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Abstract

With the aim of providing high accuracy post-Newtonian (PN) templates for the
analysis of gravitational waves generated by compact binary systems, we
complete the analytical derivation of the source type mass quadrupole moment of
compact binaries (without spins) at the fourth PN order of general relativity.
Similarly to the case of the conservative 4PN equations of motion, we show that
the quadrupole moment at that order contains a non-local (in time)
contribution, arising from the tail-transported interaction entering the
conservative part of the dynamics. Furthermore, we investigate the infra-red
(IR) divergences of the quadrupole moment. In a previous work, this moment has
been computed using a Hadamard partie finie procedure for the IR divergences,
but the knowledge of the conservative equations of motion indicates that those
divergences have to be dealt with by means of dimensional regularization. This
work thus derives the difference between the two regularization schemes, which
has to be added on top of the previous result. We show that unphysical IR poles
start to appear at the 3PN order, and we determine all of these up to the 4PN
order. In particular, the non-local tail term comes in along with a specific
pole at the 4PN order. It will be proven in a companion paper that the poles in
the source-type quadrupole are cancelled in the physical radiative type
quadrupole moment measured at future null infinity.