# Detecting the Hadron-Quark Phase Transition with Gravitational Waves

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## Abstract

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## 1. Introduction

## 2. GW170817—The Long-Awaited Event

## 3. Hypermassive Neutron Stars and the QCD Phase Diagram

`Einstein Toolkit`[60] where a fourth-order finite-differencing code

`McLachlan`[61,62] had been used. The code is based on the

`BSSNOK`conformal traceless formulation of the Einstein equations [63,64,65] using a “$1+log$” slicing condition and a “Gamma-driver” shift condition [66,67]. The covariant conservation of energy, momentum, and rest mass, formulated within the general-relativistic hydrodynamics equations [68], are cast in the conservative Valencia formulation [69]. The evolution of these hydrodynamics equations is done using the

`WhiskyTHC`code [70,71]. A numerical grid with an mesh refinement approach based on the

`Carpet`mesh-refinement driver [72] is used to both increase resolution and extend the spatial domain. A purely hadronic model of the EOS (

`LS220`,73]) had been used and an equal-mass binary with a mass of $1.35{M}_{\odot}$ for each star was selected. However, the results of other purely hadronic EOSs and/or different initial conditions show qualitatively a similar behaviour, as described below.

## 4. Detecting the Hadron-Quark Phase Transition with Gravitational Waves

`LS220-M135`simulation to several times of normal nuclear matter (see Figure 4). For such high densities, the EOS is still poorly constrained by observations from heavy-ion collisions. By analyzing the power spectral density profile of the post-merger emission of a future event within the current observing run of the LIGO/VIRGO collaboration, the GW signal can set tight constraints on the high density regime of the EOS of elementary matter [75]. Numerical simulations that include a density/temperature and composition dependent EOS with a HQPT, the so called hybrid star merger simulations, have only been performed recently.

## 5. Summary and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Spatial distribution of the rest-mass density (

**left**) and temperature (

**middle**) of the

`LS220-M135`simulation at several time snapshots within the early post-merger phase. (

**right**) The pictures on the right side show the density-temperature profiles inside the inner region of the HMNS in the style of a T-$\rho $ QCD phase diagram.

**Figure 2.**Same as Figure 1 but for later time snapshots within the early post-merger phase.

**Figure 3.**Same as Figure 2 but for later time snapshots within the transition segment from the early to the middle part of the post-merger phase.

**Figure 4.**Same as Figure 3 but for later time snapshots.

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**MDPI and ACS Style**

Hanauske, M.; Bovard, L.; Most, E.; Papenfort, J.; Steinheimer, J.; Motornenko, A.; Vovchenko, V.; Dexheimer, V.; Schramm, S.; Stöcker, H.
Detecting the Hadron-Quark Phase Transition with Gravitational Waves. *Universe* **2019**, *5*, 156.
https://doi.org/10.3390/universe5060156

**AMA Style**

Hanauske M, Bovard L, Most E, Papenfort J, Steinheimer J, Motornenko A, Vovchenko V, Dexheimer V, Schramm S, Stöcker H.
Detecting the Hadron-Quark Phase Transition with Gravitational Waves. *Universe*. 2019; 5(6):156.
https://doi.org/10.3390/universe5060156

**Chicago/Turabian Style**

Hanauske, Matthias, Luke Bovard, Elias Most, Jens Papenfort, Jan Steinheimer, Anton Motornenko, Volodymyr Vovchenko, Veronica Dexheimer, Stefan Schramm, and Horst Stöcker.
2019. "Detecting the Hadron-Quark Phase Transition with Gravitational Waves" *Universe* 5, no. 6: 156.
https://doi.org/10.3390/universe5060156