# Binary Neutron-Star Mergers with a Crossover Transition to Quark Matter

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## Abstract

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## 1. Introduction

## 2. Equations of State

## 3. Simulation Details

`Einstein Toolkit`[50] numerical relativity software. This includes full general relativity in three spatial dimensions with differential equations based upon the BSSN-NOK framework [51,52,53,54,55]. The hydrodynamics was evolved with the use of the

`GRHydro`code [56,57,58] based on the Valencia formulation [59,60]. The initial conditions were generated using

`LORENE`[61,62]. The thorn

`Carpet`[63,64] was used for adaptive mesh refinement based upon six mesh refinement levels and a minimum grid of 0.3125 in Cactus units (≈$461\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$). A constant adiabatic index ${\mathrm{\Gamma}}_{\mathrm{th}}=1.8$ was used to account for the thermal pressure in

`GRHydro`as described in Ref. [65].

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

`The Einstein Toolkit`(Ref. [50]; https://einsteintoolkit.org, accessed on 28 August 2023),

`LORENE`(Refs. [61,62]),

`PyCactus`(https://bitbucket.org/GravityPR/pycactus, accessed on 28 August 2023), and

`TOVsolver`(https://github.com/amotornenko/TOVsolver, accessed on 28 August 2023).

## Conflicts of Interest

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**Figure 1.**Power spectral density ($2\tilde{h}\left(f\right){f}^{1/2}$) vs. frequency f for various simulations. The the lower blue and orange curves show anticipated sensitivity of the Einstein Telescope and Cosmic Explorer, respectively, while the upper green curve shows the LIGO sensitivity. The first peak at around 1 kHz is the initial contact of the merging binaries. The second peaks near 2.5–3.5 kHz correspond to the long postmerger phase, ${f}_{peak}$.

**Figure 2.**Correlation between ${f}_{max}$ and ${f}_{peak}$. There appears to be a linear correlation for normal hadronic EoSs as indicated by the straight line. However, the existence of a crossover regime to quark matter leads to outliers from this correlation as indicated by the circled points.

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**MDPI and ACS Style**

Mathews, G.J.; Kedia, A.; Kim, H.I.; Suh, I.-S.
Binary Neutron-Star Mergers with a Crossover Transition to Quark Matter. *Universe* **2023**, *9*, 410.
https://doi.org/10.3390/universe9090410

**AMA Style**

Mathews GJ, Kedia A, Kim HI, Suh I-S.
Binary Neutron-Star Mergers with a Crossover Transition to Quark Matter. *Universe*. 2023; 9(9):410.
https://doi.org/10.3390/universe9090410

**Chicago/Turabian Style**

Mathews, Grant J., Atul Kedia, Hee Il Kim, and In-Saeng Suh.
2023. "Binary Neutron-Star Mergers with a Crossover Transition to Quark Matter" *Universe* 9, no. 9: 410.
https://doi.org/10.3390/universe9090410