In a subclass of Horndeski theories with the speed of gravity equivalent to
    that of light, we study gravitational radiation emitted during the inspiral
    phase of compact binary systems. We compute the waveform of scalar
    perturbations under a post-Newtonian expansion of energy-momentum tensors of
    point-like particles that depend on a scalar field. This scalar mode not only
    gives rise to breathing and longitudinal polarizations of gravitational waves,
    but it is also responsible for scalar gravitational radiation in addition to
    energy loss associated with transverse and traceless tensor polarizations. We
    calculate the Fourier-transformed gravitational waveform of two tensor
    polarizations under a stationary phase approximation and show that the
    resulting waveform reduces to the one in a parametrized post-Einsteinian (ppE)
    formalism. The ppE parameters are directly related to a scalar charge in the
    Einstein frame, whose existence is crucial to allow the deviation from General
    Relativity (GR). We apply our general framework to several concrete theories
    and show that a new theory of spontaneous scalarization with a higher-order
    scalar kinetic term leaves interesting deviations from GR that can be probed by
    the observations of gravitational waves emitted from neutron star-black hole
    binaries. If the scalar mass exceeds the order of typical orbital frequencies
    $\omega \simeq 10^{-13}$ eV, which is the case for a recently proposed
    scalarized neutron star with a self-interacting potential, the gravitational
    waveform practically reduces to that in GR.

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