The Mystery of the Quantum Vortex: Unveiling the Twisted Roots of Neutron Stars’ Puzzling Pulses

A recent study has revealed the origin of the mysterious “heartbeats” observed in neutron stars, linking them to disturbances caused by the dynamics of superfluid vortices.

Researchers found that these perturbations follow a power law similar to that of other complex systems. They developed a model based on quantum vortex networks that fits observed data without additional tuning.

Discovery of the heartbeat of neutron stars

Stars blinking in the code of Netflix’s “3 Body Problem” may be the stuff of science fiction. But a new study has deciphered the erratic flickering of neutron stars, revealing the twisted origins of these dead stars’ mysterious “heartbeats.”

When neutron stars, the ultra-dense remnants of massive stars that exploded in supernovae, were first discovered in 1967, astronomers thought their strange periodic pulses might be signals from an alien civilization. Although we now know that these “heartbeats” come from beams of radiation from stellar corpses, not from alien life, their precision makes them excellent cosmic clocks for studying astrophysical phenomena such as the rotation rates and internal dynamics of celestial objects.

Sometimes their clockwork is however accuracy is disrupted by pulses that arrive inexplicably earlier, suggesting a glitch or sudden acceleration in the neutron stars’ spins. While the exact causes remain unclear, glitch energies have been observed to follow the power law (also known as the scaling law)—a mathematical relationship reflected in many complex systems, from wealth inequality to frequency-magnitude patterns in earthquakes. Just as smaller earthquakes are more common than larger ones, low-energy glitches are more common than high-energy glitches in neutron stars.

By reanalyzing 533 up-to-date datasets of observations of rapidly spinning neutron stars, called pulsars, a team of physicists found that their proposed quantum vortex network fits naturally with calculations of the power-law behavior of glitch energies without requiring additional tuning, unlike previous models. Their findings are published in the journal Scientific reports.

Superfluid vortices get a new twist

“More than half a century has passed since the discovery of neutron stars, but the mechanism of why failures occur is still not understood. Therefore, we proposed a model to explain this phenomenon,” said study corresponding author Muneto Nitta, a specially appointed professor and co-principal investigator at Hiroshima University’s International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM²).

Previous studies have proposed two main theories to explain these disturbances: starquakes and superfluid vortex avalanches. Although starquakes, which behave like earthquakes, could explain the observed power law pattern, they could not explain all types of disturbances. Superfluid vortices are the widely accepted explanation.

“In the standard scenario, researchers believe that an avalanche of unfixed vortices could explain the origin of the disturbances,” Nitta said.

However, there is no consensus yet on what can trigger eddies into catastrophic avalanches.

Key insights into neutron star dynamics

“If there were no pinning, this would mean that the superfluid would release vortices one by one, allowing for a smooth adjustment of the rotational speed. There would be no avalanches and no disruptions,” Nitta said.

“But in our case, we didn’t need any pinning mechanism or additional parameters. We only had to consider the structure of p-wave and s-wave superfluids. In this structure, all the vortices in each cluster are connected to each other, so they can’t be released one by one. Instead neutron star must release a large number of vortices at the same time. That is the core of our model.”

While the superfluid core of a neutron star rotates at a constant speed, the regular component slows down its rotation rate by gravitational waves and electromagnetic pulses. Over time, their velocity difference grows, so that the star ejects superfluid vortices, which carry a fraction of its angular momentum, to restore equilibrium. However, when superfluid vortices become entangled, they drag others along with them, which explains the disturbances.

Twisted Clusters and Real-World Data Alignment

To explain how vortices form twisted clusters, researchers proposed the existence of two types of superfluids in neutron stars. S-wave superfluidity, which dominates the relatively tame environment of the outer core, supports the formation of integer-quantized vortices (IQVs). In contrast, p-wave superfluidity, which prevails in the extreme conditions of the inner core, favors half-quantized vortices (HQVs). As a result, each IQV in the s-wave outer core splits into two HQVs as it enters the p-wave inner core, creating a cactus-like superfluid structure known as a boojum. As more HQVs split off from IQVs and connect via boojums, the dynamics of vortex clusters become increasingly complex, like cactus arms sprouting and intertwining with neighboring branches, forming intricate patterns.

The researchers performed simulations and found that the exponent for the power-law behavior of glitch energies in their model (0.8±0.2) closely matched the observed data (0.88±0.03). This indicates that their proposed framework accurately reflects real neutron star glitches.

“Our argument, though simple, is very powerful. Even though we cannot directly observe the p-wave superfluid inside, the logical consequence of its existence is the power-law behavior of the cluster sizes obtained from simulations. By translating this into a corresponding power-law distribution for glitch energies, we found that it matches the observations,” said co-author Shigehiro Yasui, a postdoctoral researcher at WPI-SKCM² and associate professor at Nishogakusha University.

“A neutron star is a very special situation because the three fields of astrophysics, nuclear physics and condensed matter physics meet at one point. It is very difficult to observe directly because neutron stars exist far away from us, so we need to make a deep connection between the internal structure and some observational data of the neutron star.”Reference: “Pulsar glitches from quantum vortex networks” by Giacomo Marmorini, Shigehiro Yasui and Muneto Nitta, April 3, 2024, Scientific reports.
DOI: 10.1038/s41598-024-56383-w

Yasui and Nitta are also affiliated with Keio University’s Department of Physics and the Research and Education Center for Natural Sciences. Another collaborator on the study is Giacomo Marmorini from both Nihon University’s Department of Physics and Aoyama Gakuin University’s Department of Physics.