Adding documentation for the PNBMS frame fixing method#116
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keefemitman
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keefemitman
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Thanks for doing this @akhairna! I have one comment regarding your phase definition.
| # The convention for choosing the phase from h_{21} mode and the factor of | ||
| # pi/2 is described in <https://arxiv.org/abs/2603.24661>. | ||
| h_21 = h.data[:, h.index(2, 1)] | ||
| θ = -1 * np.unwrap(np.angle(-h_21) - np.pi / 2) |
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Won't this fail for symmetric systems? Isn't it better to use the time-integral of the angular velocity vector?
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For ω (below) we could use angular_velocity() instead of this θ . What we need θ for is determining the "orbital" phase, and we need to break the π degeneracy appearing in the (2,2) mode. Suggestions welcome if there is a more robust way to do this! But note that in the equal mass case, there is no way to break the π degeneracy even in principle (but I guess we wouldn't care which choice we made there)
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Yup totally agree an odd m mode is needed to break this degeneracy. I usually use the (3,3) mode, but I think the (2,1) mode is totally fine. I was just concerned about defining the phase from the (2,1) mode.
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The (3,3) mode has the same problem that it vanishes in the equal mass limit, as it's also proportional to (m_1-m_2)/m...
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Yes I know I meant for breaking the
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For breaking the (3,3) mode is a bit louder and less spin-dependent, but besides that there's no real advantage. My main concern is that you should not use an odd m mode for extracting the phase since this will fail for symmetric systems since the odd m modes are zero.
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Yes, I agree with that. I tested how much close to q=1 I can get, before this issue makes a difference. That's why the smallest q is 1.28 in the paper. I will try if I can push it lower using (3,3) mode.
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No I mean that's fine, I just think in this tutorial we shouldn't use the (2,1) mode to extract the phase and should instead use the angular velocity so that people down the line don't try this for
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Yeah, you're right about that! I will try using angular velocity, and make the changes in the docs.
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I am now using the angular velocity from the news. However for the initial phase, I have added a comment that this will fail for q=1 systems. I don't know any better way than checking the (2,2) mode phase and inferring the choice of phase difference (0 or pi) from it.
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Hi @moble, @duetosymmetry, and @keefemitman. I have added some documentation for the PNBMS frame fixing method. Please review it. If you think something is missing or incorrect, please let me know.