  We study gravitational waves emitted by a binary system of non-spinning
bodies in a quasi-circular inspiral within the framework of Einstein-aether
theory. In particular, we compute explicitly and analytically the expressions
for the time-domain and frequency-domain waveforms, gravitational wave
polarizations, and response functions for both ground- and space-based
detectors in the post-Newtonian approximation. We find that, when going beyond
leading-order in the post-Newtonian approximation, the non-Einsteinian
polarization modes contain terms that depend on both the first and the second
harmonics of the orbital phase. We also calculate analytically the
corresponding parameterized post-Einsteinian parameters, generalizing the
existing framework to allow for different propagation speeds among scalar,
vector and tensor modes, without assumptions about the magnitude of its
coupling parameters, and meanwhile allowing the binary system to have relative
motions with respect to the aether field. Such results allow for the easy
construction of Einstein-aether templates that could be used in Bayesian tests
of General Relativity in the future.
