State Of Cold Nuclear Matter Research Articles

Neutron star mass estimates from gamma-ray eclipses in spider millisecond pulsar binaries

Reliable neutron star mass measurements are key to determining the equation of state of cold nuclear matter, but such measurements are rare. Black widows and redbacks are compact binaries consisting of millisecond pulsars and semi-degenerate companion stars. Spectroscopy of the optically bright companions can determine their radial velocities, providing inclination-dependent pulsar mass estimates. Although inclinations can be inferred from subtle features in optical light curves, such estimates may be systematically biased due to incomplete heating models and poorly understood variability. Using data from the Fermi Large Area Telescope, we have searched for gamma-ray eclipses from 49 spider systems, discovering significant eclipses in 7 systems, including the prototypical black widow PSR B1957+20. Gamma-ray eclipses require direct occultation of the pulsar by the companion, and so the detection, or significant exclusion, of a gamma-ray eclipse strictly limits the binary inclination angle, providing new robust, model-independent pulsar mass constraints. For PSR B1957+20, the eclipse implies a much lighter pulsar (1.81 ± 0.07 solar masses) than inferred from optical light curve modelling.

Nuclear matter properties at finite temperatures from effective interactions

We study if commonly used nucleon-nucleon effective interactions, obtained from fitting the properties of cold nuclear matter and of finite nuclei, can properly describe the hot dense nuclear matter produced in intermediate-energy heavy-ion collisions. We use two representative effective interactions, i.e., an improved isospin- and momentum-dependent interaction with its isovector part calibrated by the results from the \emph{ab initio} non-perturbative self-consistent Green's function (SCGF) approach with chiral forces, and a Skyme-type interaction fitted to the equation of state of cold nuclear matter from chiral effective many-body perturbation theory and the binding energy of finite nuclei. In the mean-field approximation, we evaluate the equation of state and the single-nucleon potential for nuclear matter at finite temperatures and compare them to those from the SCGF approach. We find that the improved isospin- and momentum-dependent interaction reproduces reasonably well the SCGF results due to its weaker momentum dependence of the mean-field potential than in the Skyrme-type interaction. Our study thus indicates that effective interactions with the correct momentum dependence of the mean-filed potential can properly describe the properties of hot dense nuclear matter and are thus suitable for use in transport models to study heavy-ion collisions at intermediate energies.

Relativistic mean-field models with scaled hadron masses and couplings: Hyperons and maximum neutron star mass

An equation of state of cold nuclear matter with an arbitrary isotopic composition is studied within a relativistic mean-field approach with hadron masses and coupling constants depending self-consistently on the scalar mean-field. All hadron masses decrease universally with the scalar field growth, whereas meson–nucleon coupling constants can vary differently. More specifically we focus on two modifications of the KVOR model studied previously. One extension of the model (KVORcut) demonstrates that the equation of state stiffens if the increase of the scalar-field magnitude with the density is bounded from above at some value for baryon densities above the saturation nuclear density. This can be realized if the nucleon vector–meson coupling constant changes rapidly as a function of the scalar field slightly above the desired value. The other version of the model (MKVOR) utilizes a smaller value of the nucleon effective mass at the nuclear saturation density and a saturation of the scalar field in the isospin asymmetric matter induced by a strong variation of the nucleon isovector–meson coupling constant as function of the scalar field. A possibility of hyperonization of the matter in neutron star interiors is incorporated. Our equations of state fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, direct Urca constraint, gravitational-baryon mass constraint for the pulsar J0737-3039B, and the constraint on the maximum mass of the neutron stars.

Probing the equation of state for cold nuclear matter in fusion reactions

To probe the nuclear equation of state, several fusion cross-sections have been analyzed using microscopic nucleus-nucleus potentials calculated in the framework of the Hamiltonian energy density approach through the well-known Skyrme nucleon-nucleon effective interaction with eighteen different parameterizations which express various equations of state. Three density-dependent M3Y-Paris effective forces are examined also within the double-folding model. The various effective forces give incompressibility modulus values which vary over a rather wide range between 188MeV and 372MeV. The extracted fusion barrier distributions are examined too with the same aim. The most successfully investigated interactions in deriving satisfactory fusion excitation functions as well as barrier distributions are those giving equations of state with nuclear incompressibility values in the range of 230-241MeV, according to the isospin asymmetry of the interacting nuclei.

Merger of binary neutron stars with realistic equations of state in full general relativity

We present numerical results of three-dimensional simulations for the merger of binary neutron stars in full general relativity. Hybrid equations of state are adopted to mimic realistic nuclear equations of state. In this approach, we divide the equations of state into two parts as $P={P}_{\mathrm{cold}}+{P}_{\mathrm{th}}$. ${P}_{\mathrm{cold}}$ is the cold part for which we assign a fitting formula for realistic equations of state of cold nuclear matter slightly modifying the formula developed by Haensel and Potekhin. We adopt the SLy and FPS equations of state for which the maximum allowed Arnowitt-Deser-Misner (ADM) mass of cold and spherical neutron stars is $\ensuremath{\approx}2.04{M}_{\ensuremath{\bigodot}}$ and $1.80{M}_{\ensuremath{\bigodot}}$, respectively. ${P}_{\mathrm{th}}$ denotes the thermal part which is written as ${P}_{\mathrm{th}}=({\ensuremath{\Gamma}}_{\mathrm{th}}\ensuremath{-}1)\ensuremath{\rho}(\ensuremath{\epsilon}\ensuremath{-}{\ensuremath{\epsilon}}_{\mathrm{cold}})$, where $\ensuremath{\rho}$, $\ensuremath{\epsilon}$, ${\ensuremath{\epsilon}}_{\mathrm{cold}}$, and ${\ensuremath{\Gamma}}_{\mathrm{th}}$ are the baryon rest-mass density, total specific internal energy, specific internal energy of the cold part, and the adiabatic constant, respectively. Simulations are performed for binary neutron stars of the total ADM mass in the range between $2.4{M}_{\ensuremath{\bigodot}}$ and $2.8{M}_{\ensuremath{\bigodot}}$ with the rest-mass ratio ${Q}_{M}$ to be in the range $0.9\ensuremath{\lesssim}{Q}_{M}\ensuremath{\le}1$. It is found that if the total ADM mass of the system is larger than a threshold ${M}_{\mathrm{thr}}$, a black hole is promptly formed in the merger irrespective of the mass ratios. In the other case, the outcome is a hypermassive neutron star of a large ellipticity, which results from the large adiabatic index of the realistic equations of state adopted. The value of ${M}_{\mathrm{thr}}$ depends on the equation of state: ${M}_{\mathrm{thr}}\ensuremath{\sim}2.7{M}_{\ensuremath{\bigodot}}$ and $\ensuremath{\sim}2.5{M}_{\ensuremath{\bigodot}}$ for the SLy and FPS equations of state, respectively. Gravitational waves are computed in terms of a gauge-invariant wave extraction technique. In the formation of the hypermassive neutron star, quasiperiodic gravitational waves of a large amplitude and of frequency between 3 and 4 kHz are emitted. The estimated emission time scale is $\ensuremath{\lesssim}100\text{ }\text{ }\mathrm{ms}$, after which the hypermassive neutron star collapses to a black hole. Because of the long emission time, the effective amplitude may be large enough to be detected by advanced laser interferometric gravitational wave detectors if the distance to the source is smaller than $\ensuremath{\sim}100\text{ }\text{ }\mathrm{Mpc}$. Thermal properties of the outcome formed after the merger are also analyzed to approximately estimate the neutrino emission energy.

Gravitationally redshifted absorption lines in the X-ray burst spectra of a neutron star.

The fundamental properties of neutron stars provide a direct test of the equation of state of cold nuclear matter, a relationship between pressure and density that is determined by the physics of the strong interactions between the particles that constitute the star. The most straightforward method of determining these properties is by measuring the gravitational redshift of spectral lines produced in the neutron star photosphere. The equation of state implies a mass-radius relation, while a measurement of the gravitational redshift at the surface of a neutron star provides a direct constraint on the mass-to-radius ratio. Here we report the discovery of significant absorption lines in the spectra of 28 bursts of the low-mass X-ray binary EXO0748-676. We identify the most significant features with the Fe XXVI and XXV n = 2-3 and O VIII n = 1-2 transitions, all with a redshift of z = 0.35, identical within small uncertainties for the respective transitions. For an astrophysically plausible range of masses (M approximately 1.3-2.0 solar masses; refs 2-5), this value is completely consistent with models of neutron stars composed of normal nuclear matter, while it excludes some models in which the neutron stars are made of more exotic matter.

Reconstructing the equation of state for cold nuclear matter from the relationship of any two properties of neutron stars

A direct method is developed to reconstruct the equation of state for high-density nuclear matter from the relationship between any two properties of neutron stars, such as masses, radii, moments of inertia, baryonic masses, binding energies, gravitational redshifts, and their combinations.

The equation of state for cold nuclear matter as seen in nucleus-nucleus scattering

The equation of state for cold nuclear matter is determined by the effective, density-dependent interaction between bound nucleons at temperatureT = 0. This interaction can be probed in elastic nucleus-nucleus collisions at various density overlaps which may extend to several times the normal matter density. For this purpose the elastic scattering of16O ions on16O has been measured at incident energies from 250 to 1120 MeV with high accuracy. From these data, which sample both diffractive and refractive scattering processes, we extract the underlying scattering potentials utilizing model-unrestricted analysis methods. These potentials fit very well into the systematics found in light-ion scattering and compare very favorably with microscopic calculations, if these are based on a weak density dependence of the effective NN interaction, resulting in a soft equation of state for cold nuclear matter.

Nuclear equation of state

We present a discussion of the equation of state of cold nuclear matter predicted by our recently completed Thomas-Fermi model. The equation is in the form of a three-term polynomial in the cube root of the density, with coefficients that are functions of the relative neutron excess \ensuremath{\delta}. The coefficients are tabulated in the range from $\ensuremath{\delta}=0$ (standard nuclear matter) to $\ensuremath{\delta}=1$ (neutron matter), making it very easy to calculate, for a given $\ensuremath{\delta}$, the pressure, compressibility, saturation binding, and any other property of the Thomas-Fermi equation of state. We discuss the empirical information concerning abnormal densities and large neutron excess that is contained in the measured values of the surface energy, surface diffuseness, and the neutron skin.

A microscopic energy- and density-dependent effective interaction and its test by nucleus-nucleus scattering

An effective nucleon-nucleon interaction calculated in nuclear matter from the Bonn potential has been parametrized in terms of a local density- and energy-dependent two-body interaction. This allows to calculate the real part of the nucleus-nucleus scattering potential and to test this effective interaction over a wide region of densities ( ϱ ≤ 3 ϱ 0) produced dynamically in scattering experiments. Comparing our calculations with empirical potentials extracted from data on light and heavy ion scattering by model-unrestricted analysis methods, we find quantitative agreement with the exception of proton scattering. The failure in this case may be traced back to the properties of the effective interaction at low densities, for which the nuclear matter results are not reliable. The success of the interaction at high overlap densities confirms the empirical evidence for a soft equation of state for cold nuclear matter.

Equation of state for cold nuclear matter from refractive 16O+16O elastic scattering.

The nuclear density overlap, which occurs during refractive heavy-ion scattering, opens an alternative approach to study the equation of state (EOS) for cold nuclear matter. For this purpose elastic [sup 16]O+[sup 16]O scattering at incident enegies of 145, 250, 350, and 480 MeV has been measured very accurately, up to large angles. A systematic folding analysis of these data has been performed using an effective density dependent interaction based on the [ital G]-matrix elements of the Paris nucleon-nucleon potential. We find, with the observed refractive scattering patterns, that a soft EOS (with the nuclear incompressibility [ital K] around 200 MeV) is the most realistic one.

Equation of state of cold nuclear matter extracted from nuclear masses by the droplet model.

The information of the equation of state of cold nuclear matter is extracted from the experimental nuclear masses by the droplet model. The result shows the asymmetry dependence of the equation of state in a more direct way than has been done before. It shows that the spherical or the deformed nuclear region appears alternately as the bulk nucleon density of the core of nuclei increases. An explanation of why the rms fit of the droplet model to the nuclear masses gives a very broad minimum region of the nuclear compressibility is possible based on this work.

Equation of state of dense nuclear matter

An equation of state for cold nuclear matter for the region of densities ρ nm−4 ρ nm, where ρ nm is empirical nuclear-matter density, is constructed. We begin from the detailed calculation of Day and Wiringa for the two-body interactions; these give a saturation density of ∼2 ρ nm. This density is brought down to ρ nm by the addition of relativistic corrections. Additional binding is obtained from three-body forces. A reasonable picture is obtained with the Day-Wiringa compression modulus for the two-body calculation, but the picture can be further improved by choosing this to be smaller. Our equation of state is similar to that of Friedman and Pandharipande in the region of nuclear matter denstiy ρ nm, but, due to higher-order terms in the loop correction, is substantially softer at high density. Basically what happens is that the many-body effects saturate with increasing density, leaving only the two-body interactions. With this equation of state, prompt supernova explosions are very powerful when the compression modulus of neutron-rich matter (twice as many neutrons as protons) is ∼150 MeV, which corresponds to K nm ∼ 190 MeV for symmetric nuclear matter. Analysis shows that hot nuclear matter formed in heavy ion collisions demands a very stiff equation of state. We understand this as arising from the strong velocity dependence in the real part of the optical model potential which follows chiefly from the Lorentz character of the interactions, the vector mean field growing with increasing density and the scalar one decreasing. This gives a substantial repulsive contribution to the energy per particle and produces a stiff effective equation of state for several hundred MeV heavy-ion collisions. With increasing degree of equilibration the magnitude of the repulsive energy decreases since equilibration decreases the effective momentum. Given the strong velocity dependence in the interaction, the hot equation of state can be reconciled with the cool one.

Parametrizing the equation of state of cold and dense nuclear matter.

Various functional parametrizations of the equation of state of cold nuclear matter are considered with regard to both their degree of stiffness and their causal behavior at high density. We show that (i) the inferred nuclear compressibility K is strongly parametrization dependent when the measured pion multiplicity in central heavy ion collisions is fitted, and (ii) most of the commonly used equations of state are acausal at high density.