Constraints on the equation of state of ultra - dense matter from observations of neutron stars

I discuss constraints on the equation of state of matter at supra-nuclear densities that can be derived from observations of neutron stars. I focus on recent work on Vela X-1, which may well be substantially more massive than the canonical 1.4 M ⊙ , and on the prospects offered by the 'isolated' or 'thermally-emitting' neutron stars. 1. The equation of state for ultra-dense matter To understand the core collapse of massive stars, the supernova phenomenon, and the existence and properties of neutron stars, requires knowledge of the equation of state (EOS) for matter at supra-nuclear density. The EOS is determined by the behaviour of elementary particles at close proximity to each other and hence is of fundamental physical interest. It is modeled using quantum-chromodynamics calculations, but these are not developed well enough to determine the densities at which, e.g., meson condensation and the transition between the hadron and quark-gluon phases occur. At densities slightly higher than nuclear and at high temperatures, the model predictions can be compared with the results of heavy-nuclei collision experiments. For higher densities and low temperatures , however, this is not possible; the models can be compared only with neutron-star parameters. Recent reviews of our knowledge of the EOS, and the use of neutron stars for constraining it, are given by Heiselberg & Pandharipande The different models for the EOS predict highly different mass-radius relations , and a direct constraint on the EOS would be set by a simultaneous measurement of the radius and mass of a neutron star. This has not yet been possible, and observational tests have been limited to predictions for extrema, such as the maximum possible mass and the minimum possible spin or orbital period. For instance, for EOS with a phase transition at high densities, such as Kaon condensation (Brown and Bethe 1994), only neutron stars with mass < 1.5 M ⊙ could exist (for larger masses, a black hole would be formed). So far, susceptibility to systematic errors and modeling uncertainties have befuddled most attempts to constrain the EOS observationally (e.g., radius de-terminations from X-ray bursts, Lewin et al. 1993; innermost stable orbit from kHz QPOs, Van der Klis 2000). The only accurate measurements are the fastest spin period and some precise masses. The former, 1.5 ms, excludes the stiffest EOS (PSR B1937+214; Backer et al. 1982); the latter I discuss below.