With a density thousands of billions of times that of the densest element on Earth, neutron stars are among the most extreme and fascinating objects known to exist in our universe.
What's fascinating is neutron stars have a mass that is as much as twice that of the sun but a radius of only a dozen kilometers at most. However, eventually these stars reach a mass that forces them to collapse into a black hole. But when exactly does this happen?
Researchers from the Goethe University of Frankfurt, Germany, found a simple formula for calculating the maximum mass of neutron stars.
Unlike normal stars, the mass of neutron stars cannot grow without bound. In other words, when the mass of a non-rotating star increases, so does its density. While the star can live stably in this state for thousands of years, this process does eventually reach a tipping point, at which time the star will reach a mass above which no physical pressure can prevent it from collapsing to a black hole. This, researchers explained, is known as the star's critical or maximum mass.
Rather than collapsing into a black hole, neutron stars can also start rotating to support their larger mass, as the additional centrifugal force helps balance the gravitational force.
However, every neutron star has an absolute maximum mass. This means that an increase in mass must be accompanied by an increase in rotation, but there is a limit to how fast a star can rotate before breaking apart.
Until now, determining the maximum rotating mass of a neutron star was virtually impossible because it largely depends on the star's matter. However, by taking into account the maximum mass of a neutron star's corresponding non-rotating configuration, researchers have found that it is actually quite simple to predict the maximum mass of a rapidly rotating neutron star.
"It is quite remarkable that a system as complex as a rotating neutron star can be described by such a simple relation," said professor Luciano Rezzolla, one of the study authors and chair of theoretical astrophysics at the Goethe University in Frankfurt. "Surprisingly, we now know that even the fastest rotation can at most increase the maximum mass of 20 percent at most."
While previous studies have computed a number of stellar models to predict when a neutron star will collapse to a black hole, it is not until recently that scientists learned that if represented with a proper normalization, the data behaves in a universal manner. In other words, a neutron star's maximum mass is not dependent on the star's matter.
"This result has always been in front of our eyes, but we needed to look at it from the right perspective to actually see it," added Cosima Breu, a masters student at the University of Frankfurt.
Researchers also found a new method for expressing the moment of inertia of these rotating stars in terms of their compactness, which will allow scientists to measure the stellar radius of a neutron star with a precision of 10 percent or less.
"We hope to find more equally exciting results when studying the largely unexplored grounds of differentially rotating neutron stars," Rezzolla concluded.
Their study was recently published in the Monthly Notices of Royal Astronomical Society.
