NRTidalv2 spinning paper-D composition through the merger taper

Scope and status

Specification nrtidalv2-spinning-paper-d-composition/v1 checks the dominant-mode, aligned-spin amplitude_variant="paper_2019" option relative to each frontend's existing IMRPhenomD carrier. It composes the independent scalar tidal phase, self-spin, and merger/taper references. The frozen gate crosses both printed taper boundaries with positive deformabilities and nonzero spins, for Torch and JAX CPU FP64. It is a conditional printed-equation qualification, not a full waveform or physical validation.

Inputs, conventions, and options

Dietrich et al. (2019), Eqs. (17)–(21), (25)–(29), Table II give the tidal phase, self-spin phase, Planck window, and D/Pv2 model distinction. Dietrich et al. (2018), Eq. (11) gives the printed merger-frequency fit, with the paper's stated kappa_eff^T substitution. Wade et al. (2014), Eq. (5) gives the mass-weighted deformability.

Mathematics and components

With x=(pi M_sec f)^(2/3), the tested quotient is

\[ \frac{h^{\rm BNS}_{+,\times}(f)}{h^{\rm BBH}_{+,\times}(f)} =W(f;f_{\rm mrg})\exp\left[-i\left( \psi_T(f)+S_2(f)+S_3(f)\right)\right]. \]

The paper-D option has no Eq. (24) tidal amplitude and excludes the Pv2 3.5PN self-spin/cubic-spin component (Table II). The carrier quotient removes the inherited BBH amplitude and phase while checking the actual complex BNS composition in both polarizations. No alignment, amplitude rescaling, or parameter fit is permitted. The gate uses phasing_convention="coalescence", so the separate native reference-frequency subtraction is outside this slice.

Implementation mapping

The independent mpmath/SymPy modules diffgw_reference.nrtidalv2_phase, diffgw_reference.nrtidalv2_self_spin, and diffgw_reference.nrtidalv2_amplitude compute the right-hand side. The maintained test compares it against Torch/JAX IMRPhenomD_NRTidalv2 divided by each frontend's IMRPhenomD. Neither frontend imports these references.

Evidence and limitations

Frozen systems and limit

The three systems (m1,m2;chi1,chi2;Lambda1,Lambda2), in solar masses, are (1.35,1.35;0.20,-0.12;350,350), (1.6,1.2;0.08,-0.12;250,800), and the body-exchanged copy of the second. Distance is 100 Mpc, inclination 0.4 rad, coalescence phase and time zero. For each case, the scalar printed-fit merger frequency defines the Hz grid: 100, 800, then f/f_mrg = 0.75, 0.99, 1, 1.025, 1.05, 1.1, 1.15, 1.195, 1.2, 1.25. The absolute complex quotient limit is 1e-10 at every sample for both polarizations; the two native polarization quotients must also agree within that limit. The strictly post-endpoint quotient must be exactly zero. An ulp-sized mismatch between independently rounded merger frequencies is allowed at the nominal 1.2 f_mrg endpoint under the same limit. At 300 Hz for the unequal spinning case, the frequency derivative of the unwrapped local quotient phase is checked against the differentiated printed tidal phase plus a high-precision derivative of the 2PN+3PN self-spin phase, with 1e-8 relative and 1e-10 rad/Hz absolute limits. The JAX value and derivative paths are JIT compiled on CPU FP64.

Interpretation and open conflicts

The execution receipt records the strict result. This extends the earlier component gates across the taper as a single complex composition check. It does not establish agreement with a public binary implementing exactly this paper-D contract: the pinned LALSuite 7.26.15 D binary has a nonzero-tide amplitude, contrary to Table II, and its nonzero-tide effective taper boundary differs by about 25 ppm from the printed fit (source audit). No binary gate is asserted for this option. Further, the paper's Fig. 7 example for Lambda=350 conflicts with its printed Eqs. (28)–(29); this gate follows the numbered equations and cannot resolve which quadrupole relation was intended. The historical binary_compatible default and its existing gates are unchanged.

Reproduce the checks

With the reference, Torch, JAX, and pytest dependencies installed, run PYTHONPATH=src:tests JAX_ENABLE_X64=1 python -m pytest -q tests/test_nrtidalv2_paper_d_composition_math_reference.py.