Final answer:
One star is captured and the other is ejected in a binary system near a SMBH due to the distribution of energy as a result of the gravitational interaction with the black hole. Tidal forces can strip matter from the star forming an accretion disk, which emits X-rays. The dynamics of binary motion make simultaneous capture or ejection less likely.
Step-by-step explanation:
The Hills mechanism suggests that when a stellar binary system comes close to a supermassive black hole (SMBH), the intense tidal forces can result in one star being captured by the black hole while the other star is ejected at high speeds. The reason one star is captured and the other is ejected is due to the distribution of energy within the binary system when it interacts with the SMBH's gravitational field. The tidal forces can be so extreme that they can strip matter from one star, forming an accretion disk around the black hole which glows in X-ray emissions due to the intense heating of the stripped material.
It is theoretically possible for a SMBH to capture both stars or eject both, but in practice, this is much less likely due to the dynamics involved. The binary stars are typically in motion around their common center of mass, and when they approach the SMBH, one star may get captured due to losing kinetic energy to the other, which gains enough energy to be propelled away from the black hole.
While black holes are often thought of as all-consuming voids, they are also known for the intense tidal forces they exert on nearby objects, which frequently leads to one star of a binary system being torn apart while the other star might escape the gravitational pull.