What is the key observation needed to determine whether a compact object in question is a neutron star or a black hole?

Similar in many ways to black holes, neutron stars are degenerate objects created when the iron core of a massive star collapses under the force of gravity.

They are both massive and small, with the ability to spin and be charged, and they both radiate.

A mass of less than or equal to three solar masses is most likely that of a neutron star; a mass greater than or equal to three solar masses is most likely that of a black hole.

This is because of a quantum effect known as neutron degeneracy pressure, which maintains the separation of neutrons even at high temperatures and pressures. If a neutron star has a mass greater than three solar masses, the gravitational pressure is so strong that the star will continue to collapse into a black hole.

If there is something in orbit around an object, its mass can be easily calculated if the semi major axis distance and orbiting body's period can be worked out.

Mass is a crucial characteristic that distinguishes a compact object from a black hole or neutron star.