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Equation of state

The equation of state of neutron stars is not currently known. This is because neutron stars are the second most dense known object in the universe, only less dense than black holes. The extreme density means there is no way to replicate the material on earth in laboratories, which is how equations of state for other things like ideal gases are tested. The closest neutron star is many parsecs away, meaning there is no feasible way to study it directly. While it is known neutron stars should be similar to a degenerate gas, it cannot be modeled strictly like one (as white dwarfs are) because of the extreme gravity. General relativity must be considered for the neutron star equation of state because Newtonian gravity is no longer sufficient in those conditions. Effects such as quantum chromodynamics (QCD), superconductivity, and superfluidity must also be considered.

At the extraordinarily high densities of neutron stars, ordinary matter is squeezed to nuclear densities. Specifically, the matter ranges from nuclei embedded in a sea of electrons at low densities in the outer crust, to increasingly neutron-rich structures in the inner crust, to the extremely neutron-rich uniform matter in the outer core, and possibly exotic states of matter at high densities in the inner core.

Understanding the nature of the matter present in the various layers of neutron stars, and the phase transitions that occur at the boundaries of the layers is a major unsolved problem in fundamental physics. The neutron star equation of state encodes information about the structure of a neutron star and thus tells us how matter behaves at the extreme densities found inside neutron stars. Constraints on the neutron star equation of state would then provide constraints on how the strong force of the standard model works, which would have profound implications for nuclear and atomic physics. This makes neutron stars natural laboratories for probing fundamental physics.

For example, the exotic states that may be found at the cores of neutron stars are types of QCD matter. At the extreme densities at the centers of neutron stars, neutrons become disrupted giving rise to a sea of quarks. This matter's equation of state is governed by the laws of quantum chromodynamics and since QCD matter cannot be produced in any laboratory on Earth, most of the current knowledge about it is only theoretical.

Different equations of state lead to different values of observable quantities. While the equation of state is only directly relating the density and pressure, it also leads to calculating observables like the speed of sound, mass, radius, and Love numbers. Because the equation of state is unknown, there are many proposed ones, such as FPS, UU, APR, L, and SLy, and it is an active area of research. Different factors can be considered when creating the equation of state such as phase transitions.

Another aspect of the equation of state is whether it is a soft or stiff equation of state. This relates to how much pressure there is at a certain energy density, and often corresponds to phase transitions. When the material is about to go through a phase transition, the pressure will tend to increase until it shifts into a more comfortable state of matter. A soft equation of state would have a gently rising pressure versus energy density while a stiff one would have a sharper rise in pressure. In neutron stars, nuclear physicists are still testing whether the equation of state should be stiff or soft, and sometimes it changes within individual equations of state depending on the phase transitions within the model. This is referred to as the equation of state stiffening or softening, depending on the previous behavior. Since it is unknown what neutron stars are made of, there is room for different phases of matter to be explored within the equation of state.