Neutron Star Structure and the Equation of State
TL;DR: In this article, Buchdahl and Tolman showed that the moment of inertia and the binding energy of a neutron star are nearly universal functions of the star's compactness, which can be understood by considering two analytic, yet realistic, solutions of Einstein's equations.
Abstract: The structure of neutron stars is considered from theoretical and observational perspectives We demonstrate an important aspect of neutron star structure: the neutron star radius is primarily determined by the behavior of the pressure of matter in the vicinity of nuclear matter equilibrium density In the event that extreme softening does not occur at these densities, the radius is virtually independent of the mass and is determined by the magnitude of the pressure For equations of state with extreme softening or those that are self-bound, the radius is more sensitive to the mass Our results show that in the absence of extreme softening, a measurement of the radius of a neutron star more accurate than about 1 km will usefully constrain the equation of state We also show that the pressure near nuclear matter density is primarily a function of the density dependence of the nuclear symmetry energy, while the nuclear incompressibility and skewness parameters play secondary roles In addition, we show that the moment of inertia and the binding energy of neutron stars, for a large class of equations of state, are nearly universal functions of the star's compactness These features can be understood by considering two analytic, yet realistic, solutions of Einstein's equations, by, respectively, Buchdahl and Tolman We deduce useful approximations for the fraction of the moment of inertia residing in the crust, which is a function of the stellar compactness and, in addition, the pressure at the core-crust interface
Citations
More filters
TL;DR: Radio timing observations of the binary millisecond pulsar J1614-2230 that show a strong Shapiro delay signature are presented and the pulsar mass is calculated to be (1.97 ± 0.04)M⊙, which rules out almost all currently proposed hyperon or boson condensate equations of state.
Abstract: Neutron stars comprise the densest form of matter known to exist in our Universe, but their composition and properties are uncertain. Measurements of their masses and radii can constrain theoretical predictions of their composition, but so far it has not been possible to rule out many predictions of 'exotic' non-nucleonic components. Here, radio timing observations of the binary millisecond pulsar J1614-2230 are presented, allowing almost all currently proposed hyperon or boson condensate equations of state to be ruled out.
3,338 citations
TL;DR: This analysis expands upon previous analyses by working under the hypothesis that both bodies were neutron stars that are described by the same equation of state and have spins within the range observed in Galactic binary neutron stars.
Abstract: On 17 August 2017, the LIGO and Virgo observatories made the first direct detection of gravitational waves from the coalescence of a neutron star binary system. The detection of this gravitational-wave signal, GW170817, offers a novel opportunity to directly probe the properties of matter at the extreme conditions found in the interior of these stars. The initial, minimal-assumption analysis of the LIGO and Virgo data placed constraints on the tidal effects of the coalescing bodies, which were then translated to constraints on neutron star radii. Here, we expand upon previous analyses by working under the hypothesis that both bodies were neutron stars that are described by the same equation of state and have spins within the range observed in Galactic binary neutron stars. Our analysis employs two methods: the use of equation-of-state-insensitive relations between various macroscopic properties of the neutron stars and the use of an efficient parametrization of the defining function pðρÞ of the equation of state itself. From the LIGO and Virgo data alone and the first method, we measure the two neutron star radii as R1 ¼ 10.8 þ2.0 −1.7 km for the heavier star and R2 ¼ 10.7 þ2.1 −1.5 km for the lighter star at the 90% credible level. If we additionally require that the equation of state supports neutron stars with masses larger than 1.97 M⊙ as required from electromagnetic observations and employ the equation-of-state parametrization, we further constrain R1 ¼ 11.9 þ1.4 −1.4 km and R2 ¼ 11.9 þ1.4 −1.4 km at the 90% credible level. Finally, we obtain constraints on pðρÞ at supranuclear densities, with pressure at twice nuclear saturation density measured at 3.5 þ2.7 −1.7 × 1034 dyn cm−2 at the 90% level.
1,595 citations
TL;DR: In this article, it was shown that most long-duration soft-spectrum gamma-ray bursts are accompanied by massive stellar explosions (GRB-SNe) and that most of the energy in the explosion is contained in nonrelativistic ejecta (producing the supernova) rather than in the relativistic jets responsible for making the burst and its afterglow.
Abstract: Observations show that at least some gamma-ray bursts (GRBs) happen simultaneously with core-collapse supernovae (SNe), thus linking by a common thread nature's two grandest explosions. We review here the growing evidence for and theoretical implications of this association, and conclude that most long-duration soft-spectrum GRBs are accompanied by massive stellar explosions (GRB-SNe). The kinetic energy and luminosity of well-studied GRB-SNe appear to be greater than those of ordinary SNe, but evidence exists, even in a limited sample, for considerable diversity. The existing sample also suggests that most of the energy in the explosion is contained in nonrelativistic ejecta (producing the supernova) rather than in the relativistic jets responsible for making the burst and its afterglow. Neither all SNe, nor even all SNe of Type Ibc produce GRBs. The degree of differential rotation in the collapsing iron core of massive stars when they die may be what makes the difference.
1,389 citations
TL;DR: In 2019, the LIGO Livingston detector observed a compact binary coalescence with signal-to-noise ratio 12.9 and the Virgo detector was also taking data that did not contribute to detection due to a low SINR but were used for subsequent parameter estimation as discussed by the authors.
Abstract: On 2019 April 25, the LIGO Livingston detector observed a compact binary coalescence with signal-to-noise ratio 12.9. The Virgo detector was also taking data that did not contribute to detection due to a low signal-to-noise ratio, but were used for subsequent parameter estimation. The 90% credible intervals for the component masses range from to if we restrict the dimensionless component spin magnitudes to be smaller than 0.05). These mass parameters are consistent with the individual binary components being neutron stars. However, both the source-frame chirp mass and the total mass of this system are significantly larger than those of any other known binary neutron star (BNS) system. The possibility that one or both binary components of the system are black holes cannot be ruled out from gravitational-wave data. We discuss possible origins of the system based on its inconsistency with the known Galactic BNS population. Under the assumption that the signal was produced by a BNS coalescence, the local rate of neutron star mergers is updated to 250-2810.
1,189 citations
Cites background from "Neutron Star Structure and the Equa..."
...The EoS, i.e., the relation that links the star’s internal pressure to its density, can be mapped to a relationship between macroscopic observables of NSs such as their mass, radius, moment of inertia, and tidal deformability (Lattimer & Prakash 2001)....
[...]
TL;DR: This work analyzed the flow of matter to extract pressures in excess of 1034 pascals, the highest recorded under laboratory-controlled conditions, and ruled out strongly repulsive nuclear equations of state from relativistic mean field theory and weakly repulsive equation of state with phase transitions at densities less than three times that of stable nuclei.
Abstract: Nuclear collisions can compress nuclear matter to densities achieved within neutron stars and within core-collapse supernovae. These dense states of matter exist momentarily before expanding. We analyzed the flow of matter to extract pressures in excess of 10 34 pascals, the highest recorded under laboratory-controlled conditions. Using these analyses, we rule out strongly repulsive nuclear equations of state from relativistic mean field theory and weakly repulsive equations of state with phase transitions at densities less than three times that of stable nuclei, but not equations of state softened at higher densities because of a transformation to quark matter.
1,119 citations
References
More filters
TL;DR: In this paper, a first-order QCD phase transition that occurred reversibly in the early universe would lead to a surprisingly rich cosmological scenario, which is at least conceivable that the phase transition would concentrate most of the quark excess in dense, invisible quark nuggets, providing an explanation for the dark matter in terms of QCD effects only.
Abstract: A first-order QCD phase transition that occurred reversibly in the early universe would lead to a surprisingly rich cosmological scenario. Although observable consequences would not necessarily survive, it is at least conceivable that the phase transition would concentrate most of the quark excess in dense, invisible quark nuggets, providing an explanation for the dark matter in terms of QCD effects only. This possibility is viable only if quark matter has energy per baryon less than 938 MeV. Two related issues are considered in appendices: the possibility that neutron stars generate a quark-matter component of cosmic rays, and the possibility that the QCD phase transition may have produced a detectable gravitational signal.
2,553 citations
TL;DR: In this article, a method is developed for treating Einstein's field equations, applied to static spheres of fluid, in such a manner as to provide explicit solutions in terms of known analytic functions.
Abstract: A method is developed for treating Einstein's field equations, applied to static spheres of fluid, in such a manner as to provide explicit solutions in terms of known analytic functions. A number of new solutions are thus obtained, and the properties of three of the new solutions are examined in detail. It is hoped that the investigation may be of some help in connection with studies of stellar structure. (See the accompanying article by Professor Oppenheimer and Mr. Volkoff.)
2,264 citations
"Neutron Star Structure and the Equa..." refers background or methods in this paper
...Solid lines labelled “Inc”, “Buch” and “T VII” show predictions for an incompressible fluid, the solution of Buchdahl (1967), and the Tolman (1939) VII solution, respectively....
[...]
...The third analytic solution (which we will refer to as “T VII”) was discovered by Tolman (1939) and corresponds to the case when the mass-energy density ρ varies quadratically, that is, ρ = ρc[1 − (r/R)2]....
[...]
...The curves labelled “Inc”, “T VII”, “Buch” and “RP” are for an incompressible fluid, the Tolman (1939) VII solution, the Buchdahl (1967) solution, and an approximation of Ravenhall & Pethick (1994), respectively....
[...]
1,314 citations
TL;DR: In this paper, an equation of state for hot, dense matter is presented in a form that is sufficiently rapid to use directly in hydrodynamical simulations, for example, in stellar collapse calculations.
1,188 citations
TL;DR: The Argonne ${v}_{14}$ plus Urbana VII Hamiltonian produces a softening in the neutron matter equation of state localized around twice nuclear matter density which may indicate a neutral pion condensate.
Abstract: We report microscopic calculations of the equation of state for dense nuclear and neutron matter. The calculations are performed for five Hamiltonians: the Argonne ${v}_{14}$ and Urbana ${v}_{14}$ two-nucleon potentials, both alone and with the Urbana VII three-nucleon potential, and the density-dependent Urbana ${v}_{14}$ plus three-nucleon interaction model of Lagaris, Friedman, and Pandharipande. The beta-stable equation of state and neutron star structure are also calculated for three of the models. The models with the three-nucleon potential bracket the density-dependent model and are significantly stiffer than those with an unmodified two-nucleon potential only. The Argonne ${v}_{14}$ plus Urbana VII Hamiltonian produces a softening in the neutron matter equation of state localized around twice nuclear matter density which may indicate a neutral pion condensate.
767 citations