# Binary Neutron Star Merger Simulations with a Calibrated Turbulence Model

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. WhiskyTHC

`WhiskyTHC`code [91,92,93,94].

`WhiskyTHC`separately evolves the proton and neutron number densities:

`CTGamma`code [97,98], which is part of the

`Einstein Toolkit`[99,100].

`CTGamma`and

`WhiskyTHC`are coupled using the method of lines. For this work, we use the optimal strongly stability-preserving third-order Runge–Kutta scheme [101] as the time integrator. Mesh adaptivity is handled using the

`Carpet`mesh driver [102], which implements Berger–Oliger-style adaptive mesh refinement (AMR) with subcycling in time and refluxing [103,104,105].

#### 2.2. GRLES

#### 2.3. Models and Simulation Setup

`Lorene`code [114], while the evolution was performed with

`WhiskyTHC`using the setup discussed in [58]. We simulated the same binary multiple times: once with the calibrated ${\ell}_{\mathrm{mix}}$ from Section 2.2 and then with fixed constant values for ${\ell}_{\mathrm{mix}}$: 0, 5 m, 25 m, and 50 m. Additionally, each configuration was run twice: with and without the inclusion of neutrino reabsorption in the simulations. Neutrino cooling was instead always included. The resolution in the finest refinement level of the grid, which covered the NSs during the inspiral and the MNS after merger, was $185\phantom{\rule{4pt}{0ex}}\mathrm{m}$. Finally, to quantify finite-resolution effects, we also reran the simulations with no neutrino reabsorption also at the lower resolution of $246\phantom{\rule{4pt}{0ex}}\mathrm{m}$. The results presented here were thus based on a total of 15 simulations for a total cost of about 3M CPU hours. The simulations with constant ${\ell}_{\mathrm{mix}}$ were already presented (however, we reran the ${\ell}_{\mathrm{mix}}=0$ simulation with neutrino reabsorption, which we now continued for a longer time after merger than in our previous work) in [58,81,88]. In [65], postmerger profiles from the ${\ell}_{\mathrm{mix}}=0$ no neutrino reabsorption binary were mapped into a high-resolution grid and simulated with the inclusion of a magnetic field. The simulations with the calibrated turbulence model were new. For clarity, we only included the high-resolution simulations in the figures. If not otherwise specified, the figures refer to the simulations that included both neutrino emission and neutrino reabsorption. The low-resolution data followed the same qualitative trends, although there were quantitative differences.

## 3. Results

#### 3.1. Qualitative Dynamics

#### 3.2. Gravitational Waves

#### 3.3. Outflows

## 4. Discussion

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Mixing length evaluated from the general-relativistic magnetohydrodynamics (GRMHD) simulations of Kiuchi et al. [75] (dots) and the fit employed in this work (red line). Shown also are the other values of ${\ell}_{\mathrm{mix}}$ employed in this and in our previous works. GRMHD simulations favor relatively small values ${\ell}_{\mathrm{mix}}$, in agreement with the simple analytic estimate in Equation (20).

**Figure 2.**Maximum density evolution for the models computed without neutrino heating. We use nuclear saturation density (${\rho}_{0}=2.7\times {10}^{14}\phantom{\rule{4pt}{0ex}}\mathrm{g}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{-3}$) as the density scale. The inclusion of turbulent viscosity can drastically alter the lifetime of the MNS.

**Figure 3.**Remnant disk and massive neutron star (MNS) in the ${\ell}_{\mathrm{mix}}=0$ and ${\ell}_{\mathrm{mix}}={\ell}_{\mathrm{mix}}\left(\rho \right)$ models at four representative times. In each panel, we show color-coded values of entropy ($x<0$) and electron fraction ($x>0$) in the meridional plane. The bottom panel shows the disk configuration at the end of the simulation, when the MNS has collapsed to a BH. The white lines are the ${10}^{8},{10}^{9},{10}^{10},{10}^{11},{10}^{12},{10}^{13},$ and ${10}^{14}$ $\mathrm{g}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{-3}$ isocontours of the rest-mass density. Turbulent viscosity mixes material from the mantle of the MNS and the inner disks and smooths the structure of the disk.

**Figure 4.**Effective strain of the frequency domain for the dominant $\ell =2,m=2$ gravitational wave (GW) multipole for selected models. We window the GW strain data using a Hann window on the interval $-10\phantom{\rule{4pt}{0ex}}\mathrm{ms}<t-{t}_{\mathrm{mrg}}<20\phantom{\rule{4pt}{0ex}}\mathrm{ms}$. We show the effective strain for an optimally-oriented binary at $D=100\phantom{\rule{4pt}{0ex}}\mathrm{Mpc}$. Shown also are the design noise curves for Adv. LIGO, in the high laser power zero detuning configuration, and the Einstein Telescope, in the ET-Dconfiguration. The effective strain is normalized so that the ratio between the signal and the noise curve is equal to the signal-to-noise ratio density in frequency space. Turbulent viscosity results in only modest shifts of the dominant postmerger emission frequency. However, the subdominant features in the GW spectrum are strongly impacted.

**Figure 5.**Outflow rate for the baseline and the calibrated turbulence models. The thin lines denote simulations that did not include neutrino reabsorption. For clarity, we smooth the data using a rolling average with amplitude $0.5\phantom{\rule{4pt}{0ex}}\mathrm{ms}$. Turbulent dissipation has a modest impact on the dynamical ejecta mass and is subdominant in comparison to neutrino heating.

**Figure 6.**Histograms of the composition of the outflows from selected models. The thin lines denote simulations that did not include neutrino reabsorption. Turbulent viscosity and dissipation tend to increase the average electron fraction of the ejecta. However, this effect is subdominant compared to the effect of neutrino reabsorption.

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**MDPI and ACS Style**

Radice, D.
Binary Neutron Star Merger Simulations with a Calibrated Turbulence Model. *Symmetry* **2020**, *12*, 1249.
https://doi.org/10.3390/sym12081249

**AMA Style**

Radice D.
Binary Neutron Star Merger Simulations with a Calibrated Turbulence Model. *Symmetry*. 2020; 12(8):1249.
https://doi.org/10.3390/sym12081249

**Chicago/Turabian Style**

Radice, David.
2020. "Binary Neutron Star Merger Simulations with a Calibrated Turbulence Model" *Symmetry* 12, no. 8: 1249.
https://doi.org/10.3390/sym12081249