The collapsing remains of enormous stars that had undergone supernova explosions are known as neutron stars. These celestial objects, which are made up of neutron balls that are closely packed and have masses higher than the Sun, are among the densest in the universe. Their radius is barely a few kilometers. They offer a rare chance to investigate the strong force (or strong interaction), one of the four fundamental forces of nature. This force only manifests itself when specific elementary particles, like the neutrons and protons that make up atomic nuclei, are in close proximity to one another. It is currently quite challenging to investigate these items and their interactions in a scientific setting because to their microscopic size, though.

Finding macroscopic things that have a significant contribution from the strong force is therefore very desired. Neutron stars are the ideal testbed because of their incredible density, which corresponds to very small distances between particles. They provide a practical way to investigate this strong interaction at low energies and aid in the development of quantum chromodynamics, a theory that describes the behavior of this strong force. To accomplish this, researchers must first comprehend the basic characteristics of neutron stars, especially their structure. This is done by running a variety of complex computer simulations to learn more about how the neutrons that make up these stars interact in such a hostile environment.

Here’s where a group of researchers from Hungary step in. They intend to assess the precision of three of the most effective computer models of spinning neutron stars, as well as the accuracy of our present knowledge of the physics behind this type of star. According to Balázs Kacskovics, researcher at the Wigner Researcher Centre for Physics at the University of Pécs and lead author of the study, “we compared three of the most popular methodologies: 1) Hartle—Thorn slow-rotation approximation, 2) Numerical fast-rotating approach, and 3) Tolman—Oppenheimer—Volkov equation solver.” While we employed techniques created by ourselves and other researchers for 1 and 3, we used a well-known fast-rotating code package for 2.

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The purpose of this comparison, he continued, is to assess the discrepancy between the outputs of various numerical algorithms in order to increase the accuracy of recently created codes. The physicists used various techniques in their study, which was published in Astronomical Notes, to determine how the mass of a star changes depending on the velocity of its revolution. They then compared the results to see how closely they matched. We have demonstrated the applicability limit of the popular slow-rotation strategy by calculating the neutron star’s mass using each method as a function of rotational frequency and matter energy density, according to Kacskovics. The likelihood that the algorithms would yield the right findings increased with the proximity of the calculated masses to one another.

The models that had stars with rotation velocities close to the theoretical maximum—that is, stars that were revolving as quickly as was physically possible—were the most accurate. The researchers would gain the most insight into the correctness of the algorithms at such speeds because it is anticipated that the differences between the results produced by different algorithms will be the most substantial. Centrifugal force, a force that forces an object moving in a circular path to move out and away from the center of its path, accounts for this physical restriction on the maximum rotation velocity of a star (including not just neutron stars). This force, working on the star’s outer layers of matter, can overcome gravity if the star rotates too swiftly and simply rips away material. The rotation speed and frequency must stay below a theoretical limit for the star to survive.

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The Keplerian frequency is the maximum rate of angular rotation, and the magnitude of this frequency is strongly influenced by the characteristics of the rotating object. Because neutron stars are extremely dense and have extremely powerful gravitational fields, their Keplerian frequencies can approach hundreds of hertz. We have estimated the maximum rotational frequency that a star with a particular mass may rotate without losing mass due to centrifugal force, also known as the Keplerian frequency, according to Kacskovics.

The researchers were able to quantify the accuracy of this common computer model, known as the slow-rotation approximation, because it turned out that the difference between the masses calculated by the various methods was biggest for rotation at the Keplerian frequency, as was predicted. The physicists claim that despite being a step forward, there are still several opportunities to further enhance their study. In addition to the rotational frequency, “we may include the temperature as a new parameter, for instance,” stated Kacskovics. Other enhancements can include boosting the accuracy of our calculations. This should aid in our understanding of the physics of the fundamental particles that make up these particular celestial bodies, in addition to the large-scale physical events that control them.

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