Binary Neutron Star Merger Simulations

**Principal Investigator:**

Tim Dietrich

**Affiliation:**

University of Potsdam, Dutch National Institut for Subatomic Physics Amsterdam

**Local Project ID:**

pr48pu

**HPC Platform used:**

SuperMUC and SuperMUC-NG of LRZ

**Date published:**

The first direct detection of a gravitational-wave signal from the coalescence of two black holes inaugurated a new era in astronomy. After this breakthrough, the observational campaigns of the LIGO Scientific- and Virgo Collaborations (LVC) observed a variety of compact binary systems including the multi-messenger observation of a binary neutron star merger on the 17th of August 2017, GW170817 [1], and the detection of gravitational waves from two merging neutron stars on the 25th of April 2019, GW190425 [2]; cf. Fig. 1. In particular, the detection of GW170817 and the observation of its electromagnetic counterparts, covering all wavelengths ranging from radio frequencies to gamma-rays initiated a new era of multi-messenger astronomy and allowed an unambiguous connection of kilonovae and short gamma-ray-burst to the merger of two neutron stars.

To interpret the observed data, one needs reliable models that describe the binary coalescence, the emitted gravitational-wave signal, and potential electromagnetic counterparts. Our project aims towards the construction of these models.

To enable a correct description when gravitational fields are strongest and the velocity of the stars is largest, i.e., shortly before their merger, full 3+1D numerical-relativity simulations are required. These allow us to find solutions to Einstein's Field Equations and the equations of general relativistic hydrodynamics.

Due to the complexity of these nonlinear partial differential equations and the requirement to cover multiple scales, from the neutron star interior to the distant gravitational-wave zone, one needs state-of-the-art programs and high-performance computing resources.

For several years, our collaboration has developed new tools and codes to perform numerical-relativity simulations for binary neutron star systems. These simulations are fundamental to describe the emitted gravitational-wave signal as well as the observable electromagnetic counterpart.

**Computational Setup**

For our work, we are using two numerical-relativity codes, the BAM and the THC code. Both codes combine state-of-the-art methods to deal with black hole spacetimes, provide shock capturing methods for general relativistic hydrodynamics simulations, and allow high-order convergence for smooth problems. The codes use the method of lines with an explicit Runge-Kutta time integration and they are both based on an adaptive mesh refinement framework.

To allow a scientific assessment of our simulations, we need to perform simulations at multiple resolutions to quantify errors introduced by the numerical discretization. Every individual simulation runs on a few hundred to a few thousand processors depending on the resolution and parameters of the system that we simulate. In total, we consumed 140 million CPUhs within the project pr48pu. We produced ~250 million files and used a maximum of ~120TB of storage.

A video showing the simulation of the neutron star coalescence GW190425 is available here.

**Scientific results **

With the help of the computational resources granted through the project pr48pu, we have written 17 peer-reviewed articles and we received the “Heinz Billing Prize for the advancement of scientific computation“. Some of our research highlights will be discussed in the following.

*Binary Neutron Star Parameter Space Coverage: *

A central point of our work was the characterization of the imprint of intrinsic properties (masses, spins, eccentricity, and the internal composition of the neutron stars) on the gravitational-wave and electromagnetic radiation. Because of an improved formulation to construct initial conditions, we could explore previously inaccessible regions of the binary neutron star parameter space.

These simulations included high mass ratio configurations, the first consistent simulations of spinning and precessing binary neutron star mergers, as well as the only simulations of binary neutron stars on highly eccentric orbits based on consistent initial data.

Our studies resulted in several hundred simulations for various parameter combinations. To support the emerging field of gravitational-wave astronomy, we made all data publicly available in the first binary neutron star database (http://www.computational-relativity.org) [3].

*Waveform model development: *

Although we can simulate generic binary neutron star systems and have studied a large number of configurations, numerical-relativity simulations are computationally too expensive to be directly employed for gravitational-wave astronomy. Typically, one needs to compute hundreds of millions of gravitational-wave templates spanning thousands of gravitational-wave cycles to extract the parameters from a possible detection. Based on a small number of highly accurate simulations combined with analytical expressions using post-Newtonian theory, describing the early inspiral when the two stars are still far apart, and the so-called *effective-one-body* approach, we developed an analytic framework which models the entire gravitational-wave signal from the early inspiral up to the merger of the two stars [4]. The evaluation time is about 10 billion times smaller than pure numerical-relativity simulations.

Its efficiency and accuracy have made the proposed model to the standard framework to interpret binary neutron star gravitational-wave signals and it was employed for the analysis of the first and second gravitational-wave detection connected to binary neutron star mergers.

*Modeling Electromagnetic Signals*

In addition to the emitted gravitational waves, neutron star mergers are of particular interest because of their electromagnetic footprint. In particular, the origin of the kilonova, a counterpart observable for a few hours to weeks after the merger, is matter ejected from the system. Numerical-relativity simulations allow a connection between the intrinsic parameters of the binary and the amount of ejected material from the collision of two neutron stars. Based on the increasing coverage of the binary neutron star parameter space, it was possible to link the amount of ejected material to the masses and internal composition of the two stars.

This allowed us to study the amount of matter which became unbound from GW170817. Combining this knowledge with models forecasting the properties of the thermal kilonova places constraints on the internal structure of the neutron stars from electromagnetic observations.

*Determining the Merger Outcome*

In addition, some of the resources have been used to simulate binaries in which immediately after the merger of the two stars a black hole is formed. Based on our data, we could find the threshold mass where this happens and we could derive the probability of prompt black hole formation in neutron star merger by analyzing the inspiral gravitational-wave signal solely.

Our method was applied for the analysis of GW170817 and GW190425 and we concluded that GW190425, which is associated to a high total mass, had a probability of prompt collapse of about 96%. This might explain why no electromagnetic signal was detected for this event.

A simulation of a Binary Neutron Star merger showing the emitted gravitational waves, the evolution of the supranuclear matter of the neutron stars, and material ejected during and after the merger can be seen below:

*Search for Dark Matter*

Over the last years, there has been a growing interest in the study of potential black hole or neutron star mimickers that consist of ultralight particles and that could explain the presence of dark matter in our Universe.

Instead of focusing purely on the merger of exotic compact objects, we investigated the possibility that a neutron star or a black hole merges with an exotic compact object; cf. Fig. 2. For this study, we extended the existing infrastructure of our code to allow the simultaneous evolution of the Einstein Equations, the equations for general relativistic hydrodynamics, and the relativistic Klein-Gordon equations.

We found that the collision of neutron stars with exotic compact objects can lead to a variety of observables ranging from gravitational waves, optical transients, fast radio bursts, radio flares, gamma-ray bursts, to neutrinos. Thus, we can not rule out the (nevertheless unlikely) scenario that GW170817 and GW190425 involved some kind of exotic compact object.

While continuing our study of binary neutron star mergers within the project pn56zo, we are also developing a new pseudospectral code, BAMPS. BAMPS includes already routines for general relativistic hydrodynamics within the framework of discontinuous Galerkin methods and will likely replace our finite differencing codes BAM and THC in the next years.

[1] LIGO Scientific and Virgo Collaborations, (2017) Phys.Rev.Lett. 119 16

[2] LIGO Scientific and Virgo Collaborations, (2020) Astrophys.J.Lett. 892 L3

[3] T. Dietrich et al., (2018) Class.Quant.Grav. 35 24, 24LT01

[4] T. Dietrich, S. Bernuzzi, and W. Tichy, (2017) *Phys. Rev.* D.96, 12, 121501.

[5] T. Dietrich, F. Day, K. Clough, M. Coughlin, J. Niemeyer, (2019) Mon.Not.Roy.Astron.Soc. 483 1, 908-914

**Researchers**

S. Bernuzzi, B. Brügmann, S. V. Chaurasia, K. Clough, T. Dietrich (PI), R. Dudi, F. Fabbri, N. Madrigal, N. Ortiz, D. Radice, W. Tichy, M. Ujevic, F. Zappa

**Project Partners**

Max Planck Institute for Gravitational Physics, University of Parma, University of Jena, Federal University of the ABC, Florida Atlantic University, University of Oxford

**Scientific Contact**

Prof. Dr. Tim Dietrich

Dutch National Institut for Subatomic Physics Amsterdam*since 2020:*

University of Potsdam

Institut for Physics and Astrophysics

Karl-Liebknecht-Str. 24/25, D-14476 Potsdam OT Golm (Germany)

e-mail: tim.dietrich [@] uni-potsdam.de

*LRZ project ID: pr48pu*

*July 2020*