IMRPhenomNSBH branch amplitude factors

Scope and status

Specification nsbh-branch-amplitude-fits/v1 covers the adjusted ringdown frequency, the four fit coordinates, and the three dimensionless branch factors from Thompson et al. (2020), Appendix A Eqs. (20)–(24), (30), and Table I. It excludes the Table I joining frequencies, Eq. (26) and (29) corrections, PhenomC carrier, amplitude windows, remnant/QNM provider, phase, and assembled waveform. This specification fixes the grid and limits before native comparison.

Inputs, conventions, and options

\(q=m_1/m_2\ge1\), \(\eta=q/(1+q)^2\), \(\chi\) is the black-hole spin, \(C\) is neutron-star compactness, \(T=M_{b,\rm torus}/M_{b,\rm NS}\) is the nonnegative carrier ratio, and \(f_{\rm tide},f_{\rm RD}>0\) use the same units. \(\Lambda\ge0\) is the neutron-star tidal deformability. The paper's fitted domain is \(1\le q\le15\), \(|\chi|\le0.5\), \(0\le\Lambda\le5000\).

The synthetic grid fixes \(q=2\), \(\chi=0.2\), \(C=0.17\), \(f_{\rm tide}=1000\) Hz, \(f_{\rm RD}\in\{800,1000,1200\}\) Hz, \(T\in\{0,0.05\}\) and \(\Lambda\in\{0,0.5,1,2,800\}\): 30 cases. It exercises all four Table I classes, equality, and both Eq. (20) branches. The composition grid uses the 60 already specified physical inputs \(q\in\{1,2,5,10,15\}\), \(\chi\in\{-0.5,0,0.5\}\), \(\Lambda\in\{300,800,2600,5000\}\), independent scalar \(C\), \(f_{\rm tide}\) and clipped \(T\), and controlled \(f_{\rm RD}/f_{\rm tide}\in\{0.8,1,1.2\}\): 180 cases. This is not a test of the remnant-derived ringdown frequency. Both native gates use CPU FP64.

Mathematics and components

Thompson et al. (2020), Appendix A Eqs. (20)–(24), (30) and Table I print

[ \widetilde f_{\rm RD}=0.98f_{\rm RD} \begin{cases}1-0.02\Lambda+0.01\Lambda^2,&\Lambda\le1,\0.99,&\Lambda>1,\end{cases} \quad u=\left(\frac{f_{\rm tide}-\widetilde f_{\rm RD}} {\widetilde f_{\rm RD}}\right)^2, ] [ x_{\rm ND}=u-0.571505C-0.00508451\chi,\quad x'{\rm ND}=u-0.657424C-0.0259977\chi, ] [ x=T+0.424912C+0.363604\sqrt\eta-0.060559\chi, ] [ x'_{\rm D}=T-0.132754C+0.576669\sqrt\eta-0.0603749\chi -0.0601185\chi^2-0.0729134\chi^3. ]

With \(\omega^\pm_{x_0,d}(x)=[1\pm\tanh(4(x-x_0)/d)]/2\), Table I assigns

Class	\(\epsilon_{\rm tide}\)	\(\epsilon_{\rm ins}\)	\(\sigma_{\rm tide}\)
non-disruptive, no torus	\(\omega^+_{-0.0796251,0.0801192}(x_{\rm ND})\)	1	\(\omega^-_{-0.206465,0.226844}(x'_{\rm ND})\)
mildly disruptive, torus	same	\(1.29971-1.61724x_{\rm D}\)	same
mildly disruptive, no torus	0	\(1.29971-1.61724x_{\rm D}\)	half the sum of the high-branch value and \(0.137722-0.293237x'_{\rm D}\)
disruptive, torus	0	\(1.29971-1.61724x_{\rm D}\)	\(0.137722-0.293237x'_{\rm D}\)

The Table I note and Eq. (30) require the half factor in each window. The torus ratio's nonnegative clip is an existing carrier adapter, not Eq. (23).

Implementation mapping

An independent high-precision scalar evaluator implements the printed equations. Torch and JAX approximants.imrphenom_nsbh expose a helper used by the production amplitude assembly. It consumes the already gated branch predicates and numeric inputs; neither native module imports the scalar reference.

Evidence and limitations

Before comparison, the gate fixes maximum relative error \(2\times10^{-13}\) for \(\widetilde f_{\rm RD}\) and maximum absolute error \(2\times10^{-12}\) for each of \(x_{\rm ND},x'_{\rm ND},x_{\rm D}, x'_{\rm D},\epsilon_{\rm tide},\epsilon_{\rm ins},\sigma_{\rm tide}\). The 70- versus 90-digit scalar results must agree within \(10^{-30}\) absolutely. No tolerance may be enlarged after observing the native output. The existing disruption and torus gates support the composition inputs; this gate does not certify those fits' physical calibration, the remnant/QNM model, joining frequencies, amplitude assembly, or a binary waveform.

Reproduce the checks

Run JAX_ENABLE_X64=1 PYTHONPATH=src pytest -q tests/test_nsbh_branch_amplitude_fits_math_reference.py with reference, Torch and JAX extras on CPU. The validation receipt records measured results and versions.