A neutron star is what remains after a massive star goes supernova.

Composed entirely of neutrons, this compact star possesses a radius of only a dozen kilometers (approx. 7 miles) but has a mass that is up to two times that of our Sun — an incredible density for such a small star.

One distinguishing property of neutron stars from normal stars is that, if they go through a change in mass, they could turn into black holes. This critical mass limit is referred to by scientists as maximum mass.

Astrophysicists have long been trying to figure out when or where a neutron star makes its final transformation.

Now, a new study by Goethe University in Germany has found a possible way to determine the absolute maximum mass required for a neutron star to collapse and give birth to a new black hole.

How Neutron Stars Transform Into Black Holes

Neutron stars are the densest of all objects in the known Universe. Because of this, their mass cannot grow without bound, and any increase in mass will consequently cause an increase in density.

This is not unusual for a neutron star because this process will simply cause the neutron star to reach a new state of equilibrium.

The nonrotating neutron star will begin to spin, allowing for a stable state for longer than it could hold otherwise. The extra centrifugal force — the outward force apparent in a rotating frame — helps balance out the extreme gravitational force at work in the interior of the star.

But this cannot last forever.

Professor Luciano Rezzolla, one of the researchers of the study, said that the mass of nonrotating neutron stars is not difficult to calculate, but it is not the largest possible mass.

If the neutron star is rotating, it can still sustain more mass than a nonrotating neutron star. Still, Rezzolla said there is a limit to how much a neutron star can rotate before being torn apart from the centrifugal force.

Therefore, the true largest mass of a rapidly rotating model is called "maximum mass of a maximally rotating configuration" or M_max.

Once a single atom is added to a neutron star that has achieved its M_max, the star would then collapse into a black hole and break apart if continually spun.

Finding the Real Limit

Here comes the tricky part: determining the value of this limit is difficult because a maximum value is strongly dependent on the thermodynamic equation of the state of the matter that composes the neutron star.

Although scientists have long been able to establish, with a degree of certainty, the maximum mass of nonrotating neutron stars, calculating the maximum mass of rotating neutron stars has been less successful.

Now, Rezzolla and colleague Cosima Breu argue that it is now possible to infer what the maximum mass could be before the neutron star collapses to a black hole. It can be done by simply considering what the maximum mass is for the corresponding nonrotating configuration.

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

Both scientists said what was essential in their discovery was to look at the data in a proper way. They needed to look from a different perspective to finally see the results: through a universal manner independent of the existence of the thermodynamic equation.

The findings of this study, which is featured in the Monthly Notices of the Royal Astronomical Society, contributes to a larger class of universal relations for neutron stars.

Rezzolla and Breu's study has also improved methods to express the moment of inertia of rotating neutron stars in terms of compactness. It will allow experts to measure stellar radius with 10 percent precision.

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