Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian Order

The rate of gravitational-wave energy loss from inspiralling binary systems of compact objects of arbitrary mass is derived through second post-Newtonian (2PN) order $O\left(\right({Gm/rc}^2{)}^2)$ beyond the quadrupole approximation. The result has been derived by two independent calculations of the (source) multipole moments. The 2PN terms, and, in particular, the finite mass contribution therein (which cannot be obtained in perturbation calculations of black hole spacetimes), are shown to make a significant contribution to the accumulated phase of theoretical templates to be used in matched filtering of the data from future gravitational-wave detectors.