Resonant locking between binary systems induced by gravitational waves

The interaction of gravitational waves (GWs) with matter is thought to be typically negligible in the Universe. We identify an exception in the case of resonant interactions, where GWs emitted by a background binary system, such as an inspiraling supermassive black hole (SMBH) binary, cause a resonant response in a stellar-mass foreground binary and the frequencies of the two systems become, and remain, synchronized. We point out that this previously unexplored dynamical phenomenon is not only possible, but can lead to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="script">O</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>30</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> binary systems becoming resonantly locked in the host galaxy of merging SMBHs of mass <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msup> <f:mn>10</f:mn> <f:mrow> <f:mn>8.5</f:mn> <f:mo>−</f:mo> <f:mn>11</f:mn> </f:mrow> </f:msup> <f:msub> <f:mi>M</f:mi> <f:mo stretchy="false">⊙</f:mo> </f:msub> </f:math> , each of which has a significantly reduced merger time. We predict <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi mathvariant="script">O</i:mi> <i:mo stretchy="false">(</i:mo> <i:msup> <i:mn>10</i:mn> <i:mn>10</i:mn> </i:msup> <i:mo stretchy="false">)</i:mo> </i:math> binary systems have been locked in the Universe’s history. Resonant locking could be detected through anomalous inspiral of binary systems.