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It has long been known that gravitational waves from compact binarycoalescing sources are responsible for a first-order displacement memory effectexperienced by a pair of freely falling test masses. This constant displacementis sourced from the non-vanishing final gravitational-wave strain present inthe wave's after-zone, often referred to as the non-linear memory effect, andis of the same order of magnitude as the strain from the outgoing quadrupoleradiation. Hence, this prediction of general relativity is verifiableexperimentally by measurement of the final relative separation between testmasses that comprise gravitational-wave detectors. In a separate context,independent calculations have demonstrated that exact, sandwich, plane wavespacetimes exhibit a velocity memory effect: a non-zero relative velocity,gained by a pair of test masses in free fall, after the passage of agravitational wave. In this paper, we find that in addition to the knownconstant displacement memory effect test masses experience, a velocity memoryeffect at leading order arises due to the non-linear nature of gravitationalwaves from compact binary sources. We discuss the magnitude of the first-ordervelocity memory effect in the context of observing gravitational-wave radiationfrom super massive binary black hole mergers in LISA.

The First-Order Velocity Memory Effect from Compact Binary Coalescing Sources