Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order

This article provides the details on the technical derivation of the gravitational waveform and total gravitational-wave energy flux of non-spinning compact binary systems to the 4PN (fourth post-Newtonian) order beyond the Einstein quadrupole formula. In particular: (i) we overview the link between the radiative multipole moments measured at infinity and the source moments in the framework of dimensional regularization; (ii) we compute special corrections to the source moments due to "infrared" commutators arising at the 4PN order; (iii) we derive a "post-adiabatic" correction needed to evaluate the tail integral with 2.5PN relative precision; (iv) we discuss the relation between the binary's orbital frequency in quasi-circular orbit and the gravitational-wave frequency measured at infinity; (v) we compute the hereditary effects at the 4PN order, including those coming from the recently derived tails-of-memory; and (vi) we describe the various tests we have performed to ensure the correctness of the results. Those results are collected in an ancillary file.