NRTidalv2 Pv2 inherited remnant-spin component

Scope and status

Specification nrtidalv2-pv2-remnant-spin/v1 is a conditional component gate, frozen before comparing the native backends. It does not qualify the complete BNS waveform or determine its time and reference-frequency origin.

Inputs, conventions, and options

The aligned remnant parameter is supplied. The bounded domain is finite positive masses with \(m_1\ge m_2\), \(0\le\chi_p\le 0.5\), and \(0<a_{f,\parallel}<1\). This restriction avoids using the published magnitude equation to adjudicate the native signed retrograde branch. Tidal deformabilities do not enter this inherited map.

Mathematics and components

Dietrich et al. (2019), Sec. III.4, retain the IMRPhenomPv2 precession dynamics for IMRPhenomPv2_NRTidalv2. The Pv2 technical note, Eqs. (29)–(30), (46), (51), and the text below Eq. (51), specifies the effective in-plane spin and the implemented remnant-spin choice. For ordered component masses \(m_1\ge m_2>0\), define

\[ A_1=2+3m_2/(2m_1),\quad A_2=2+3m_1/(2m_2),\quad \chi_p={\max(A_1m_1^2|\boldsymbol\chi_{1\perp}|, A_2m_2^2|\boldsymbol\chi_{2\perp}|)\over A_1m_1^2}. \]

For a supplied positive aligned-spin IMRPhenomD final Kerr parameter \(a_{f,\parallel}\), the Pv2 prescription assigns all in-plane spin to the larger body and sets the note's \(\lambda=M_f/M_i\). Equation (46) therefore reduces to

\[ a_{f,\mathrm{Pv2}}=\sqrt{a_{f,\parallel}^2+ [\chi_p(m_1/(m_1+m_2))^2]^2}. \]

The aligned remnant fit and QNM conversion are separate inputs to this gate; neither is inferred from this equation.

Implementation mapping

The independent diffgw_reference.nrtidalv2_pv2_remnant scalar evaluator uses arbitrary-precision arithmetic and only the printed equations. The production Torch and JAX Pv2 drivers call native remnant-spin helpers.

Evidence and limitations

Three BNS-scale, unequal/equal-mass, double-spin cases compare the Torch and JAX helpers to it, with absolute error at most 2e-15 for both \(\chi_p\) and \(a_{f,\mathrm{Pv2}}\), CPU FP64, without alignment or fitting. A public-BBH waveform smoke/regression check follows the helper extraction.

This gate does not settle the published angle-map conflict: the Pv2 technical note Eq. (32) sets the NNLO longitudinal input to the larger body's aligned spin, whereas the native drivers use a mass-weighted effective spin mapping selected by earlier binary compatibility checks. The note's Eq. (26) and Pratten et al. (2020), Eq. (27) also print different 2PN orbital-angular-momentum coefficients; the native drivers use a mixed public-compatibility coefficient. These must remain distinct from the present remnant-spin component and cannot yet support a paper-exact public BNS dispatch. The BNS carrier's remnant-frequency spline time shift and reference-frequency phase origin also require a separate contract.

Source: Dietrich et al. (2019), Sec. III.4.

Reproduce the checks

Run JAX_ENABLE_X64=1 PYTHONPATH=src:tests python -m pytest -q tests/test_nrtidalv2_pv2_remnant_spin_math_reference.py on CPU FP64.