# Fluid dynamic simulations could reveal secrets of dense nuclear matter

EU-funded scientists shed more light on the extreme interiors of the densest and weirdest objects in space – neutron stars spiralling in towards each other.

Inside a neutron star, gravity squeezes matter to greater densities than those typical of an atomic nucleus, creating a fertile ground for probing new physics beyond the Standard Model. Such extreme densities cannot be experimentally measured. So when the Universe agreed to help out, astronomers grabbed the chance and in 2017, the Laser Interferometer Gravitational-Wave Observatory (LIGO)-Virgo collaboration picked up gravitational waves from a binary neutron star inspiral 140 million light years from Earth.

## Tidal deformations in neutron star surfaces

As the two neutron stars orbit around each other, radiating energy as gravitational waves, they also raise tidal distortions on the other. Leaving a distinct imprint on the emitted gravitational waves, these revealed unique information about the exotic interior of neutron stars. Using an equation of state (EoS), astronomers can mathematically describe how the internal structure of a neutron star reacts to changes in density and pressure. “Binary neutron stars are like astrophysical-scale colliders, allowing astronomers to probe physics phenomena impossible to replicate in terrestrial particle colliders and, especially, strong nuclear forces which are governed by quantum chromodynamics,” notes Ulrich Sperhake, coordinator of the EU-funded ACFD project. This theory determines the EoS in the neutron star innards where matter densities can be 10 times higher than ordinary nuclear matter. A stiff EoS, where the pressure increases rapidly with density, yields stars with large radii and tidal effects on the inspiral waveform. Furthermore, highly deformable stars circle toward mutual doom more rapidly. “Measuring the neutron star deformation caused by tidal forces with high precision would allow us to tightly constrain the EoS and realise LIGO’s potential for breakthrough discoveries regarding extremely dense matter,” explains Dr Charalampos Markakis. The project team conducted numerical simulations to estimate the neutron-star EoS parameters from gravitational wave observations. They confirmed phase transitions (for example, neutrons dissolving into strange quarks) in the core lead to measurably softer EoS. “Measuring tidal effects from different neutron-star inspirals with second- and third-generation gravitational-wave observatories will allow us to measure their EoS,” adds Markakis.

## Mathematical theorems leaving their imprints on gravitational waves

Using Kelvin’s circulation theorem and its corollary – Helmholtz’s third theorem – the scientists further probed how matter behaves at extreme densities. They demonstrated that both theorems hold during a binary neutron star inspiral. A new constraint-damping scheme, based on Hamiltonian fluid dynamics, can preserve these laws during supercomputer simulations. They also noted that the Hamiltonian is nearly constant for binaries on circular orbits. This could facilitate physicists in extracting high-precision gravitational wave templates. “It is marvellous that mathematical theorems that characterise the highly relativistic flows of neutron stars in curved spacetime are imprinted on the gravitational waves that we detect here on Earth, though they are 140 million light years away,” enthuses Markakis.

## A step closer to resolving an open problem

ACFD found a promising remedy to the long-standing problem of the Euler-Einstein equations which break down at the interface between fluids (dense matter) and vacuum. In mathematical terms, this breakdown causes a loss of pointwise convergence in binary neutron star inspiral simulations. Project research aimed to mathematically and computationally explore how nature operates on scales where current understanding breaks down. Fluid dynamic simulations can reveal more about the elusive state of matter in neutron star cores.

## Keywords

ACFD, gravitational waves, equation of state (EoS), binary neutron stars, inspiral, fluid dynamics, dense matter, Kelvin’s circulation theorem