Inspiral gravitational waveforms from charged compact binaries with scalar hair

We investigate gravitational waveforms from compact binary systems in Einstein-scalar-Maxwell (ESM) theories, where a scalar field $\phi$ couples to a $U(1)$ gauge field $A_\mu$ through a field-dependent function $\mu(\phi)$. In this framework, compact objects -- black holes (BHs), neutron stars (NSs), and exotic compact objects (ECOs) -- can carry both vector and scalar charges, with the latter arising as secondary hair induced by the former. Modeling the binary as electrically charged point particles with scalar-field-dependent masses, we derive the conservative dynamics in the near zone and compute the radiative fields in the far zone. The tensor waveform is modified through the effective dynamics and radiation-reaction-driven phase evolution, while scalar and vector modes introduce additional energy-loss channels. From the energy fluxes of tensor, scalar, and vector radiation, we construct the frequency-domain waveform using the stationary phase approximation. Dipole radiation sourced by differences in scalar and vector charge-to-mass ratios yields a leading $-1$ post-Newtonian correction. The deviation from general relativity is characterized by a single parameter $b$, which controls both amplitude and phase modifications. We further examine constraints from the orbital-period decay of binary pulsars, showing that current observations already place stringent bounds on $b$ for neutron star binaries. In addition, we evaluate $b$ for representative BH-BH, NS-NS, ECO-ECO binaries realized in ESM theories. Our results provide a unified framework for gravitational-wave signatures of charged compact binaries and offer a means of testing dark-sectorscalar and vector charges with current and future observations.