We may soon be able to “see” inside a neutron star and learn what extreme matter governed by exotic physics lurks there, thanks to the imprint of tidal interactions on gravitational waves emitted by pairs of neutron stars that are headed for explosive fusion.
“One hope is that we will be able to get some information about the neutron star equation of state at densities found in the inner core of a neutron star,” Nicolás Yunes of the University of Illinois, who led the research, said in a statement. “Is there really one quark core, as some have recently argued? Are there phase transitions happening inside that we don’t know about yet?”
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But deeper down in a neutron star, near the core, things can be even weirder. Gravitational pressure can be so extreme that it smashes neutrons into their building blocks, which are fundamental particles called quarks and gluons which usually bind quarks together to form protons and neutrons.
Scientists call this state a quark-gluon plasma. This state of matter existed during the first fraction of a second after Big Bangand outside of particle accelerator experiments, the only other place in the universe where quark-gluon plasma can exist is inside neutron stars.
If scientists could understand the interior of neutron stars, they could therefore learn more about the state of matter immediately after the Big Bang.
Binary neutron stars have long been considered the best bet for deciphering what lurks within. These pairs of neutron stars spiral around each other in elliptical orbits, moving ever closer until they collide and merge into a kilonova. Crucially, their in-spiral sees the release of gravitational waves.
Now, researchers led by Yunes and Abhishek Hegade of Princeton University believe they have figured out how to decipher the frequency of these gravitational waves to interpret the internal structure of neutron stars.
“As they get closer, tidal forces from one (neutron) star begin to deform the other and vice versa,” Hegade said. “The amount of deformation depends on what’s inside these stars.”
The problem is that extreme gravity and high speed (up to 40% of the speed of light) of the neutron stars as they spin around each other means that scientists have to watch out Albert Einstein‘s general relativity for solutions. This is a complex endeavor, but Yunes and Hegade believe they now have the answer.
As the binary neutron stars deform the shape and structure of each other through gravitational tides, they trigger oscillations in their interior, like the ringing of a clock. The patterns of these oscillations are called modes, and the frequency of these modes is imprinted on the gravitational waves emitted by the binary neutron stars.
A complete set of modes is necessary to understand the binary system. However, distinguishing these modes is complicated by the fact that the tidal forces are dynamic: they change as the neutron stars orbit each other, and the effects of each neutron star overlap, making it even more difficult to distinguish what is happening.
“Without a full set of modes, it’s entirely possible that you could miss part of the tidal response when you model it, since there could possibly be other parts you’re leaving out of the mathematical description of the response that’s needed to capture all the physics,” Yunes said.
Newtonian physics – that is, the basic physics of gravity according to Isaac Newtonthe law of gravitation – contains a complete set of oscillating modes for an ordinary object. These modes are referred to as a damped harmonic oscillator. In relativistic physics, however, it has not been clear whether all the modes could be derived. For example, gravitational waves that radiate away energy from binary neutron stars are a phenomenon of general relativity, which succeeded Newtonian gravity, and as such are not considered by Newtonian physics.
“If your system loses energy, the modes cannot be complete,” Hegade said.
The solution was to break down the problem, considering each neutron star individually, and its companion as just one source of gravitational tides. Yunes and Hegade’s team then divided each neutron star into separate regions of varying gravitational strength on different scales, describing strong gravity and weaker gravity. They found approximate solutions for each scale and then combined them. They even found that the loss of energy from gravitational waves effectively canceled out. This allowed them to derive a solution that described all oscillating modes in a neutron star’s interior, and furthermore how these modes would be imprinted on the frequency of the resulting gravitational waves.
“We showed two important things,” Hegade said. “First, we were able to subtract radiation, and found that a neutron star’s modes actually form a complete set. Second, we found that if you consistently solve a certain set of equations using a tidal field that is sufficiently ‘smooth’, it is a solution to the interior of a star, and you can do all the same things in general gravity as in Newtonian gravity.”
This is not the end of the story. The work of Yunes and Hegade’s team is purely theoretical at this stage, and current gravitational wave detectors are not sensitive enough at higher frequencies to detect this imprint. However, Yunes and Hegade are optimistic that the next generation of detectors will do the trick.
The findings were published on 18 February in the journal Physical review letters.
