Nuclear matter and its role in supernovae, neutron stars and compact object binary mergers☆
Introduction
The equation of state (EOS) of dense matter plays an important role in the supernova phenomenon and in the structure and evolution of neutron stars. Matter in the collapsing core of a massive star at the end of its life is compressed from white dwarf-like densities of about to two or three times the nuclear saturation density, about or ns=0.16 baryons fm−3. The central densities of neutron stars may range up to 5–10ns. At densities around ns and below matter may be regarded as a mixture of neutrons, protons, electrons and positrons, neutrinos and antineutrinos, and photons. At higher densities, additional constituents, such as hyperons, kaons, pions and quarks may be present, and there is no general consensus regarding the properties of such ultradense matter. Fortunately for astrophysics, however, the supernova phenomenon and many aspects of neutron star structure may not depend upon ultradense matter, and this article will focus on the properties of matter at lower densities.
The main problem is to establish the state of the nucleons, which may be either bound in nuclei or be essentially free in continuum states. Neither temperatures nor densities are large enough to excite degrees of freedom, such as hyperons, mesons or quarks. Electrons are rather weakly interacting and may be treated as an ideal Fermi gas: at densities above , they are relativisitic. Because of their even weaker interactions, photons and neutrinos (when they are confined in matter) may also be treated as ideal gases.
At low enough densities and temperatures, and provided the matter does not have too large a neutron excess, the relevant nuclei are stable in the laboratory, and experimental information may be used directly. The so-called Saha equation may be used to determine their relative abundances. Under more extreme conditions, there are a number of important physical effects which must be taken into account. At higher densities, or at moderate temperatures, the neutron chemical potential increases to the extent that the density of nucleons outside nuclei can become large. It is then important to treat matter outside nuclei in a consistent fashion with that inside. These nucleons will modify the nuclear surface, decreasing the surface tension. At finite temperatures, nuclear excited states become populated, and these states can be included by treating nuclei as warm drops of nuclear matter. At low temperatures, nucleons in nuclei are degenerate and Fermi-liquid theory is probably adequate for their description. However, near the critical temperature above which the dense phase of matter inside nuclei can no longer coexist with the lighter phase of matter outside nuclei, the equilibrium of the two phases of matter is crucial.
The fact that at subnuclear densities the spacing between nuclei may be of the same order of magnitude as the nuclear size itself will lead to substantial reductions in the nuclear Coulomb energy. Although finite-temperature “plasma” effects will modify this, the zero-temperature Wigner–Seitz approximation employed by Baym et al. [1] is usually adequate. Near the nuclear saturation density, nuclear deformations must be dealt with, including the possibilities of “pasta-like” phases and matter turning “inside-out” (i.e., the dense nuclear matter envelopes a lighter, more neutron-rich, liquid). Finally, the translational energy of the nuclei may be important under some conditions. This energy is important in that it may substantially reduce the average size of the nuclear clusters.
An acceptable way of bridging the regions of low density and temperature, in which the nuclei can be described in terms of a simple mass formula, and high densities and/or high temperatures in which the matter is a uniform bulk fluid, is to use a compressible liquid droplet model for nuclei in which the drop maintains thermal, mechanical, and chemical equilibrium with its surroundings. This allows us to address both the phase equilibrium of nuclear matter, which ultimately determines the densities and temperatures in which nuclei are permitted, and the effects of an external nucleon fluid on the properties of nuclei. Such a model was originally developed by Lattimer et al. [2] and modified by Lattimer and Swesty [3]. This work was a direct result of David Schramm's legendary ability to mesh research activities of various groups, in this case to pursue the problem of neutron star decompression. After the fact, the importance of this topic for supernovae became apparent.
Section snippets
Nucleon matter properties
The compressible liquid droplet model rests upon the important fact that in a many-body system the nucleon–nucleon interaction exhibits saturation. Empirically, the energy per particle of bulk nuclear matter reaches a minimum, about –16 MeV, at a density . Thus, close to ns, its density dependence is approximately parabolic. The nucleon–nucleon interaction is optimized for equal numbers of neutrons and protons (symmetric matter), so a parabolic dependence on the neutron excess or
The equation of state and the collapse of massive stars
Massive stars at the end of their lives are believed to consist of a white-dwarf-like iron core of 1.2–1.6M⊙ having low entropy (s≤1), surrounded by layers of less processed material from shell nuclear burning. The effective Chandrasekhar mass, the maximum mass the degenerate electron gas can support, is dictated by the entropy and the average lepton content, YL, believed to be around 0.41–0.43. As mass is added to the core by shell Si-burning, the core eventually becomes unstable and collapses.
The structure of neutron stars
The theoretical study of the structure of neutron stars is crucial if new observations of masses and radii are to lead to effective constraints on the EOS of dense matter. This study becomes ever more important as laboratory studies may be on the verge of yielding evidence about the composition and stiffness of matter beyond ns. To date, several accurate mass determinations of neutron stars are available, and they all lie in a narrow range (1.25–1.44M⊙). There is some speculation that the
The merger of a neutron star with a low-mass black hole
The general problem of the origin and evolution of systems containing a neutron star and a black hole was first detailed by Lattimer and Schramm [37], although the original motivation was due to Schramm. Although speculative at the time, Schramm insisted that this would prove to be an interesting topic from the points of view of nucleosynthesis and gamma-ray emission. The contemporaneous discovery [38] of the first-known binary system containing twin compact objects, PSR 1913+16, which was also
Acknowledgements
We thank Ralph Wijers for discussions concerning accretion disks.
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Partially supported by USDOE Grants DE-AC02-87ER40317 and DE-FG02-88ER-40388, and by NASA ATP Grant # NAG 52863.