Constraints on a phenomenologically parameterized neutron-star equation of state

Abstract: We introduce a parameterized 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 should be smaller than the number of neutron-star properties that have been measured or will have been measured in the next several years. And the set must be large enough to accurately approximate the large set of candidate EOSs. We find that a parameterized 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 solar mass 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. In particular, we emphasize potentially stringent constraints on the EOS parameter space associated with two measured properties of a single star; and we find that a measurement of the moment of inertia of PSR J0737-3039A can strongly constrain the maximum 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.

• The paper presents a 4-parameter piecewise polytropic model that reproduces candidate neutron-star EOS with an average rms error of about 4%.
• The study categorizes 34 EOS candidates, contrasting ordinary nuclear matter models with those including exotic components.
• The methodology integrates astrophysical constraints such as maximum mass and spin, offering predictions for future gravitational-wave observations.

Overview of Constraints on a Phenomenologically Parameterized Neutron-Star Equation of State

This paper discusses a methodology to systematize the study of constraints on the neutron-star Equation of State (EOS) using a parameterized high-density EOS. The primary focus is on providing a manageable set of parameters that can accurately describe the complex nature of the neutron-star matter captured by various candidate EOSs while being constrained by current and anticipated astrophysical observations.

The proposed parameterization employs a piecewise polytropic EOS with two notable features: first, the EOS has up to four free parameters, which is fewer than the number of measurable neutron-star properties; second, it is crafted to approximate existing candidate EOSs with high fidelity, yielding an average root mean square (rms) error of about 4%. By choosing three specific density intervals with fixed division points at $10^{14.7}$ and $10^{15.0}$ g/cm$^3$, the authors effectively reduce the parameter space to a more tangible 4-dimensional space without compromising the accuracy of representation.

Key Results and Discussion

The work extensively tests the proposed parameterization against 34 EOS candidates, categorizing them into those with only ordinary nuclear matter (e.g., $npe\mu$ matter models) and those including exotic components such as hyperons, meson condensates, and quarks. Exceptionally low rms errors are reported for ordinary nuclear matter EOSs, whereas configurations involving exotic matter see an increase but remain within an acceptable range.

Astrophysical constraints evaluated include the effects of causality, maximum observed neutron-star mass, maximum spin, and gravitational redshift. Observational limits such as a 1.7 $M_\odot$ neutron-star mass and rotational frequencies up to 716 Hz are used as benchmarks for ruling out certain regions of the parameter space. Of particular theoretical interest is the insight offered into the implications of future measurements of the moment of inertia for pulsar PSR~J0737-3039A, as such measurements could significantly constrain the parameter space.

Additionally, the methodology presents an efficient algorithm for determining points of marginal stability and maximum angular velocity of stable models, a critical aspect for studying rapidly rotating neutron stars. The paper underscores the utility of assessing multiple observables from single stars due to the intensified constraints they can impose on the EOS parameter space.

Implications and Future Prospects

The approach offers a systematic exploration of the neutron-star EOS, with parameterizations that suggest couplings between high-density behavior and measured neutron-star properties. The implication for theoretical models is that precise measurements of neutron-star observables could deliver stringent constraints on the EOS, minimizing the range of plausible models. Practically, the anticipation of gravitational-wave observations presents an avenue for further refining these constraints.

The research adopts a cautious tone regarding the interpretative strength of various astrophysical measurements, especially in light of systematic uncertainties, thus providing a robust baseline for interpreting future high-fidelity observations. The integration of gravitational-wave data stands as a promising means of further constraining the EOS, particularly as interferometers reach their designed sensitivities.

In conclusion, this work provides a comprehensive and quantitative method for assessing neutron-star EOSs, bridging theoretical predictions with observational data. It offers a promising foundation for further explorations in both neutron-star astrophysics and high-density matter physics, particularly as more precise observational data become available.