# How loud are neutron star mergers?

Authors: Sebastiano Bernuzzi, David Radice, Christian D. Ott, Luke F. Roberts, Philipp Mosta and Filippo Galeazzi

First Author’s Institution: University of Parma, Parma, Italy

Status: Published in Phys. Rev. D, open access

In September 2015, gravitational waves (GWs) were detected for the first time by LIGO (Laser Interferometer Gravitational Observatory). Gravitational waves are ripples in spacetime produced by the acceleration of massive objects. To read more about this monumental discovery and gravitational wave astronomy in general, see this astrobite. This first signal was generated in the final fraction of a second before two black holes merged into a single object.  Neutron star mergers are also likely candidates for gravitational wave production and the authors of this paper are particularly interested in the emission of gravitational waves after the neutron stars have merged — they demonstrate that the first 10 ms of this post-merger phase is the most GW-“luminous” period of the neutron star binary evolution.

### Gravitational waves from coalescing binaries

Gravitational waves produced by the merging of pairs of compact objects (like neutron stars or black holes) are called Compact Binary Inspiral Gravitational Waves (CBIGWs). As the objects orbit each other, they produce gravitational waves which carry away the orbital energy of the system. Therefore, they “inspiral” closer to each other, emitting progressively stronger gravitational waves until they finally merge. The phases of evolution for a coalescing binary are (1) inspiral, (2) merger and (3) post-merger.

There are some significant differences between black hole and neutron star mergers. Firstly, black holes are more compact than neutron stars and therefore can inspiral for a longer time before merging. Also, tidal effects occur during the neutron star inspiral which determine the wave’s phase during the merger. Tides depend on the equation of state (the relationship between density and pressure) which is governed by the micro-physics inside the star. The exact equation of state for neutron star matter is not known; astrophysicists use theoretical models and observational measurements to constrain it. Photons and neutrinos can be emitted as neutron stars merge, meaning that the neutron star binaries can also be spotted using conventional astronomy methods (not just through gravitational waves). This approach of matching the gravitational wave event with an electromagnetic counterpart is called “multi-messenger astronomy”, a developing field which is discussed in this astrobite.

### What happens after neutron stars merge?

Figure 1: The density (in red) and temperature (in blue) for three characteristic time points in the post-merger neutron star binary evolution. Merger time is $t_0$. The “two-core” structure in the first image transitions into a single-core HMNS in the final image. Figure 1 in the paper.

Figure 1 depicts the post-merger phase of a neutron star binary. After the merger occurs at $t_0$, a “hot, differentially rotating hypermassive neutron star” (HMNS) forms, which is a super-dense short-lived object (lasts for tens of milliseconds) that subsequently collapses into a black hole.  Broadly speaking, gravitational waves are emitted by massive objects whose acceleration is not exactly spherically or rotationally symmetric, i.e. there is some “non-axisymmetry” in their motion. There are severe non-axisymmetries in the shape of the very dense HMNS, which can lead to significant gravitational wave emission.

### So, how loud are neutron star mergers?

Figure 2: Binding energy $E_b$ vs. angular momentum $j$ of the binary neutron star system after inspiral. Figure 2 in the paper.

Now that we have some background, let’s get to the root of our question! We will address it in two parts: (1) “What is the loudest phase of the neutron star binary evolution?” and (2) “How loud is a neutron star merger compared to a similar black hole merger?” Figure 2 answers both of these questions. Here, the “loudness” of a gravitational wave refers to the size of its amplitude.

The black curve in Fig. 2 is a comparison curve showing the evolution of a binary black hole system. The other three curves (blue, green and red) correspond to neutron star binaries with different equations of state (LS220, DD2 and SFHo respectively).  The binary evolves in the direction shown on the plot by the arrow; initially, the stars are well-separated with large angular momentum $j$. The largest change in binging energy $E_b$ is where we find the greatest gravitational wave luminosity. As noted previously, you can see that the actual merging event takes place later for the black hole than the neutron star binaries.

Firstly, in the first 10 ms after the neutron stars have merged, the most luminous gravitational wave signals are produced out of the whole history of the binary (a factor of two greater than the inspiral signal). Secondly, in comparison to non-spinning equal mass black hole binaries, the total GW energy emitted by binary neutron star mergers is similar or sometimes even greater. The equation of state influences the results, with, for example, the DD2 equation of state generating less gravitational wave energy.

All in all, due to the extremely high density and non-axisymmetry of the HMNS object, neutron star binaries produce “loud” gravitational wave signals after merging (relative to the earlier neutron star binary evolution, and also relative to  comparable black hole binaries). Also, in theory, the equation of state could be constrained by combining a single gravitational wave energy observation with results from this paper, although more simulations are probably necessary to make this feasible.