗

Inference of Multichannel r -process Element Enrichment in the Milky Way Using Binary Neutron Star Merger Observations

Observations of GW170817 strongly suggest that binary neutron star (BNS) mergers produce rapid neutron-capture nucleosynthesis ( r -process) elements. However, it remains an open question whether these mergers can account for all the r -process element enrichment in the Milky Way’s history. Here, we constrain the contributions of the BNS channel using astrophysical neutron star observations. The rate and mass distributions are constrained by LIGO/Virgo/Kagra through the latest catalog GWTC-3, the neutron star equation of state by gravitational-wave, radio, and X-ray observations, and the delay time distribution by short gamma-ray burst (GRB) host galaxy associations. We present a Bayesian framework to consistently combine these observations with abundance information to quantify the contribution and uncertainties of single and multiple astrophysical enrichment sources, and obtain a distribution of per-event BNS r -process element yields consistent with geophysical and astrophysical abundance constraints. We then adopt a Galactic chemical evolution model assuming an instantaneous and fixed amount of Fe enrichment from core-collapse supernovae, and show that BNS-only enrichment scenarios remain inconsistent with the observed r-process abundance trend of disk stars in the Galaxy even with the uncertainties in BNS merger observations. Using stellar abundance observations instead of the short GRB constraints, we can infer a shorter BNS delay time distribution with power-law index α ≤ −2.0 and minimum delay time ${t}_{{\rm{\min }}}\leqslant 40$ Myr at 90% confidence, consistent with detailed Galactic chemical evolution models. Such delay times are in tension with those predicted by standard BNS formation models. Alternatively, we confirm that a two-channel scenario, in which the second channel tracks the star formation history without significant delay, can account for both Galactic stellar and short GRB observations. We estimate that 45%–90% of the r -process abundance in the Milky Way today would have been produced by this star formation-tracking channel, rather than BNS mergers with significant delay times.

gravitational wave astronomy↗

Josephson currents in neutron stars

We demonstrate that the interface between S-wave and P-wave paired superfluids in neutron stars induces a neutron supercurrent, a charge-neutral analog of the Josephson junction effect in electronic superconductors. The proton supercurrent entrainment by the neutron superfluid generates, in addition to the neutral supercurrent, a charged current across the interface. Beyond this stationary effect, the motion of the neutron vortex lines responding to secular changes in the neutron star’s rotation rate induces a time-dependent oscillating Josephson current across this interface when proton flux tubes are dragged along with them. We show that such motion produces radiation from the interface once clusters of proton flux tubes intersect the interface. The power of radiation exceeds by orders of magnitude the Ohmic dissipation of currents in neutron stars. As a result, this effect appears to be phenomenologically significant enough to heat the star and alter its cooling rate during the photon cooling era.

79 ASTRONOMY AND ASTROPHYSICS↗

The Impact of Classical and General Relativistic Obliquity Precessions on the Habitability of Circumstellar Neutron Stars’ Planets

Recently, it has been shown that rocky planets orbiting neutron stars can be habitable under plausible circumstances. If a distant, point-like source of visible light, such as a Sun-like main-sequence star or the gravitationally-lensed accretion disk of a supermassive black hole is present, possible temporal variations Δε{sub p}(t) of the planet’s axial tilt ε {sub p} to the ecliptic plane should be included in the overall habitability budget since the obliquity determines the insolation at a given latitude on a body’ s surface. I point out that, for rather generic initial spin–orbit initial configurations, general relativistic and classical spin variations induced by the post-Newtonian de Sitter and Lense–Thirring components of the field of the host neutron star and by its pull to the planetary oblateness J{sub 2}{sup p} may induce huge and very fast variations of ε {sub p} that would likely have an impact on the habitability of such worlds. In particular, for a planet’s distance of, say, 0.005 au from a 1.4 M {sub ⊙} neutron star corresponding to an orbital period P {sub b} = 0.109 day, obliquity shifts Δε {sub p} as large as ε{sub p}{sup max}−ε{sub p}{sup min}≃50{sup ∘}--100{sup ∘} over characteristic timescales as short as 10 days (J{sub 2}{sup p}) to 3 Myr (Lense–Thirring) may occur for arbitrary orientations of the orbital and spin angular momenta L, S {sub ns}, S {sub p} of the planet-neutron star system. In view of this feature of their spins, I dub such hypothetical planets as “nethotrons.”.

79 ASTRONOMY AND ASTROPHYSICS↗

Geometric and thermodynamic characterization of binary neutron star accretion discs

Accretion disks formed in binary neutron star mergers play a central role in many astrophysical processes of interest, including the launching of relativistic jets or the ejection of neutron-rich matter hosting heavy element nucleosynthesis. In this work we analyze in detail the properties of accretion disks from 44 ab initio binary neutron star merger simulations for a large set of nuclear equations of state, binary mass ratios, and remnant fates, with the aim of furnishing reliable initial conditions for disk simulations and a comprehensive characterization of their properties. We find that the disks have a significant thermal support, with an aspect ratio decreasing with the mass ratio of the binary from ~0.7 to 0.3. Even if the disk sample spans a broad range in mass and angular momentum, their ratio is independent from the equation of state and from the mass ratio. This can be traced back to the rotational profile of the disk, characterized by a constant specific angular momentum (as opposed to a Keplerian one) of 3 – 5×10 16 cm 2 s –1 . The profiles of the entropy per baryon and of the electron fraction depend on the mass ratio of the binary. For more symmetric binaries, they follow a sigmoidal distribution as a function of the rest mass density, for which we provide a detailed description and a fit. Furthermore, the disk properties discussed in this work can be used as a robust set of initial conditions for future long-term simulations of accretion disks from binary neutron star mergers, posing the basis for progress in the quantitative study of the outflow properties.

79 ASTRONOMY AND ASTROPHYSICS↗

GW190814: Impact of a 2.6 solar mass neutron star on the nucleonic equations of state

Is the secondary component of GW190814 the lightest black hole or the heaviest neutron star ever discovered in a double compact-object system? This is the central question animating this paper. Covariant density functional theory provides a unique framework to investigate both the properties of finite nuclei and neutron stars, while enforcing causality at all densities. By tuning existing energy density functionals we were able to: (i) account for a 2.6 M ⊙ neutron star, (ii) satisfy the original constraint on the tidal deformability of a 1.4 M ⊙ neutron star, and (iii) reproduce ground-state properties of finite nuclei. Yet, for the class of models explored in this work, we find that the stiffening of the equation of state required to support supermassive neutron stars is inconsistent with either constraints obtained from energetic heavy-ion collisions or from the low deformability of medium-mass stars. Furthermore, we speculate that the maximum neutron star mass can not be significantly higher than the existing observational limit and that the 2.6 M ⊙ compact object is likely to be the lightest black hole ever discovered.

79 ASTRONOMY AND ASTROPHYSICS↗

Reverse phase transitions in binary neutron-star systems with exotic-matter cores

Multimessenger observations of binary neutron-star mergers provide a unique opportunity to constrain the dense-matter equation of state. Although it is known from quantum chromodynamics that hadronic matter will undergo a phase transition to exotic forms of matter—e.g., quark matter—the onset density of such a phase transition cannot be computed from first principles. Hence, it remains an open question if such phase transitions occur inside isolated neutron stars or during binary neutron-star mergers, or if they appear at even higher densities that are not realized in the cosmos. Here, in this article, we perform numerical relativity simulations of neutron-star mergers and investigate scenarios in which the onset density of such a phase transition is exceeded in at least one inspiraling binary component. Our simulations reveal that shortly before the merger, it is possible that such stars undergo a “reverse phase transition”—i.e., densities decrease and the quark core inside the star disappears, leaving a purely hadronic star at merger. After the merger, when densities increase once more, the phase transition occurs again and leads, in the cases considered in this work, to the rapid formation of a black hole. We compute the gravitational-wave signal and the mass ejection for our simulations of such scenarios and find clear signatures that are related to the postmerger phase transition—e.g., smaller ejecta masses due to the softening of the equation of state through the quark core formation. Unfortunately, we do not find measurable imprints of the reverse phase transition.

79 ASTRONOMY AND ASTROPHYSICS↗

Extreme matter meets extreme gravity: Ultraheavy neutron stars with phase transitions

The speed of sound of the matter within neutron stars may contain nonsmooth structure related to first- or higher-order phase transitions. Here we investigate what are the observable consequences of structure in the speed of sound, such as bumps, spikes, step functions, plateaus, and kinks. One of the main consequences is the possibility of ultraheavy neutron stars (with masses larger than 2.5 solar masses), mass twins in heavy (with masses larger than 2 solar masses) and ultraheavy neutron stars. These stars pass all observational and theoretical constraints, including those imposed by recent LIGO/Virgo gravitational-wave observations and NICER x-ray observations. Here we thoroughly investigate other consequences of this structure in the speed of sound to develop an understanding of how nonsmooth features affect astrophysical observables, such as stellar radii, tidal deformability, moment of inertia, and Love number. Our results have important implications for future gravitational wave and x-ray observations of neutron stars and their impact in nuclear astrophysics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Quantifying modeling uncertainties when combining multiple gravitational-wave detections from binary neutron star sources

Here, with the increasing sensitivity of gravitational-wave detectors, we expect to observe multiple binary neutron-star systems through gravitational waves in the near future. The combined analysis of these gravitational-wave signals offers the possibility to constrain the neutron-star radius and the equation of state of dense nuclear matter with unprecedented accuracy. However, it is crucial to ensure that uncertainties inherent in the gravitational-wave models will not lead to systematic biases when information from multiple detections is combined. To quantify waveform systematics, we perform an extensive simulation campaign of binary neutron-star sources and analyze them with a set of four different waveform models. For our analysis with 38 simulations, we find that statistical uncertainties in the neutron-star radius decrease to ± 250 m (2% at 90% credible interval) but that systematic differences between currently employed waveform models can be twice as large. Hence, it will be essential to ensure that systematic biases will not become dominant in inferences of the neutron-star equation of state when capitalizing on future developments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Constraining neutron-star matter with microscopic and macroscopic collisions

Interpreting high-energy, astrophysical phenomena, such as supernova explosions or neutron-star collisions, requires a robust understanding of matter at supranuclear densities. However, our knowledge about dense matter explored in the cores of neutron stars remains limited. Fortunately, dense matter is not probed only in astrophysical observations, but also in terrestrial heavy-ion collision experiments. Here we use Bayesian inference to combine data from astrophysical multi-messenger observations of neutron stars and from heavy-ion collisions of gold nuclei at relativistic energies with microscopic nuclear theory calculations to improve our understanding of dense matter. We find that the inclusion of heavy-ion collision data indicates an increase in the pressure in dense matter relative to previous analyses, shifting neutron-star radii towards larger values, consistent with recent observations by the Neutron Star Interior Composition Explorer mission. Our findings show that constraints from heavy-ion collision experiments show a remarkable consistency with multi-messenger observations and provide complementary information on nuclear matter at intermediate densities. This work combines nuclear theory, nuclear experiment and astrophysical observations, and shows how joint analyses can shed light on the properties of neutron-rich supranuclear matter over the density range probed in neutron stars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗