SEOBNRv5HM_ROM_NRTidalv3_NSBH Waveform Model

• SEOBNRv5HM_ROM_NRTidalv3_NSBH is a frequency-domain gravitational-wave model for quasi-circular, aligned-spin NSBH binaries that incorporates tidal effects and higher-order modes.
• It combines an effective-one-body baseline with NRTidalv3 tidal prescriptions calibrated to numerical relativity, ensuring accurate modeling across inspiral, merger, and ringdown phases.
• The model uses reduced-order compression to deliver millisecond-scale evaluations in LALSuite, making it highly suitable for large-scale parameter estimation and population studies.

Searching arXiv for the cited model paper and key related waveform/ROM papers. SEOBNRv5HM_ROM_NRTidalv3_NSBH is a frequency-domain gravitational-wave model for quasi-circular, aligned-spin neutron star–black hole binaries that includes higher-order modes beyond the dominant quadrupole, tidal effects in both phasing and amplitude, and a reduced-order compression designed for millisecond-scale evaluation (Vidal et al., 3 Jun 2026). It is constructed by “dressing up” the aligned-spin, higher-mode Effective-One-Body baseline SEOBNRv5HM with tidal effects from the NRTidalv3 framework and then compressing the resulting waveform family into a Reduced-Order Model (ROM). Within the model, the BBH baseline supplies the resummed EOB dynamics and multimode structure, while the NSBH-specific sector supplies tidal dephasing and amplitude suppression calibrated to numerical relativity simulations. The resulting model is implemented in LALSuite under the name SEOBNRv5HM_ROM_NRTidalv3_NSBH (Vidal et al., 3 Jun 2026).

1. Conceptual basis and model identity

SEOBNRv5HM_ROM_NRTidalv3_NSBH belongs to the SEOBNR family of waveform models and is specifically an aligned-spin, higher-mode, inspiral–merger–ringdown construction for NSBH systems. Its defining ingredients are threefold: the SEOBNRv5HM Effective-One-Body description of compact-binary dynamics, the NRTidalv3 prescription for tidal matter effects, and a ROM compression step that turns the full model into a fast frequency-domain approximant (Vidal et al., 3 Jun 2026).

The model is presented alongside IMRPhenomXHM_NSBH and IMRPhenomXPHM_NSBH as part of the first two frequency-domain models for gravitational-wave signals from quasi-circular, aligned-spin neutron star–black hole binaries including higher-order modes beyond the dominant quadrupole; IMRPhenomXPHM_NSBH extends the former model to the spin-precessing case (Vidal et al., 3 Jun 2026). In this context, SEOBNRv5HM_ROM_NRTidalv3_NSBH is the EOB-based aligned-spin realization.

Its stated purpose is to provide accurate multimode IMR waveforms for NSBH binaries while remaining computationally practical for large-scale parameter estimation and population studies. This practicality derives from the ROM compression, whereas the physical content derives from the combination of a state-of-the-art EOB BBH baseline with closed-form, high-PN tidal dephasing and amplitude suppression ansätze (Vidal et al., 3 Jun 2026).

A plausible implication is that the model occupies a methodological middle ground between fully time-domain EOB evolution and more aggressively phenomenological frequency-domain ansätze: it preserves the SEOBNRv5HM baseline physics while exposing the waveform directly in a form optimized for inference pipelines.

2. Effective-One-Body dynamics and aligned-spin structure

At the core of the SEOB construction lies a Hamiltonian $H_{\rm EOB}(Q,P;\chi_1,\chi_2)$ describing two spinning compact bodies in quasi-circular motion. The two-body dynamics are mapped onto an effective test-mass problem by introducing an effective Hamiltonian $H_{\rm eff}$ for a particle of mass $\mu = m_1 m_2 /(m_1+m_2)$ moving in a deformed Kerr metric parameterized by the total mass $M = m_1+m_2$ and EOB potentials $A(r)$, $B(r)$, and $Q(r,p_r)$. The real Hamiltonian is then written as

$$H_{\rm EOB} = M \sqrt{1 + 2\eta\left[\frac{H_{\rm eff}}{\mu}-1\right]}, \qquad \eta \equiv \mu/M .$$

In the test-mass limit $\eta \to 0$, the exact Schwarzschild/Kerr geodesic Hamiltonian is recovered (Vidal et al., 3 Jun 2026).

Spin–orbit and spin–spin interactions are introduced through additional gyro-gravitomagnetic functions $G_S(r)$ and $H_{\rm eff}$0, calibrated to high-order post-Newtonian results and to numerical relativity. The mapping onto $H_{\rm eff}$1 is designed so that known test-mass results are exactly respected, while finite-$H_{\rm eff}$2 effects enter through a resummed PN expansion of the EOB potentials (Vidal et al., 3 Jun 2026).

Gravitational-wave dissipation is incorporated by a non-conservative radiation-reaction force $H_{\rm eff}$3 added to the Hamilton equations for the canonical momenta. The associated flux at infinity is expressed as

$H_{\rm eff}$4

with each mode flux $H_{\rm eff}$5 written in terms of factorized inspiral amplitude and phase functions $H_{\rm eff}$6 and $H_{\rm eff}$7 and, when spins are present, further spin-dependent corrections. In SEOBNRv5HM, the leading $H_{\rm eff}$8 flux is augmented by higher modes up to $H_{\rm eff}$9, and aligned spins $\mu = m_1 m_2 /(m_1+m_2)$0 enter both inspiral phasing and amplitude through spin–orbit and spin–spin corrections up to next-to-next-to-leading PN order (Vidal et al., 3 Jun 2026).

These features define the BBH baseline onto which NSBH-specific matter effects are superimposed. This suggests that, within the model architecture, the NSBH sector is treated as an extension of a pre-existing high-fidelity BBH dynamical description rather than as a wholly separate dynamical system.

3. Tidal sector from NRTidalv3

In NSBH systems, matter effects first enter the waveform phasing through the tidal dephasing $\mu = m_1 m_2 /(m_1+m_2)$1. For the dominant $\mu = m_1 m_2 /(m_1+m_2)$2 mode, the NRTidalv3 prescription writes

$\mu = m_1 m_2 /(m_1+m_2)$3

where $\mu = m_1 m_2 /(m_1+m_2)$4 is the leading-PN coefficient, $\mu = m_1 m_2 /(m_1+m_2)$5 gives the dynamical tidal coupling, and $\mu = m_1 m_2 /(m_1+m_2)$6 is a Padé-resummed rational function that reproduces the known 7.5PN series at low $\mu = m_1 m_2 /(m_1+m_2)$7 and is fitted to 55 BNS NR waveforms up to merger (Vidal et al., 3 Jun 2026).

Beyond the quadrupole, the model uses the scaling ansatz

$\mu = m_1 m_2 /(m_1+m_2)$8

Spin-squared and spin-cubed EOS-dependent terms, up to 3.5PN, are added in $\mu = m_1 m_2 /(m_1+m_2)$9 and are likewise scaled for higher modes (Vidal et al., 3 Jun 2026).

The construction also includes a regularization procedure for the tidal phase. To avoid pathological poles or inflection points beyond the calibration region, the model switches at a limiting frequency $M = m_1+m_2$0, chosen just before the nearest pole or inflection, to a second-order Taylor extrapolation in $M = m_1+m_2$1, ensuring that $M = m_1+m_2$2 is $M = m_1+m_2$3 continuous in frequency (Vidal et al., 3 Jun 2026). This regularization is directly tied to stated limitations of the model at large $M = m_1+m_2$4 or far beyond the strongest calibration region.

The tidal sector is not limited to phase corrections. The abstract explicitly states that the new models incorporate tidal effects in both the gravitational-wave phasing and amplitude using a higher-mode extension of NRTidalv3 as well as dedicated amplitude models calibrated to NR simulations (Vidal et al., 3 Jun 2026). In this sense, SEOBNRv5HM_ROM_NRTidalv3_NSBH is not a phase-only tidal dressing of the BBH baseline.

4. Higher-order modes and NSBH amplitude ansatz

SEOBNRv5HM_ROM_NRTidalv3_NSBH retains the same set of harmonics as its BBH baseline: $M = m_1+m_2$5, $M = m_1+m_2$6, $M = m_1+m_2$7, $M = m_1+m_2$8, $M = m_1+m_2$9, $A(r)$0, and $A(r)$1 (Vidal et al., 3 Jun 2026). For each mode,

$A(r)$2

the phase is written as

$A(r)$3

with $A(r)$4 given by the NRTidalv3 higher-mode scaling (Vidal et al., 3 Jun 2026).

The amplitude is factorized as

$A(r)$5

For the $A(r)$6 mode, the NSBH correction factor is

$A(r)$7

where

$A(r)$8

is a smooth step (Hann–tanh) between $A(r)$9 and $B(r)$0, with $B(r)$1 (Vidal et al., 3 Jun 2026).

The function $B(r)$2 is represented as a superposition of tanh transitions,

$B(r)$3

with $B(r)$4 determined by fitting to NR waveforms in four regimes: non-disruptive, disruptive with torus, disruptive without torus, and mildly disruptive, as in Matas et al. Higher modes are then obtained by the frequency-rescaling prescription

$B(r)$5

where $B(r)$6 plus small corrections are fitted to NR (Vidal et al., 3 Jun 2026).

The amplitude ansatz therefore combines a mode-by-mode BBH baseline with an NSBH suppression factor that is explicitly tied to disruption phenomenology. A plausible implication is that the model encodes tidal disruption signatures primarily through waveform amplitude structure near merger, while relying on the underlying SEOBNRv5HM dynamics for the broader IMR morphology.

5. Reduced-order compression and computational realization

The ROM is introduced to deliver millisecond-scale waveforms. Its offline compression of the aligned-spin SEOBNRv5HM_NRTidalv3 family proceeds through four named stages: Greedy Reduced Basis, Empirical Interpolation, Parameter Interpolation, and Online Evaluation (Vidal et al., 3 Jun 2026).

In the greedy reduced-basis stage, a training set of waveforms is constructed over the intrinsic parameter grid $B(r)$7, and a greedy algorithm selects an orthonormal basis $B(r)$8 such that every waveform is approximated to within a prescribed error $B(r)$9, given as an example of $Q(r,p_r)$0 in norm. In the empirical-interpolation stage, a set of interpolation nodes $Q(r,p_r)$1 is identified so that the reduced-basis expansion can be evaluated by sampling the full model only at these nodes. In the parameter-interpolation stage, each basis coefficient $Q(r,p_r)$2 is assigned a cheap interpolant, for example polynomial or Chebyshev, in the four-dimensional parameter space $Q(r,p_r)$3, with residuals required to remain below $Q(r,p_r)$4. In the online stage, the query parameters are mapped to the coefficients via the fast interpolants, the waveform is reconstructed as

$Q(r,p_r)$5

and the full frequency grid is filled in $Q(r,p_r)$6 operations with $Q(r,p_r)$7–$Q(r,p_r)$8 (Vidal et al., 3 Jun 2026).

The practical implementation is in LALSuite (lalsimulation) under the exact name SEOBNRv5HM_ROM_NRTidalv3_NSBH. The model can be called through $H_{\rm eff}$08 with required inputs consisting of masses in $Q(r,p_r)$9, aligned-spin components, tidal deformabilities, and the frequency range and resolution; for a black hole, one sets $$H_{\rm EOB} = M \sqrt{1 + 2\eta\left[\frac{H_{\rm eff}}{\mu}-1\right]}, \qquad \eta \equiv \mu/M .$$0 if appropriate for the BH slot in the chosen ordering. The implementation returns frequency-domain plus/cross polarizations or individual modes, requires no external data files beyond those shipped with LALSuite, is thread-safe, and supports MLDC frequency resolution and merging with heterodyning or multibanding (Vidal et al., 3 Jun 2026).

Typical runtime figures reported for the implementation are 1–3 ms on a modern CPU for an aligned-spin full-mode waveform and $$H_{\rm EOB} = M \sqrt{1 + 2\eta\left[\frac{H_{\rm eff}}{\mu}-1\right]}, \qquad \eta \equiv \mu/M .$$1 ms for $$H_{\rm EOB} = M \sqrt{1 + 2\eta\left[\frac{H_{\rm eff}}{\mu}-1\right]}, \qquad \eta \equiv \mu/M .$$2-only generation (Vidal et al., 3 Jun 2026). These numbers are consistent with the ROM’s intended use in inference settings where repeated likelihood evaluations dominate the cost.

6. Calibration, validation, parameter space, and limitations

Calibration uses 162 SACRA $$H_{\rm EOB} = M \sqrt{1 + 2\eta\left[\frac{H_{\rm eff}}{\mu}-1\right]}, \qquad \eta \equiv \mu/M .$$3 waveforms and 25 high-quality BAM+SACRA+SXS waveforms with subdominant modes $$H_{\rm EOB} = M \sqrt{1 + 2\eta\left[\frac{H_{\rm eff}}{\mu}-1\right]}, \qquad \eta \equiv \mu/M .$$4 hybridized to a tidal inspiral (DALI) down to approximately 20 Hz. The parameter ranges spanned in calibration are $$H_{\rm EOB} = M \sqrt{1 + 2\eta\left[\frac{H_{\rm eff}}{\mu}-1\right]}, \qquad \eta \equiv \mu/M .$$5, $$H_{\rm EOB} = M \sqrt{1 + 2\eta\left[\frac{H_{\rm eff}}{\mu}-1\right]}, \qquad \eta \equiv \mu/M .$$6, neutron-star $$H_{\rm EOB} = M \sqrt{1 + 2\eta\left[\frac{H_{\rm eff}}{\mu}-1\right]}, \qquad \eta \equiv \mu/M .$$7, and neutron-star mass approximately $$H_{\rm EOB} = M \sqrt{1 + 2\eta\left[\frac{H_{\rm eff}}{\mu}-1\right]}, \qquad \eta \equiv \mu/M .$$8–$$H_{\rm EOB} = M \sqrt{1 + 2\eta\left[\frac{H_{\rm eff}}{\mu}-1\right]}, \qquad \eta \equiv \mu/M .$$9. The amplitude–phase ansätze are then fitted mode-by-mode across this space (Vidal et al., 3 Jun 2026).

Validation against a separate set of NR + NRSurTidal hybrids yields median mismatches (unfaithfulness) below $\eta \to 0$0 over $\eta \to 0$1, $\eta \to 0$2, and $\eta \to 0$3, across 36 extrinsic configurations varying inclination, phase, and polarization. Time-domain comparisons show sub-radian phase differences up to merger for both quadrupole and higher modes, together with amplitude discrepancies below $\eta \to 0$4 (Vidal et al., 3 Jun 2026).

Single-core speed benchmarks report that the full SEOBNRv5HM_ROM_NRTidalv3_NSBH waveform with $\eta \to 0$5 modes over $\eta \to 0$6 Hz and $\eta \to 0$7 Hz requires approximately $\eta \to 0$8 ms. The uncompressed time-domain SEOBNRv5HM with identical physics would take $\eta \to 0$9 s, corresponding to a reported $G_S(r)$0 speedup (Vidal et al., 3 Jun 2026).

The allowed intrinsic ranges are broader than the strongest calibration region:

Quantity	Allowed intrinsic range
$G_S(r)$1	$G_S(r)$2
$G_S(r)$3	$G_S(r)$4
Mass ratio	$G_S(r)$5
$G_S(r)$6	$G_S(r)$7 aligned
$G_S(r)$8	$G_S(r)$9 aligned
$H_{\rm eff}$00	$H_{\rm eff}$01

Model fidelity is stated to degrade for $H_{\rm eff}$02 or for $H_{\rm eff}$03 with large $H_{\rm eff}$04, chiefly because of potential poles in $H_{\rm eff}$05 for $H_{\rm eff}$06. The implementation automatically detects and excises these pathologies using the Taylor-extrapolation switch at $H_{\rm eff}$07 (Vidal et al., 3 Jun 2026). This distinction between nominal domain of use and strongest calibration support is important: it clarifies that the model has explicit extrapolation controls, but these should not be conflated with equally strong calibration evidence across the entire nominal parameter space.

The broader study reports that the new models show clear improvements over their predecessors in analyses of simulated signals, while yielding results consistent with the literature when applied to real events from the GWTC-3 and GWTC-4 catalogs (Vidal et al., 3 Jun 2026). For SEOBNRv5HM_ROM_NRTidalv3_NSBH, this places the model simultaneously in two roles: as a calibrated representation of multimode aligned-spin NSBH coalescences, and as a computationally efficient tool intended for production-scale gravitational-wave data analysis.