NRTidalv2 nonspinning tidal phase
Scope and status
Specification nrtidalv2-nonspinning-tidal-phase/v1 covers only the additive
frequency-domain NRTidalv2 tidal phase of the dominant (2,2) mode, with zero
component spins, CPU FP64 and the declared 30–800 Hz binaries below the merger
taper. The independent scalar reference
has component IDs nrtidalv2.phase.lambda_tilde.v1, .pade.v1, .tidal.v1
and .frequency_derivative.v1. It imports no Torch, JAX or LAL code.
Inputs, conventions, and options
Dietrich et al., Phys. Rev. D 100, 044003 (2019), arXiv:1905.06011v2, Eqs. (17)–(21) prints the NRTidalv2 phase, Padé form, PN constraints and four calibrated decimals. Wade et al., Phys. Rev. D 89, 103012 (2014), Eq. (5) defines the mass-weighted dimensionless deformability. The four free decimals are kept exactly as printed: \(n_{5/2}=90.550822\), \(n_3=-60.253578\), \(d_1=-15.111208\), and \(d_2=8.0641096\). They are empirical fit inputs, not values derived from PN theory. The reference asserts the published PN expansion independently of either native implementation.
Mathematics and components
Let \(M=m_1+m_2\), \(\delta=(m_1-m_2)/M\), \(\eta=(1-\delta^2)/4\), \(M_{\rm sec}=GM/c^3\), and \(x=(\pi M_{\rm sec}f)^{2/3}\), where \(f\) is positive GW frequency in Hz. The inputs Λ₁ and Λ₂ are nonnegative dimensionless quadrupolar deformabilities, with no equation-of-state relation imposed. Wade's Eq. (5), using signed δ so that either body order is allowed, is
Dietrich's Eqs. (17)–(18) give
The remaining coefficients follow Eqs. (19)–(20), with \(c_1=3115/1248\), \(c_{3/2}=-\pi\), \(c_2=28024205/3302208\), \(c_{5/2}=-4283\pi/1092\): \(n_1=c_1+d_1\), \(n_{3/2}=(c_1c_{3/2}-c_{5/2}-c_{3/2}d_1+n_{5/2})/c_1\), \(n_2=c_2+c_1d_1+d_2\), and \(d_{3/2}=-(c_{5/2}+c_{3/2}d_1-n_{5/2})/c_1\). The waveform multiplier is \(\exp(-i\psi_T)\). The phase is not shifted at \(f_{\rm ref}\); with zero spins, the finite-reference point-particle carrier cancels in the BNS/BBH quotient. Symbolic differentiation defines \(d\psi_T/df\) with masses and deformabilities fixed.
Implementation mapping
The maintained math tests
compare the unit complex quotient IMRPhenomD_NRTidalv2 / IMRPhenomD from
Torch and JAX with the independent high-precision phase. The denominator
removes the inherited point-particle carrier; normalization removes the
tidal amplitude. The same quotient is built from the installed LALSuite
7.26.15 binary by its public waveform-sequence API in the
binary test. There is no
phase/time alignment or fitting to that binary. The oracle is used only for
agreement, never to choose coefficients.
Evidence and limitations
The frozen systems \((m_1,m_2;\Lambda_1,\Lambda_2)\), in solar masses, are \((1.35,1.35;400,400)\), \((1.6,1.2;200,800)\), its body-exchanged copy, and \((1.35,1.35;0,0)\). Paper-value frequencies are 30, 100, 300, 500 and 800 Hz. At every point each frontend's unit-complex residual must be at most \(10^{-10}+10^{-11}|\psi_T|\). At 300 Hz, Torch/JAX autodifferentiated \(d\psi_T/df\) must agree with the independent symbolic derivative within relative \(10^{-8}\) and absolute \(10^{-10}\) rad/Hz.
The LAL grid is 30–800 Hz in 5 Hz steps. For each case, the unaligned unit
complex quotient must have relative complex \(L_2\le10^{-6}\) and maximum
pointwise phase residual \(\le10^{-5}\) rad against the paper reference;
Torch and JAX quotients must meet the same limits against the LAL quotient.
Run with DIFFGW_REQUIRE_LAL_BINARY=1 to fail instead of skip when the pinned
binary is unavailable. These limits are fixed before the binary run and are
not adjusted in response to failures.
The qualification receipt records the exact host, checkout, command, binary versions, metrics and outcome. Passing this gate establishes only literature transcription, native implementation and named-binary agreement for the declared slice. It does not establish physical accuracy, an equation-of-state relation, amplitude Eq. (24), merger frequency and taper Eq. (25), self-spin Eqs. (26)–(29), spinning binaries, other modes, FP32/GPU behavior or the full family.
Reproduce the checks
Run DIFFGW_REQUIRE_LAL_BINARY=1 PYTHONPATH=src:tests python -m pytest -q
tests/test_nrtidalv2_phase_math_reference.py
tests/test_nrtidalv2_phase_lal_binary.py with LALSuite 7.26.15 installed.