NRTidal v1 nonspinning merger taper and carrier composition
Scope and status
Specification nrtidalv1-nonspinning-merger-taper/v1 composes the
independently checked v1 tidal phase with the published
merger-frequency fit and descending Planck taper for zero-spin,
dominant-mode IMRPhenomD_NRTidal on CPU FP64. The paper-to-Torch/JAX
factor and the premerger full carrier agree on six declared systems. The
pinned LALSuite 7.26.15 binary has a nonzero-tide taper-boundary discrepancy,
so this specification does not qualify its tapered full waveform.
Inputs, conventions, and options
Component masses are in solar masses for Torch/JAX and in seconds
\(M_{\rm sec}=G(m_A+m_B)/c^3\) for the scalar reference. Frequency is in Hz;
\(\Lambda_A,\Lambda_B\ge0\), \(\chi_A=\chi_B=0\), \(f_{\rm ref}=30\) Hz,
\(D=100\) Mpc, and inclination is \(0.4\) rad. The v1 phase uses the
documented carrier_rounded=True realization of the published fit.
The native option is apply_merger_taper=True. The binary test uses the
public SimInspiralChooseFDWaveformSequence API without phase or time
alignment. Both polarizations have the same tidal multiplicative factor;
the numerical gates use \(h_+\).
The six declared \((m_A,m_B;\Lambda_A,\Lambda_B)\) systems are \((1.35,1.35;400,400)\), \((1.6,1.2;200,800)\), its body-exchanged copy, \((1.35,1.35;0,0)\), \((1.48,1.22;600,250)\), and \((1.25,1.25;900,900)\). The merger-window fractions are \(f/f_{\rm mrg}=0.9,1,1.025,1.05,1.1,1.15,1.195,1.2,1.25\).
Mathematics and components
Dietrich et al. (2018), Eq. (11) fit the merger angular frequency and explicitly state that the previous NRTidal signal receives a Planck taper from merger to 1.2 times merger. The fit uses \(\kappa_{\rm eff}^{T}\) in place of \(\kappa_2^T\) for the LAL implementation, as the paragraph before Eq. (11) explains. With \(X_A=\max(m_A,m_B)/(m_A+m_B)\), \(X_B=\min(m_A,m_B)/(m_A+m_B)\), and \(\kappa_{\rm eff}^{T}=3\widetilde\Lambda/16\), the printed fit is
Dietrich et al. (2019), Eq. (25) and adjacent text confirm that the 1-to-1.2 merger taper is unchanged from the previous NRTidal implementation. The descending branch is McKechan et al. (2010), Eq. (7), which the 2018 paper cites as its Planck-taper source. Setting its endpoints to the stated frequencies and writing \(z=(f-f_{\rm mrg})/(0.2f_{\rm mrg})\) gives
The independently specified v1 phase \(\psi_T\) gives the paper-derived tidal factor \(F_T(f)=\exp[-i\psi_T(f)]W(f)\), so that the native nonspinning carrier is \(h_+^{\rm BNS}=h_+^{\rm IMRPhenomD}F_T\).
| Component ID/version | Primary source | Scalar reference | Frontends | Evidence |
|---|---|---|---|---|
nrtidal.shared.merger_frequency.eq11.v1 |
Dietrich 2018 Eq. (11) | nrtidalv2_amplitude.merger_frequency |
_bns_merger_frequency |
six-case frequency and body-exchange |
nrtidal.shared.planck_taper.v1 |
Dietrich 2018 after Eq. (11), McKechan 2010 Eq. (7); 2019 Eq. (25) | nrtidalv2_amplitude.taper |
_planck_taper_window |
endpoints, monotonicity, native factor |
nrtidalv1.composed_tidal_factor.v1 |
Dietrich 2017 Eq. (7) plus 2018 Eq. (11) | nrtidalv1_taper.factor |
IMRPhenomD_NRTidal |
Torch/JAX complex quotient, pinned binary premerger |
Implementation mapping
The v1 scalar composition
reuses the existing independent merger/taper expressions in
diffgw_reference.nrtidalv2_amplitude: these are shared published components,
not NRTidalv2-specific fits. A symbolic test verifies their effective tidal
coupling is exactly the v1 paper coupling. The math tests
check Torch and JAX's complete complex BNS/BBH quotient against \(F_T\),
including both window endpoints. The binary tests
compare the full unaligned \(h_+\) through merger, the premerger quotient,
and the zero-tide taper against the named public binary.
Evidence and limitations
The predeclared merger-frequency relative gate is \(10^{-11}\) and the Torch/JAX complex factor absolute gate is \(10^{-10}\). Premerger binary frequencies are 30–800 Hz in 5 Hz steps, plus \(0.9f_{\rm mrg}\) and \(f_{\rm mrg}\); the full \(h_+\) relative complex \(L_2\) gate is \(10^{-8}\). The binary factor maximum absolute gate is \(5\times10^{-5}\). The zero-tide binary taper has the same \(5\times10^{-5}\) absolute gate.
The 27 September 2026 receipt records the strict passing tests and a separate, frozen nonzero-tide taper failure diagnostic. For the five nonzero-tide systems, the pinned binary amplitude quotient differs from the published window by \(2.77\times10^{-4}\) to \(5.36\times10^{-4}\) at the declared fractions. Those values exceed the \(5\times10^{-5}\) boundary gate. No coefficient was inferred or adjusted from the binary. The premerger success does not establish agreement within the nonzero-tide taper, nor physical agreement with independent numerical-relativity data. Spins, self-spin, other modes, FP32, accelerators, and parameter-domain coverage remain separate. The full tapered unaligned \(h_+\) comparison also exceeds its frozen relative complex \(L_2\le10^{-6}\) gate on both holdouts.
The convention diagnostic finds the published Planck shape to numerical precision after inferring one merger frequency from the binary's central taper sample. The inferred frequencies are \(2.5\times10^{-5}\) to \(4.9\times10^{-5}\) below the printed fit for nonzero tides. The paper's printed precision admits this size of shift, but does not identify the binary's full-precision coefficients. Substituting \(\kappa_2^T\) for \(\kappa_{\rm eff}^T\) does not account for the discrepancy. The inferred frequencies are diagnostic data, not inputs to the scalar reference or a passing binary gate.
The historical boundary diagnostic measured the failed gates outside the
required strict test selection without qualifying the mismatch. A separate
historical convention diagnostic tested window shape, merger frequency,
and the explicit alternative coupling. Their one-off replay scripts are
not maintained; their methods and numerical conclusions are recorded in
the linked receipts. The maintained boundary gate remains
tests/test_nrtidalv1_taper_lal_binary.py.
Reproduce the checks
On CPU FP64 with pinned LALSuite 7.26.15, run
DIFFGW_REQUIRE_LAL_BINARY=1 JAX_ENABLE_X64=1 PYTHONPATH=src:tests
python -m pytest -q tests/test_nrtidalv1_phase_math_reference.py
tests/test_nrtidalv1_phase_lal_binary.py
tests/test_nrtidalv1_taper_math_reference.py
tests/test_nrtidalv1_taper_lal_binary.py.
Strict mode makes missing reference or binary dependencies fatal. The
published merger/taper expression and its binary discrepancy require
separate review before any broader qualification claim.