Post-Newtonian dynamics of compact binaries with mass transfer

TL;DR

This work investigates mass transfer in inspiralling compact binaries and its impact on post-Newtonian dynamics and gravitational-wave phasing. It extends the standard two-body PN framework to include time-varying masses via a Fokker-action approach, deriving the 2PN metric, 2PN Lagrangian, and 2.5PN radiation-reaction corrections with MT. Focusing on quasi-circular orbits, it shows mass transfer induces measurable corrections to the orbital frequency evolution through angular-momentum balance, with a non-negligible 1PN MT contribution and MT-dependent terms that alter GW cycles. The results enhance GW waveform modeling for MT binaries and can improve parameter estimation, including individual masses and MT properties, for space-based detectors; the formalism also accommodates higher MT rates and future extensions to noncircular orbits.

Abstract

Taking into account the mass transfer effect, we derive the equations of motion of a compact binary system at the second-half post-Newtonian order. Applying such equations of motion to quasi-circular orbits, we obtain the time derivative of the orbital frequency, which is consistent with the angular momentum balance equation. Numerical estimates of the phase of gravitational waves are provided for typical mass transfer rates. Our result can be used to improve the waveforms of gravitational waves emitted by compact binaries with mass transfer.

Figures (1)

• Figure 1: The contribution of MT and GWs to the numbers of cycles at the Newtonian-order and the 1PN order. The red lines denote the contribution of MT while the black lines denote the contribution of GWs. The Newtonian order is plotted as dashed lines, and the 1PN order as solid lines. The parameters of the binary system are the same as those of the first column and the second column of Table \ref{['Table']}. The MT contribution at the Newtonian order is much smaller than the GW contribution at the Newtonian order, but larger than the GW contribution at the 1PN order. Given that the cumulative 1PN order MT contribution to the GW phase shift may exceed 2$\pi$ radians, this effect becomes observable provided the signal-to-noise is high enough.