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:
A comparsion with the provided (thanks to Valentin) NR waveform is shown here. Initial values: m1=m2=r0=10 Msun, the binary is circular, D=500 Mpc.
Here we plot the output of CBwaves (left column) and the code of the Columbia group (right column) together with the NR data.
Issues:
The properties of the two different RR gauges BT and DD can be easily analyzed with CBwaves. To give a more detailed explanation of the above results we show additional plots generated by CBwaves.
The waveform and the evolution of the orbtial separation in the BT and DD gauges
The evolution of the total energy and the post-Newtonian parameter v^2
Ninja2 waveforms are hibrydized and available for comparsion. The plot below shows the /BAM_D11spp50_96.T4.hyb.n2.gwf waveform compare with CBwaves as an example. Parameters are:
Comparsion is not straightforward because:
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 at 2.5PN and 3.5PN leaving the formulas for energy and angular momentum flux invariant. CBwaves and the code of the Columbia group use different gauges BT and DD, but CBwaves can also analyize the DD gauge thanks to the built-in and configurable gauge transformation. With the appropriate coordinate transformation x'=x+δx (applied at 2.5PN order in the figure below for a circular binary with m1=m2=r0=10 Msun) we can change from one system to the other.
I | Attachment | History | Action | Size | Date | Who | Comment |
---|---|---|---|---|---|---|---|
jpg | comparsion.jpg | r1 | manage | 81.2 K | 2012-11-15 - 15:18 | GergelyDebreczeni | |
jpg | comparsion2.jpg | r1 | manage | 63.8 K | 2012-11-15 - 15:22 | GergelyDebreczeni | Hybrid PN comparsion |