There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

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

https://iopscience.iop.org/article/10.1086/319702/pdf

Neutron Star Structure and the Equation of State

Composition and structure of protoneutron stars

Systematic calculations of asymmetric nuclear matter have been performed in the framework of the Brueckner-Bethe-Goldstone approach in a wide range of both density and asymmetry parameter. The empirical parabolic law fulfilled by the binding energy per nucleon is confirmed by the present results in all the range of the asymmetry parameter values. The predominant role of the $^{3}$${\mathit{S}}_{1\mathrm{\ensuremath{-}}}^{3}$${\mathit{D}}_{1}$ component of the NN interaction is elucidated. A linear variation of the proton and neutron single-particle potentials is found as increasing the neutron excess; a deviation from the phenomenological potentials occurs for highly asymmetric matter as an effect of the self-consistency. The present calculations of the incompressibility predict a strong softening of the equation of state going from symmetric to asymmetric nuclear matter. The proton fraction in equilibrium with neutron matter has been determined from the beta-stability condition and its relevance to the superfluidity of neutron stars has been investigated.

Asymmetric nuclear matter equation of state

https://arxiv.org/pdf/astro-ph/9810065.pdf

Strange Stars with Realistic Quark Vector Interaction and Phenomenological Density-dependent Scalar Potential

The possibility of strange stars is one of the most important issues in the study of compact objects. Here we use the observations of the newly discovered millisecond x-ray pulsar SAX J1808.4-3658 to constrain the radius of the compact star. Comparing the mass-radius relation of SAX J1808.4-3658 with theoretical models for both neutron stars and strange stars, we argue that a strange star model could be more consistent with SAX J1808.4-3658, and suggest that it is a likely strange star candidate. Our results are useful in constraining microscopic chiral symmetry restoration parameters in the quantum chromodynamics (QCD) modeling of strange matter.

Is SAX J1808.4-3658 a Strange Star ?

The properties of isospin-asymmetric nuclear matter have been investigated in the framework of the extended Brueckner-Hartree-Fock approximation at zero temperature. Self-consistent calculations using the Argonne ${V}_{14}$ interaction are reported for several values of the asymmetry parameter $\ensuremath{\beta}=(N\ensuremath{-}Z)/A,$ ranging from symmetric nuclear matter to pure neutron matter. The binding energy per nucleon fulfills the ${\ensuremath{\beta}}^{2}$ law in the whole asymmetry range. The symmetry energy is calculated for different densities and discussed in comparison with other predictions. At the saturation point it is in fairly good agreement with the empirical value. The present approximation, based on the Landau definition of quasiparticle energy, is investigated in terms of the Hugenholtz--Van Hove theorem, which is proved to be fulfilled with a good accuracy at various asymmetries. The isospin dependence of the single-particle properties is discussed, including mean field, effective mass, and mean free path of neutrons and protons. The isospin effects in nuclear physics and nuclear astrophysics are briefly discussed.

Ignazio Bombaci

Papers

Composition and structure of protoneutron stars

Asymmetric nuclear matter equation of state

Strange Stars with Realistic Quark Vector Interaction and Phenomenological Density-dependent Scalar Potential

Is SAX J1808.4-3658 a Strange Star ?

Asymmetric nuclear matter from an extended Brueckner-Hartree-Fock approach