In a binary star system, the two stars can indeed come closer to each other and orbit each other faster over time. This phenomenon is known as orbital decay or inspiral. However, the process by which they get faster is a bit more complex than simply losing energy through gravitational waves.
Gravitational waves do play a role in the overall evolution of a binary star system, but they are not the primary mechanism responsible for the stars getting closer and orbiting faster. Gravitational waves are ripples in spacetime caused by the acceleration of massive objects, such as the two stars in a binary system. When a binary star system emits gravitational waves, it loses energy and angular momentum, causing the stars to gradually spiral inward over time.
However, the loss of energy and angular momentum due to gravitational waves is a relatively slow process. In most binary systems, other factors are more dominant in driving the increase in orbital speed. The primary mechanism responsible for the stars getting closer and orbiting faster is mass transfer or mass loss.
In a binary system, one star may be more massive than the other. As the more massive star evolves and expands, it can transfer mass to its companion through various mechanisms such as stellar winds or Roche lobe overflow. This mass transfer affects the orbital dynamics of the system.
When mass is transferred from one star to the other, the recipient star gains mass, which increases its gravitational pull. This increased gravitational attraction causes the stars to move closer to each other and speeds up their orbital motion. As the stars become closer, their gravitational interaction becomes stronger, leading to an acceleration in their orbital velocity.
So, in summary, while gravitational waves do contribute to the overall evolution of a binary star system, the primary mechanism causing the stars to get closer and orbit faster is mass transfer or mass loss between the stars.