### Abstract

Observations of isolated neutron stars place constraints on the equation of state (EOS) of cold, neutron-rich matter, while nuclear physics experiments probe the EOS of hot, symmetric matter. Many dynamical phenomena, such as core-collapse supernovae, the formation and cooling of proto-neutron stars, and neutron star mergers, lie between these two regimes and depend on the EOS at finite temperatures for matter with varying proton fractions. In this paper, we introduce a new framework to accurately calculate the thermal pressure of neutron-proton-electron matter at arbitrary density, temperature, and proton fraction. This framework can be expressed using a set of five physically motivated parameters that span a narrow range of values for realistic EOS and are able to capture the leading-order effects of degenerate matter on the thermal pressure. We base two of these parameters on a new approximation of the Dirac effective mass, with which we reproduce the thermal pressure to within ≲30% for a variety of realistic EOS at densities of interest. Three additional parameters, which are based on the behavior of the symmetry energy near the nuclear saturation density, allow us to extrapolate any cold EOS in β-equilibrium to arbitrary proton fractions. Our model thus allows a user to extend any cold nucleonic EOS, including piecewise polytropes, to arbitrary temperature and proton fraction for use in calculations and numerical simulations of astrophysical phenomena. We find that our formalism is able to reproduce realistic finite-temperature EOS with errors of ≲20% and offers a 1-3 orders-of-magnitude improvement over existing ideal-fluid models.

Original language | English (US) |
---|---|

Article number | 12 |

Journal | Astrophysical Journal |

Volume | 875 |

Issue number | 1 |

DOIs | |

State | Published - Apr 10 2019 |

### Fingerprint

### Keywords

- Equation of state
- gravitational waves
- stars: Neutron
- supernovae: General

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*875*(1), [12]. https://doi.org/10.3847/1538-4357/ab08ea

**Finite-temperature Extension for Cold Neutron Star Equations of State.** / Raithel, Carolyn A.; Ozel, Feryal; Psaltis, Dimitrios.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 875, no. 1, 12. https://doi.org/10.3847/1538-4357/ab08ea

}

TY - JOUR

T1 - Finite-temperature Extension for Cold Neutron Star Equations of State

AU - Raithel, Carolyn A.

AU - Ozel, Feryal

AU - Psaltis, Dimitrios

PY - 2019/4/10

Y1 - 2019/4/10

N2 - Observations of isolated neutron stars place constraints on the equation of state (EOS) of cold, neutron-rich matter, while nuclear physics experiments probe the EOS of hot, symmetric matter. Many dynamical phenomena, such as core-collapse supernovae, the formation and cooling of proto-neutron stars, and neutron star mergers, lie between these two regimes and depend on the EOS at finite temperatures for matter with varying proton fractions. In this paper, we introduce a new framework to accurately calculate the thermal pressure of neutron-proton-electron matter at arbitrary density, temperature, and proton fraction. This framework can be expressed using a set of five physically motivated parameters that span a narrow range of values for realistic EOS and are able to capture the leading-order effects of degenerate matter on the thermal pressure. We base two of these parameters on a new approximation of the Dirac effective mass, with which we reproduce the thermal pressure to within ≲30% for a variety of realistic EOS at densities of interest. Three additional parameters, which are based on the behavior of the symmetry energy near the nuclear saturation density, allow us to extrapolate any cold EOS in β-equilibrium to arbitrary proton fractions. Our model thus allows a user to extend any cold nucleonic EOS, including piecewise polytropes, to arbitrary temperature and proton fraction for use in calculations and numerical simulations of astrophysical phenomena. We find that our formalism is able to reproduce realistic finite-temperature EOS with errors of ≲20% and offers a 1-3 orders-of-magnitude improvement over existing ideal-fluid models.

AB - Observations of isolated neutron stars place constraints on the equation of state (EOS) of cold, neutron-rich matter, while nuclear physics experiments probe the EOS of hot, symmetric matter. Many dynamical phenomena, such as core-collapse supernovae, the formation and cooling of proto-neutron stars, and neutron star mergers, lie between these two regimes and depend on the EOS at finite temperatures for matter with varying proton fractions. In this paper, we introduce a new framework to accurately calculate the thermal pressure of neutron-proton-electron matter at arbitrary density, temperature, and proton fraction. This framework can be expressed using a set of five physically motivated parameters that span a narrow range of values for realistic EOS and are able to capture the leading-order effects of degenerate matter on the thermal pressure. We base two of these parameters on a new approximation of the Dirac effective mass, with which we reproduce the thermal pressure to within ≲30% for a variety of realistic EOS at densities of interest. Three additional parameters, which are based on the behavior of the symmetry energy near the nuclear saturation density, allow us to extrapolate any cold EOS in β-equilibrium to arbitrary proton fractions. Our model thus allows a user to extend any cold nucleonic EOS, including piecewise polytropes, to arbitrary temperature and proton fraction for use in calculations and numerical simulations of astrophysical phenomena. We find that our formalism is able to reproduce realistic finite-temperature EOS with errors of ≲20% and offers a 1-3 orders-of-magnitude improvement over existing ideal-fluid models.

KW - Equation of state

KW - gravitational waves

KW - stars: Neutron

KW - supernovae: General

UR - http://www.scopus.com/inward/record.url?scp=85067271323&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067271323&partnerID=8YFLogxK

U2 - 10.3847/1538-4357/ab08ea

DO - 10.3847/1538-4357/ab08ea

M3 - Article

AN - SCOPUS:85067271323

VL - 875

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1

M1 - 12

ER -