A neutron star is the ultra-dense remnant of a supernova explosion, whose existence was predicted by Fritz Zwicky back in the 1930s. Later, Jocelyn Bell Burnell detected them as pulsars — rotating sources of strictly periodic radio signals.
The precise radius of a neutron star depends on the stiffness of nuclear matter — its ability to resist compression. This quantity can’t be measured directly for the star, but it can be calculated in the lab. The atomic nucleus is like a sponge: squeeze it, and its compressibility tells you how soft the star-sphere is in distant space. Chandrasekhar laid the groundwork for such a connection; recent work found a universal rule that equates the behavior of protons and neutrons in a nucleus to the properties of stellar matter — and all this fits within the standard model.
Measurements on lead nuclei showed: if the star weighs as much as 1.4 Suns, its radius is roughly 12 kilometers. The tiniest change in the nucleus's deformability shifts this estimate by kilometers. So, by squeezing a tiny sample in an earthly lab, physicists refine the size of an object thousands of light-years away. The cosmos and the microcosmos have come together not in fiction, but in precise calculation.
Due to the monstrous gravity of a neutron star, its surface is almost perfectly smooth: mountains there can't be taller than a few millimeters — any bump gets instantly crushed.
In the sci-fi novel 'Dragon's Egg', a civilization is described living on a neutron star, where time flows thousands of times faster than on Earth.