London, April 10 (IANS) A formula taking into account the maximum mass of non-rotating neutron star has made it possible for scientists to calculate the critical mass when a rotating neutron star would collapse to become a black hole.

"It is quite remarkable that a system as complex as a rotating neutron star can be described by such a simple relation," said Luciano Rezzolla from the Goethe University in Frankfurt, one of the authors of the study.

Neutron stars have a mass that is up to twice that of the sun but a radius of only a dozen km, making them thousands of billions of times denser than that of the densest element on the Earth. 

But their mass cannot grow without bound. Indeed, if a non-rotating star increases its mass, its density also will increase. Normally this will lead to a new equilibrium and the star can live stably in this state for thousands of years. 

This process, however, cannot repeat indefinitely and the accreting star will reach a mass above which no physical pressure will prevent it from collapsing to a black hole. 

The critical mass when this happens is called the "maximum mass" and represents an upper limit to the mass that a non-rotating neutron star can be.

However, once the maximum mass is reached, the star also has an alternative to the collapse: It can rotate. 

A rotating star, in fact, can support a mass larger than if it was non-rotating, simply because the additional centrifugal force can help balance the gravitational force. 

Also in this case, however, the star cannot be arbitrarily massive because an increase in mass must be accompanied by an increase in rotation and there is a limit to how fast a star can rotate before breaking apart. Hence, for any neutron star there is an absolute maximum mass and is given by the largest mass of the fastest-spinning model.

Determining this value from first principles is difficult because it depends on the equation of state of the matter composing the star and this is still essentially unknown. Because of this, the determination of the maximum rotating mass of a neutron star has been an unsolved problem for decades. 

Scientists had to compute a very large number of stellar models to find the result, published recently in the journal Monthly Notices of the Royal Astronomical Society.

"Surprisingly, we now know that even the fastest rotation can at most increase the maximum mass of 20 percent at most," Rezzolla noted.

"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," said Cosima Breu, a research student at the University of Frankfurt, who performed the analysis of the data during her bachelor thesis.

This simple but powerful result opens the prospects for more universal relations to be found in rotating stars. "We hope to find more equally exciting results when studying the largely unexplored grounds of differentially rotating neutron stars," Rezzolla said.​