(r5) PNComparison < RmiVirgo

RmiVirgo Web>CBwaves>PNComparison (revision 5) (raw view)~~EditAttach~~

---+ Comparison of CBwaves, Columbia, NR and hybrid waveforms

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---+ RMKI Virgo group (Budapest, Hungary)

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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:

   * <strong> Equations of motion </strong><br />- PN terms: PN, 2PN, 3PN are identical<br />- Spin terms: SO (PN-SO), SS (PN-SS), RRSO (3.5PN-SO), RRSS (3.5PN-SS) are identical<br /><span style="white-space: pre;"> </span> in the latest verion of CBwaves we have included the 1PN correction to the SO term: PNSO (2PN-SO) which gives non negligible <a target="_blank" href="http://www.grid.kfki.hu/afs/vasuth/web/Janna/PNSO.pdf">contribution</a><br />- Radiation reaction: use of BT (CBwaves) and DD (Columbia) gauges at 2.5PN and 3.5PN
   * <strong>Spin precession</strong><br />In addition to the usual SO and SS terms CBwaves contains the 1PN correction to the SO term in spin precession
   * <strong>Waveform</strong><br />In CBwaves <a target="_blank" href="http://www.grid.kfki.hu/afs/vasuth/web/Janna/wform.pdf">all the contributions</a> from the leading 2.5PN order quadruplole term up to 4.5PN are included.

---++ NR waveforms

A comparsion with the provided NR waveform is shown here.
<table align="center" border="0"> <tbody> <tr> <td><img width="480" alt="" src="http://www.grid.kfki.hu/afs/vasuth/web/Janna/CBwavesNR.jpg" height="360" /><br /></td> <td><img width="480" alt="" src="http://www.grid.kfki.hu/afs/vasuth/web/Janna/JNR1.jpg" height="360" /><br /></td> </tr> <tr> <td></td> <td><img width="480" alt="" src="http://www.grid.kfki.hu/afs/vasuth/web/Janna/JNR2.jpg" height="360" /><br /></td> </tr> </tbody> </table>

Issues:
   * One has to check the "hybridisation" region of NR waveforms. We should exactly know how they were hybridized.

Domain of validity
<table align="center" border="0"> <tbody> <tr> <td><img width="480" alt="" src="http://www.grid.kfki.hu/afs/vasuth/web/Janna/EBT.jpg" height="360" /></td> <td><img width="480" alt="" src="http://www.grid.kfki.hu/afs/vasuth/web/Janna/EDD.jpg" height="360" /></td> </tr> </tbody> </table>
---++ Hybrid waveforms

The

---++ RR gauges

The radiation reaction terms at 2.5PN and 3.5PN depends on 2 and 6 parameters, see e.g. <a target="_blank" href="http://adsabs.harvard.edu/abs/1995PhRvD..52.6882I">IyerWill95</a>. These arbitrary parameters represent the residual gauge freedom in the relative coordinate <strong>x=x</strong>1<strong>-x</strong>2 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 (applied at 2.5PN order in the figure below) we can change form one system to the other.

<img width="480" alt="" src="http://www.grid.kfki.hu/afs/vasuth/web/Janna/BTtransf.jpg" height="360" />

Topic revision: r5 - 2012-11-15 - GergelyDebreczeni

RmiVirgo

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