Neutron stars are found in a variety of binary stars, which provides a means to determine their masses using Kepler's Laws -- possibly modified to tske into account relativity.
A much more accurate technique using the Shapiro Delay (named after Harvard Professor Irwin Shapiro) is possible for the double neutron stars in which one star is a radio pulsar. If the path of the radio pulse passes close to the companion star it will be delayed by a tiny amount, which is measurable with very accurate clocks on Earth. The technique can also be applied to white dwarf-pulsar systems with reduced accuracy due to the weaker gravitational field of a white dwarf star.
As an example, the famous binary known as PSR B1913+16 is made up of neutron stars with 1.441 and 1.387 times the mass of our Sun. Surprisingly, these kinds of stars often turn out to have masses very close to 1.4 times the Sun's mass. The new observation of 1.97+/-0.04 times the Sun's mass for J1614-2230 is all the more remarkable, and provides new clues to physicists studying the interiors of neutron stars.
Double neutron star systems are also unique laboratories for testing General Relativity. The first one to be discovered, PSR1913+16 won Russell Hulse and Joseph Taylor the 1993 Nobel Prize in Physics. In 2004 an international team including scientists at Manchester University in the UK discovered an even rarer double pulsar.
Links
Astronomy Now article by Keith Cooper.
Ars Technica news story.
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