Final answer:
The most difficult X-ray binary companion star to observe is a neutron star due to their compactness and weak visible light emission. Spectral analysis and X-ray observations are key in identifying them in binary systems. Discussions about binary system evolution, such as Sirius and its white-dwarf companion, help in understanding the mass and evolutionary differences within these systems.
Step-by-step explanation:
The most difficult type of X-ray binary companion star to observe is the neutron star. Due to their compact nature, and the fact that they do not emit much visible light, neutron stars are challenging to detect directly. Instead, their presence is typically inferred from their interactions with other stars, such as accretion of material that emits X-rays, or the gravitational effects they have on their binary companions.
To distinguish a binary system containing a main-sequence star and a white dwarf from one containing a main-sequence star and a neutron star, astronomers would utilize observations of X-ray emissions and look for Doppler shifts in spectral lines to determine the mass of the unseen companion. As an example, the first black hole binary system discovered, Cygnus X-1, was identified through such methods. If the unseen companion's mass exceeds the Chandrasekhar limit but does not exhibit a radius commensurate with a white dwarf, it could be a neutron star or possibly a black hole.
In the case of Sirius, which has a white-dwarf companion, discussions about how the white dwarf evolved before Sirius, despite the two stars forming at the same time, suggest that the white dwarf's initial mass was larger than Sirius', allowing it to evolve faster. This demonstrates the significance of mass in stellar evolution within binary systems. Massive stars evolve rapidly and end their lives as white dwarfs, neutron stars, or, in some cases, black holes, depending on their initial mass.