James M. Lattimer

Neutron Star Structure and the Equation of State

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 stars compactness. These features can be understood by considering two analytic, yet realistic, solutions of Einsteins 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.

The physics of neutron stars

Neutron stars are some of the densest manifestations of massive objects in the universe. They are ideal astrophysical laboratories for testing theories of dense matter physics and provide connections among nuclear physics, particle physics, and astrophysics. Neutron stars may exhibit conditions and phenomena not observed elsewhere, such as hyperon-dominated matter, deconfined quark matter, superfluidity and superconductivity with critical temperatures near 1010 kelvin, opaqueness to neutrinos, and magnetic fields in excess of 1013 Gauss. Here, we describe the formation, structure, internal composition, and evolution of neutron stars. Observations that include studies of pulsars in binary systems, thermal emission from isolated neutron stars, glitches from pulsars, and quasi-periodic oscillations from accreting neutron stars provide information about neutron star masses, radii, temperatures, ages, and internal compositions.

Neutron star observations: Prognosis for equation of state constraints

Abstract We investigate how current and proposed observations of neutron stars can lead to an understanding of the state of their interiors and the key unknowns: the typical neutron star radius and the neutron star maximum mass. We consider observations made not only with photons, ranging from radio waves to X-rays, but also those involving neutrinos and gravity waves. We detail how precision determinations of structural properties would lead to significant restrictions on the poorly understood equation of state near and beyond the equilibrium density of nuclear matter. To begin, a theoretical analysis of neutron star structure, including general relativistic limits to mass, compactness, and spin rates is made. A review is the made of recent observations such as pulsar timing (which leads to mass, spin period, glitch and moment of inertia estimates), optical and X-ray observations of cooling neutron stars (which lead to estimates of core temperatures and ages and inferences about the internal composition), and X-ray observations of accreting and bursting sources (which shed light on both the crustal properties and internal composition). Next, we discuss neutrino emission from proto-neutron stars and how neutrino observations of a supernova, from both current and planned detectors, might impact our knowledge of the interiors, mass and radii of neutron stars. We also explore the question of how superstrong magnetic fields could affect the equation of state and neutron star structure. This is followed by a look at binary mergers involving neutron stars and how the detection of gravity waves could unambiguously distinguish normal neutron stars from self-bound strange quark matter stars.

A generalized equation of state for hot, dense matter

Abstract 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. It contains an adjustable nuclear force that accurately models both potential and mean-field interactions, and it allows for the input of various nuclear parameters, some of which are not yet experimentally well-determined. These include the bulk incompressibility parameter, the bulk and surface symmetry energies, the symmetric matter surface tension, and the nucleon effective masses. This permits parametric studies of the equation of state in astrophysical situations. The equation of state is modelled after the Lattimer, Lamb, Pethick and Ravenhall LLPR compressible liquid-drop model for nuclei, and includes the effects of interactions and degeneracy of the nucleons outside nuclei. Account is also taken of nuclear deformations and the phase transitions from nuclei to uniform nuclear matter at subnuclear densities. Comparisons of this equation of state are made to the results of the LLPR model and the Cooperstein-Baron equation of state. The effects of varying the bulk incompressibility are also investigated.

Effects of Dietary Fiber and Its Components on Metabolic Health

Dietary fiber and whole grains contain a unique blend of bioactive components including resistant starches, vitamins, minerals, phytochemicals and antioxidants. As a result, research regarding their potential health benefits has received considerable attention in the last several decades. Epidemiological and clinical studies demonstrate that intake of dietary fiber and whole grain is inversely related to obesity, type two diabetes, cancer and cardiovascular disease (CVD). Defining dietary fiber is a divergent process and is dependent on both nutrition and analytical concepts. The most common and accepted definition is based on nutritional physiology. Generally speaking, dietary fiber is the edible parts of plants, or similar carbohydrates, that are resistant to digestion and absorption in the small intestine. Dietary fiber can be separated into many different fractions. Recent research has begun to isolate these components and determine if increasing their levels in a diet is beneficial to human health. These fractions include arabinoxylan, inulin, pectin, bran, cellulose, β-glucan and resistant starch. The study of these components may give us a better understanding of how and why dietary fiber may decrease the risk for certain diseases. The mechanisms behind the reported effects of dietary fiber on metabolic health are not well established. It is speculated to be a result of changes in intestinal viscosity, nutrient absorption, rate of passage, production of short chain fatty acids and production of gut hormones. Given the inconsistencies reported between studies this review will examine the most up to date data concerning dietary fiber and its effects on metabolic health.

The Equation of State from Observed Masses and Radii of Neutron Stars

We determine an empirical dense matter equation of state (EOS) from a heterogeneous data set of six neutron stars: three Type-I X-ray bursters with photospheric radius expansion, studied by ?zel et?al., and three transient low-mass X-ray binaries. We critically assess the mass and radius determinations from the X-ray burst sources and show explicitly how systematic uncertainties, such as the photospheric radius at touchdown, affect the most probable masses and radii. We introduce a parameterized EOS and use a Markov chain Monte Carlo algorithm within a Bayesian framework to determine nuclear parameters such as the incompressibility and the density dependence of the bulk symmetry energy. Using this framework we show, for the first time, that these parameters, predicted solely on the basis of astrophysical observations, all lie in ranges expected from nuclear systematics and laboratory experiments. We find significant constraints on the mass-radius relation for neutron stars, and hence on the pressure-density relation of dense matter. The predicted symmetry energy and the EOS near the saturation density are soft, resulting in relatively small neutron star radii around 11-12?km for M = 1.4 M ?. The predicted EOS stiffens at higher densities, however, and our preferred model for X-ray bursts suggests that the neutron star maximum mass is relatively large, 1.9-2.2 M ?. Our results imply that several commonly used equations of state are inconsistent with observations.

The Nuclear Equation of State and Neutron Star Masses

Neutron stars are valuable laboratories for the study of dense matter. Recent observations have uncovered both massive and low-mass neutron stars and have also set constraints on neutron star radii. The largest mass measurements are powerfully influencing the high-density equation of state because of the existence of the neutron star maximum mass. The smallest mass measurements, and the distributions of masses, have implications for the progenitors and formation mechanisms of neutron stars. The ensemble of mass and radius observations can realistically restrict the properties of dense matter and, in particular, the behavior of the nuclear symmetry energy near the nuclear saturation density. Simultaneously, various nuclear experiments are progressively restricting the ranges of parameters describing the symmetry properties of the nuclear equation of state. In addition, new theoretical studies of pure neutron matter are providing insights. These observational, experimental, and theoretical constraints of dense matter, when combined, are now revealing a remarkable convergence.

Composition and structure of protoneutron stars

Abstract We investigate the structure of neutron stars shortly after they are born, when the entropy per baryon is of order 1 or 2 and neutrinos are trapped on dynamical timescales. We find that the structure depends more sensitively on the composition of the star than on its entropy, and that the number of trapped neutrinos play an important role in determining the composition. Since the structure is chiefly determined by the pressure of the strongly interacting constituents and the nature of the strong interactions is poorly understood at high density, we consider several models of dense matter, including matter with strangeness-rich hyperons, a kaon condensate and quark matter. In all cases, the thermal effects for an entropy per baryon of order 2 or less are small when considering the maximum neutron star mass. Neutrino trapping, however, significantly changes the maximum mass due to the abundance of electrons. When matter is allowed to contain only nucleons and leptons, trapping decreases the maximum mass by an amount comparable to, but somewhat larger than, the increase due to finite entropy. When matter is allowed to contain strongly interacting negatively charged particles, in the form of strange baryons, a kaon condensate, or quarks, trapping instead results in an increase in the maximum mass, which adds to the effects of finite entropy. A net increase of order 0.2 M ⊙ occurs. The presence of negatively-charged particles has two major implications for the neutrino signature of gravitational collapse supernovae. First, the value of the maximum mass will decrease during the early evolution of a neutron star as it loses trapped neutrinos, so that if a black hole forms, it either does so immediately after the bounce (accretion being completed in a second or two) or it is delayed for a neutrino diffusion timescale of ~ 10 s . The latter case is most likely if the maximum mass of the hot star with trapped neutrinos is near 1.5 M ⊙ . In the absence of negatively-charged hadrons, black hole formation would be due to accretion and therefore is likely to occur only immediately after bounce. Second, the appearance of hadronic negative charges results in a general softening of the equation of state that may be observable in the neutrino luminosities and average energies. Further, these additional negative charges decrease the electron fraction and may be observed in the relative excess of electron neutrinos compared to other neutrinos.

Isospin asymmetry in nuclei and neutron stars

Abstract The roles of isospin asymmetry in nuclei and neutron stars are investigated using a range of potential and field-theoretical models of nucleonic matter. The parameters of these models are fixed by fitting the properties of homogeneous bulk matter and closed-shell nuclei. We discuss and unravel the causes of correlations among the neutron skin thickness in heavy nuclei, the pressure of beta-equilibrated matter at a density of 0.1 fm - 3 , the derivative of the nuclear symmetry energy at the same density and the radii of moderate mass neutron stars. Constraints on the symmetry properties of nuclear matter from the binding energies of nuclei are examined. The extent to which forthcoming neutron skin measurements will further delimit the symmetry properties is investigated. The impact of symmetry energy constraints for the mass and moment of inertia contained within neutron star crusts and the threshold density for the nucleon direct Urca process, all of which are potentially measurable, is explored. We also comment on the minimum neutron star radius, assuming that only nucleonic matter exists within the star.

Equation of State in the Gravitational Collapse of Stars

Abstract The equation of state in stellar collapse is derived from simple considerations, the crucial ingredient being that the entropy per nucleon remains small, of the order of unity (in units of k), during the entire collapse. In the early regime, ρ∼1010−1013 g/cm3, nuclei partially dissolve into α-particles and neutrons; the α-particles go back into the nuclei at higher densities. At the higher densities, nuclei are preserved right up to nuclear matter densities, at which point the nucleons are squeezed out of the nuclei. The low entropy per nucleon prevents the appearance of drip nucleons, which would add greatly to the net entropy. We find that electrons are captured by nuclei, the capture on free protons being negligible in comparison. Carrying the difference of neutron and proton chemical potentials μn−μp in our capture equation forces the energy of the resulting neutrinos to be low. Nonethelesd, neutrino trapping occurs at a density of about ρ = 1012 g/cm3. The fact that the ensuing development to higher densities is adiabatic makes our treatment in terms of entropy highly relevant. The resulting equation of state has an adiabatic index of roughly 4 3 coming from the degenerate leptons, but lowered slightly by electrons changing into neutrinos and by the nuclei dissolving into α-particles (although this latter process is reversed at the higher densities), right up to nuclear matter densities. At this point the equation of state suddenly stiffens, with Γ going up to Γ ≈ 2.5 and bounce at about three times nuclear matter density. In the later stages of the collapse, only neutrinos of energy ⪅10 MeV are able to get out into the photosphere, and these appear to be insufficient to blow off the mantle and envelope of the star. We do not carry our description into the region following the bounce, where a shock wave is presumably formed, and, therefore, we cannot answer the question as to whether the shock wave, in conjunction with neutrino transport, can dismantle the star, but a one-dimensional treatment shows the shock wave to be very promising in this respect.