Comparison of CBwaves, Columbia, NR and hybrid waveforms

RMKI Virgo group (Budapest, Hungary)

Both CBwaves and the code of the Columbia group developed by Janna Levin use the PN equations to describe the evolution and the emitted waveforms of binary systems. The main differences in the applied approximation can be summarized as:

• Equations of motion
  - PN terms: PN, 2PN, 3PN are identical
  - Spin terms: SO (PN-SO), SS (PN-SS), RRSO (3.5PN-SO), RRSS (3.5PN-SS) are identical
  in the latest verion of CBwaves we have included the 1PN correction to the SO term: PNSO (2PN-SO) which gives non negligible contribution
  - Radiation reaction: use of BT (CBwaves) and DD (Columbia) gauges at 2.5PN and 3.5PN
• Spin precession
  In addition to the usual SO and SS terms CBwaves contains the 1PN correction to the SO term in spin precession
• Waveform
  In CBwaves all the contributions from the leading 2.5PN order quadruplole term up to 4.5PN are included.

NR waveforms

The

Domain of validity

Hybrid waveforms

The

RR gauges

The radiation reaction terms at 2.5PN and 3.5PN depends on 2 and 6 parameters, see e.g. IyerWill95. These arbitrary parameters represent the residual gauge freedom in the relative coordinate x=x1-x2 leaving the formulas for energy and angular momentum flux invariant. CBwaves and the code of the Columbia group use different gauges BT and DD. The DD gauge can be easily analyzed within CBwaves. With the appropriate coordinate transformation (applied at 2.5PN order in the figure below) we can change form one system to the other.