Final answer:
A compact object in an X-ray binary is classified as a black hole rather than a neutron star if its mass is greater than about eight solar masses, as observed through detailed measurements of companion stars' motion and X-ray emissions.
Step-by-step explanation:
To classify the compact object in an X-ray binary as a black hole rather than a neutron star, astronomers consider the object's mass. If the X-ray emissions and the observed motion of companion stars indicate a mass greater than about eight solar masses, the compact object is likely a black hole.
This is because neutron stars cannot sustain masses above this threshold without collapsing into a black hole due to the resistance provided by the strong force. For example, the binary system Cygnus X-1 contains an object with a mass estimated at around 15 solar masses, which is too massive to be a neutron star and is thus classified as a black hole.
Additionally, observations using X-ray telescopes like the Chandra X-ray Observatory help to accurately determine the masses of these compact objects by studying the motion of matter around them. Such detailed measurements are necessary because real-life calculations involving Kepler's law only provide the combined mass of the two stars in a binary system.
Astronomers must also examine the properties of the X-rays emitted to distinguish between a black hole and neutron star, as neutron stars can have accretion disks that produce X-rays as well.