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Discontinuities in PhenomXPHM

This is to summarize what is known about the discontinuities observed in XPHM.

XPHM presents discontinuities in some regions of parameter space with high mass ratio, negative spins and more often when close to aligned-spins. These cases have the initial L+S_{∣∣}<0.

For these cases the opening angle \beta can be larger than pi/2, causing the PN Euler angles to be pathological. This is well known and a warning message is printed for those cases (lal.ClobberDebugLevel(2)).

image

In particular, the discontinuities occur because the 3PN angular momentum has an unphysical growth towards merger that flips the sign of cosbeta. This discontinuity in cosbeta is propagated to the Wigner matrices and provokes the change of power between positive/negatives frequencies.

This can be observed in

  • XPHM default (223)
  • XPHM NNLO (102)
  • XPHM_SpinTaylor (320) ONLY when it defaults to either MSA or NNLO

During the XPHM review this was not an issue since the sign of cosbeta was not tracked, but that changed here.

The region affected by the flip of sign is in blue

flip_cos_beta

TODOs

[ ] A long-term solution would be e.g. calibrating the angular momentum L or use calibrated angles as XO4a.

[ ] There has been a feature request to implement an option that returns a hard error when \beta>0 and this is on the way.

Edited by Cecilio Garcia-Quiros