# Neutron-Star-Merger Equation of State

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## Abstract

**:**

## 1. Introduction

## 2. Subnuclear Density

## 3. Supranuclear Density

**are not**going to allow for such relaxation (equivalent to considering a large surface tension between the phases) to study the maximum effect the phase transition can have in binary mergers. We are also going to use a neutrino-leakage scheme to evolve the charge fraction of matter, which will allow us to go beyond the initially chemically equilibrated data.

`Frankfurt/IllinoisGRMHD`code (

`FIL`) [21,22,23,24] including weak-interactions via the neutrino-leakage scheme [25,26,27]. The binaries are initially placed at a distance of 45 km in quasi-circular orbit and perform around five orbits before the merger. These simulations include two setups with equal-mass neutron stars with a combined total mass of $M=2.8$ and $2.9\phantom{\rule{0.166667em}{0ex}}{M}_{\odot}$. For each of these systems, two identical scenarios were simulated either employing the standard CMF EOS, where quarks and a strong first-order PT are included, or a purely hadronic variant, in which the quarks are artificially suppressed.

## 4. Discussion and Outlook

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**$\alpha $-particle mass fraction ${X}_{\alpha}=4{n}_{\alpha}/n$ as a function of baryon density for different electron fractions at T = 10 MeV shown for the APR/excluded volume and virial approaches.

**Figure 2.**Mass fraction ${X}_{i}={A}_{i}{n}_{i}/n$ (

**left**) and pressure (

**right**) as a function of baryon density for different electron fractions at T = 5 MeV shown for the APR/EV approach. The subscripts d, $\tau $, 3, $\alpha $, e, and o correspond to contributions from deuterons, tritons, ${}^{3}$He, alpha particles, electrons and outside nucleons (nucleons not bound in nuclei). The total mass fraction (=1) and total pressure are given by ${X}_{tot}$ and ${P}_{tot}$, respectively.

**Figure 3.**Mass fraction ${X}_{i}={A}_{i}{n}_{i}/n$ (

**left**) and pressure (

**right**) as a function of baryon density for different electron fractions at T=10 MeV shown for the APR/EV approach. The subscripts d, $\tau $, 3, $\alpha $, e, and o correspond to contributions from deuterons, tritons, ${}^{3}$He, alpha particles, electrons and outside nucleons (nucleons not bound in nuclei). The total mass fraction (=1) and total pressure are given by ${X}_{tot}$ and ${P}_{tot}$, respectively.

**Figure 4.**

**Left**: QCD Phase diagram resulting from the CMF model. The lines represent first-order transitions. The circles mark the critical end-points. Isospin-symmetric matter refers to zero isospin and strangeness constraints, while neutron-star matter stands for charged neutral matter in chemical equilibrium. The shaded regions exemplify some of the different regimes that can be described within the model.

**Right**: EoS for star matter at T = 0 under different charge neutrality conditions calculated with the CMF model.

**Figure 5.**

**Left**: merger simulations performed using the CMF model without (top) and with the suppression of quarks (bottom) for a high-mass binary at a time shortly before the collapse to a black hole (figure extracted from Ref. [20]).

**Right**: time evolution of the maximum normalized baryon density region (diamonds) and maximum temperature region (circles) after the merger for the low-mass binary using the CMF EoS. The gray-shaded area shows the first-order PT being crossed.

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**MDPI and ACS Style**

Dexheimer, V.; Constantinou, C.; Most, E.R.; Papenfort, L.J.; Hanauske, M.; Schramm, S.; Stoecker, H.; Rezzolla, L.
Neutron-Star-Merger Equation of State. *Universe* **2019**, *5*, 129.
https://doi.org/10.3390/universe5050129

**AMA Style**

Dexheimer V, Constantinou C, Most ER, Papenfort LJ, Hanauske M, Schramm S, Stoecker H, Rezzolla L.
Neutron-Star-Merger Equation of State. *Universe*. 2019; 5(5):129.
https://doi.org/10.3390/universe5050129

**Chicago/Turabian Style**

Dexheimer, Veronica, Constantinos Constantinou, Elias R. Most, L. Jens Papenfort, Matthias Hanauske, Stefan Schramm, Horst Stoecker, and Luciano Rezzolla.
2019. "Neutron-Star-Merger Equation of State" *Universe* 5, no. 5: 129.
https://doi.org/10.3390/universe5050129