## Gravitational Waves from Neutron Stars Mergers

### arXiv:1703.02046

*Effect of turbulent dissipation on the evolution of a binary neutron
star merger remnant. Turbulence is modeled using a general-relativistic
extension of the classical mixing length prescription. We consider four
value of the mixing length parameter ℓ _{mix} : from 0 (no
turbulent dissipation) to 50 meters (extremely efficient turbulence). We
show temperature and density in the meridional plane. The time is in
milliseconds after merger. The white lines are the iso-density contours
for ρ = 10^{10}, 10^{11}, 10^{12}, 10^{13},
10^{14}, and 5·10^{14} g·cm^{−3}.*

Neutron star merger simulations are extremely computationally challenging. WhiskyTHC requires 6 hours of calculation on 512 cores to simulate one millisecond of evolution of a binary. This is for our standard resolution of 180 meters. Doubling the resolution increases the computational cost by a factor 16. Unfortunately, we know that, during the merger, there are small-scale magnetohydrodynamical instabilities that generate turbulence with typical driving scales of few meters or less. These are scales that are unaccessible to our simulations, even when running on the World's largest supercomputers. How can we model their effect in simulations?

Our approach is to use turbulence models initially developed for weather forecast and other "terrestrial" applications. Indeed, WhiskyTHC is the first, and so far only, code to include an effective, sub-grid scale, treatment of turbulence. This is based on the general-relativistic (GR) extension of the large-eddy simulations (LES) method, which we recently introduced.

For our first GRLES simulations, we adopted the so-called mixing-length
closure of turbulence and we studied the impact of (sub-grid scale) turbulent
mixing in the evolution of the merger remnant. We found that turbulence could
have a potentially very important role in the evolution of the binary after
contact and might alter the gravitational-wave and neutrino signals from the
binary. On the other hand, for the most conservative values of the mixing
length parameter ℓ_{mix}, we found that these effects are
minor. This is very good news for all existing models of the
gravitational-wave emissions from merging neutron star, which did not include
any turbulence model. However, the final words will have to wait until
we will be able to actually measure ℓ_{mix} by means of more
restricted, but much higher resolution, GRMHD simulations.

### arXiv:1612.06429

*Gravitational wave strain and spectra generated during the collision
of two neutron stars modeled with two different nuclear equations of
state. The DD2 equation of state includes only "normal" nuclear matter,
while the BHBΛφ also includes Λ-hyperons.*

Can we use coming gravitational-waves observations of merging neutron stars to detect the appearance of exotic particles or phase transitions in nuclear matter at several times nuclear density?

The answer to this question is "yes" according to our most recent simulations. The typical outcome of neutron star mergers is the formation of an object, called hypermassive neutron star, which survives only for short time before collapsing to form a black hole. The densities in this remnant can be several times larger than the density in the neutron stars before they collide. Now, we expect that phase transitions or other changes in the nature of matter in the remnant will be the result of the system re-arranging to find a new energy minimum. Where does the energy difference go? In gravitational waves! As a consequence, gravitational waves can be used to confirm or rule out the appearance of exotic states of matter in these extreme conditions.

### arXiv:1603.05726

*Binary neutron star merger simulations showing the development and
saturation of the one-armed spiral instability for both "soft" and "stiff"
equations of state.*

We recently performed a series of high-resolution simulations of the late inspiral and merger of neutron star binaries using the high-order methods implemented in WhiskyTHC.

We studied the development and saturation of an hydrodynamical instability that has been recently discovered in eccentric neutron star mergers that included neutron star spin by Paschalidis and collaborators. We found that this instability is not restricted to eccentric or spinning neutron star mergers, but that the development of the one-armed spiral instability is a generic outcome of the merger. Furthermore, if detected in gravitational-waves, this instability would help constrain unknown parameters of the equation of state of matter at super-nuclear densities.

*Complete gravitational wave spectrum for an M1 = M2 = 1.35 Msun
binary neutron star merger at 10 Mpc with edge-on orientation. We use the
MS1b interaction model to describe the equation of state of neutron stars
(the "stiff" case above).*

For this study, we constructed hybrid waveforms by combining our numerical-relativity waveforms with state-of-the-art effective-one-body waveforms we generated using a publicly available code. Using these waveforms, we studied the detectability of this instability and of other components of the gravitational-wave signal by ground-based gravitational wave observatories. Unfortunately, we find that the detection of this instability by Advanced LIGO is unlikely, but might be possible for third generation detectors such as the Einstein Telescope.

We released the complete hybrid gravitational waveforms on Zenodo.