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Add new well-measured phase parameter

Colm Talbot requested to merge new-phase-parameter into master

I've noticed that with many waveforms we get a cross-hatched posterior for phase and polarisation, specifically recently with IMRPhenomXPHM but I think I've seen it before with one of the surrogates.

This is basically the sum of two lines one with phase + psi = constant and one with phase - psi = constant. Whether it is +/- depends on the sign of cos inclination, basically, the polarisation rotation mimics a rotation of the (2, 2) spherical harmonic modes and the relative sign of the plus and cross response changes when you go above/below the orbital plane.

My suggestion is to define a new parameter

delta_phase = phase - sign(cos_theta_jn) * psi.

This parameter is really well measured into a few Gaussian peaks with two detectors at modest SNR.

Here's an example 2D plot

image

I'm eager to get feedback on whether we think this is useful and if there's a sensible name to include. I hope think that it could make sampling much easier without phase marginalisation on.

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