Everything around us is constructed of atoms, which themselves consist of electrons and nucleons (i.e. protons and neutrons). This familiar structure of matter is, however, disrupted when matter is compressed to very high densities that reach beyond the density of an atom, called the nuclear density. It is one of the prime pursuits of modern physics to understand what happens to matter beyond this point. It is not possible to generate supra-nuclear densities in terrestrial laboratories on Earth. However, neutron stars are extreme objects in which matter is compressed to enormously high densities. These stellar bodies therefore serve as exciting, natural laboratories to further our understanding of the fundamental behavior of matter.
Neutron stars are the remnants of once massive stars that ended their life in a supernova explosion. A defining property of neutron stars is that these objects are very compact; while being roughly a factor of 1.5 more massive than our Sun, their radius is almost 100.000 times smaller. Due to their extreme compactness, neutron stars are the densest, directly observable stellar objects in our universe. These fascinating objects come in a wide range of manifestations, e.g. as single stars or as part of a binary, and can be detected at different wavelengths.
Unfortunately it is not possible to travel to a neutron star to conduct experiments of how their interiors look like. However, the macroscopic properties of neutron stars, such as their mass, radius and rotation rate, provide indirect yet powerful information about their interiors. The electromagnetic radiation coming directly from the surface of neutron stars, or from matter that revolves around them, can be used to measure these macroscopic properties. These observational constraints can then be used to infer for instance how high their central density is, what kind of particles are present, and what the superfluid properties of their interior are.
We recently reviewed how different types of electromagnetic observations can be employed to learn more about the interior of neutron stars. This included commonly used techniques of combining radio pulsar timing with optical spectroscopic studies to measure neutron star masses, as well as various techniques to measure neutron star radii from X-ray data. In addition, we touched upon various techniques that have not yielded strong constraints to date, but have great potential to be further developed in the future and can be particularly interesting when combined with other methods. Finally, we provided an outlook of the potential for neutron star research of the future generation of ground-based observatories such as the Square Kilometer Array and the new class of 30-m telescopes, as well as new and upcoming X-ray facilities such as NICER, eXTP, Athena and X-ray polarimetry missions.
Degenaar & Suleimanov 2018, book chapter in The Physics and Astrophysics of Neutron Stars, Springer Astrophysics and Space Science Library: Testing the equation of state of neutron stars with electromagnetic observations
Paper link: ADS
Artist impression of the Square Kilometer Array (SKA), which is currently in the design phase. This radio facility is expected to be transformable in many areas of science, including measuring the masses (and spins) of neutron stars.
Nathalie Degenaar 
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