Scientists discover surprising importance of 'I Love Q' for understanding neutron stars

Scientists can learn a tremendous amount about neutron stars and quark stars without understanding their internal structure in detail, according to two Montana State University scientists who published their findings in the July 26 issue of "Science."

"The stars could be the softest or the hardest in their kind, and it wouldn't matter," said Nicolas Yunes, assistant professor in MSU's Department of Physics.

The reason – discovered by Yunes and postdoctoral scholar Kent Yagi—is almost universal relations among three intrinsic properties of these highly compressed stars. These relations will allow astrophysicists to learn about the shape and degree of deformation of these stars without knowing the details of their internal structure.

These relations – described in Yunes and Yagi's paper titled "I Love Q" – are realized among the moment of inertia ("I"), the "Love number" and the quadrupole moment ("Q").

The first quantity describes how fast a star can rotate. The larger the number, the slower the spin rate.

"Think of twirling ice skaters," Yagi said. "If they bring their arms close to their bodies, the skaters' moment of inertia decreases, and so they spin faster."

The Love number relates to the deformability of a star when squished. The larger the number, the more deformed the star is. The third quantity, "Q," refers to the changing shape of a star.

A measurement of any one of these three quantities would allow astrophysicist to infer the other two to amazing precision without actually measuring them, according to the MSU researchers.

"It doesn't matter if the star is made of different proportions of neutrons, quarks and other particles. In the end, how much the star can be squeezed will be a direct function of its moment of inertia," Yagi said.

Yunes and Yagi used mathematical equations and computer models to discover that I, Love and Q satisfy these universal relations.

This is the first time that Yunes and Yagi have published their work in "Science," the world's leading journal of scientific research, global news and commentary. The weekly publication is read by an estimated 1 million readers. It is the academic journal of the American Association for the Advancement of Science.

"Getting a paper accepted into 'Science' is very difficult," Yunes said. "It's a great honor to be accepted. This encourages us to continue working hard to make new, important discoveries."

Neutron stars and quark stars are extremely compact. They contain an enormous amount of mass in a tiny radius. Because of that, they are so dense that they exert an insanely strong gravitational pull, Yunes said.

"Just imagine a ball the size of the sun being squeezed until it's the size of Bozeman," he said. "All the gravity of the sun, but amplified by factors of thousands."

Astrophysicists believe that these stars produce waves that vibrate through the universe, as the stars spiral into each other and collide. The scientists predict that they will be able to detect these "gravitational waves" by the end of this decade. If they are successful, they will have a whole new way of understanding the universe.

"To make a simple analogy, these waves are like the soundtrack to the universe, and their detection will be like transitioning from mute pictures to modern cinema," Yunes has said in the past.

Yunes and Yagi believe that these I-Love-Q relations they have found will aid in the gravitational wave effort.

"For instance, this universal relation could be used to test Einstein's Theory of General Relativity without contamination due to our ignorance of their internal structure," Yunes said. "You could also use these relations to tell whether what you have observed is a neutron star or a strange quark star."

Not understanding the internal structure of neutron stars has presented a major challenge to certain astrophysical studies, but the "I Love Q relations show that you can proceed without that knowledge," Yunes said.