IMRPhenomXHM default ringdown cutting frequencies
Scope and status
xhm.frequency.ringdown-cut.default.v1 specifies the default amplitude and
phase ringdown cuts for the (2,1), (3,3), (3,2), and (4,4) modes. This
is a supplied-QNM frequency algebra gate, not a QNM-fit, attachment, or
whole-waveform qualification. The paper notes exceptional (3,2) cut
adjustments for high-mass, high-spin cases; those are outside this default
slice.
Before comparison with native code, fix CPU float64 value tolerance to
rtol=0, atol=2e-15 and all input Jacobian tolerance to rtol=0,
atol=2e-14. The fixed three-row input grid is below. Both frontends must
agree with the independent 70-digit scalar evaluator and the analytic sparse
Jacobian, including zero cross-row and unused (3,2) QNM derivatives.
Inputs, conventions, and options
Frequencies are positive dimensionless Mf. r_lm and d_lm are supplied
fundamental QNM ring and damping frequencies, respectively. Rows are ordered
(22,21,33,32,44); no QNM provider or intrinsic binary parameterization is
specified by this component.
| Row | r22,r21,r33,r32,r44 |
d22,d21,d33,d32,d44 |
|---|---|---|
| 1 | .080,.075,.095,.091,.120 |
.012,.012,.015,.014,.018 |
| 2 | .087,.079,.100,.095,.130 |
.010,.010,.013,.012,.016 |
| 3 | .075,.072,.088,.086,.110 |
.015,.014,.018,.017,.020 |
Mathematics and components
García-Quirós et al., arXiv:2001.10914v2, Sec. V, Eq. (36) and Table 2
give f_RD = delta_RD * r_lm + epsilon_RD, with distinct amplitude and phase
choices. The eight default cuts are
| Mode | Amplitude cut | Phase cut |
|---|---|---|
| 21 | 0.75 r21 |
r21 - d21 |
| 33 | 0.95 r33 |
r33 - d33 |
| 32 | r22 |
r22 - 0.5 d22 |
| 44 | 0.90 r44 |
r44 - d44 |
The Jacobian follows directly: each displayed coefficient is the partial
derivative with respect to its input, with -1 for each non-mixing phase
damping frequency and -0.5 for d22 in the (3,2) phase cut. All other
partials are zero.
Implementation mapping
The independent mpmath evaluator is
diffgw_reference.imrphenomxhm_ringdown_cuts. Torch and JAX each call their
own _ringdown_cut_frequencies helper from the production XHM waveform path;
neither native frontend imports the scalar reference. The native helper
returns separate amplitude and phase cut dictionaries keyed by mode string.
Evidence and limitations
The gate compares all eight outputs and their full cross-mode and cross-row
Jacobian for three supplied-QNM rows. This checks the published default
frequency selection that feeds the intermediate and ringdown attachment
paths. It does not validate a QNM provider, exceptional (3,2) cut rules,
the fitted collocation targets, or the attached phase/amplitude itself.
The adjacent non-mixing ringdown phase coefficient rule in Eq. (45) is not
qualified here. That equation leaves the mode constants w_lm unspecified,
whereas the existing Torch/JAX paths use independently calibrated per-mode
coefficient surfaces rather than an explicit Eq. (45) rescaling. Equating
those without an independently sourced calibration would change the claim.