A3 Compact Binary Fusion

Topic

The central feature of this model is the pair of compact objects that merge into one.

Two compact objects—neutron stars, black holes, or a combination of both—orbiting each other lose orbital energy by radiating gravitational waves; this energy loss reduces the separation between the objects, and that reduced separation, in turn, increases the intensity of the radiation, creating a self-reinforcing feedback loop: less separation leads to more radiation, and more radiation leads to even less separation, inevitably culminating in the merger of the two objects into one.

The frequency of the gravitational wave emitted during this final spiral is always twice the orbital frequency of the pair itself; consequently, both frequencies rise in tandem—accelerating rapidly—during the final moments leading up to the merger.

The wave's amplitude upon reaching Earth decreases with the distance between Earth and the source, while increasing with both the system's mass and the speed of the merging bodies; yet, the amplitude is so minute that detecting it requires measuring a change in length—within the arms of an interferometer spanning several kilometers—that is far smaller than the size of an atomic nucleus.

Two black holes, each with a mass thirty times that of the Sun, orbiting with a separation of just one-tenth of an astronomical unit, would take millions of years to merge on their own; this confirms that the events actually detected represent only the final stage of a much longer, much slower spiral. Thus, from the pair of compact objects with which this document begins to the final detected phase with which it concludes—taking in the self-reinforcing loop and the wave frequency linked to the orbital frequency—the merger of compact binaries causes millions of years of silent orbiting to culminate, in their final moments, in a mere fraction of a second of catastrophic merger.

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