Constraints on a phenomenologically parametrized neutron-star equation of state

We introduce a parametrized high-density equation of state (EOS) in order to systematize the study of constraints placed by astrophysical observations on the nature of neutron-star matter. To obtain useful constraints, the number of parameters must be smaller than the number of EOS-related neutron-star properties measured, but large enough to accurately approximate the large set of candidate EOSs. We find that a parametrized EOS based on piecewise polytropes with 3 free parameters matches, to about 4% rms error, an extensive set of candidate EOSs at densities below the central density of $1.4{M}_{\ensuremath{\bigodot}}$ stars. Adding observations of more massive stars constrains the higher-density part of the EOS and requires an additional parameter. We obtain constraints on the allowed parameter space set by causality and by present and near-future astronomical observations with the least model dependence. Stringent constraints on the EOS parameter space are associated with the future measurement of the moment of inertia of PSR J0737-3039A combined with the maximum known neutron-star mass. We also present in an appendix a more efficient algorithm than has previously been used for finding points of marginal stability and the maximum angular velocity of stable stars.