NRTidalv2 Pv2 tidal-amplitude mode normalization
Scope and status
Specification nrtidalv2-pv2-tidal-mode-normalization/v1 covers the
conversion of the published signed Eq. (24) face-on plus-strain amplitude
into the positive-frequency (2,-2) input of the Pv2 rotation. It composes
the already-gated aligned finite-size term and positive-22 projector at a
supplied set of Euler angles. It does not qualify a complete native
IMRPhenomPv2_NRTidalv2 waveform.
Inputs, conventions, and options
The signed complex face-on finite-size term is
T=A_T W exp[-i(psi_T+S_2+S_3+S_3.5)], with the masses, distance, spin,
tidal deformability, and frequency conventions of the
aligned additive-term specification.
The target is the positive-frequency h^L_{2,-2} supplied to the
Pv2 projector. The angles
alpha, gamma, beta, theta_JN, and zeta are supplied independently;
this gate does not predict their BNS dynamics. CPU FP64 and positive
frequencies are in scope.
Mathematics and components
Dietrich et al. (2019), Eqs. (22)–(25) obtain Eq. (24) by preserving the low-frequency coefficient of Eq. (22). Immediately below Eq. (22), the authors say they substitute luminosity distance for the effective distance of their cited source. That source, Hotokezaka et al. (2016), Eqs. (15), (17), and (24), defines the Fourier quantity as the plus polarization and puts detector and inclination response in the effective distance. Thus, the Eq. (24) coefficient has face-on plus-strain normalization. The introductory description of a dominant 2,2 mode in Dietrich et al. does not itself fix its mode-to-strain normalization; the cited derivation does.
For the Pratten et al. (2020), Eqs. (11)–(13) positive-22 projector, zero Euler and basis-rotation angles give
Consequently the source-normalized aligned tidal input is
At zero Euler and basis angles, arbitrary inclination has the independent
closed form Delta h_plus=T(1+cos(theta)^2)/2 and
Delta h_cross=-i T cos(theta). The complex sign of T is retained.
| Component ID/version | Source | Variant | Status | Scalar reference | Torch/JAX boundary | Check |
|---|---|---|---|---|---|---|
nrtidalv2-pv2-tidal-mode-normalization/v1 |
Dietrich (2019), Eqs. (22)–(25); Hotokezaka (2016), Eqs. (15), (17), (24); Pratten (2020), Eqs. (11)–(13) | Published Pv2 finite-size term, supplied angles | Conditional executable | nrtidalv2_pv2_projection.mode_from_face_on_strain and project_positive_22 |
Pv2 face_on_to_positive_22 and positive-22 projectors |
test_nrtidalv2_pv2_tidal_mode_normalization_math_reference.py |
Implementation mapping
The scalar reference uses mpmath and the previously versioned aligned-term reference. Torch and JAX each implement the conversion in their native Pv2 driver, which also uses it for its existing BBH face-on carrier. The maintained test feeds the independently evaluated finite-size term and the native Eq. (24)/phase term through that same conversion and each native projector. No LAL source, binary residual, or fitted conversion enters.
Evidence and limitations
The frozen systems are (1.35,1.35;chi=0.20,-0.12;Lambda=350,350),
(1.6,1.2;0.08,-0.12;250,800), and the exchanged version, all at 100 Mpc.
Frequencies are 100 Hz, 800 Hz, 1.05 f_mrg, and 1.25 f_mrg. Two angle
sets are used: zero rotation with theta_JN=0,0.4,1.1 for the analytic
polarization limit, and nondegenerate precession/basis angles as frozen in
the test. Both complex polarizations must agree with the scalar reference
to 1e-10, normalized pointwise by the nonzero |A_T W|; the post-taper
term must be exactly zero. No alignment or output rescaling is permitted.
The receipt
records the result.
This gate fixes the Eq. (24) normalization at the supplied-mode boundary. It does not implement the native Pv2 BNS carrier, prove the paper's tidal amplitude fit against NR, determine spin-dependent precession angles or reference-frequency anchoring, resolve the merger-frequency/source Fig. 7 conflict, or establish binary parity. The existing D paper and historical binary-compatible variants remain distinct.
Reproduce the checks
With mpmath, Torch, JAX, and pytest installed on CPU FP64:
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