New Tool Uses Gravitational Waves to Peer Inside Neutron Stars

Imagine taking a star with twice the mass of the Sun and crushing it down to the size of Manhattan. The result would be a neutron star—one of the densest objects found anywhere in the Universe. In fact, they exceed the density of any material found naturally on Earth by a factor of tens of trillions. Although neutron stars are remarkable astrophysical objects in their own right, their extreme densities may also allow them to function as laboratories for studying fundamental questions of nuclear physics, under conditions that could never be reproduced on Earth.

Because of these exotic conditions, scientists still do not understand what exactly neutron stars themselves are made from, their so-called “equation of state” (EoS). Determining this is a major goal of modern astrophysics research. A new piece of the puzzle, constraining the range of possibilities, has been discovered by a pair of scholars at the Institute for Advanced Study (IAS): Carolyn Raithel, John N. Bahcall Fellow in the School of Natural Sciences; and Elias Most, Member in the School and John A. Wheeler Fellow at Princeton University. Their paper was published recently in The Astrophysical Journal Letters.

Neutron star merger and the gravity waves it produces. Credit: NASA/Goddard Space Flight Center

Ideally, astrophysicists would like to look inside these exotic objects, but they are too small and distant to be imaged with standard telescopes. Researchers instead rely on indirect properties that they can measure—such as the mass and radius of a neutron star—to calculate the EoS. This is much like how one might use the length of two sides of a right-angled triangle to work out its hypotenuse. However, one issue here is that the radius of a neutron star is very difficult to measure precisely. A promising alternative for future observations is to instead use a quantity called the “peak spectral frequency” (or f₂) in its place.

But how is f₂ measured? Collisions between neutron stars, which are governed by the laws of Einstein’s Theory of Relativity, lead to strong bursts of gravitational wave emission. In 2017, scientists directly measured such emissions for the first time. “At least in principle, the peak spectral frequency can be calculated from the gravitational wave signal emitted by the wobbling remnant of two merged neutron stars,” says Most.

Doomed neutron stars whirl toward their demise in this animation. Gravitational waves (pale arcs) bleed away orbital energy, causing the stars to move closer together and merge. As the stars collide, some of the debris blasts away in particle jets moving at nearly the speed of light, producing a brief burst of gamma rays (magenta). In addition to the ultra-fast jets powering the gamma rays, the merger also generates slower-moving debris. An outflow driven by accretion onto the merger remnant emits rapidly fading ultraviolet light (violet). A dense cloud of hot debris stripped from the neutron stars just before the collision produces visible and infrared light (blue-white through red). The UV, optical, and near-infrared glow is collectively referred to as a kilonova. Later, once the remnants of the jet directed toward us had expanded into our line of sight, X-rays (blue) were detected. This animation represents phenomena observed up to nine days after GW170817. Credit: NASA’s Goddard Space Flight Center/CI Lab

It was previously expected that f₂ would be a reasonable proxy for radius, since—until now—researchers believed that a direct, or “quasi-universal,” correspondence existed between them. However, Raithel and Most have demonstrated that this is not always true. They have shown that determining the EoS is not like solving a simple hypotenuse problem. Instead, it is more akin to calculating the longest side of an irregular triangle, where one also needs a third piece of information: the angle between the two shorter sides. For Raithel and Most, this third piece of information is the “slope of the mass-radius relation,” which encodes information about the EoS at higher densities (and thus more extreme conditions) than the radius alone.

This new finding will allow researchers working with the next generation of gravitational wave observatories (the successors of the currently operating LIGO) to better utilize the data obtained following neutron star mergers. According to Raithel, this data could reveal the fundamental constituents of neutron star matter. “Some theoretical predictions suggest that within neutron star cores, phase transitions could be dissolving the neutrons into sub-atomic particles called quarks,” stated Raithel. “This would mean that the stars contain a sea of free quark matter in their interiors. Our work may help tomorrow’s researchers determine whether such phase transitions actually occur.”

Reference: “Characterizing the Breakdown of Quasi-universality in Postmerger Gravitational Waves from Binary Neutron Star Mergers” by Carolyn A. Raithel and Elias R. Most, 13 July 2022, The Astrophysical Journal Letters.
DOI: 10.3847/2041-8213/ac7c75

Credit: NASA’s Goddard Space Flight Center/CI Lab

Imagine taking a star with twice the mass of the Sun and crushing it down to the size of Manhattan. The result would be a neutron star—one of the densest objects found anywhere in the Universe. In fact, they exceed the density of any material found naturally on Earth by a factor of tens of trillions. Although neutron stars are remarkable astrophysical objects in their own right, their extreme densities may also allow them to function as laboratories for studying fundamental questions of nuclear physics, under conditions that could never be reproduced on Earth.

Because of these exotic conditions, scientists still do not understand what exactly neutron stars themselves are made from, their so-called “equation of state” (EoS). Determining this is a major goal of modern astrophysics research. A new piece of the puzzle, constraining the range of possibilities, has been discovered by a pair of scholars at the Institute for Advanced Study (IAS): Carolyn Raithel, John N. Bahcall Fellow in the School of Natural Sciences; and Elias Most, Member in the School and John A. Wheeler Fellow at Princeton University. Their paper was published recently in The Astrophysical Journal Letters.

Neutron star merger and the gravity waves it produces. Credit: NASA/Goddard Space Flight Center

Ideally, astrophysicists would like to look inside these exotic objects, but they are too small and distant to be imaged with standard telescopes. Researchers instead rely on indirect properties that they can measure—such as the mass and radius of a neutron star—to calculate the EoS. This is much like how one might use the length of two sides of a right-angled triangle to work out its hypotenuse. However, one issue here is that the radius of a neutron star is very difficult to measure precisely. A promising alternative for future observations is to instead use a quantity called the “peak spectral frequency” (or f₂) in its place.

But how is f₂ measured? Collisions between neutron stars, which are governed by the laws of Einstein’s Theory of Relativity, lead to strong bursts of gravitational wave emission. In 2017, scientists directly measured such emissions for the first time. “At least in principle, the peak spectral frequency can be calculated from the gravitational wave signal emitted by the wobbling remnant of two merged neutron stars,” says Most.

Doomed neutron stars whirl toward their demise in this animation. Gravitational waves (pale arcs) bleed away orbital energy, causing the stars to move closer together and merge. As the stars collide, some of the debris blasts away in particle jets moving at nearly the speed of light, producing a brief burst of gamma rays (magenta). In addition to the ultra-fast jets powering the gamma rays, the merger also generates slower-moving debris. An outflow driven by accretion onto the merger remnant emits rapidly fading ultraviolet light (violet). A dense cloud of hot debris stripped from the neutron stars just before the collision produces visible and infrared light (blue-white through red). The UV, optical, and near-infrared glow is collectively referred to as a kilonova. Later, once the remnants of the jet directed toward us had expanded into our line of sight, X-rays (blue) were detected. This animation represents phenomena observed up to nine days after GW170817. Credit: NASA’s Goddard Space Flight Center/CI Lab

It was previously expected that f₂ would be a reasonable proxy for radius, since—until now—researchers believed that a direct, or “quasi-universal,” correspondence existed between them. However, Raithel and Most have demonstrated that this is not always true. They have shown that determining the EoS is not like solving a simple hypotenuse problem. Instead, it is more akin to calculating the longest side of an irregular triangle, where one also needs a third piece of information: the angle between the two shorter sides. For Raithel and Most, this third piece of information is the “slope of the mass-radius relation,” which encodes information about the EoS at higher densities (and thus more extreme conditions) than the radius alone.

This new finding will allow researchers working with the next generation of gravitational wave observatories (the successors of the currently operating LIGO) to better utilize the data obtained following neutron star mergers. According to Raithel, this data could reveal the fundamental constituents of neutron star matter. “Some theoretical predictions suggest that within neutron star cores, phase transitions could be dissolving the neutrons into sub-atomic particles called quarks,” stated Raithel. “This would mean that the stars contain a sea of free quark matter in their interiors. Our work may help tomorrow’s researchers determine whether such phase transitions actually occur.”

Reference: “Characterizing the Breakdown of Quasi-universality in Postmerger Gravitational Waves from Binary Neutron Star Mergers” by Carolyn A. Raithel and Elias R. Most, 13 July 2022, The Astrophysical Journal Letters.
DOI: 10.3847/2041-8213/ac7c75