NRTidalv2 Pv2 aligned-frame additive finite-size terms

Scope and status

Specification nrtidalv2-pv2-aligned-additive-terms/v1 covers the signed tidal-amplitude contribution with the full printed self-spin phase, before the precession rotation. This is a conditional component-composition gate, not an IMRPhenomPv2_NRTidalv2 waveform qualification. It follows Dietrich et al. (2019), Eqs. (17)–(21), (24)–(29), Table II and Sec. III.4, with the printed merger fit. The paper says to add finite-size corrections to the underlying aligned-spin model before rotation. It assigns both Eq. (24) and the 3.5PN spin terms to Pv2, whereas the D gate omits both.

Inputs, conventions, and options

The three (m1,m2;chi1,chi2;Lambda1,Lambda2) systems 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 exchanged second system. Distance is 100 Mpc; the diagnostic D quotient uses inclination 0.4 rad, zero coalescence phase/time, and phasing_convention="coalescence". Frequencies are 100 and 800 Hz plus the scalar-fit fractions 0.75, 0.99, 1.0, 1.025, 1.05, 1.10, 1.15, 1.25 of merger frequency. CPU FP64 is required.

Mathematics and components

For positive deformabilities, aligned spins, and coalescence phasing, the tested signed complex contribution is

\[ T(f)=A_T(f)W(f;f_{\rm mrg})\exp\{-i[\psi_T(f)+S_2(f)+S_3(f)+S_{3.5}(f)]\}. \]

Here A_T has the absolute, distance-dependent Eq. (24) normalization. Consequently T is an additive amplitude term, not a BBH amplitude ratio or a complete strain.

Implementation mapping

The independent mpmath/SymPy reference is src/diffgw_reference/nrtidalv2_pv2_terms.py, composed from the separate phase, self-spin, and amplitude references. The native diagnostic composes the actual paper-D pre-taper BNS/BBH quotient, the native 3.5PN component, native Eq. (24) amplitude, and native taper in each frontend. It does not import the reference in Torch or JAX.

Evidence and limitations

Both Torch and JAX must satisfy |T_native-T_ref|/(|A_T,ref| W_ref) <= 1e-10 at nonzero-window bins, without time/phase alignment, rescaling or fitting. At the strictly post-taper bin, both must return exact complex zero. The two polarization routes must agree at the same normalized limit.

No native IMRPhenomPv2_NRTidalv2 class currently composes these terms with the aligned-spin carrier and twists them into plus/cross polarizations. The paper's Sec. III.4 specifies the order of operations but does not turn this component test into a polarization or precession validation. A full Pv2 gate still needs that native assembly and a pinned binary or independent physical comparison with a matching convention. The Fig. 7 versus Eqs. (28)–(29) Love–Q conflict and the printed-fit versus pinned-LAL merger boundary difference remain open in the linked component receipts. The supplied-mode projection operator has a separate positive-22 gate. A subsequent normalization gate resolves the Eq. (24) supplied-mode scale. The subsequent conditional aligned-carrier gate composes this correction with a supplied BBH carrier; public Pv2 BNS angle and reference conventions remain unresolved. The historical binary_compatible default is unchanged.

Reproduce the checks

Run JAX_ENABLE_X64=1 PYTHONPATH=src:tests python -m pytest -q tests/test_nrtidalv2_pv2_aligned_additive_terms_math_reference.py with Torch and JAX CPU FP64. The execution receipt records the full len command and dependency versions.

The execution receipt records the outcome under this frozen limit.