Kicks and memory with a massless scalar field

A scalar field coupled conformally and disformally to matter affects both the linear memory effect for binary systems on hyperbolic orbits, as well as the kick velocity for binaries on bound or unbound orbits. We study these corrections in detail, their order of magnitude, and discuss their detectability. In particular, we find that the disformal interaction does not contribute to the memory effect and the emitted power spectrum at zero frequency. The conformal interaction corrects the GR linear memory and the quadrupole emitted power at zero frequency resulting in a breaking of the GR memory-power spectrum relationship. On the other hand, disformal interactions give rise to a change of momentum for the center of mass. Hence, measuring both the linear memory effect and the kicks for hyperbolic orbits would give access to the conformal and disformal couplings of nearly massless scalars to matter.